communication, such as IEEE 1344 in 1995, IEEE C37.118, IEEE C37.118.1-2011 and IEEE ... IEEE format bus-branch network model such as two-area system, Western Electricity ...... âHelpâ button directs user to the LSE manual. A status ...... 102. [20]. R. R. Shoults and E. Barrera-Cardiel, âUse of a Graphical User Interface.
VALIDATION, TESTING AND IMPLEMENTATION OF THE LINEAR STATE ESTIMATOR IN A REAL POWER SYSTEM
By LIN ZHANG
A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITY School of Electrical Engineering and Computer Science August 2014
To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation of LIN ZHANG find it satisfactory and recommend that it be accepted.
_____________________________ Anjan Bose, Ph.D., Chair
_____________________________ Chen-Ching Liu, Ph.D.
____________________________ Mani Venkatasubramanian, Ph.D.
ii
ACKNOWLEDGEMENT I would like to express my sincere gratitude to my advisor Dr. Anjan Bose for offering me the precious opportunity to work with him on this dissertation at Washington State University, and the continuous support of my Ph.D. studies and research. I feel very grateful for his patience, motivation, enthusiasm, and immense knowledge, which guided me throughout my research and also the writing of this thesis. The entire PhD experience is unforgettable to me. I would also like to express my appreciation to the rest of my committee members, Dr. Chen-Ching Liu and Dr. Mani Venkatasubramanian for their encouragement, insightful comments, and useful feedback during my research. My sincere thanks also go to Dr. Jay Giri and Dr. Anil Jampala from Alstom Grid and Dr Vahid Madani from Pacific Gas & Energy, for offering me a great opportunity to work on the Pacific Gas & Energy Linear State Estimator project. I specially thank Dr. Anil Jampala, with whom I have been working, for giving me all the helps during the internships in the last two summers as my manger. This work was supported by the Pacific Gas & Energy (PG&E) and Alstom Grid and I sincerely acknowledge the financial support extended to this project by the sponsors. I am also indebted to my many colleagues in the power group who have supported me over these years. Special thanks to Dr. Tao Yang, Dr. Kai Yin Kenny Poon, Dr. Haoen Li, Meng Ming, Tuo Ji, Simon Guo, Alex Ning and Lily Wu. I would like to express my heartfelt thanks to every member of my family for their love, support and encouragement over the years.
iii
VALIDATION, TESTING AND IMPLEMENTATION OF THE LINEAR STATE ESTIMATIOR IN A REAL POWER SYSTEM ABSTRACT
by Lin Zhang, Ph.D. Washington State University August 2014
Chair: Anjan Bose
With the advent of phasor measurement unit, the synchro-phasor data related application at control center has been researched in recent decades. Time-stamped phasor data can benefit in the applications in modern power system, such as state estimation, voltage stability, oscillation monitoring and so forth. As one of the key applications in Energy Management System (EMS), state estimation utilizing synchro-phasor data is the major objective of this dissertation. As more and more Phasor Measurement Units (PMUs) are coming on-line, validation of PMU data becomes important. As part of PG&E smart grid project design and implementation, validation of such data as well as preparing end users for various scenario (e.g. loss of PMU signal and its impact) is a necessity. PG&E has chosen to integrate Linear State Estimator (LSE) into their next generation EMS. One of the business use cases of LSE is validation of PMU data. It is important that system dispatchers trust LSE from day one, as much as they do their SCADA. A linear state estimation algorithm in control center environment is presented in this dissertation. The LSE algorithm contains four major functionalities: topology processor,
iv
observability analysis, state estimation and bad data detection and identification, all of which functionalities are explored in detail. The LSE user interface is presented and some of the snapshots of the UI are displayed as well. Moreover, the data flow in EMS for LSE is designed in this project. The LSE application makes use of network model from EMS, PMU data from PDC and breaker/switch status information from EMS/SCADS through the web service. The validation and testing of the LSE application has been carried on with different data set, simulated steady state data, simulated RTDS data and field PMU data. Various conditions of testing of LSE successfully demonstrate the correctness of the LSE algorithm and provide the useful practical information of integrating LSE application. All the implementation experience is also helpful on how to integrate “smart grid” application for future power grid.
Keywords: PMU, linear state estimation, EMS
v
TABLE OF CONTENTS
ACKNOWLEDGEMENT ............................................................................................................. iii ABSTRACT ................................................................................................................................... iv TABLE OF CONTENTS ............................................................................................................... vi LIST OF TABLES ......................................................................................................................... ix LIST OF FIGURES ........................................................................................................................ x 1.
2.
INTRODUCTION .................................................................................................................. 1 1.1.
Motivation ................................................................................................................. 1
1.2.
Objective and Findings ............................................................................................. 3
1.3.
Outline....................................................................................................................... 5
PHASOR MEASUREMENT UNITS AND LINEAR STATE ESTIMATOR ...................... 8 2.1.
Supervisory Control and Data Acquisition ............................................................... 8
2.2.
Phasor Measurement Unit ......................................................................................... 9
2.3.
Power System Linear State Estimator..................................................................... 15
2.3.1. Traditional Power System State Estimation ............................................................ 15 2.3.2. Linear State Estimator ............................................................................................. 18 3.
LINEAR STATE ESTIMATOR IN THE CONTROL CENTER ENVIRONMENT .......... 21 3.1.
Control Center Level Linear State Estimator.......................................................... 21
vi
3.2.
Linear State Estimation Algorithm ......................................................................... 22
3.2.1. Power System and PMUs ........................................................................................ 22 3.2.2. Topology Processor ................................................................................................. 25 3.2.2.1.
Map breaker/switch data to network model ...................................................... 25
3.2.2.2.
Build bus model from breaker/switch data ....................................................... 29
3.2.2.3.
Case Study of Topology Processor ................................................................... 33
3.2.3. Observability Analysis ............................................................................................. 36 3.2.3.1.
Numerical Observability ................................................................................... 36
3.2.3.2.
Topological Observability ................................................................................ 37
3.2.3.3.
Phasor Measurements ....................................................................................... 38
3.2.3.4.
Case Study of Observability Analysis .............................................................. 41
3.2.4. Linear State Estimation Equations and Solutions .................................................... 42 3.2.4.1.
Impact of Series Capacitors on LSE formulation ............................................. 45
3.2.4.2.
LSE formulation in observable islands ............................................................. 46
3.2.5. Bad Data Detection and Identification..................................................................... 47 3.3. 4.
EMS Data Flow....................................................................................................... 50
VISUALIZATION ................................................................................................................ 56 4.1.
Software Development Tools ................................................................................. 56
4.2.
Configure The Linear State Estimator .................................................................... 56
4.3.
Run The Linear State Estimator .............................................................................. 60
vii
4.4. 5.
Display The Output of The Linear State Estimator ................................................ 62
Testing................................................................................................................................... 66 5.1.
Testing on Simulated Steady State Data ................................................................. 68
5.1.1. LSE retrieving PMU data from openPDC ............................................................... 69 5.1.2. LSE retrieving data from EMS using a web service ................................................ 72 5.1.3. LSE sending output to EMS and adapted for multi-host environment .................... 74 5.1.4. Characteristic Problems of PMU Data..................................................................... 75 5.1.5. Case Study ............................................................................................................... 77 5.2.
Testing on Simulated RTDS Data........................................................................... 82
5.2.1. LSE Application Context ......................................................................................... 82 5.2.2. Case Study ............................................................................................................... 83 5.3. 6.
Testing on Field PMU Data .................................................................................... 87
Conclusions and Future Works ............................................................................................. 96 6.1.
Conclusions ............................................................................................................. 96
6.2.
Future Works .......................................................................................................... 98
REFERENCES ....................................................................................................................... 100
viii
LIST OF TABLES TABLE I.
Detail of 500 kV substation diagram ....................................................................... 24
TABLE II.
Node Index ........................................................................................................... 28
TABLE III.
Device Connection List ........................................................................................ 28
TABLE IV.
Tabulated Result of Topology Processor on Sample System ............................... 34
TABLE V.
openPDC signal reference versus Scada analog name ......................................... 71
TABLE VI.
LSE test result on simulated RTDS data .............................................................. 84
ix
LIST OF FIGURES Figure 1.
Architecture for a SCADA system. ........................................................................... 9
Figure 2.
A typical configuration of a PMU ........................................................................... 11
Figure 3.
PMU installation at US & Canada ........................................................................... 12
Figure 4.
LSE algorithm and data flow at control center ........................................................ 22
Figure 5.
500 kV substation diagram ...................................................................................... 24
Figure 6.
Definition of Node or Bus section ........................................................................... 26
Figure 7.
A Typical Substation Level Description of a Power System ................................... 27
Figure 8.
A Sample Breaker and a Half Configuration ........................................................... 27
Figure 9.
Diagram of Substation Topology Processor ............................................................ 30
Figure 10.
Diagram of System Level Topology Processor ....................................................... 32
Figure 11.
Example of Topology Processor on Sample System ............................................... 34
Figure 12.
Example of Topology Processor on PG&E System ................................................ 35
Figure 13.
Numerically observable versus algebraically observable ........................................ 37
Figure 14.
Voltage Phasor Measurement .................................................................................. 39
Figure 15.
Flow Current Phasor Measurement ......................................................................... 39
Figure 16.
Injection Current Phasor Measurement ................................................................... 40
Figure 17.
Observability Analysis on Sample System .............................................................. 41
Figure 18.
Observability Analysis on PG&E System ............................................................... 42
Figure 19.
Branch Modeling with Pi Model.............................................................................. 44
Figure 20.
LSE formulation on series capacitor ........................................................................ 45
Figure 21.
LSE Solving in Each of Observable Islands ............................................................ 47
Figure 22.
Traditional SE Data Flow in Existing EMS ............................................................. 51
x
Figure 23.
Snapshot of Part of Static File ................................................................................. 52
Figure 24.
Snapshot of Sample PMU data ................................................................................ 53
Figure 25.
Snapshot of Sample Dynamic File ........................................................................... 54
Figure 26.
LSE data flow for EMS............................................................................................ 54
Figure 27.
LSE UI TAB - Configure ......................................................................................... 57
Figure 28.
Web Service ............................................................................................................. 59
Figure 29.
LSE UI TAB - Connect............................................................................................ 60
Figure 30.
LSE UI TAB – Internal Measurement ..................................................................... 63
Figure 31.
LSE UI TAB - Analyze............................................................................................ 63
Figure 32.
LSE Real Time Chart ............................................................................................... 64
Figure 33.
User Interface of PMU Simulator ............................................................................ 69
Figure 34.
openPDC User Interface .......................................................................................... 70
Figure 35.
PMU data flow ......................................................................................................... 70
Figure 36.
Web service in EMS ................................................................................................ 72
Figure 37.
LSE retrieving the latest dynamic file ..................................................................... 73
Figure 38.
LSE in multi-host environment ................................................................................ 75
Figure 39.
Constant Phase Angle Bias ...................................................................................... 76
Figure 40.
Sudden Phase Angle Jumps ..................................................................................... 76
Figure 41.
Saw-Tooth Behavior ................................................................................................ 76
Figure 42.
LSE test on steady-state base case ........................................................................... 78
Figure 43.
LSE test result on two line outage ........................................................................... 79
Figure 44.
LSE test result on angle bias .................................................................................... 80
Figure 45.
LSE test result on magnitude error .......................................................................... 81
xi
Figure 46.
LSE application context ........................................................................................... 82
Figure 47.
PMU connection tester user interface ...................................................................... 83
Figure 48.
LSE real time chart – topology error ....................................................................... 86
Figure 49.
LSE result at substation 8 ........................................................................................ 89
Figure 50.
Voltage measurement (AC) ..................................................................................... 90
Figure 51.
Voltage measurement (BD) ..................................................................................... 91
Figure 52.
Current measurement (AC) from substation 8 to 11 ................................................ 92
Figure 53.
Current measurement (BD) from substation 8 to 11 ................................................ 92
Figure 54.
Current measurement (AC) from substation 8 to 4 .................................................. 93
Figure 55.
Current measurement (BD) from substation 8 to 4 .................................................. 93
Figure 56.
Current measurement (AC) from substation 8 to 10 ................................................ 94
Figure 57.
Current measurement (BD) from substation 8 to 10 ................................................ 95
xii
1. INTRODUCTION 1.1. Motivation Power system state estimation has been playing a vital role in Energy Management System (EMS) since it was first introduced in 1960s [1]-[3]. It is a digital processing scheme which provides a real-time data base for many of the central control and dispatch functions in a power system. Its purpose is to permit improvements in system security and data accuracy and to reduce measurement and telemetry cost [4]-[5]. The real-time digital and analog measurements for state estimator come from the Supervisory Control and Data Acquisition (SCADA) system, which is acquired through Remote Terminal Units (RTUs) or intelligent electronic devices (IEDs) installed in substations. Its output serves as a reliable, consistent and accurate data base which is fed into other down-streaming key functions in EMS, such as Contingency Analysis, Optimal Power Flow, Unit Commitment and Security Monitoring. Power system SCADA networks are part of the nation’s critical electric infrastructure. A variety of threats exists in SCADA networks today and affects the performance, reliability, flexibility and safety of distributed SCADA systems [6]. Power system state estimator can functions as a filter to eliminate the bad data and give the true state of the power system network. Another issue with the SCADA system is that its periodicity is very low, whose sampling rate is not fast enough to run state estimation as a true real-time application. Moreover, traditional power system state estimator uses voltage magnitude, injection real and reactive power, and real and reactive power flow. The relationship between power and voltage is
1
nonlinear, so the iteration is required to solve the nonlinear equations, which normally takes more time than solving linear equations. This is also a bottle neck for state estimation coming online as a real time application. A phasor measurement unit (PMU) or synchrophasor is a device which measures the electrical phasors on an electricity grid, using a Global Positioning System (GPS) as a common time source for synchronization. It was developed in mid 1980s [7]. These devices can produce phasors that are synchronized across widely dispersed locations [8]. PMUs provide the possibility and feasibility of measuring the state vector directly, rather than estimating it from SCADA measurements. The phasor measurement from PMUs are collected and transferred to the down-streaming application by Phasor Data Concentrators (PDCs. The PDC purpose is to combine synchrophasor measurements from many phasor measurement units (PMUs) into a single time synchronized data stream [9]. There are several protocols for phasor data communication, such as IEEE 1344 in 1995, IEEE C37.118, IEEE C37.118.1-2011 and IEEE C37.118.2-2011 invented for PDC [10]. Linear State Estimator is one of the key applications in EMS which can benefit from the phasor data from PMUs. There has been a lot of research in this field since the first PMU invented in 1980s. Sponsored by Dominion Virginia Power and the Department of Energy (DOE), Virginia Polytechnic Institute & State University (VT) has implemented its three-phase linear state estimator at Dominion’s 500kV network [11]. The Super Calibrator, a fully distributed state estimator by Georgia Institute of Technology, has also been implemented on the US Virgin Islands St. Thomas and St. John power system of the USVI Water and Power Authority [12]. A two-level linear
2
state estimator has been developed in GridSim project at Washington State University (WSU) [13]-[14]. It is based on PMU data and requires algorithmic processing at the substation level, fast communication of the substation results to the control center, and synchronization of the data at the control center before it finally calculates a state estimate (SE) for the whole system [15]. Sponsored by US Smart Grid Investment program (SGIG) [16], Pacific Gas and Energy (PG&E) collaborates with Alstom Grid and WSU to implement our LSE on PG&E EMS network model.
1.2. Objective and Findings The two-level linear state estimation algorithm at WSU has been tested on the IEEE format bus-branch network model such as two-area system, Western Electricity Coordinating Council (WECC) [17] 179 bus system and the whole WECC system. The real time PMU simulated measurements are generated by Transient Security Assessment Tool (TSAT), which is a leading-edge full time-domain simulation tool designed for comprehensive assessment of dynamic behavior of complex power systems [18]. The two-level LSE algorithm shows very great performance on the two study system without considering communication and computation delay [19]. This dissertation is mainly focused on the validation, testing and implementation of the linear state estimator in the power system network at PG&E. The EMS network model at PG&E, of a real power system, is a practical node-breaker model, which varies from IEEE format bus-branch model. Moreover, the real-time phasor measurements come from actual field PMUs concentrated by PDC and then fed into LSE at EMS. The linear state estimator is designed to stay at EMS, taking raw PMU data from PDC as input, doing the calculation and feeding the clean phasor data as 3
output to EMS in the end. Hence, the main task is to adapt our linear state estimation algorithm and implement it at PG&E network model. With the continually installation of PMUs in real power system, the linear state estimation running in EMS becomes possible. In order to solve a typical state estimation problem, it requires enough observability of the network and certain redundancy to obtain a good SE result. Preliminary off-line observability analysis has been done and proves that the PG&E network has adequate observability for SE to solve. LSE Data flow structure in EMS environment is another major task in this dissertation. LSE makes use of the PMU data from PDC, which varies from the traditional state estimator receiving measurements from SCADA. However, LSE still needs to use the network model from the EMS system and the real time breaker/switch status information to do topology processor. After the calculation is done, the output of LSE will be fed back into EMS. Therefore, the data flow structure has to be designed and built up in the first place. As a product, which will be used in practical EMS at a control center, LSE has to have its own user interface. This interface allows the user full control over the application and provides facilities for the study of the response of the simulated system. The software structure has to contain a special man-machine interface designed with a graphical user interface approach [20]. Windows Presentation Framework (WPF) has been used to build up the user interface. The last major task in this dissertation is to validate and test the LSE algorithm and application by utilizing the simulated steady state data and Real Time Digital
4
Simulator (RTDS) data [21], and field PMU data. The interface of LSE application was designed to be able to make use of these various format data for the LSE core algorithm. Many testing has been carried on to prove the success of the LSE project at PG&E. In conclusion, the following contributions are achieved in this study: •
A linear state estimator algorithm and data flow structure for EMS are presented and implemented in a real power system. The LSE algorithm is consists of topology processor, observability analysis, state estimation and bad data detection. The novel data flow structure is designed and developed to interact with EMS and PDC.
•
A LSE application with user interface and algorithm has been built up. The new generation user interface development tool WPF has been used. And the LSE application has been delivered to user.
•
As a real time application, LSE has been tested on simulated steady state data and RTDS data, and field PMU data. Various scenarios, such base case, fault, one line outage, double line outage, topology error, have been tested. LSE shows great performance in these testing.
1.3. Outline This dissertation comprises 6 chapters and is outlined as follows. The motivation behind the research in this dissertation along with the objectives is described in Chapter 1. A short review of PMU and WAMS and linear state estimation are included in Chapter 2. The history, operation, technical review and implementation are provided 5
in this chapter. A control center level linear state estimator diagram is presented and introduced as well. The linear state estimator algorithm and data structure in EMS are introduced in Chapter 3. The real power system at PG&E and PMUs location in the network are presented first, following up with the detail LSE algorithm, such as topology processor, observability analysis, LSE equations and solutions, and bad data detection and identification. The second part of this chapter is to provide the new data structure of LSE in EMS, versus the traditional state estimation data flow. In Chapter 4, the visualization of LSE application is introduced and explained in detailed. The settings, control and functions of the application are included as well. The inner mechanism of data flow and behind logics of the software is also discussed in this chapter. The major work of validation and testing of LSE is placed in Chapter 5. This chapter is divided into three parts: 1) Testing on Simulated Steady State Data EMS generates steady state power flow solution for LSE to test. With the help of PMU simulator, PDC can stream the steady state solution to LSE in the format of PMU data. 2) Testing on Simulated RTDS Data A 100-bus model is built up in RTDS based on the EMS model. PMU connection tester is used to capture PMU data from RTDS. Then PDC streams the data to LSE for purpose of testing. 3) Testing on field PMU data
6
The actual field PMU data is collected and concentrated at PDC and then fed into LSE for testing. The testing results are also provided in this chapter. A summary of the findings in this dissertation and the future work are provided in Chapter 6.
7
2. PHASOR MEASUREMENT UNITS AND LINEAR STATE ESTIMATOR In this chapter, the architecture of SCADA system is briefly introduced at first. The invention and configuration of typical PMU device is also introduced. We review many application of PMU in power system since it was invented as well. And we also review the major four logic elements of traditional state estimation very shortly, such as topology processor, observability analysis, state estimation and bad data detection and identification. At the end of this chapter, the algorithm of linear state estimation is introduced. 2.1. Supervisory Control and Data Acquisition It is necessary to briefly introduce the architecture of EMS/SCADA before digging into Phasor Measurement Units. The fundamental functions of SCADA are the acquisition of data, the processing of those data for use by the operator, and operator control of remote devices [22]. Supervisory control and data acquisition (SCADA) is a complex monitor and control system consisting of a central host or master, known as master terminal unit (MTU); several field data gathering and control units or remotes known as remote terminal units (RTUs); and a collection of standard and/or custom software used to monitor and control remotely located field data elements [23]. A quality SCADA solution is central to effective operation of a utility's most critical and costly distribution, transmission, and generation assets [24]. Figure 1 shows the architecture for a SCADA system. The Data Acquisition System (DAS) gathers information from the MTU, generates and stores alerts that needs attention from the operator because it
8
can cause impact on the system. The Human Machine Interface (HMI) gathers information from the DAS and provides the interface where the operator logs on to monitor the variables of the system [25]. The utilities are facing the challenges of the competitive market and increased levels of real time data exchange that comes with various kinds of new applications and functions added to the complex system which is already very complicated in the first place. A well planned and implemented SCADA system plays an important role in terms of delivering power reliably and safely to the customers and lowering costs and achieving higher customer satisfaction. Therefore, the challenge for SCADA system needs the change and improvement of it. More will be explored in the latter chapter in the view of state estimation regarding SCADA system.
RTU
RTU
RTU
MTU
HMI
DAS
Figure 1. Architecture for a SCADA system.
2.2. Phasor Measurement Unit 9
A phasor measurement unit (PMU) is basically a digital recorder with synchronized time stamp provided by GPS. Time synchronization allows synchronized real-time measurements of multiple remote measurement points on the grid [26]. A PMU can be a dedicated device, or the PMU function can be incorporated into a protective relay or other device [27]. It was invented in 1988 by Dr. Arun G. Phadke and Dr. James S. Thorp at Virginia Tech. A PMU can measure 50/60 Hz AC waveforms for both voltages and currents, typically at a rate of 48 samples per cycle (2880 samples per second). In the field of power system engineering, phasor stands for both the magnitude and phase angle of the sine waves found in electricity. The term synchrophasor is used to refer to the phasor measurements occurring at the same time. Phasor measurement units are typically sampled from various widely dispersed locations in a power system network and synchronized from the common time source GPS. Synchrophasor technology can be used as a tool for power grid operators and planners to measure the state of the electrical system directly. Figure 2 shows a typical configuration of a PMU [28]. The analog AV waveform input signals obtained from the secondary of the voltage and current transformers are firstly introduced to anti-aliasing filter to eliminate aliasing errors. The output signals are then sampled by 16 bit A/D converter, in the reference of GPS time signal which has been processed by a phase-lock oscillator. The digital signals are then sent to phasor microprocessor to calculate the values of the phasor. Finally, the calculated phasors along with other information are transmitted to appropriate remote locations through the modems.
10
Figure 2. A typical configuration of a PMU
It has been decades since the first PMU was invented. Hundreds of PMUs have been installed all across the United States. There are many organizations and association, which make joint effort to advance the application of SynchroPhasor technologies. The North American SynchroPhasor Initiative (NASPI) is a collaboration between the electric industry, the North American Electric Reliability Corporation (NERC), and the U.S. Department of Energy (DOE) to advance the use of synchrophasor technology to enhance grid reliability and economics through highspeed, wide-area measurement, monitoring, and control [29]. Figure 3 shows PMU installations at US and Canada by March 2011 [30].
11
Figure 3. PMU installation at US & Canada
With more and more PMUs installed in power system, a lot of potential applications utilizing PMU data in terms of power system monitoring, protection, control and linear state estimation have been studied. The authors in [31] introduced the features of the PMU based WAMS (wide area measurement system) and proposed an estimation method of interconnected power system parameters from the monitored power oscillation information based on PMU data. The paper [32] provides a methodology to characterize the accuracy of PMU data (GPS-synchronized) and the applicability of this data for monitoring system stability. The researchers focus on the application of transient stability monitoring and propose an approach that is based on the energy functions (Lyapunov indirect method). PMU are also used to monitor the
12
dynamics and events of power systems [33]-[35]. There are some researches going on the aspects of voltage stability using PMU measurements as well [36]-[38]. Reference [39] presents an application of microprocessor-based phasor measurements to novel adaptive protection schemes. The possibilities for applications of PMU measurements synchronized sampling over an entire power system to simultaneously obtain the phasor values of voltages and currents at particular instants of time, in protection and control tasks of the future are explored [40]. A concept for local monitoring of the onset of voltage collapse, protective, and emergency control in the presence of voltage-sensitive loads utilizing voltage and current phasors measurements is presented in [41]. The paper [42] compares two protection schemes: one protection scheme is based solely on the protective relays while the other protection scheme utilizes both the protective relays and the PMUs. The paper [43] presents loss of mains (LOM) protection using a model that is representative of a distribution network incorporating DG. A new current differential protection scheme has been suggested for transmission line protection using synchronized measurements [44]. The main contribution of [45] is to integrate local and wide area control and protection systems by implementing the WAMS function and substation protections into one system to identify the overload caused by flow transfer from isolation of main trunk line. The scheme that makes use of the positive-sequence voltage and current phasors at both ends of a transmission line to determine the parameter of the transmission line and the location of a fault on the transmission line is presented in [46].
13
The paper [47] develops an integrated strategy for handling the challenging problem of maintaining voltage stability for online applications by using of real-time measurements via phasor measurement unit (PMU) technology. It is discussed that the problem of determining phase during a transition from one cyclic state to another by making use of PMU measurements [48]. The work reported in the paper [49] investigated the ability of synchronized phase angle measurements to identify impending instabilities through real time measurement, and to trigger remedial actions in time to prevent major power system outages. In paper [50], it is discussed that two practical considerations in the design of a PMU-based wide-area damping control system for power grid inter-area oscillations. The first consideration is the selection of PMU measurements. The second consideration is the selection of PMU data reporting rates. The stability control flow based on PMU for interconnected power system, which is a real-time stability control, is proposed in [51]. The presented scheme which is designed to a closed-loop rolling control process involving a preventive control, emergency control and corrective control, can protect the stability of power system. The paper [52] presents a new adaptive control approach to power system secondary voltage control (SVC) problem using synchronized phasor measurements as control feedback. In this paper [53], the application of synchrophasor for power system islanding and restoration is explored and the feasibility of PMUs for controlled separation is demonstrated in a real power system as well. The Duality Element Relative Fuzzy Evaluation Method (DERFEM) is used to evaluate quantitatively security vulnerabilities within cyber systems of power systems and a System Stability Monitoring and Response System (SSMARS) is
14
developed to monitor the impact of intrusion scenarios on power system dynamics in real time based on PMU measurements [54]. As introduced in chapter 1, there has been plenty of research going on the linear state estimation [13]-[14] [55]-[57] with sychrophasor data since the very first PMU invent. In the following section of this chapter, the linear state estimation algorithm will be explored in detail. 2.3. Power System Linear State Estimator The key application state estimation in EMS becomes linear, benefitting from more and more PMUs installation in power grid. PMUs provide the possibility of measuring the state vector directly, rather than estimating it from SCADA measurements. 2.3.1. Traditional Power System State Estimation Before exploring linear state estimation, it’s necessary to briefly introduce traditional state estimation. As a key function in EMS, traditional state estimation has been playing a vital role in observing the state of power system. It consists of four major parts of logic: topology processor, observability analysis, state estimation, bad data detection and identification. The purpose of topology processor is to build network model using breaker/switch status from SCADA system. In the static database of EMS/SCADA system, there are all the equipment, such as generators, load feeders, shunt capacitors, transformers, transmission lines, etc, and devices such as circuit breakers and switches. The equipment has impedance between the nodes, while the case is different for the devices. It is zero impedance when closed and open circuit when open. The output of topology processor is a table that describes a bus-branch model 15
of the network. In essence, the major work of topology processor is to convert nodebreaker topology into bus-branch topology. In practice, the tree search algorithm has been widely used [58]. To be able to solve state estimation, the power system must be observable if the measurements made on it allow determination of complex bus voltage at every node of the network [59]. Preliminary off-line observability study needs to perform before on-line implementation of state estimation. The process is to assure that it is still a reliable state estimate even under some contingencies like loss of some measurements. Online observability analysis is to make sure that the state estimation can be solved in every run of the whole procedure. In practice, there are different kinds of observability which need to be explained here. Generally speaking, it can be categorized as topological observability and numerical observability for a power network in the sense of topology and numeral. The network is topologically observable with respect to the given measurements if it is algebraically observable. The power system is numerically observable if the state estimation can be solved from a flat start while it is algebraically observable if the measurement function matrix has rank of 2n-1 (n represents the number of state) [59]. The static state of a power system can be described by the vector of complex voltage. The so-called state estimation is to calculate the states from inherent network parameters, and an adequate set of voltage and power flow measurements. The Weighted Least Square solution is the best estimate for an overdetermined system. The measurement function can be described as follows: 𝑍 = ℎ(𝑋) + 𝜎
16
(2.1)
Where Z represents the vector of measurements consisting of voltage magnitude, power flow and power injections; X represents the vector of complex voltage; 𝜎 is the measurement error vector. The set of equations are nonlinear so the Jacobian matrix is obtained by taking partial derivatives of ℎ(𝑋),
𝐻=
𝜕ℎ(𝑋) 𝜕𝑋
(2.2)
The solution of this over determined nonlinear equations has to be iterative and numerical with a criterion for convergence. 𝑋𝑘+1 = 𝑋𝑘 + 𝐺𝐻 𝑇 𝑊 −1 (𝑍 − ℎ(𝑋))
(2.3)
Where 𝑋𝑘+1 is the next iterate of the state, 𝑋𝑘 is the start iterate; the Gain matrix is: 𝐺 = (𝐻 𝑇 𝑊 −1 𝐻)−1
(2.4)
𝑊 is the covariance matrix. The last logic of the whole state estimation is a functionality that can eliminate the bad data among the raw measurements. Bad data detection and identification serves to remove the measurement with large errors. It highly relies on the redundancy of the measurements. Chi-square distribution has been widely used to detect the bad measurement. A measurement is critical if deletion of this measurement makes loss of observability of the entire network. It is proven that a measurement is detectable and identifiable if and only if the measurement is not critical and does not belong to any critical pairs. This provides a guideline for the strategy of placing the measurements [60]-[61].
17
All in all, traditional state estimation has been serving as indispensable to the operation of power system. It is the truth that many fault and black out come along with the malfunction of state estimation. Hence, to make state estimation function is very important. However, in practice, state estimation sometimes encounters convergence difficulty; this is a big threat for the operation of power system. With the advent of PMU, the measurement function becomes linear and there is no iteration while solving over determined linear equations. Therefore, the convergence needs not to be a concern. This is one big advantage of linear state estimation. Obviously, it can also save a lot of computation time. 2.3.2. Linear State Estimator PMU has the capability to directly measure the magnitude and angle of bus voltage and current. If enough voltage and current phasors are measured to make the network observable, state estimation could become linear. The measurements are voltage phasor and current phasor, and states are voltage phasor. The relationship between measurement and state is linear on the condition when the phasors are in the form of rectangular coordinate [62]. The measurement vector Z is given by 𝜎𝑉 𝑉 𝑍 = [ ] + [𝜎 ] 𝐼 𝐼
(2.5)
Where V and I are the vectors of true values of bus voltage and branch current measurements while 𝜎𝑉 and 𝜎𝐼 are the measurement error vectors. The covariance matrix W can be expressed by, 𝑊=[
𝑊𝑉 0
0 ] 𝑊𝐼
The relationship between V and I can be shown as, 18
(2.6)
𝐼 =𝑌∗𝑉
(2.7)
Where Y can be obtained through network admittance matrix and note that I in equation (2.8) is identity matrix, so 𝜎𝑉 𝐼 𝑍 = [ ] 𝑉 + [𝜎 ] 𝑌 𝐼
(2.8)
𝑍 = 𝐻𝑉 + 𝜎
(2.9)
The weighted least squares of estimate for the state vector V can be easily calculated, 𝑉 = (𝐻 𝑇 𝑊𝐻)−1 𝐻 𝑇 𝑊𝑍
(2.10)
Where the Gain matrix is shown 𝐺 = 𝐻 𝑇 𝑊𝐻
(2.11)
Without the necessity of iteration, linear state estimator (LSE) can run at subsecond cycle. PMU is able to stream phasor data measurements as fast as 30 frames per second. With the rate of microprocessor becomes much faster than ever before, LSE should be able to take advantage of the capacity of PMU. As more and more Phasor Measurement Units are coming on-line, a linear state estimator utilizing only PMU data becomes possible. As in the traditional state estimator, this linear state estimator requires sufficient redundancy for the solution to provide good estimates as well. Moreover, The topology processor is still an important part for LSE. Observability analysis, no matter preliminary off line study or on-line real time checking, are also key to be able to successfully solve the linear state estimation problem. The bad data detection and identification logic should also function in every execution of the state estimator calculation cycle. In next chapter, the detailed of linear state estimation algorithm will
19
be presented and explored carefully. Plus, the data flow issue at the control center will also be discussed. The new architecture of data flow in EMS for linear state estimator will be presented.
20
3. LINEAR STATE ESTIMATOR IN THE CONTROL CENTER ENVIRONMENT In this chapter, the power system and PMUs are introduced, including ten 500kV substations and the locations of PMUs. The algorithm of linear state estimator, which has the four major elements: topology processor, observability analysis, state estimation, bad data detection and identification, is presented and explained very carefully. In the end of this chapter, the LSE data flow for EMS is designed and explored in detail. 3.1. Control Center Level Linear State Estimator As introduced in chapter 1, Washington state university has developed a twolevel state estimator for GridSim project. The layered architecture of databases, communications and application programs are required to support this two-level linear state estimator. However, the project of Pacific Gas and Energy (PG&E) LSE needs to be run using the database at the control center. There is no distributed substation database and no state estimation at any of the substations. Hence, the twolevel LSE algorithm and data flow has to be changed and adapted to control center level only LSE in the EMS environment. Fig 4 shows the basic algorithm and data flow of the LSE at the control center. Basically, LSE takes input from EMS and openPDC to establish the static and real-time database. The LSE algorithm makes use of the information to run the core logics of linear state estimation, such as topology processor, observability analysis, state estimation, bad data detection and identification. Finally, the output of LSE is sent back to EMS for the down streaming
21
applications. Detail of each block in this diagram is to be explained in following sections. Network model from EMS
PMU data OpenPDC
LSE Static database (Read once when LSE starts)
Breaker status(EMS)
LSE Real time database
LSE Input
LSE Database
Topology Processor
Observablity Analysis
LSE formulation
LSE Algorithm
Control Center LSE X=(
Bad Data Detection
Bad Data?
YES
Eliminate the bad data and its corresponding row of H and W matrix
NO LSE output to EMS
LSE Output
Figure 4. LSE algorithm and data flow at control center 3.2. Linear State Estimation Algorithm Before exploring the algorithm of the linear state estimator, it is necessary to take a look at the real power system at PG&E network. More importantly, the location of PMUs needs to be identified so preliminary observability can be carried out. 3.2.1. Power System and PMUs The PG&E EMS network model has approximately 4,000 buses and tens of PMUs to be installed at ten 500 kV substations. The preliminary work was to extract all the ten 500 kV substations which have PMUs installed from the entire PG&E 22
system to a simpler and smaller power system. Fig 5 shows the diagram of this particular power system with the marks of PMU locations.
23
Figure 5. 500 kV substation diagram
TABLE I.
Detail of 500 kV substation diagram
Number of
Seires
Number of
Voltage
Current
Lines
Capacitor
PMUs
Phasor
Phasor
1
4
Yes
0
0
0
2
2
Yes
3
3
3
3
4
Yes
2
2
2
4
3
Yes
2
2
2
5
2
No
2
2
2
6
2
No
2
2
2
7
4
Yes
2
2
2
8
6
Yes
6
6
6
9
3
No
3
3
3
10
4
Yes
3
3
3
11
7
Yes
4
4
4
Substation
Table I describes the PMU configuration and locations in the substations. Note that substation 1 does not belong to PG&E system, so we are not able to receive any PMU data from substation 1. Preliminary off-line observability checking was done manually based on this table. There are 32 PMUs, 38 branches in this system. These PMUs measure line-side voltage and current phasors instead of bus voltage and current phasors. Each PMU is able to measure three-phase voltage and current phasor
24
and positive sequence, negative sequence and zero sequence voltage and current phasor. In the table, it only shows the number of positive sequence voltage and current phasors. The number of state variable varies in different network topology, such as split bus, on/off series capacitor, maintenance of lines or equipment and so forth. In the situation of base case (with all the circuit break and series capacitor on), there is 36 states variable and 80 measurements so the redundancy is 2.22 and it’s relatively adequate in the view of state estimation. Hence, when each PMU has one backup, then the redundancy becomes double, which is good for the accuracy of linear state estimator.
3.2.2. Topology Processor The LSE algorithm begins with that the static and real time database have been generated. The goal of topology processor is to use breaker/switch status from EMS/SCADA to obtain the real time network model of power system. The static and real time database have the topology information of each substation, analog measurements from openPDC and breaker/switch status from EMS. The LSE topology processor takes all these substation connectivity information and breaker/switch status to build up the network bus-branch model from the nodebreaker model. The whole process of topology processor can be divided into major two sections: 1. Map breaker/switch data to network model 2. Build bus model from breaker/switch data 3.2.2.1.
Map breaker/switch data to network model 25
First of all, it is necessary to show a typical Substation Level Description of a Power System in Figure 7. This is a real small power system with all the nodes (or bus sections), equipment and device, which can be defined as follows: •
Node or bus sections: Physically individual zero impedance link to which equipment is connected
Figure 6. Definition of Node or Bus section •
Equipment: Impedance between nodes: – Line, Transformer, series reactor, series capacitor – Source/sink of power: load, generator, shunt capacitor, shunt reactor
•
Device: – Connects nodes to form a bus •
Circuit breaker
•
Disconnect switch
– Zero impedance when closed – Open circuit when open
26
Figure 7. A Typical Substation Level Description of a Power System
This is a typical breaker and a half substation configuration. By extracting the main bus section, the sample substation is shown in Figure 8. N1
D1 A
D6
N2
C
N6
D2 B
D5
N3
D
N5
D3
D4 N4 N1...N6 Nodes (Bus Sections) D1...D6 Devices (Breakers/Switches) Sample Substation
Figure 8. A Sample Breaker and a Half Configuration
27
As seen, the configuration has six nodes, six breakers and four lines. It can be tabulated as two tables: TABLE II.
Node Index
Node ID Devices connected with N1
D1, D6
N2
D1, D2, A
N3
D2, D3, B
N4
D3, D4
N5
D4, D5, D
N6
D5, D6, C
TABLE III.
Device Connection List
Device ID From Node To Node
Status
D1
N1
N2
Closed
D2
N2
N3
Closed
D3
N3
N4
Closed
D4
N4
N5
Open
D5
N5
N6
Open
D6
N6
N1
Closed
All these information received from EMS/SCADA can be stored in the real time database of linear state estimator as the input of topology processor.
28
3.2.2.2.
Build bus model from breaker/switch data
The topology program runs with substation data only, one substation by one substation in sequence, as shown in figure 9. And then it connects the entire bus branch model in all the substations with the transmission lines to islands at system level, as shown in figure 10. Note that the topology processor program runs in control center, so here the substation topology processor only means it runs with substation data only rather than at a real substation remotely. It is important to restate the input and output of the network topology program. Input:
breaker/switch status Physical description of network at substation level
Output: bus branch network model Hence, the topology processor has two major parts: substation topology processor connects all the nodes with closed devices while system level topology processor connects all the buses (results from substation topology processor) with the branches, such as transmission lines, series capacitors and so on.
29
Device Connection List Device ID FromNode ToNode D1
N1 N2 N3
D2 D3
Status Closed Closed Open
N2 N3 N4
NO
Closed?
Removed from the list
YES Device Connection List Device ID D1
FromNode ToNode N1 N2
D2
N2 N3
Status Closed Closed
Loop the list
The two end Nodes belong to same island
No island has the two end nodes
The two end nodes belong to different islands
One node belongs to one island, the other node belongs to no island
Add the branch to the island: parallel branch
Create a new island: islandNum = islandNum + 1
Merge the two islands and delete the duplicate one
Append the branch to the island
Connect equipment to each island Bus Branch Model at Substation Island(Bus)
Nodes
Devices
Equipments
Bus 1
N1, N2 ... D1, D2, ...
E1, E2..
Bus 2
N2, N3 ...
D2, D3, ...
E3, E4..
Figure 9. Diagram of Substation Topology Processor
30
The diagram in figure 9 shows the details of the substation topology processor. Note that the term “island” in this diagram actually refers to bus in the aspect of bus branch model. The whole process of the algorithm is explained as follows: Step 1: Build the device connection list table; Step 2: Loop the device connection list table; If (Status is Open), removed from the list; Step 3: Loop the new device connection list table If (The two end Nodes belong to same island), add the branch to the island: parallel branch; If (No island has the two end nodes), create a new island: islandNum = islandNum + 1; If (The two end nodes belong to different islands), merge the two islands and delete the duplicate one; If (One node belongs to one island, the other node belongs to no island), append the branch to the island; Step 4: Connect equipment to each island and form the Bus Branch Model at Substation.
The diagram in figure 10 shows the details of the system level topology processor. Each substation runs substation topology processor and sends the results to system level topology processor, which runs the similar algorithm to connect all the buses and branches to islands.
31
Bus Model at substation 1 Island(Bus) Nodes Bus 1 Bus 2
Devices Equipments N1, N2 ... D1, D2, ... E1, E2.. N2, N3 ... D2, D3, ... E3, E4..
Bus Model at substation N
Bus Model at substation 2 Island(Bus) Nodes
Devices Equipments N1, N2 ... D1, D2, ... E1, E2.. N2, N3 ... D2, D3, ... E3, E4..
Bus 1 Bus 2
Island(Bus) Nodes Bus 1 Bus 2
Devices Equipments N1, N2 ... D1, D2, ... E1, E2.. N2, N3 ... D2, D3, ... E3, E4..
Branch Connection List Branch FromBus ToBus Bus 1 Bus 2 Br1 Bus 2 Br2 Bus 3 Loop the list
The two end buess belong to same island
No island has the two end buses
The two end buses belong to different islands
One bus belongs to one island, the other bus belongs to no island
Add the branch to the island: parallel branch
Create a new island: islandNum = islandNum + 1
Merge the two islands and delete the duplicate one
Append the branch to the island
Bus Branch Network Model Island Buses Branches Equipments E1, E2.. Island 1 Bus 1, Bus 2.. D1, D2, ... E3, E4.. Island 2 Bus 3, Bus 4.. D2, D3, ...
Figure 10. Diagram of System Level Topology Processor
The whole process of the system level topology processor algorithm is similar with the algorithm of substation topology processor and explained as follows: Step 1: Build the branch connection list table based on the results of substation topology processor; Step 2: Loop the branch connection list table; If (The two end buses belong to same island), add the branch to the island: parallel branch;
32
If (No island has the two end buses), create a new island: islandNum = islandNum + 1; If (The two end buses belong to different islands), merge the two islands and delete the duplicate one; If (One bus belongs to one island, the other bus belongs to no island), append the branch to the island; Step 4: Identify the islands: eliminate the island without branches or any equipment At the end of the entire program, all the equipment connected to the buses is tabulated. The connectivity of the equipment to the buses can be established. And the present connectivity of the system can be determined. 3.2.2.3.
Case Study of Topology Processor
Below are the examples to demonstrate the functionality of topology processor of the linear state estimator algorithm. Figure 11 presents an example to show how topology processor connects the closed breaker/switch to form a bus-branch model. The uppercase letters represent node/bus sections while the lowercase letters represent circuit breakers. There are two breaker and a half scheme substations as shown. The bypass breakers of series capacitors at substation 1 are all open, which means that the statuses of series capacitors are in. Hence, node G, H, N and O become bus 3, 4, 5 and 6 respectively. And the circuit breakers a, d and f at substation 1 are open, so this voltage level becomes split bus, bus 1 and 2. Bus 1 consists of node B, E and bus 2 consists of node A, C, D and F. For substation 2, all the breakers are closed, so this voltage level becomes single bus 7. This is only a demonstration of the logic the 33
topology processor. In the real power system, there are not only circuit breaker, but also switch and other devices to be taken into account. After topology processing, LSE can have a bus-branch model of the whole network. Table Ⅳ shows the tabulated result. E
I c
N
f
a B
b
C
J
G
d D
A
h
Transimission Line
g
H
k
i
Transimission Line
M
O
K
e
m
j
F
L
Substation 1
Substation 2 Closed Open
Bus 1 (B, E)
Bus 3 (G)
Bus 5 (N) Bus 7 (I, J, K, L,M) Transimission Line
Bus 2 (A, C, D, F) Bus 4 (H)
Bus 6 (O)
Figure 11. Example of Topology Processor on Sample System TABLE IV.
Tabulated Result of Topology Processor on Sample System Bus ID
Node ID
1
B, E
2
A, C, D, F
3
G
4
H
5
N
6
O
7
I, J, K, L, M
34
Another example is to run the topology processor at PG&E system. As to the real power system, the result of topology processor is given here. The figure 12 shows the topology processor running on base case with all the series capacitors switched on. ST 3
ST 2 LN
BUS SC LN LN
Line
ST 7 LN
ST 5
LN
ST 4
LN LN
LN
LN
LN
ST 6
ST 9
LN
ST 8
LN
LN
LN
LN ST 10 LN LN
ST 11
Figure 12. Example of Topology Processor on PG&E System
As seen in this figure, series capacitors add more buses to the power system. Hence, while formulating the linear state estimation problem, we need to take into account the cases with on/off series capacitors. Once the status of any series capacitors changes, the topology processor has to be able to detect and build new bus
35
branch model for the following state estimation. But before heading to state estimation, the real time observability check has to be done first to make sure the state estimation can be solved.
3.2.3. Observability Analysis The result of topology processor provides the present connectivity of the power system. The real time observability analysis is to correlate the PMU measurement with the network topology, so that LSE is able to figure out how many observable islands there are and how the buses are connected in each observable island. As introduced in chapter 2, there are basically two kinds of observabilities in the aspect of topology and numeral. 3.2.3.1.
Numerical Observability
The power system is algebraically observable with respect to the given measurements if the Jacobian matrix H(x) has the rank equals to number of state. However, numerically observable is defined as the state estimator can be iteratively solved from a flat start [59]. In some cases, the Jacobian matrix H(x) may have the rank equals to number of state, but the matrix is ill-conditioned so the state estimation problem is not able to be solved. Hence, if the system is numerically observable, then it must be algebraically observable, but the converse may not hold. That is how these two can be distinguished as shown in figure 13. The numerical observability analysis looks conceptually simple and by checking the rank of Jacobian matrix H(x), we can make sure the state estimation problem is algebraically observable or not. However, as a numerical algorithm, the round-off
36
errors may make the process difficult if the diagonal entry of Jacobian matrix H(x) has zeros.
algebraically observable
numerically observable
Figure 13. Numerically observable versus algebraically observable
3.2.3.2.
Topological Observability
Unlike numerical method, topological method makes use of topology information from topology processor. The basic idea of topological observability is to find an observable spanning tree, given a set of measurements and the topology of the power system. A spanning tree of the network graph is an observable spanning tree (OST) if and only if it is possible to assign a measurement of to each one of the tree branches, such that no two branches are associated with the same measurement [63][64]. If it is not able to find an OST for the network, the topological observability analysis program has to find a maximal forest with multiple trees and each one of them in the forest is an observable spanning tree by using pseudo-measurements or virtual measurements to create such a spanning tree of the network to meet the requirement of the observability. The topological observability analysis program can be divided into two steps:
37
Step 1: given the measurement set M, construct a fundamental spanning forest by assigning each line flow measurement to the corresponding branches to and identify the boundary buses which connect these trees and unmeasured buses. Step 2: assign injection measurements to one selected branch. As the injection measurement can be correlated with any of the branches incident to the measured bus, so there are several ways to assign it. In reference [59], a practical algorithm using network topology was presented. The algorithm can locate the observable islands, and what measurements can be added to make the entire network observable. The topology method is straightforward and easy to implement in program compared with numerical method. Hence, in our linear state estimation program, we use topology method to do the real time on line observability check. 3.2.3.3.
Phasor Measurements
As introduced above, phasor measurement unit is able to measure both voltage and current phasors at the same reference. And the current phasor measurement contains flow current measurement and injection current measurement. These measurements form the input of linear state estimator, so the program needs to identify and correlate these measurements with the present topology. Voltage Phasor: the voltage phasor measurement measures the voltage of node/bus section at one substation. Voltage phasor measurement is actually a state measurement, because the measurement itself is a state. The same logic applies to the bus-branch model. The bus becomes an observable bus if there is a voltage phasor measurement on this bus.
38
PMU
Node
Figure 14. Voltage Phasor Measurement
Flow Current Phasor: the flow current phasor measurement is taken on any branch, such as transmission line, series capacitor, shunt, or any other equipment with current flowing through. Figure 15 gives an example of flow current phasor measurement on a branch. Pi model is introduced here to represent the branch.
V1
PMU I12
V2 R
X
B/2
B/2 Ground
Figure 15. Flow Current Phasor Measurement
The PMU can measures the phasors of 𝑉1 and 𝐼12 , the direction of which is shown in figure 15. Equation (3.1) provides the relationship between 𝐼12 and 𝑉1 , 𝑉2. 𝐵
𝐼12 = 𝑌12 (𝑉1 − 𝑉2 ) + 𝑉1 ∗ 𝑗 2
(3.1)
𝑅−𝑗𝑋
where 𝑌12 = 𝑅2 +𝑋 2, is the relationship between two buses; If 𝑉1 and 𝐼12 are given, then this branch is observable because 𝑉2 can be calculated with equation (3.1).
39
Injection Current Phasor: the injection current measurement is taken at the injection point in power system, like generator, load, shunt capacitor and so forth. Figure 16 provides an example of injection current phasor measurement at one injection node of network. As seen in the figure, the PMU measures the voltage phasor 𝑉1 and injection current phasor 𝐼1 .
VN
I1N V3 I13
I12 V1 PMU
V2 I1
Figure 16. Injection Current Phasor Measurement
Applying Kirchhoff's current law (KCL) at injection node 1, we can obtain the equation: 𝐼1 = 𝐼12 + 𝐼13 + ⋯ + 𝐼1𝑁 𝐼1 = ∑𝑁 1 (𝑌1𝑁 (𝑉1 − 𝑉𝑁 ) + 𝑉1 ∗ 𝑗 Where 𝑌1𝑁 and 𝐵1𝑁 can be obtained from Y bus.
40
(3.2) 𝐵1𝑁 2
)
(3.3)
Hence, the injection current phasor measurement can be assigned at any branch associated with the injection node. It can be used to add to any network to render observability. 3.2.3.4.
Case Study of Observability Analysis
Two examples are given here to demonstrate the observability analysis program. Bus 1 (B, E)
Bus 3 (G)
Bus 5 (N) Bus 7 (I, J, K, L,M) Transimission Line
Bus 2 (A, C, D) Bus 4 (H)
Bus 6 (O)
PMU Current Measurement
Figure 17. Observability Analysis on Sample System
Figure 17 shows an example of the sample system. Since PMU is located at line side, the observability analysis program has to extend the current measurement to its adjacent series capacitors to make the series capacitor branch observable. There is a PMU measuring voltage and current phasors at bus 5, the program extends the current to bus 3 and 1 so that the two series capacitor branches also are observable. Bus 7 can be calculated by its neighboring bus 5 in state estimation, so it is also observable. To the contrary, there is no PMU at bus 6, so bus 6, 4 and 2 are not observable in this case and neither do the corresponding branches. The other example in figure 18 is to apply the observability analysis program on PG&E system. By extending all the line side current to its adjacent series capacitors,
41
the whole system is able to gain the observability. Therefore, linear state estimation problem can be formulated and solved. This is the base case of the PG&E system; with the topology changes the observability analysis program may detect multiple observable islands, in which we need to formulate the linear state estimation problem. It is carefully explored in next section. ST 3
BUS SC
LN LN LN ST 2
LN
Current Measurement
ST 7 LN
ST 5
Line
ST 4
LN LN
LN
LN
LN
ST 6
ST 9
LN
ST 8
LN
LN
LN
LN ST 10 LN LN
ST 11
Figure 18. Observability Analysis on PG&E System
3.2.4. Linear State Estimation Equations and Solutions
42
The purpose of state estimation is to provide the best state variables of the whole network. The analog quantities measured by the meter system are sent to control center, where it has computer units to process these data through communication links. However, the quantities are not freedom of noise or errors, so we never know the true state and can only obtain the best possible estimate. A weighted least square algorithm (WLS) has been widely used to solve the state estimation problem for the over determined system. It can be formulated as follows: 2 Min 𝑱(𝒙) = ∑𝑚 𝑖=1(𝒛𝑖 − 𝒉𝒊 (𝒙)) /𝑹𝑖𝑖
s. t. 𝒛𝑖 = ℎ𝑖 (𝒙) + 𝜎𝑖
(3.4) (3.5)
Where 𝒙 is the vector of state, voltage vector V namely; 𝑹𝑖𝑖 is the diagonal entry of the covariance matrix and m is the number of measurement, 𝑾 = 1/𝑹
(3.6)
As introduced in previous sections, the measurement function becomes linear so the solution has iterations. In this dissertation, the measurement inputs are the bus ̂ , flow current vector 𝑰̂𝒇 and injection current vector 𝑰̂𝒊 : voltage vector 𝑽 𝑉1 𝑉 ̂ = [ 2] 𝑽 ⋮ 𝑉𝑛
(3.7)
𝐼𝑓𝑙𝑜𝑤,1 𝐼 𝑰̂𝒇 = 𝑓𝑙𝑜𝑤,2 ⋮ 𝐼 [ 𝑓𝑙𝑜𝑤,𝑖 ]
(3.8)
𝐼𝑖𝑛𝑗,1 𝐼 𝑰̂𝒊 = 𝑖𝑛𝑗,2 ⋮ [𝐼𝑖𝑛𝑗,𝑗 ]
(3.9)
43
Where i and j are the number of flow measurement and injection measurement respectively; In this linear state estimator project, there is no injection current measurement. Hence, the injection measurement model is ignored under the circumstance and the measurement function can be formulated as follows: ̂ ̂ = [ 𝑽 ] = 𝑯𝑽 ̂ + 𝝈 = [𝑰] 𝑽 ̂+𝝈 𝒁 ̂ 𝑰𝒇 𝒀
(3.10)
Where 𝑰 is the identity matrix, 𝝈 is the measurement error vector, 𝒀 represent the relationship between two buses and it can be obtained from network parameters. Pi model is introduced here again to represent the branch in figure 19.
V1
I12
R
I21
X
B/2
V2
B/2 Ground
Figure 19. Branch Modeling with Pi Model
If all the phasor are defined in complex plane, we can make some transformation to equation (3.1), 𝐵
𝑅−𝑗𝑋
𝐵
𝑅−𝑗𝑋
𝐼12 = 𝑌12 (𝑉1 − 𝑉2 ) + 𝑉1 ∗ 𝑗 2 = (𝑅2 +𝑋 2 + 𝑗 2 ) 𝑉1 − 𝑅2 +𝑋 2 𝑉2
𝐼12,𝑟𝑒𝑎𝑙 [ ]= 𝐼12,𝑖𝑚𝑎𝑔
44
(3.11)
𝑅 𝑉 𝑅 2 +𝑋 2 1,𝑟𝑒𝑎𝑙 [ 𝐵 𝑋
𝐵
𝑋
−𝑅
𝑋
𝑋
−𝑅
− ( 2 − 𝑅2 +𝑋 2 ) 𝑉1,𝑖𝑚𝑎𝑔 + 𝑅2 +𝑋 2 𝑉2,𝑟𝑒𝑎𝑙 − 𝑅2 +𝑋 2 𝑉2,𝑖𝑚𝑎𝑔 𝑅
( 2 − 𝑅2 +𝑋 2 ) 𝑉1,𝑟𝑒𝑎𝑙 + 𝑅2 +𝑋 2 𝑉1,𝑖𝑚𝑎𝑔 + 𝑅2 +𝑋 2 𝑉2,𝑟𝑒𝑎𝑙 + 𝑅2 +𝑋 2 𝑉2,𝑖𝑚𝑎𝑔
]
(3.12)
Hence, the equation (3.10) can be expressed in the complex plane as follows: ̂ 𝒓𝒆𝒂𝒍 𝑽 ̂ 𝒊𝒎𝒂𝒈 𝑽 𝑰̂𝒇
𝒓𝒆𝒂𝒍
̂ [𝑰𝒇 𝒊𝒎𝒂𝒈 ]
𝑰 𝟎 = [𝒀 𝟏 𝒀𝟑
𝟎 ̂ 𝒓𝒆𝒂𝒍 𝑽 𝑰 ] [ 𝒀𝟐 𝑽 ̂ 𝒊𝒎𝒂𝒈 ] + 𝝈 𝒀𝟒
(3.13)
The matrix 𝒀𝟏 , 𝒀𝟐 , 𝒀𝟑 , 𝒀𝟒 can be calculated using equation (3.12). Once these measurement functions are formulated, it's easy to use equation (2.10) to solve the LSE problem.
3.2.4.1.
Impact of Series Capacitors on LSE formulation
Of particular interest are the series-compensated lines, where PMUs are installed on line-side. The status of compensators (in or out) will impact the results. It’s already discussed regarding the impact of series capacitors on observability analysis. In this section, the impact of series capacitors on LSE formulation is explored.
PMU
V3
I1
I1
XC
XC V2
I1
V1
Figure 20. LSE formulation on series capacitor
45
As seen in figure 20, the PMU is located on line side. So 𝑉1 and 𝐼1 are directly measured by PMU. Hence, it is easy to obtain the measurement function, 𝑉1 = 𝑉1 𝐼1 = −𝑗 ∗ 𝑋𝐶 (𝑉2 − 𝑉1 ) 𝐼1 = −𝑗 ∗ 𝑋𝐶 (𝑉3 − 𝑉2 ) States: 𝑉1, 𝑉2 and 𝑉3 Measurements: 𝑉1, 𝐼1 between bus 1 and 2, 𝐼1 between bus 2 and 3
It is obvious that the formulation is solvable. However, it only meets the observability with no redundancy.
3.2.4.2.
LSE formulation in observable islands
The last issue needs to be explained here is that how the linear state estimator behaves when there are multiple observable islands existing. One of the big advantages of our linear state estimator program is that it is able to formulate the LSE equations and solve the problems in each of the observable island, as of how many of them depend on the result of observability analysis program. Hence, even if one or several PMUs are missing, we can still be able to formulate the equations and solve the LSE and the only difference is that the observable island becomes smaller. Figure 21 provides an example that LSE is solved in different observable islands. The figure also shows the part of the power network which is not observable and LSE can’t be solved if there is no PMU installed in any of the unobservable islands or no enough observability. Further research needs to be carried on in the field of PMU
46
placement strategy, which tries to gain the maximum observable island with limited number of PMUs. Observable Island
Observable Island
Internal system
Unobservable Island Observable Island External system 1
Figure 21. LSE Solving in Each of Observable Islands
3.2.5. Bad Data Detection and Identification If the power system network model and acquired data measurement from EMS/SCADA are accurate, there is good reason to believe that state estimate can provide the best estimates calculated by the weighted least square algorithm. However, there is still a chance that a measurement is grossly erroneous or so-called bad data. The linear state estimator should be able to detect, identify and finally remove those bad data. Hence, bad data detection and identification becomes essential function of state estimator in EMS. In this dissertation, LSE also has this built-in feature to filter out the bad data. It is known that the performance of bad data detection and identification relies on the measurement redundancy. In this section, the widely used method Chi-squares test is
47
applied to detect bad data, and the other method Largest Normalized Residual (LRN) is used to identify bad data. These two methods are based on the random theory. As mentioned in previous section, we never know the true state of the system. Neither is the true measurement error 𝑒𝑗 . The best we can do is to calculate the estimated error, ̂ = 𝒁 − 𝑯𝑽 = [𝑰 − 𝑯𝑮−𝟏 𝑯𝑻 𝑾]𝒆 𝒆̂ = 𝒁 − 𝒁
(3.14)
The mean of the estimated error 𝒆̂𝒋 , ̂ ) = 𝑬(𝒁 − 𝑯𝑽) = [𝑰 − 𝑯𝑮−𝟏 𝑯𝑻 𝑾]𝑬(𝒆) = 𝟎 𝑬(𝒆̂) = 𝑬(𝒁 − 𝒁
(3.15)
The expected value of 𝒆𝒆𝑻 can be easily obtained, 𝑬(𝒆𝒆𝑻 ) = 𝑹
(3.16)
As to the expected value of estimated measurement error 𝒆̂𝒆̂𝑻 , ̂ )(𝒁 − 𝒁 ̂ )𝑇 = [𝑰 − 𝑯𝑮−𝟏 𝑯𝑻 𝑹−𝟏 ]𝒆𝒆𝑻 [𝑰 − 𝑹−𝟏 𝑯𝑮−𝟏 𝑯𝑻 ] 𝒆̂𝒆̂𝑻 = (𝒁 − 𝒁 Hence, the covariance matrix of the estimated error can be given, 𝑬(𝒆̂𝒆̂𝑻 ) = 𝑬([𝑰 − 𝑯𝑮−𝟏 𝑯𝑻 𝑹−𝟏 ]𝒆𝒆𝑻 [𝑰 − 𝑹−𝟏 𝑯𝑮−𝟏 𝑯𝑻 ]) = [𝑰 − 𝑯𝑮−𝟏 𝑯𝑻 𝑹−𝟏 ]𝑬(𝒆𝒆𝑻 )[𝑰 − 𝑹−𝟏 𝑯𝑮−𝟏 𝑯𝑻 ] = 𝑹 − 𝑯𝑮−𝟏 𝑯𝑻 = 𝑹′ (3.17)
The WLS algorithm is applied here so we substitute estimated error 𝑒𝑗 in the objective function of state estimation, which is also known as the weighted sum of square 𝑓̂ [65] ̂ 𝒋𝟐 𝑓̂ = ∑𝒎 𝒋=𝟏 𝒘𝒋 𝒆
(3.18)
Where m is the is number of measurement and the weighting factor 𝑤𝑗 is set equal to 1⁄ 2 . 𝜎𝑗
48
Based on random process theory, 𝒆̂𝒋 is a Gaussian random variable with zero mean, so the weighted sum of square 𝑓̂ is also a random variable that has a chi-square probability distribution, with the number of degrees of freedom 𝑚 − 𝑛 (number of state variable), ̂ 𝒋𝟐 = 𝒎 − 𝒏 𝑬[ 𝑓̂] = ∑𝒎 𝒋=𝟏 𝒘𝒋 𝒆
(3.19)
Therefore, chi-square test has been used to detect bad data as a built-in feature of the linear state estimator program. The whole procedure is as follows,
1. Solve the linear state estimator, then calculate the weighted least squares estimates of state 𝑽; ̂ =𝑯∗𝑽 ̂ , hence the estimated 2. Substitute estimates of states to the equation 𝒁 ̂; error 𝒆̂ = 𝒁 − 𝒁 ̂ 𝒋𝟐; 3. Evaluate the weighted sum of squares 𝑓̂ = ∑𝒎 𝒋=𝟏 𝒘𝒋 𝒆 4. For 𝑘 = 𝑚 − 𝑛, and a specified probability α, determine whether or not the value of 𝑓̂ is less than the critical value corresponding to α. In practice, this 2 means we check the inequality 𝑓̂ < 𝜒𝑘,𝛼 2 5. If 𝑓̂ > 𝜒𝑘,𝛼 , then bad data is detected; otherwise no bad data
The next step is to identify the bad data and remove it from the measurements, if there is bad data detected. Largest Normalized Residue (LNR) method which uses the properties of the residue is widely used today’s single bad data identification program. The procedure is shown below,
49
1. Solve the WLS linear state estimation problem and then calculate the residue ̂; of measurement 𝒆̂ = 𝒁 − 𝒁 2. Calculate the covariance matrix of the estimated measurement error 𝑹′ = (𝑰 − 𝑯 ∗ 𝑮−𝟏 ∗ 𝑯𝑻 ∗ 𝑹−𝟏 ) ∗ 𝑹; 3. 𝑅𝑗𝑗 ′ is the diagonal element of 𝑹′ , then the normalized residues: 𝑟𝑖 𝑁 =
𝑟𝑖 𝑅𝑗𝑗 ′
;
4. Find the largest normalized residue and compare it with pre-set threshold, if 𝑟𝑖 𝑁 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 , then remove it; 5. Go to step 1 again, until 𝑟𝑖 𝑁 < 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
One of the drawbacks of this Largest Normalized Residue method is that the residues can be strongly correlated. Its performance can be impacted if there exist multiple bad data. Another one is that the threshold value is set based on the engineer’s experience. If the threshold is too high, then it decreases the accuracy of state estimation; on the contrast, if the threshold is too low, then some reasonably good measurement may be flagged as bad data and be removed. It can be as further research.
3.3. EMS Data Flow Power system state estimation is one of the key applications in modern energy management system at control center. The purpose of state estimation is to obtain the best estimate of the real time model of power system [67]-[68]. For SE to be solved, it needs a static database and a real time data base.
50
A static database in EMS provides network configuration data such as line impedance, transformer impedance, generator model, device connectivity and so forth. Traditional state estimator makes use of measurements from supervisory control and data acquisition system. A real-time database in SCADA is acquired through RTUs and IEDs. SCADA provides one snapshot of the system measurements including analog and digital measurements. Analog measurement comprises voltage magnitude, power injections and power flows. Digital measurement comprises topology information such as breaker status, switch status and so forth. The traditional power system state estimator data flow in existing EMS is shown in Figure 22. SE Breaker Status(EMS) Static Database R, X, B...
SCADA Real Time Database
RTU
RTU
IED
Topology Processor
IED
Figure 22. Traditional SE Data Flow in Existing EMS
LSE is to use PMU data from openPDC, so the data flow structure has to be changed and redesigned. Figure 4 shows how the LSE databases are generated. The static database is generated from EMS network model while the real time database consists of PMU data and breaker/switch status from EMS.
51
In this linear state estimator project at PG&E, LSE makes use of a customized network topology file, which is called as a static file. The static file contains an EMS node breaker model of the ten 500 kV substations. Plus, it is a CSV ("Comma Separated Value") format file, interfaced with the main LSE program. Each substation contains all the equipment description such as generator, transformer, transmission line, breaker, switch, series capacitor, shunt capacitor and so forth. Moreover, it also has the location of PMUs at each substation, which is a key for topology process and observability analysis afterwards. All these information are processed by the LSE interface and stored in its own static data base for the next step processing. One snapshot of part of this static file is shown in figure 23. ST,3 ,SWTC,BRKR ,612 ,5002,5003,500 ST,3 ,SWTC,BRKR ,712 ,5005,5006,500 : : : ST,3 ,SWTC,SW ,611 ,5000,5002,500 ST,3 ,SWTC,SW ,613 ,5003,5004,500 : : ST,3 ,CAPR,SHUNT_CAP_5 ,5024,500,2.43 ST,3 ,CAPR,SHUNT_CAP_6 ,5026,500,2.43 : : ST,3 ,XFMR,1_500WND ,5017,9999,500,1,0.00018,0.01668,0,0.38 :
Figure 23. Snapshot of Part of Static File
The openPDC is a complete set of applications for processing streaming timeseries data in real-time. It stands for "open source phasor data concentrator" and was 52
originally designed for the concentration and management of real-time streaming synchrophasors [69]-[70]. OpenPDC has the capability to collect and send over PMU data as fast as 30 frames per second [71]. LSE receives the PMU data from PDC to generate the real time database. One snapshot of sample PMU data is shown in figure 24, and there are both magnitude and angle for voltage and current.
Voltage1 Angle 147.6971581 147.6971854 147.6971717 Current7 Angle -34.84570245 -34.84599273 -34.84599956
Voltage1 Magnitude 315786.625 315790.3438 315786.5625 : Current7 Magnitude 496.9590454 496.9672852 496.9586792 :
Figure 24. Snapshot of Sample PMU data
The other major element of the LSE real time database contains the breaker/switch status. A web service is applied to transfer a dynamic file which contains all the breaker/switch status from SCADA through communication network to LSE program. The detail of how we make use of web service will be explained in the next chapter. Here, it is necessary to mention that SCADA updates the breaker status much slower than LSE running, which is designed to run 30 times per second. Hence, when the topology changes for some reason, LSE may not be able to receive the latest dynamic file in time and the LSE output could be problematic in a small time interval. Figure 25 provides an example of snapshot of the dynamic file.
53
ST,3 ,SWTC,BRKR ,612 ,CLOSED ST,3 ,SWTC,BRKR ,712 ,CLOSED : ST,3 ,SWTC,CAPSEG,SERIES_CAP1 ,OPEN : ST,3 ,SWTC,SW ,611 ,CLOSED ST,3 ,SWTC,SW ,613 ,CLOSED :
Figure 25. Snapshot of Sample Dynamic File
We have already discussed about all the inputs that are needed for the linear state estimator program. The whole LSE data flow in EMS at control center is shown in figure 26.
ST,3 ,SWTC,BRKR ,612 ST,3 ,SWTC,BRKR ,712
,5002,5003,500 ,5005,5006,500
ST,3 ,SWTC,SW ,611 ST,3 ,SWTC,SW ,613
,5000,5002,500 ,5003,5004,500
ST,3 ,CAPR,SHUNT_CAP_5 ,5024,500,2.43 ST,3 ,CAPR,SHUNT_CAP_6 ,5026,500,2.43
ST,3 ,XFMR,1_500WND
,5017,9999,500,1,0.00018,0.01668,0,0.38
Network model from EMS
Voltage1 Angle 147.6971581 147.6971854 147.6971717
Voltage1 Magnitude 315786.625 315790.3438 315786.5625
Current7 Angle -34.84570245 -34.84599273 -34.84599956
Current7 Magnitude 496.9590454 496.9672852 496.9586792
ST,3 ,SWTC,BRKR ,612 ST,3 ,SWTC,BRKR ,712
ST,3 ,SWTC,CAPSEG,SERIES_CAP1 ,OPEN ST,3 ,SWTC,SW ,611 ST,3 ,SWTC,SW ,613
Breaker status(EMS) PMU data OpenPDC
LSE
Figure 26. LSE data flow for EMS
54
,CLOSED ,CLOSED
,CLOSED ,CLOSED
As seen in figure 26, the static and dynamic file come from the EMS at control center while the PMU data are from openPDC. Note that every data source has different sampling rate, LSE has to be able to handle it. Before diving to the testing of our LSE program, it is meaningful to introduce the user interface next chapter, which has been developed for the utility customer.
55
4. VISUALIZATION The basic user interface of the linear state estimator program is presented in this chapter. The functionalities of the LSE program are explored in detail, including the configuration, running, display and output of the LSE. The behind logic of designing the program is also discussed in this section. Some pictures of user interface are given here as well.
4.1. Software Development Tools As an actual application, LSE needs a basic user interface which can give some visualization to user. Windows Presentation Framework (WPF) is used to build up the UI. WPF is a Computer Software graphical subsystem for rendering user interfaces in Windows-based applications by Microsoft [72]. A setup package of LSE has been created by using InstallShield from Flexera Software [73]. InstallShield is a software development tool for creating installers or software packages. It is primarily used for installing software for Microsoft Windows desktop and server platforms [74]. Some new technologies, such as Web Service, XML, ISD and so forth, are also applied here to enhance the performance and functionalities of the LSE. 4.2. Configure The Linear State Estimator
56
Figure 27. LSE UI TAB - Configure
Figure 27 gives the snapshot of the LSE UI TAB – Configure. There are three sections under the TAB.
1. PDC Configuration:
57
LSE is a stand-alone application and this version of LSE is designed to work for TCP/UDP connection for the input stream obtained from PDC. Configuration frames are received through TCP connection while Data frames are received via UDP connection. The user needs to enter: Access ID: ID code of the input stream/device ID UDP Port: Port which receives Data packets TCP Port: Port for command channel communication (Configuration File etc) TCP IP: IP address for TCP connection Interface: Interface is left with 0.0.0.0 for now, save it for the use in future
2. LSE Configuration Load Static Information: Static file contains the network model Load Static Information: Dynamic file (breaker status information) and Load Mapping File: Mapping file between PMU name from openPDC and EMS name are needed. Details of how the mapping is done will be explained in the next chapter. Using Web Service: Enable/Disable the web service module; figure 28 gives a brief example of how the web service works. A web service is a method of communications between two electronic devices over a network. It serves as a software function provided at a network address over the web with the service always on as in the concept of utility computing [75]. More of detail of how the web service functionality has been applied for LSE in EMS environment will be explored in the next chapter.
58
Request Message
Internet
Client
Response Message
Server
Figure 28. Web Service
Logging: Enable/Disable the log functionality of LSE, which can save all the operation activities of LSE for the analysis afterwards. IPAddress 1-4: IP address for web service, four IP address provides four different server addresses. Check Availability of WebService: before connecting to server, check the availability of web service.
3. SCADA configuration SCADA configuration is used to set up parameters of inter site delivery (ISD) link, with which the output of LSE are sent back to EMS. It is an existing software function plugged in to LSE by other IT talent. Hence, the detail of these parameters is not going to be explained in this dissertation.
LSE also provides an easy way to configure the parameters by making use of XML file for the continence of the users. Hence, user can either edit the XML file directly to change the parameters or enter the parameters on the user interface itself.
59
Extensible Markup Language (XML) is a markup language that defines a set of rules for encoding documents in a format that is both human-readable and machinereadable. It provides simplicity, generality, and usability for transferring data over the Internet [76].
4.3. Run The Linear State Estimator
Figure 29. LSE UI TAB - Connect 60
The user interface provides two ways of running LSE. One utilizes data from PDC while the other one makes use of data from Dispatcher Training Simulator (DTS). A dispatcher training simulator (DTS) is able to simulate the behavior of the electrical network forming the power system under various operating conditions [77].
1. Connect to PDC: There are two ways of retrieving dynamic file: 1> Using local dynamic file: Enter the parameters needed for connecting to PDC, Load static, dynamic, mapping files, then click “connect to PDC” button, and click “Start LSE” button. 2> Using web service to transfer dynamic file: Enter the parameters needed for connecting to PDC, Check the “Using webservice” checkbox, then Load static, mapping files, input up to four IP addresses in each textbox, and click “Check Availability of Webservice” button, finally click “connect to PDC” button, and click “Start LSE” button.
2. Connect to DTS: Load static, mapping files, it will always use the IP address in the textbox IPAddress 1, then click “connect to DTS” button, and click “Start LSE” button. The advantage of DTS is that it can simulate various operation conditions under which LSE can be tested. It helps to validate the LSE algorithm.
61
Plus, the user interface also provides the functionalities such as Connect to/Disconnect from PDC, Start/Pause LSE and Connect to/Disconnect from SCADA. “Help” button directs user to the LSE manual. A status bar at the bottom is added to keep track of the operation of LSE. Some additional testing features which are useful to let engineer be able to test LSE are added. One is disable/enable PMU signal, so user can simulate the condition when some PMU signals are not available and under these circumstances whether LSE is able to handle it or not. The other feature is adding Gaussian noise to PMU signal. So by using these functionalities, user can toggle availability of measurements and add noise to measurements including magnitude and angle. All the PMU signals are organized in a tree view. User can disable/enable one PMU signal or multiple PMU signal in one substation or multiple substations. There are two slides in right side of UI, which can let user to add particular percentage of phasor magnitude with standard normal distribution and add certain degree bias to phasor angle.
4.4. Display The Output of The Linear State Estimator Once LSE starts, click the “TAB InternalMeasurement”, it goes to figure 30. The table will be updated continuously. User can change the refresh rate of the table on the scale of second. With the Combobox, user can pause the table refreshing and get a snapshot of the input and output of LSE and save it as a file for further analysis.
62
Figure 30. LSE UI TAB – Internal Measurement
Under the Analyze tab, there is another table as shown in figure 31, which can show the statistics of LSE such as number of topological island, observable island, bus, branch, voltage, current and sum of voltage magnitude error and so forth.
Figure 31. LSE UI TAB - Analyze
63
A real time display chart was created to show the trajectory of input and output of LSE as shown in figure 32. From this chart, LSE is able to show the transient states of a power system, which could be very useful to operator and dispatcher at control center.
Figure 32. LSE Real Time Chart
This chart shows one testing case with RTDS simulated PMU data. The detail of testing of LSE will be explored in next chapter.
Window Title: display of current PDC data frame rate
64
Horizontal Axis: time in the format of Date Time Vertical Axis: magnitude for both the voltage and current phasors Legend: phasor IDs
This chart serves as a trending function which can keeps track the state of power system in real time. Further enhancement can be made to the user interface, such as Capture “Events” - detect an event and dump data for certain duration; playback feature - read the dumped data and play back one frame at a time, and so on. With the help of the LSE user interface, it is very convenient to perform the testing of the LSE algorithm, which is the major part of this dissertation and is going to be explored in next chapter.
65
5. Testing Linear State Estimator is a key new application that makes use of synchrophasor data only. LSE, by design, is capable of running at sub-second intervals, as opposed to traditional state estimators in EMS that run every few minutes. As part of PG&E smart grid project architecture, LSE is to be integrated in to the next generation energy management system. Alstom Grid worked with Washington State University to integrate LSE in to the EMS. Some of the challenges in integration were presented in [78]. Integration, by design, included validation and training. It was decided to use PG&E network model in the validation from the beginning itself. In the early stages, the deployment location of LSE is deferred. One choice is to run LSE on the enabled (Primary) EMS every few seconds (at SCADA scan rate). The other choice is to run LSE on the same machine as the openPDC which will have all the PMU data. Each has its own data requirements. The latter was chosen in order to run LSE as often as possible, with the minimum requirement of four times per second. In order to validate the linear state estimation algorithm and test the performance of the user interface, a lot of testing has been carried on under various data set and system operation conditions in major three settings in this chapter:
Testing on simulated steady state data,
Testing on simulated RTDS data and
Testing on field PMU data.
66
It is natural that the testing sequence is starting from steady state data, and then moving to the dynamic. This chapter is going to be divided by the three testing settings; in the meantime, some related functionality and performance of the user interface is also mentioned. In addition to LSE’s own User Interface, LSE send its output to SCADA database. This information is displayed on wide-area situational displays [79]-[80] for operators. In addition, a Parallel State Estimator (SE) is setup in EMS to run using only PMU data; the Parallel SE can run using either raw PMU data or LSE data and uses the conventional non-linear state estimation. This allows the needed flexibility to compare various scenarios: LSE output versus traditional SE output, etc. As introduced in previous section, LSE is adapted to run on PG&E system from WSU two-level LSE. In summary, there are some key enhancements made in the process of adapting,
LSE’s core logic was based on bus-branch model and it was adapted to use node-breaker model.
LSE is capable of running at substation level and control center level. Because of limited availability of PMU data, LSE was redesigned to run at control center level.
LSE is enhanced to take series compensator into consideration since the PMU measurements are on the line-side; the impedance of series compensators and the PMU data is used to augment the data as needed.
67
The key to the success of this effort was the ease of adapting software to meet the practical needs.
5.1. Testing on Simulated Steady State Data Steady state validation allows the core logic of LSE to be validated. Steady-state power-flow solution corresponding to various topological conditions (e.g. single lineout, double line-out, etc.) is generated into files,
Static file: network model from EMS; Dynamic file: the status of breaker/switch Solution file: the power flow solution.
LSE would process these input files and in the absence of noise, etc. LSE’s output should match that of input for all the conditions studied. Several tests had been run and LSE showed good performance. The percentage error between measurements and estimates is very small. Before we show the results, it is necessary to see the issues to implement this testing and how they are resolved. The whole integration involves four steps:
1. LSE retrieving PMU data from OpenPDC 2. LSE retrieving data from EMS using a web service 3. LSE sending data to EMS using an existing library (which is the same library used for sending OpenPDC data to SCADA)
68
4. Adapting LSE for use in multi-host environment.
5.1.1. LSE retrieving PMU data from openPDC The goal is to use the power flow solution as make-up PMU data in the form of C37.118. So LSE’s interface is able to take the C37.118 PMU format data and run its algorithm. Then we can verify the accuracy of LSE algorithm by checking the output of LSE. The solution file is fed into a PMU Simulator (a tool that can take a CSV file and customized configure file as input and stream out C37.118 PMU data). Figure 33 shows the snapshot of the PMU simulator. It is a very useful tool developed by Alstom [81]. PMU simulator is able to take CSV file as input and output the C37.118 format PMU data.
Figure 33. User Interface of PMU Simulator
69
The final goal of the validation is to make LSE use the phaosr data from openPDC as data source. The snapshot of openPDC user interface is shown in figure 34 [70].
Figure 34. openPDC User Interface
Hence, the output data from PMU simulator is then fed into openPDC. The whole PMU data flow is then shown in figure 35, PMU Simulator
OpenPDC
LSE
Figure 35. PMU data flow
70
In order to complete the loop, there are obviously several issues that need to be resolved. As seen in figure 35, the PMU data goes through the three steps. It requires addressing various interface issues such as:
OpenPDC signal reference versus Scada Analog names: LSE needs to process data from OpenPDC and send it to SCADA and these use different identifiers. So, a mapping of the two is needed.
OpenPDC voltage values are in volts (phase to neutral) and SCADA analog values are in kV (line to line).
OpenPDC angle values are in radians and SCADA analog values are in degrees.
TABLE V.
openPDC signal reference versus Scada analog name
OpenPDC signal
Scada analog name
Phasor magnitude substation ID device type device ID analog (magnitude) Phasor angle
substation ID device type device ID
analog (angle)
TABLE V gives an example of the mapping process. Hence, a mapping file is introduced here, which explains that user needs to load a mapping file in the LSE user interface in last chapter. As to the scale conversion issue, LSE’s interface is able to handle it. Actually, all the phasor value will be transformed into per unit value for the calculation in the LSE algorithm.
71
5.1.2. LSE retrieving data from EMS using a web service A web service which can transfer two files (dynamic file and solution file) between EMS server and client has been integrated in the LSE application. The fast topology processor (QKNET), which runs at SCADA scan rates, is adapted to produce these two files which will be storage in a file system. LSE makes inquiry to obtain the latest dynamic and solution files through web service. Fig 36 shows the flow chart of how LSE makes use of the web service. EMS Hosts Solution producer – QKNET – Fast Topology Processor
Dynamic File, Solution File
Webservice
Network model database
Notification And Solution Export
Client – Solution consumer (LSE)
File System
Figure 36. Web service in EMS
The web service at server provides two functionalities to the client, 1. ListAvailable: list all the solution files with its entire information such as a file created date time and reference ID 2. Export: transfer the specific solution files using the reference ID
72
Run ListAvailable of web service
Find Latest Time Stamp Solution
(Latest Time Stamp ) no later than (Current Time Stamp) Compare Time Stamp
(Latest Time Stamp) later than (Current Time Stamp)
Current Time Stamp = Latest Time Stamp
Still use the breaker/switch status from Current Time Stamp dynamic file
Generate real time database with new dynamic file
Figure 37. LSE retrieving the latest dynamic file
Hence, the logic of LSE using the functionalities of web service is shown in figure 37, Step 1: make connection with server, run the ListAvailable of web service; Step 2: find the latest time stamp solution; Step 3: Compare the time stamp;
73
If ((Latest Time Stamp) later than (Current Time Stamp)), then go to step 4, If ((Latest Time Stamp) no later than (Current Time Stamp)), then go to step 6 Step 4: set Current Time Stamp = Latest Time Stamp Step 5: generate real time database with new dynamic file, skip step 6, go to next section of LSE program Step 6: still use the breaker/switch status from Current Time Stamp dynamic file
The advantage of the web service is that LSE can obtain the latest topology information from remote EMS servers. However, there are some disadvantages: 1. LSE has to make inquiry continuously, which is a waste of resource and a burden for the whole program 2. The fast topology processor runs at SCADA scan rate, which is much slower than LSE. It is problematic for LSE running with outdated topology information at a very small time interval when LSE could not be able to get the latest one after topology changes.
5.1.3. LSE sending output to EMS and adapted for multi-host environment LSE’s output is transmitted to SCADA in EMS using the same library that OpenPDC uses for sending PMU data to SCADA. Separate analog records are created in SCADA so that raw data (from PMUs) is distinct from output of LSE.
74
The EMS provides site redundancy as well as redundancy at each site. Thus, any of the four machines (two sites and two machines at each site) can take over the ‘enabled’ (primary) role. The set up is as shown in figure 38. LSE is enhanced to process data from the enabled machine and sends its output to SCADA on the enabled machine. Situational awareness displays show all PMU information, both raw and LSE’s output.
Enabled EMS
EMS
EMS
EMS
Site 2
Site 1
LSE
Figure 38. LSE in multi-host environment
5.1.4. Characteristic Problems of PMU Data In practice, PMU data at times may exhibit charactestic problems. So LSE needs to test on these cases.
Constant Phase Angle Bias (e.g. 30 degrees, 120 degrees)
75
Phasor Angle
30 degree
Time
Figure 39. Constant Phase Angle Bias
Sudden Phase Angle Jumps Phasor Angle
Time
Figure 40. Sudden Phase Angle Jumps
Saw-Tooth Behavior Phasor
Time
Figure 41. Saw-Tooth Behavior
76
Random Noise
PMU data is a measurement taken by CT, PT in the telemetered system. So it also has some noise as well. In this testing process, we add the Gaussian noise to the raw measurement to simulate the raw PMU data.
5.1.5. Case Study Several tests had been run and LSE showed good performance. The percentage error between measurements and estimates is very small. a) Base case The base case is the situation with all the breaker closed and series capacitors on. Results, in the form of bar charts are shown in Figure 42 for voltage magnitude and angle. 550
Voltage Magnitude
545 Voltage Magnitude Estimated
540 535 530 525
520 515 510 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17
1) Voltage Magnitude Measurements vs. Estimates
77
25 Voltage Angle
20 Voltage Angle Estimated
15 10 5
0 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17
2) Voltage Angle Measurements vs. Estimates Figure 42. LSE test on steady-state base case
As shown in the bar chart, estimated values are very close to raw value as expected because these raw data are clean data without noise.
b) Two line outage Several line outage cases have been tested. The purpose of doing this validation is to verify that LSE still works properly when it encounters topology changes. By changing breaker status, various topology scenarios are generated. Here, figure 43 shows the estimated currents.
78
1600 1400 Current Magnitude 1200 1000
Current Magnitude Estimated
800 600 400 200 0
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031323334353637
1) Current Magnitude Measurements vs. Estimates 250 Current Angle 200
Current Angle Estimated
150 100 50 0 -50
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031323334353637
-100
2) Current Angle Measurements vs. Estimates Figure 43. LSE test result on two line outage
As can be seen from Figures 42 and 43, LSE’s estimates are in agreement with the measurements.
c) Bad data detection As introduced in chapter 3, LSE has a built in bad data detection and identification functionality. Hence, bad data are intentionally added to the power flow
79
solution to simulate the case with bad data. Similarly, several tests are tested under various bad data cases.
Angle bias: add 30 degree to the voltage phasor of PMU 2 in figure 5, which is located at substation 3. Figure 44 shows the test result. 550
Voltage Magnitude
545 540
Voltage Magnitude Estimated
535 530 525 520 515 510 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1) Voltage Magnitude Measurements vs. Estimates 40 35 30
Voltage Angle Voltage Angle Estimated
25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
2) Voltage Angle Measurements vs. Estimates Figure 44. LSE test result on angle bias
80
In this figure, at the index 5, it is seen that the received phasor angle from PMU is 30 degree more than the estimated one. It shows that LSE’s own bad data detection algorithm successfully detect this angle biases.
Magnitude Error: 2. add one big noise (10% of its value) to the magnitude of one phasor of PMU 2 at substation 3. 620 600
Voltage Magnitude Voltage Magnitude Estimated
580 560 540 520 500 480 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1) Voltage Magnitude Measurements vs. Estimates 25 20
Voltage Angle Voltage Angle Estimated
15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
2) Voltage Angle Measurements vs. Estimates Figure 45. LSE test result on magnitude error 81
In the figure 45, at the index 5, it is seen that the received phasor magnitude from PMU is10 percent more than the estimated one. LSE’s bad data detection logic detected this condition and corrected the measurement.
5.2. Testing on Simulated RTDS Data In order to test a real time application, only steady state data testing is not enough. Simulated RTDS data is used to further test LSE. A 100-bus model is built up in RTDS and it is very similar to the EMS model. With the flexibility of RTDS, various types of topology, measurement set cases can be simulated in real time and be fed into LSE for testing.
5.2.1. LSE Application Context The complete LSE application context involves openPDC, LSE, EMS/SCADA and QKNET, as shown in figure 46.
Figure 46. LSE application context
82
PMU connection tester [70] is a very useful tool and has been used to capture PMU data from RTDS. Once given the PMU capture file, we can just configure it at openPDC manager in local machine so as to stream PMU data out into LSE.
Figure 47. PMU connection tester user interface
5.2.2. Case Study
83
A lot of simulated RTDS data has been retrieved from POC in the form of PMU capture file. It is convenient for us to run the testing of LSE. However, it happens that some measurements show “NaN” (not a number), and even for the whole frame. LSE is still able to handle this situation. One snapshot result of simulated RTDS data is shown in the table Ⅵ. The fourth and fifth columns are the input PMU phasor measurement while the sixth and seventh columns are the estimated phasors. It is apparent that LSE manages to provide a good estimate. There is one voltage phasor whose value is NaN, but LSE is still able to be solved under this circumstance.
TABLE VI.
LSE test result on simulated RTDS data Measurement Measurement
Substation
PMU
Phasor
2
3
Voltage
2
4
Voltage
3
1
Voltage
3
2
Voltage
4
15
Voltage
4
16
Voltage
5
11
Voltage
5
12
Voltage
6
13
Voltage
6
14
Voltage
Estimated
Estimated
magnitude
angle
magnitude
angle
(kV)
(degree)
(kV)
(degree)
537.2343
266.0133
539.852
266.877
524.7022
-85.0795
525.044
-86.3201
540.2579
-82.7314
543.9556
-81.7473
535.8566
-84.0411
535.9275
-85.0497
538.2032
-89.3406
539.4234
269.5974
538.2033
-89.3406
539.4234
269.5974
530.7355
266.9569
532.4803
267.5397
530.7359
266.9571
532.4803
267.5397
533.1682
268.9373
534.5636
269.6857
533.1824
268.9368
534.5636
269.6857
84
7
5
Voltage
7
6
Voltage
7
8
Voltage
7
9
Voltage
7
10
Voltage
8
17
Voltage
8
18
Voltage
8
19
Voltage
8
20
Voltage
8
21
Voltage
8
22
Voltage
9
30
Voltage
9
31
Voltage
9
32
Voltage
10
23
Voltage
10
24
Voltage
10
25
Voltage
11
26
Voltage
11
27
Voltage
11
28
Voltage
11
29
Voltage
530.871
268.0293
533.2351
266.9816
537.1029
268.9021
538.4306
269.5679
536.9993
-89.3734
538.4306
269.5679
537.0034
268.8983
538.4306
269.5679
536.9907
268.8988
538.4306
269.5679
543.9125
-89.4643
544.1712
-88.9497
543.9119
-89.4643
544.1712
-88.9497
543.9109
-89.4641
544.1712
-88.9497
543.9159
-87.7363
544.1712
-88.9497
543.9117
-89.4646
544.1712
-88.9497
NaN
NaN
NaN
NaN
563.2886
-85.1638
566.3014
-83.2934
563.4176
-83.4376
566.3014
-83.2934
563.4176
-83.4376
566.3014
-83.2934
548.0015
268.4751
548.9783
268.8562
546.1283
267.8151
550.1115
-89.9602
544.6859
-89.1499
546.6974
-89.3304
544.5641
269.8866
544.5641
269.8866
544.5641
269.8866
546.6341
269.6718
544.5642
269.8866
546.6341
269.6718
544.5642
269.8866
546.7014
269.7066
85
Another example given here is LSE result of running for a period of time. The real time chart in LSE UI is displayed in figure 48. This chart shows the two end voltage phasors and current phasors of one line. The scenario: when web service does not function, LSE can’t obtain the latest topology information. The sequence event of the line outage is as shown below, while LSE keeps using the topology with the line in service all the time. The charts demo how LSE behaves by showing the trajectory of two end voltage and current magnitude of the line.
Figure 48. LSE real time chart – topology error
86
𝑡0 ~𝑡1 : both ends closed The estimated voltage magnitude follows the raw voltage magnitude as expected.
𝑡1 ~𝑡2 : one end (Bus 1) open 𝑡2 ~𝑡3 : both ends open 𝑡3 ~𝑡4 : one end (Bus 2) closed From 𝑡1 to 𝑡4 , LSE still uses the old topology information, the line is still closed. Hence, the bad data detection and identification algorithm detects and remove the bad data, provides an estimate instead. So obtaining the latest and accurate topology information is a key to the LSE application.
After 𝑡4 : both end closed The estimated voltage and current magnitude back to follow the raw voltage and current magnitude as expected.
5.3. Testing on Field PMU Data The final goal of this project is to implement the LSE algorithm in a real power system. LSE has to be able to run with field PMU data properly. We could be able to obtain field PMU data from four of the ten substations at this point. PG&E is still installing and integrating the PMUs to the network. Apparently, this is a complex and time-consuming work to complete. Hence, the LSE case study on four substation field PMU data is discussed in this section.
87
The four substations are substation 7, 8, 9 and 11 in figure 5. PMU connection tester is still used to capture the field PMU data for LSE testing. There is one point needs to be mentioned: in practical PG&E system, each of the 32 PMUs has one backup PMU, which uses different communication channel. Here we use AC and BD to represent the two set of PMUs. Apparently, the redundancy of the LSE has been doubled that is very good news to state estimation. Accordingly, the corresponding interface of LSE has to be changed as well. Case study: LSE running with the capture field PMU data, we take five second time windows as a demonstration. Five seconds mean 150 frames, which should be enough here. Substation 8 is geographically located at the center of the four substations, so it is a very good point to observe the behavior of LSE. In order to understand the result of state estimation at substation 8, we need to know what measurements can make effect on the state. In general, we can categorize the measurement as three parts. 1). Voltage phasor measurement at bus itself: 𝑉̂1 2). Current phasor measurement from the bus: 𝐼̂1 3). Current phasor measurement from the opposite bus: 𝐼̂2
So the state 𝑉1 is associated with, 𝑉1 ~𝑓(𝑉̂1 , 𝐼̂1 , 𝐼̂2 ) There is one bus at substation 8 in the view of bus-branch model: Number of state: 1
88
Number of 𝑉̂1: 6*2=12, including 6 backup PMUs Number of 𝐼̂1 : 6*2=12, including 6 backup PMUs Number of 𝐼̂2 : 3, there is no backup PMU data coming in this case, so one line current from substation 7, and two from substation 11. measurement
magnitude (kV & A)
600 400 200 0 0
1
2
3 time (second) state
4
5
6
0
1
2
3 time (second)
4
5
6
magnitude(kV)
548.5 548 547.5 547 546.5
Figure 49. LSE result at substation 8
This figure 49 involves two charts: the upper one is the measurement magnitude of voltage and current while the lower one is the magnitude of the state. From the observation, there are three points need to be explained here, 1. Disconnection in the curves
89
The reason why there is some disconnection in the curves is because LSE receive the no frames or the whole frame is corrupted. LSE skips the particular frame and outputs nothing.
2. Drifting of the state Due to the scaling issue, it’s hard to have a good observation on the measurement. So we separate the measurements and display them individually. Figure 50 and 51 shows the voltage measurement (AC and BD). It is obvious that the reason of the
546.8
0
2 4 6 time (second) voltage measurement (AC)
547 546.5 546
0
2 4 6 time (second) voltage measurement (AC)
547 546.5 546
0
2 4 time (second)
6
magnitude (kV)
547
magnitude (kV)
voltage measurement (AC) 547.2
magnitude (kV)
magnitude (kV)
magnitude (kV)
magnitude (kV)
drifting of state is because the drifting of the voltage measurement.
voltage measurement (AC) 547.2 547 546.8
0
2 4 6 time (second) voltage measurement (AC)
0
2 4 6 time (second) voltage measurement (AC)
547.2 547 546.8
547.2 547 546.8
0
2 4 time (second)
Figure 50. Voltage measurement (AC)
90
6
0
2 4 6 time (second) voltage measurement (BD)
549.5
549
0
2 4 6 time (second) voltage measurement (BD)
545.5
545
0
2 4 time (second)
6
magnitude (kV)
549
magnitude (kV)
549.2
magnitude (kV)
magnitude (kV) magnitude (kV) magnitude (kV)
voltage measurement (BD) 549.4
voltage measurement (BD) 545.6 545.4 545.2
0
2 4 6 time (second) voltage measurement (BD)
0
2 4 6 time (second) voltage measurement (BD)
545.6 545.4 545.2
545.4 545.2 545
0
2 4 time (second)
6
Figure 51. Voltage measurement (BD)
3. Spikes or jumps There must be an explanation on these spikes on the state curves. It is because there are jumps on current measurement. There are too many measurements; here we only show the measurement which causes the spikes. As seen in figure 52 to 55, the time of spikes of state is synchronized with these current measurements.
91
magnitude (kV or A)
current measurement (AC) from substation 8 to 11 400
200
0
0
1
2
3 time (second) state
4
5
6
0
1
2
3 time (second)
4
5
6
magnitude(kV)
549 548 547 546
Figure 52. Current measurement (AC) from substation 8 to 11
magnitude (kV or A)
current measurement (BD) from substation 8 to 11 400
200
0
0
1
2
3 time (second) state
4
5
6
0
1
2
3 time (second)
4
5
6
magnitude(kV)
549 548 547 546
Figure 53. Current measurement (BD) from substation 8 to 11
92
magnitude (kV or A)
Current measurement (AC) from substation 8 to 4 150 100 50 0
0
1
2
3 time (second) state
4
5
6
0
1
2
3 time (second)
4
5
6
magnitude(kV)
549 548 547 546
Figure 54. Current measurement (AC) from substation 8 to 4
magnitude (kV or A)
Current measurement (BD) from substation 8 to 4 150 100 50 0
0
1
2
3 time (second) state
4
5
6
0
1
2
3 time (second)
4
5
6
magnitude(kV)
549 548 547 546
Figure 55. Current measurement (BD) from substation 8 to 4
4. No PMU on the opposite bus
93
If there is no PMU in the area of opposite bus, the current measurement from the bus has no effect on the state. The result of the LSE testing illustrates the idea in figure 56. Plus, the relationship is as follows, 𝑉1 ~𝑉1 𝐼12 ~(𝑉1 , 𝑉2 ) Where 𝑉1 is the bus voltage, 𝑉2 is the opposite bus voltage and 𝐼12 is the current from the bus; It is obvious the measurement 𝑉2 has no effect on the bus state 𝑉1. Figure 56 and 57 demonstrate the theory.
magnitude (kV or A)
Current measurement (AC) from substation 8 to 10 300 200 100 0
0
1
2
3 time (second) state
4
5
6
0
1
2
3 time (second)
4
5
6
magnitude(kV)
549 548 547 546
Figure 56. Current measurement (AC) from substation 8 to 10
94
magnitude (kV or A)
Current measurement (BD) from substation 8 to 10 300 200 100 0
0
1
2
3 time (second) state
4
5
6
0
1
2
3 time (second)
4
5
6
magnitude(kV)
549 548 547 546
Figure 57. Current measurement (BD) from substation 8 to 10
All these testing and analysis prove the correctness of the LSE algorithm under various conditions, such as zero currents, topology changes and missing PMU data. The testing provides us the confidence of carrying on our study on LSE. It is promising that implementation and deployment of the LSE application. More testing on the full ten 500 kV substations are still needed to be done once we obtain the data.
95
6. Conclusions and Future Works 6.1. Conclusions In this dissertation, linear state estimation as one of the smart grid applications benefits from the synchro-phasor data has been reviewed. Linear State Estimator has been moved from the laboratory to production grade test facility in a short amount of time, while adding significant features that are needed in an EMS environment. The linear state estimation algorithm involving topology processor, observability analysis, state estimation and bad data detection and identification is presented. The tree search algorithm is used to develop the logic of the topology processor. What role of the flow measurement and injection measurement play in observability analysis are discussed. LSE formulation and equations in this PG&E system is explored in detail, especially the formulation of series capacitors. Finally, the Chisquare distribution and LNR method are used to do the bad data detection and identification. As one major focus of this dissertation, the LSE algorithm is explored in detail very carefully. The advantage of this LSE algorithm includes:
A linear solution to the system state that always guarantees a solution.
Be able to run as fast as 30 frames per second
Function in any topology changes like split bus, series capacitor on/off
Bad data detection and identification
Construct observable islands and solve the LSE on these islands
96
The LSE data flow in EMS is designed and presented in this dissertation as well. The static data base is generated from the network model from EMS while the real time data base is created from PMU data from openPDC and breaker/switch status information from EMS/SCADS with the help of web service. The basic user interface of the linear state estimator program is presented in this dissertation. The LSE UI is developed by windows presentation framework. The functionalities of the LSE UI are explained very carefully, including the configuration, running, display and output of the LSE. Some snapshots of the user interface are displayed as well. The LSE UI serves as a very good tool for us to test LSE algorithm, such as toggling availability of measurements, adding noise and so forth. Plus, it provides displays like tables and charts to present the LSE output in a very user friendly way. The other major focus of this dissertation is the validation and testing of the real time LSE application. The testing has been conducted on simulated steady state data, simulated RTDS data and field PMU data. Steady state power flow solution generated as a making up PMU data from EMS is used to test the LSE algorithm. Many testing on the data set have been conducted. Some case study is also given in this dissertation. Several issues are tackled in the process of integration, such as
LSE retrieving PMU data from OpenPDC
LSE retrieving data from EMS using a web service
LSE sending data to EMS using ISD link
Adapting LSE for use in multi-host environment.
97
RTDS model very similar with the EMS model is built up in POC. PMU connection tester is used to capture the PMU data and the entire LSE application context is developed and presented. Several testing under various conditions has been carried on. Plus, the case study of one snapshot LSE result and the real time case with topology error are discussed as well. Final testing has been conducted on field PMU data. Even though there is only four substation field PMU data and the data set is not very stable or reliable, the LSE algorithm still performance properly. It functions as normal when it encounters zero voltage or currents, spikes and missing measurement. The analysis of the case study is presented as well.
6.2. Future Works Although this dissertation contains the algorithm, data flow and user interface of linear state estimator, the work doesn’t end here. The following aspects should be studied further: 1.
PMU placement strategy needs to be studied in order to get maximum observability with limited number of PMUs. In this project, the location of PMUs has already been determined before the preliminary off-line observability analysis. It is better if reversed to ensure the observability of the whole network.
98
2.
There is no injection measurement from PMU data, so it needs to be studied once the injection measurement is coming. The injection measurement model needs to be integrated in LSE program.
3.
Once we have enough PMU at substation, the LSE at substation level is able to be activated and the whole LSE program becomes two-level linear state estimation.
4.
When all of the ten substation field PMU data coming online, more testing needs to be carried on. With more PMU data, it is believed that LSE can behave better.
5.
It is meaningful to compare the result of LSE with the traditional state estimator. It is good for the transition from traditional SE to LSE in future.
6.
Web service caused topology error issue needs to be fixed. One good method is to let PMU data packet carry the digital breaker/switch status information along with the analog measurements.
99
REFERENCES [1]. F. C. Schweppe and J. Wildes, "Power system static-state estimation, pt. I: exact model," IEEE Trans. Power Apparatus and Systems, vol. PAS-89, pp. 120-125, January 1970. [2]. F. C. Schweppe and D. Rom, "Power system static-state estimation, pt. II: approximate model," this issue, pp. 125-130, January 1970. [3]. F. C. Schweppe, "Power system static-state estimation, pt. III: implementation," this issue, pp. 130-135, January 1970. [4]. R. E. Larson, W. F. Tinney, and J. Peschon, "State estimation in power systems, pt. I: theory and feasibility," this issue, pp. 345-352, March 1970. [5]. R. E. Larson, W. F. Tinney, L. P. Hajdu, and D. S. Piercy, "State estimation in power systems, pt. II: implementation and applications," this issue, pp. 353-363, March 1970. [6]. Jian Ma, Yousu Chen, Zhenyu (Henry) Huang, and Pak Chung Wong, "Using State Estimation Residuals to Detect Abnormal SCADA Data," Transmission and Distribution Conference and Exposition, 2010 IEEE PES, pp. 1-7 [7]. A.G.Phadke and J.S.Thorp, Synch Synchronized Phasor Measurements and Their Applications. New York: Springer, 2008, pp. 150–163. [8]. A. G. Phadke, J. S. Thorp, R. F. Nuqui, and M. Zhou, “Recent developments in state estimation with phasor measurements,” in Proc. 2009 IEEE Power Systems Conference and Exposition Conf., pp. 1-7. [9]. IEEE Guide for Phasor Data Concentrator Requirements for Power System Protection, Control, and Monitoring, IEEE Standard C37.244-2013, May. 2013.
100
[10]. Hema A. Retty, " Evaluation and Standardizing of Phasor Data Concentrators," Master. thesis, Dept. Elec. Eng., Virginia. Polytechnic, Blacksburg, 2013. [11]. Kevin David Jones, "Three-Phase Linear State Estimation with Phasor Measurements," Master. thesis, Dept. Elec. Eng., Virginia. Polytechnic, Blacksburg, 2011. [12]. Meliopoulos, A.P.S. ; Cokkinides, G.J. ; Hedrington, C. ;Conrad, T.L.; “The SuperCalibrator – a Fully Distributed State Estimator” IEEE Power and Energy General Meeting, 2010, pp. 1-8. [13]. T. Yang, H. Sun, and A. Bose, “Transition to a two-level linear state estimator— Part I: Algorithm,” IEEE Trans. Power Syst., vol. 26, no.1, pp. 46–53, Feb. 2011. [14]. T. Yang, H. Sun, and A. Bose, “Transition to a two-level linear state estimator— Part II: Algorithm,” IEEE Trans. Power Syst., vol. 26, no.1, pp. 54–62, Feb. 2011. [15]. D Anderson, et al, A Virtual Smart Grid - IEEE PES Magazine - IEEE Power & Energy,
http://magazine.ieee-pes.org/january-february-
2012/a-virtual-smart-
grid/ [16]. S. Bossart and J. Bean, “Metrics and benefits analysis and challenges for smart grid field projects,” in Energy tech, 2011 IEEE, May 2011, pp. 1 –5. [17]. Western Electricity Coordinating Council website, http://www.wecc.biz [18]. Powertech website, http://www.powertechlabs.com/ areas-of-focus/smart-utility/ dsatools- software/ transient-security- assessment-tool/ [19]. Tao Yang, "Design of two-level power system linear state estimator," Ph.D. dissertation, Dept. Elec. Eng., Washington State University, Pullman, 2011.
101
[20]. R. R. Shoults and E. Barrera-Cardiel, “Use of a Graphical User Interface Approach for Digital and Physical Simulation in Power System Control Education: Application to an HVDC Transmission System Model”, IEEE Trans. OR Power System, vol. 7, pp. 1598-1603, November 1992. [21]. Real Time Digital Simulator website, http://www.rtds.com/ [22]. D. J. Gaushell and H. T. Darlington, “Supervisory control and data acquisition,” Proc. IEEE, vol. 75, no. 12, pp. 1645–1658, 1987. [23]. Haoen Li, "Wide Area Voltage Monitoring and Optimization," Ph.D. dissertation, Dept. Elec. Eng., Washington State University, Pullman, 2013. [24]. http://www.powersystem.org/scada [25]. SCADA:
A
big
challenge
for
information
security
professionals,
https://isc.sans.edu/forums/diary/SCADA+A+big+challenge+for+information+s ecurity+professionals/9436 [26]. http://en.wikipedia.org/wiki/Phasor_measurement_unit [27]. KEMA, Inc. (November 2006). Substation Communications: Enabler of Automation / An Assessment of Communications Technologies. UTC - United Telecom Council. pp. 3–40. [28]. "Phasor Advanced FAQ". CERTS, http://www.phasor-rtdm s.com /phaser co ncepts / phasor_adv _faq.html [29]. https://www.naspi.org/ [30]. Summary of the North American SynchroPhasor Initiative (NASPI) Activity Area, NASPI-U.S. Department of Energy, energy.gov
102
[31]. Y. Ota, T. Hashiguchi, H. Ukai, M. Sonoda, Y. Miwa, and A. Takeuchi, “Monitoring of interconnected power system parameters using PMU based WAMS,” inProc. 2007 IEEE Lausanne Power Tech, pp. 1718–1722. [32]. A. P. S. Meliopoulos, G. J. Cokkinides, O. Wasynczuk, E. Coyle, C. Hoffmann, C. Nita-Rotaru, T. Downar, L. Tsoukalas, and R. Gao, “ PMU data characterization and application to stability monitoring,” inProc. 2006 IEEE Power Eng. Soc. Power Systems Conf. Expo., Nov. 2006, pp. 151–158. [33]. J. Ma, Y. V. Makarov, C. H. Miller, and T. B. Nguyen, “Use multi-dimensional ellipsoid to monitor dynamic behavior of power systems based on PMU measurement,” in Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 2008 IEEE, July 2008, pp. 1 – 8. [34]. Jie Yan et sl, “A PMU-based monitoring scheme for rotor angle stability” in Power and Energy Society General Meeting 2012 IEEE, pp. 1-5 [35]. Tlusty et sl, “The monitoring of power system events on transmission and distribution level by the use of phasor measurements units (PMU)” in Electricity Distribution - Part 1, 2009. CIRED 2009, pp. 1-4 [36]. B. Milosevic, M. Begovic, "Voltage-stability protection and control using a wide-area network of phasor measurements," IEEE Transactions on Power Systems, 2003, vol. 18, pp. 121-127 [37]. H. Sangwook, B. Lee, S. Kim, Y. Moon , "Development of voltage stability index using synchro-phasor based data," Proc. Transmission & Distribution Conference & Exposition: Asia and Pacific, 2009, pp. 1-4.
103
[38]. S. Han, B. Lee, S. Kim, Y. Moon, B. Chang, J. Shin, "Voltage stability monitoring using PMU data in KEPCO system," Proc. Transmission and Distribution Conference and Exposition, 2010, pp. 1-5. [39]. J.S. Thorp, A.G. Phadke, S.H. Horowitz, and M.M. Begovic, “Some Applications of Phasor Measurements to Adaptive Protection”, IEEE Transactions on Power Systems, vol. 3, pp. 791–798, May 1998 [40]. A.G. Phadke, B. Pickett, M. Adamiak, M. Begovic, G. Benmouyal, R.O. Burnett, T.W. Cease, J. Goossens, D.J. Hansen, M. Kezunovic, L.L. Mankoff, P.G. McLaren, G. Michel, R.J. Murphy, J. Nordstrom, M.S. Sachdev, H.S. Smith, J.S. Thorp, M. Trotignon, T.C. Wang, and M.A. Xavier, “Synchronized Sampling and PhasorMeasurements for Relaying and Control”, IEEE Transactions on Power Delivery, vol. 9 , pp. 442-452, Jan. 1994. [41]. B. Milosevic, and M Begovic, “Voltage-stability Protection and Control Using a Wide-area Network of Phasor Measurements”, IEEE Transactions on Power Systems, vol. 18, pp. 121–127, Feb. 2003. [42]. Saran A, “Comparison between overcurrent relay and developed PMU based protection”, North American Power Symposium (NAPS), 2013, pp. 1-6 [43]. F. Ding, C.D. Booth, "Protection and Stability Assessment in Future Distribution Networks Using PMUs", 11th International Conference on Developments in Power Systems Protection, DPSP, Apr. 2012. [44]. Sivanagaraju, G et sl, “Uncertainty in Transmission Line Parameters: Estimation and Impact on Line Current Differential Protection”, IEEE Transactions on Instrumentation and Measurement, pp. 1-9
104
[45]. Z. Dan, Z. Chao, T. Jiancheng, B. Zhiqian, “A new scheme of control and protection based on utilizing phasor measurement technique” Chinese Control and Decision Conference (CCDC), Publication Year: 2010 , Page(s): 4154 4157 [46]. K. Z. H.; Z. Y. Li, "A novel PMU-based transmission line protection scheme design,” in Power Symposium, 2007. NAPS '07. 39th North American, pp. 1319. [47]. J.A. Momoh, Y. Xia, and G. Boswell, “Voltage stability enhancement usingPhasor Measurement Unit (PMU) technology,” Power Symposium, 2008. NAPS '08. 40th North American, pp. 1 – 6, 28-30 Sept. 2008 [48]. D.M. Laverty, D.J. Morrow, R. Best, and P.A. Crossley, “Performance of phasormeasurement units for wide area real-time control,” Power & Energy Society General Meeting, 2009. PES '09. IEEE, pp. 1 – 5, 26-30 July 2009 [49]. S.E. Stanton, C. Slivinsky, K. Martin, and J. Nordstrom, “Application of phasor measurements and partial energy analysis in stabilizing large disturbances,” IEEE Transactions on Power Systems, Vol. 10, Issue 1, pp. 297-306, Feb. 1995 [50]. Yang Zhang, Anjan Bose, “PMU-based wide-area damping control system design,” Power and Energy Society General Meeting, 2012 IEEE, pp. 1 - 7 [51]. Yi Yang et sl, “Power system stability analysis and control based on PMU,” 2011 International Conference on Computer Science and Service System (CSSS), pp. 3376-3379
105
[52]. Heng-Yi Su et sl, “An Adaptive PMU-Based Secondary Voltage Control Scheme,” IEEE transaction on Smart Grid, Vol. 04, Issue 3, pp. 1514-1522, July. 2013. [53]. Moshref, A, et sl, “PMU application in controlled islanding,” Power and Energy Society General Meeting (PES), 2013 IEEE, pp. 1-5 [54]. Jie Yan, Govindarasu M, Chen-Ching Liu et sl, “A PMU-based risk assessment framework for power control systems,” Power and Energy Society General Meeting (PES), 2013 IEEE, pp. 1-5 [55]. J.S.
Thorp,
A.G.
Phadke,
and
K.J.
Karimi,
“Real
Time
Voltage-
PhasorMeasurements for Static State Estimation”. IEEE Transactions on PAS, vol. PAS-104, pp. 1779-1787, Aug. 1985. [56]. A.G. Phadke, J.S. Thorp, and K.J. Karimi, “State Estimation with PhasorMeasurements”. IEEE Transactions on PAS, vol. PAS-105, pp. 12311237, Aug. 1986. [57]. R. Zivanovic, and C. Cairns, “Implementation of PMU Technology in StateEstimation: an Overview”. IEEE Proceedings on AFRICON 4th, vol. 2, pp. 1006-1011, July, 1996. [58]. A. Bose and K. E. Clements, "Real Time Modeling of Power Networks", Proceedings of the IEEE, vol. 75, no. 12, December 1987. [59]. G.R. Krumpholz, K.A. Clements, and P.W. Davis, “Power system observability: a practical algorithm using network topology,” IEEE Trans on PAS, Vol. PAS99, pp. 1534-1542, July/August 1980
106
[60]. K. A. Clements and P. W. Davis, “Multiple bad data detectability and identifiabilityA: geometric approach,/”€ €€ Trans. Power Delivery, vol. PWRD1, pp. 355-360, July 1986 [61]. K. A. Clements and P. W. Davis, “Power system state estimation residual analysis-An algorithm using network topology,” /€€E Trans. Power App. Syst., vol. PAS-100, pp. 1779-1787, Apr. 1981 [62]. M. Zhou, V. A. Centeno, J. S. Thorp, and A. G. Phadke, “An alternative for including phasor measurements in state estimation,” IEEE Trans. Power Syst., vol. 21, pp. 1930–1937, Nov. 2006. [63]. Costa, A.S., Lourenco, E.M., Clements, K.A. Power system topological observability analysis including switching branches. Power Systems, 2002, 17 (2):1250~1256. [64]. V. H. Quintana, A. S. Costa, and A. Mandel, “Power system topological observability using a direct graph-theoretic approach,” IEEE Trans. Power Apparatus. Syst., 1982 [65]. John J. Grainger, William D. Stevenson, JR, Power System Analysis. New York: McGraw-Hill, 2003, pp. 655-664 [66]. Chi-squared distribution Wikipedia, http://en.wikipedia.org/wiki/ Chi-squared_ distribution [67]. A. Abur and A.G. Exposito, Power System State Estimation: Theory and Implementation, Marcel Dekker Inc., 2004
107
[68]. A. Monticelli, State Estimation in Electric Power Systems – A Generalized Approach, The Kluwer International Series in Engineering and Computer Science, Kluwer Academic Publishers, 1999. [69]. openPDC Wikipedia, http://en.wikipedia.org/wiki/OpenPDC [70]. The open source phasor data concentrator homepage, http://openpdc. codeplex.com [71]. A. Gómez-Expósito, A. Abur, A. de la Villa Jaén, and C. GómezQuiles, “A multilevel state estimation paradigm for smart grids,”Proc. IEEE, no. 99, pp. 1– 25, 2011. [72]. Matthew MacDonald, Pro WPF in C# 2010: Windows Presentation Foundation in .NET 4.0. New York: Springer, 2010 [73]. InstallShield home page, http://www.flexerasoftware.com/ [74]. InstallShield Wikipedia, http://en.wikipedia.org/wiki/InstallShield [75]. Web Service Wikipedia, http://en.wikipedia.org/wiki/Web_service [76]. XML Wikipedia, http://en.wikipedia.org/wiki/XML [77]. DTS Wikipedia, http://en.wikipedia.org/wiki/Dispatcher_training_simulator [78]. A. Jampala, et al, Practical Challenges of Integrating Synchrophasor Applications into an EMS, a paper submitted to IEEE ISGT 2013 conference. [79]. J. Giri, M. Parashar, J. Trehern, V. Madani, “The Situation Room: Control Center Analytics for Enhanced Situational Awareness”, IEEE Power and Energy Magazine, vol. 10, no. 5, pp. 24-39, Sep./Oct. 2012. [80]. S. Matsumoto, Y. Serizawa, F. Fujikawa, T. Shioyama, Y. Ishihara, H. Sakashita, T. Kase, A. Ishibashi "Wide-Area Situational Awareness (WASA) System based
108
upon International Standards, " 11th International Conference on Developments in Power System Protection 23-26 April 20 12, Birmingham, UK [81]. Alstom, www.alstom.com
109
