Distributed State Estimation Based on the

2007 iREP Symposium- Bulk Power System Dynamics and Control - VII, Revitalizing Operational Reliability August 19-24, 2007, Charleston, SC, USA

Distributed State Estimation Based on the SuperCalibrator Concept – Laboratory Implementation Salman Mohagheghi, Ramiz H. Alaileh, George Cokkinides, A.P. Sakis Meliopoulos School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, GA USA

Introduction The energy management system (EMS) is the basic infrastructure that enables monitoring, optimization and control of an electric power system. A typical configuration of the EMS is illustrated in Fig. 1. The importance of the EMS lies in the fact that it can provide situational awareness in real-time, and it helps operators to prevent many major escalated disturbances and/or blackouts in the power grid.

State estimation is the heart of every EMS installation, since it provides the operators with the most accurate estimates of the state of the power system, which is uniquely defined as a set of the voltage magnitudes and phase angles at different buses in the network. The output of the state estimator is a real-time model of the power system that has various applications in Load Forecasting, optimization techniques such as Economic Dispatch or Optimal Power Flow, VAR Control, Available Transfer Capability, Security Assessment, Congestion Management, Dynamic Line Rating, Transient Stability, Visualizations and suchlike. Traditionally, the above described centralized state estimator is based on a single phase model of the power system with non-simultaneous measurements. This approach leads to a biased state estimator corrupted with asymmetry errors, unbalance errors and instrumentation errors. The centralized approach also places a burden on the communications requirements. The SuperCalibrator concept was introduced to take advantage of the characteristics of GPS-synchronized equipment (PMUs). The concept is based on a statistical estimation process that fits the GPS-synchronized measurements and all other available standard data into a three-phase, breaker-oriented, instrumentation inclusive model [1]. The basic idea is to provide a model based correction of the errors from all known sources of error. The main characteristics of the SuperCalibrator concept are:

Fig. 1. Typical configuration of EMS hardware.

A fundamental function of the EMS is data collection from various sensors and transmission of this information from the remote terminal units (RTU) to the control center, where it is processed using state estimation procedures to filter and display the data on a mimic board or other user interface system.

1-4244-1519-5/07/$25.00 ©2007 IEEE.

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It utilizes a detailed breaker-oriented model of the power system, which includes all the three phases, instrumentation channels and models of the data acquisition systems, The measurements obtained from devices such as PMUs, relays or SCADA are used in a statistical estimation method that fits the data to the detailed model,

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The bad data are identified using the confidence level of the estimated state of the system. It can be performed at the substation level leading to a distributed approach for state estimation.

This procedure is applied at the substation level and the final results are verified by a state estimation coordinator that functions as a central supervisor. Figure 2 illustrates the concept of the SuperCalibrator approach. More details are provided in the next section.

Fig. 2. SuperCalibrator concept.

A laboratory setup is presented in this paper to be used for testing and validating distributed state estimation based on the SuperCalibrator concept. The laboratory setup is built in such a way that it models the non-idealities of a power system, such as the asymmetries and voltage unbalance conditions.

Distributed State Estimation The visibility and situational awareness of an electric power system depends largely on two important procedures: state estimation and alarm processing. The state estimation problem is usually performed at a centralized location where all the raw data from SCADA are collected and then processed to provide the real time model of the system. The reliability of the state estimator on an industry wide basis is about 95%. Recently GPS synchronized measurements have been utilized to enhance the state estimator with the same basic centralized approach. The root causes of the unreliability of the centralized state estimator have been addressed in several publications and remain unaltered with or without GPS synchronized measurements: (a) (b) (c) (d)

Biases from imbalances in the system, Biases from system asymmetries, Substantial errors from instrumentation channels, Non-simultaneity of SCADA data.

The centralized state estimator has a number of additional practical disadvantages: (a) Processing all the data simultaneously at a central location generates a bottleneck resulting in longer execution times, (b) In case of existence of bad data, the detection and identification of the bad data becomes more complex and less sharp, (c) Communication requirements are excessive since all SCADA data must be sent to a central location. The introduction of the GPS-synchronized measurements opens up the possibility of distributing the state estimation function. Meliopoulos et al [1] have introduced the concept of the “SuperCalibrator” – a substation based state estimator based on a detailed three-phase breakeroriented model of the substation, with explicit representation of the instrumentation channels. The proposed approach will perform the state estimation locally at each substation and then transmit the local state to a central location. This approach will provide a more efficient and reliable state estimator, improved and sharper data detection and identification, and reduced data traffic between substations and the control center.

SuperCalibrator Concept A. Formulation The SuperCalibrator technology is based on a flexible hybrid state estimation formulation. This is a combination of the traditional state estimation formulation and the GPS-synchronized measurement formulation, which uses an augmented set of available data. In addition, it utilizes a three-phase, breaker oriented and instrumentation channel inclusive model. The set of measurements comprises of: (a) Traditional, non-synchronized measurements such as voltage magnitude, active and reactive line flows and bus injections, and other standard SCADA data, (b) GPS-synchronized measurements of voltage and current phasors for each phase, (c) Appropriate pseudo-measurements when necessary. The measurement set may include any combination of three phase and single phase measurements. Typical measurements are illustrated in Fig. 3 and listed in Table 1. The problem is formulated as: z = h(x) + η where:

(1)

vector of GPS-synchronized and nonsynchronized measurements, vector of state of the system, vector of measurement errors that are statistically described by the meter accuracy, a vector function that depends on the model of the system.

z x η h

The state of the system is defined as the phasors of the phase voltages at each phase of a bus, including the neutral node. In general, the state for a four node bus k will be:

[

~ ~ ~ ~ ~ Vk = Vk , A Vk ,B Vk ,C Vk , N

]

T

(2)

~ Vk , A  ~  Vk , B  ~  Vk ,C  ~ , ~ T ~ ~z = I v d 1,k , A + η v = C d 1,k , A  ~  + ηv Vm, A  ~  Vm, B  V~   m,C 

(4)

Where C is a matrix derived from the pi-equivalent model of the power system and relates the current to node voltages of the three phases. Pseudo-measurements for neutrals and grounds can be written as: ~z = 0 + j 0 = V~ + η~ . (5) v k ,N v Non-synchronous measurements for voltage magnitudes and active/reactive power flows are expressed as:

~ ~ zv =| Vk , A − Vk , N |2 +2η v

(6) = (Vk , A, r − Vk , N , r ) 2 + (Vk , A, i − Vk , N ,i ) 2 + 2ηv Where subscripts r and i denote the real and imaginary part of the voltage phasor respectively.

Fig. 3. Measurement definition for hybrid state estimation approach.

Table 1. List of available data for hybrid state estimation approach. GPS-synchronized Non-synchronized

~ V ~ Current Phasor I

Voltage Phasor

Current Injection Phasor ~ I inj

Voltage Magnitude V Real Power Flow Pf Reactive Power Flow Qf Real Power Injection Pinj Reactive Power Injection Qinj

Normally the measurements of neutral and ground voltages are not available. Since their values are very small under normal operating conditions, a pseudomeasurement of voltage phasor is introduced for each neutral and ground node in the system, whose value is exactly zero. The meter accuracy for this measurement is therefore assumed to be low, e.g., 10%. The measurement model equations for phase A are given below. Similar equations are given for phases B and C. Phasor measurements are as follows: ~z = V~ − V~ + η~ . v k,A k ,N v

* ~   Vk , A       ~     Vk , B       ~    ~  Vk ,C    zv = Pd 1,k , A + η v = Re Vk , A  CdT1,k , A  ~    + η v   Vm , A       ~     Vm , B      V~      m ,C     

(7)

* ~   Vk , A       ~     Vk , B       ~    ~  Vk ,C    zv = Qd 1,k , A + η v = ImVk , A  C dT1,k , A  ~    + η v   Vm , A       ~     Vm , B      V~      m ,C     

(8)

The state estimation process minimizes the following objective function which includes all the available measurement data:

J= (3)

η~v*η~v η vη v . + ∑ ∑ 2 2 v∈Phasor σ v v∈Non − synch σ v

(9)

If all the measurements are synchronized, the state estimation problem becomes linear and the solution is obtained directly. In the presence of non-synchronized measurements, the problem is quadratic, consistent with the quadratic power flow. Specifically using the quadratic formulation, the measurements can be separated into phasor and non-synchronized measurements as: zs = H s x + ηs (10)

{

additional wiring and possibly burdens. Figure 4 illustrates typical instrumentation channels, a voltage channel and a current channel. Phase Conductor

i(t) Current Transformer

v(t)

Potential Transformer

Attenuator i1(t)

}

z n = H n x + x T Qi x + η n

i2(t)

Burden

Phasor Measurement Unit

(11)

In these equations, the subscripts s and n indicate phasor measurements and non-synchronized measurements respectively. The best state estimate is given by:

v3(k)

Instrumentation Cables v1(t)

Attenuator

v2(t) Computer

Case 1: Phasor Measurements Only xˆ = ( H sTWH s ) −1 H sT Ws .z s (12) Where Ws is a diagonal matrix whose non-zero entries are equal to the inverse of the variance of the measurement errors: 1  Ws = diag  2  (13) σ v  Case 2: Phasor and non-synchronized measurements The state of the system will be derived from the following iterative solution:   z s − H s xˆ j xˆ j +1 = xˆ j + ( H T WH ) −1 H T W . j jT j  ˆ ˆ ˆ z − H x − x Q x n i  n 

{

where: 0 W W = s   0 Wn  and:  Hs  H =   H n + H qn 

}

(14)

Burden

Fig. 4. Typical instrumentation channel for data collection.

Each component of the instrumentation channel will introduce an error. The net error introduced by all the components of the instrumentation channel is of main importance. The overall error can be defined as follows: Let the voltage or current at the power system be va(t) and ia(t). An ideal instrumentation channel will generate a waveform at the output of the channel that will be an exact replica of the waveform at the power system. If the nominal transformation ratio is kv and ki for the voltage and current instrumentation channels respectively, then the output of the ideal channels will be:

videal (t ) = k v .va (t ) (15)

iideal (t ) = ki .ia (t )

.

(17)

The error is then defined as: (16)

B. Instrumentation Model PMUs, SCADA, relaying, metering and disturbance recording systems use a system of instrument transformers to scale the power system voltages and currents into instrumentation level voltages and currents. Standard instrumentation level voltages and currents are 67V or 115V and 5A respectively. These standards were established many years ago to accommodate the electromechanical relays. Today, the instrument transformers are still in use but because modern relays, metering and disturbance recording operates at much lower voltages, it is necessary to apply another transformation from the previously defined standard voltages and currents to another set of standard voltages of 10V or 2V. This means that the modern instrumentation channel consists of typically two transformations and

verror (t ) = vout (t ) − videal (t ) ierror (t ) = iout (t ) − iideal (t )

,

(18)

where the subscript out refers to the actual output of the instrumentation channel. The overall instrumentation channel error can be characterized with the frequency response of the entire channel.

Experimental Setup This paper applies the SuperCalibrator concept for estimating the states of a laboratory setup representing a three-substation scaled model. The system is built to reflect the true nature of a small size power system, along with its metering equipment. Figure 5 depicts the schematic diagram of the three-substation scaled model. It consists of a generation substation that is connected to two remote substations, yellow jackets 1 and 2, through two transmission lines. The operation voltages of the system are scaled by a factor of 1000.

the output voltage of the amplifier is limited to 56V rms, a transformer structure is built that is fed from the outputs of the amplifier and further boosts the voltage to the required 115 V for the scaled model.

Fig. 5. One line diagram of the substation scaled model.

The laboratory setup was built in the Power Systems Control and Automation Laboratory at the Georgia Institute of Technology (Fig. 6). The scaled model of the power system is built in such a way that it resembles the power system with a high degree of accuracy. This section briefly describes the main characteristics of the laboratory setup. For more details, the reader is referred to [2]. Fig. 7. Laboratory setup for the power supply.

The software developed for the source enables the user to select the required voltage magnitudes and frequencies of the three phases. These values can be fixed or varied with time. This allows for the introduction of harmonics, voltage imbalances and various types of voltage or frequency fluctuations. Therefore, the designed source is able to model the generator outputs under all possible operating conditions. Figure 8 demonstrates the generator control menu.

Fig. 6. Scaled model implementation of the system of Fig. 5.

A. Power Supply The input voltage applied to the scaled model is generated using a computer. The computer simulates a synchronous generator and feeds the results into a multi-channel A/D converter. This provides the capability to introduce source harmonic pollution as well as voltage imbalances to the system. Figure 7 illustrates the schematic diagram of the input voltage source. It consists of a PCI board that is connected to the host PC. The board is a National Instruments NI 6722 arbitrary waveform generator, which has 8 analog outputs with a range of ±10V maximum voltage. The outputs from the board are fed to an amplifier. In this laboratory setup a 7-channel Sunfire TGA-7400 amplifier with maximum power of 800W per channel is used. Since

Fig. 8. Generator control menu.

B. Transmission Line Model Lumped models of the 4-wire transmission lines are constructed that take the mutual couplings between the phases and the neutral as well as the power system asymmetries into account. The transmission lines are built using basic elements based on the design of a 2-mile 3phase transmission line with neutral conductor [3], [4]. Figure 9 illustrates the circuit model of the high-fidelity

transmission line model using basic elements. The model parameters are generated using the WinIGS software and are modified for a 2-mile section. Clearly, the lengths of the transmission lines can be increased by installing more units in series.

Fig. 11. Flow of power in the scaled model.

Fig. 9. Transmission line model.

The windings of the transmission line are located on a dielectric core build from polypropylene. The dimensions of the core are derived in such a way that the line module has the same characteristics as the high-fidelity model in Fig. 9. The capacitors are mounted on a printed circuit board (PCB) that is located on the dielectric core. Figure 10 shows the final prototype of the transmission line. This module accurately models a 2-mile section of a transmission line.

Fig. 12. Phase shifting transformer prototype.

D. Instrumentation Various instrument transformers (PTs and CTs) are installed on the laboratory setup in Fig. 6 in order to provide actual measurements of the voltages and currents at different nodes/lines. All the measurements from across the scaled model are time tagged using GPS. These measurements are then transmitted to the relays and PMUs that communicate with the setup. A list of some of the devices used appears in Table 2.

ID P142 P442 M-3425A SEL-AMS SEL-387E Fig. 10. Transmission line prototype for a 2-mile section. SEL-421

C. Flow of Power Two phase shifters are connected between the generation bus and the remote buses, yellow-jackets 1 and 2 (Fig. 11). In this way, power can be circulated throughout the system with no need for any additional supplies at the remote buses. Also, by providing individual phase shifts for the three phases, the transformers allow imposing voltage unbalance on the system. The prototype built in the laboratory is illustrated in Fig. 12.

GE-G30 GE-G60 GE-N60

Table 2: Relays ID and description. Description Areva MiCOM model P142 Feeder Management Relay Areva MiCOM model P442 Numerical Distance Protection Relay Beckwith M-3425A Generator Protection System Schweitzer SEL-AMS Adaptive Multichannel Source Schweitzer SEL-387E Current Differential and Voltage Relay Schweitzer SEL-421 High-Speed Line Protection, Automation, and Control System GE-G30 Generator Management Relay GE-G60 Generator Management Relay GE-N60 Network Stability and Synchrophasor Measurement System

Using an Ethernet network, the actual measurements acquired from the system in Fig. 6 are transmitted to a local host where the interface software and the simulation algorithms are located. This information is then used as inputs to the state estimator, which is based on the

SuperCalibrator approach, and estimates the state of the system considering all the unbalances, asymmetries and instrumentation errors. The results can then be compared with the actual measurements from the system.

substation. The measurements can be classified to two main categories:

E. Ground Potential Rise The power supply allows for the introduction of Ground Potential Rise (GPR) by applying a user-defined voltage between the neutral and the grounding network of the scale model. This is achieved by the transformer structure that connects the PCI board to the scale model (Fig. 13).

Fig. 14. One line diagram of the scaled model.

A. Substation Measurements These are the actual physical quantities measured within the substation. For the scale model shown in Fig. 14, the internal measurements are: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ V1s ,V2 s ,V3 s , I g , I1 , I 2 , I 3 , I 4 , I 5 , I 6 B. Pseudo-measurements These are measurements in addition to the actual measurements of the system. The pseudo-measurements used in this case study are: B.1. Pseudo-measurements from Kirchoff’s current law These are measurements that are derived from the Kirchoff’s current law at the substation nodes. The KCL equations are added to the state estimation model and provide additional redundancy level. For the system in Fig. 14:

Fig. 13. One line diagram of the scaled model.

Implementation of the SuperCalibrator Figure 14 illustrates the one line diagram of the scale model. The purpose of the distributed state estimation is to find the state of the main substation in Fig. 13 that consists of the generator bus and the main bus. All the other buses, including yellow-jackets 1 and 2, are considered to be remote nodes. The states of the substation are the voltage phasors V~1s , ~ ~ ~ V2 s and V3 s as the internal states and V3e as the external state. Clearly, each voltage phasor is a 4×1 complex vector as:

~ V1s ,a  ~  ~ V1s ,b  , V1s =  ~  V1s ,c  ~  V1s ,n 

(19)

Therefore the overall number of states of the system in this study is 16. Minimal metering devices have been considered in this study for measuring the voltages and the currents of the

~ ~ I1 + I g = 0 ~ ~ I 2 + I3 = 0 ~ ~ I5 + I6 = 0

(20)

B.2. Pseudo-measurements of the voltages at the neighboring substations Given the voltage measurement of V~3 s , and the current ~ I6 , and a three-phase model of the transmission line in the form of the generalized pi-equivalent form:

~ ~  I 6  Y11 Y12  V3 s  ~  =  . ~  ,  I 7  Y21 Y22  V3e 

(21)

the pseudo-measurement of the voltage at the other end of the line is determined by:

~ ~ V3epseudo = ( I − Z 22Y22 ) −1 Z 21 I 6

~ + ( I − Z 22Y22 ) −1 Z 22Y21V3 s ,

(22)

where:

 Z11 Z  21

−1

Z12  Y11 Y12  , = Z 22  Y21 Y22 

(23)

and I is the identity matrix of appropriate dimension. B.3. Pseudo-measurements of the neutral/shield wire current Given the model of a line model, the ratio of the shield/neutral current over the return current can be computed. ~ Is/n α= ~ ~ ~ , (24) − I a + Ib + Ic

(

Table 3 summarizes the available measurements for the distributed state estimator using the SuperCalibrator concept. Given the fact that the total number of system states is 16, the above 78 measurements provide a redundancy level of 5.25 or 525%.

)

This pseudo-measurement is therefore introduced for the shield/neutral current of I6 as follows: ~ ~ ~ ~ ,m I 6pseudo = −α × I 6,a + I 6 ,b + I 6 ,c , (25) ,s / n

(

)

B.4. Pseudo-measurements of the neutral/ground voltage The neutral/ground voltage is computed as the product of the substation ground impedance and the earth current. The earth current is the sum of all earth currents of all transmission lines connected to the substation. ~ ~ ~ ~ V pseudo,m = − R × ∑ (1 − α ). I + I + I , (26) s/n

formulation segregates the magnitude and phase errors of GPS-synchronized data.

[

g

i

(

i ,a

i ,b

i ,c

)]

Table 3: List of the required measurements. Quantity

~ ~ ~ ~ V1s , V2 s , V3s , V3e ~ ,~ ,~ ,~ ,~ ,~ I g I1 I 2 I 3 I 4 I 5 ~ I6 Kirchoff’s current law

~ V3e ~ I 6,s / n ~ Vs / n

z

Type

No. of Measurements

Physical Measurement

4×4=16

Physical Measurement

7×3=21

Pseudo-measurement

9

Pseudo-measurement

3

Pseudo-measurement

1

Pseudo-measurement Pseudo-measurement Total

1 11×3=33 84

i

where: substation ground resistance. In this study, the Rg ground resistance is a 9 ft AWG-10 copper wire, which runs underneath the scale model in Fig. 6 and connects to all the ground nodes. αi ratio of the shield/neutral current over the return current. Clearly the neutral/ground voltage will be negligibly small normal operating conditions. However, during a fault condition or a stuck breaker the neutral/ground voltage may be elevated to a substantial value. B.5. Segregation of Magnitude and Phase Errors In GPS-synchronized measurements, the magnitude error is typically different than the phase error. For most GPSsynchronized equipment, the phase error is much smaller than the magnitude error. Utilizing the total phasor error results in missing information and compromises the performance of the state estimator. Within the formulation of the hybrid state estimator, the phase and magnitude errors are segregated by simply introducing an additional datum. This datum is treated as a pseudo-measurement. For instance, the definition of this pseudo-measurement ~ for a voltage phasor V is:

~ ~ z pseudo = tan(δ ) × Re V − Im V + η ,

{}

{}

(27)

The standard deviation of the error η depends on the characteristics of the GPS-synchronized equipment. It expresses the error of the phase measurement. This

Summary The SuperCalibrator concept was introduced based on a statistical estimation process that fits the GPSsynchronized measurements and all other available standard data into a three-phase, breaker-oriented, instrumentation inclusive model. In this approach, the asymmetries, unbalances and the instrumentation errors are taken into account in the state estimation procedure. The laboratory setup considered in this paper is the scaled down model of a three substation power system. The model is built to mimic a power system with a high level of accuracy considering the asymmetries and unbalanced working conditions. Transmission line modules are built in such a way that they take the mutual inductances between the phases and the neutral as well as the stray capacitances into account. All the nodes and lines of the system are equipped with PTs and CTs. These actual measurements are used as inputs to the state estimator using the SuperCalibrator concept. Compensating for all the asymmetries, unbalances and the instrumentation errors, the state estimator provides the state of the system, which can then be compared with the measurements provided by the metering devices. This paper provided a general overview of the SuperCalibrator concept and how it will be implemented on the laboratory setup. This is a work in progress and the

actual experimental results of applying the SuperCalibrator concept for distributed state estimation of the laboratory setup will be presented in the authors’ follow-up work.

Arbiter Systems and Macrodyne for their generosity in donating equipment to the lab.

Acknowledgements

[1]

The authors wish to express their gratitude to Concurrent Technologies Corporation (CTC), Power Systems Engineering Research Center (PSERC), the U.S. Department of Energy (DoE), Entergy, New York Power Authority (NYPA) and National Science Foundation (NSF) for their support of the research projects that led to this project and developing this laboratory. They also would like to thank Schweitzer Engineering Laboratories (SEL), Beckwith Electric, General Electric (GE), Areva,

References

[2]

[3] [4]

A.P. Sakis Meliopoulos, G.J. Cokkinides, F. Galvan and P. Mydra, “Advances in the SuperCalibrator Concept- Practical Implementations,” in Proc. 40th Annual Hawaii Intl. Conf. on System Sciences (HICSS), Jan. 3-6, 2007. S. Mohagheghi, R.H. Alaileh, G. Cokkinides and A.P. Sakis Meliopoulos, “A Laboratory Setup for a Substation Scaled Model”, To Appear in Proc. Power Tech 2007 Conf., Lausanne, Switzerland, July 1-5, 2007. Standard Handbook for Electrical Engineers, 14th edition, edited by Donald G. Fink and H. Wayne Beaty. WinIGS Applications Guide, January 2004, available at http://www.ap-concepts.com/_downloads/IGS_AGuide.pdf.