Load Model Parameter Derivation Using an ...

1

Load Model Parameter Derivation Using an Automated Algorithm and Measured Data A. Maitra, A. Gaikwad, P. Pourbeik, D. Brooks

Abstract—This paper summaries some of the key results achieved in the second phase of a multi-year collaborative load modeling research project. After having identified suitable types of load monitoring devices, actual field data for load model development and validation were collected at appropriate locations for several months to more than a year in three different utilities. This data was post-processed using an automated methodology to filter out events suitable for load model parameter estimation. Two load model structures were then used with an automated parameter estimation algorithm to fit model parameters using the field data collected. The models thus developed were then validated using Siemens PTI PSS/ETM dynamic simulation program. This whole process resulted in some key insights and valuable conclusions for future load modeling research efforts. techniques,

In response to these needs, EPRI started a multi-year collaborative load modeling research program [4] in 2004 involving participating member utilities, and other industry experts. This program was specifically aimed at developing more representative load models and verification using available natural system disturbance data. Here we refer to this approach as measurement based since the load model for a distribution bus is derived from voltage and power measurements recorded at that bus in response to an upstream transmission system fault or a distribution fault on an adjacent feeder.

t has always been understood that the largest source for

This paper presents the results obtained during the most recent phase of this program. The analysis provided here focuses on the development of a nonlinear least-square based optimization technique to identify and derive appropriate parameters and composition percentages of static and dynamic load models directly from measurement data.

Index Terms—load modeling, identification measurement, static models, dynamic models

I. INTRODUCTION

I

detailed load models based on surveys of customer loads, together with typical model parameters, to develop complex load models that capture both the static loads and dynamic loads such as induction motors [8-10].

simulation inaccuracy for planning and operational studies is load model uncertainty [1-7]. However, modeling load has always been a difficult task because: • diversity in the types of loads connected to the power system at any given moment • accurate information on the composition and mix of loads on continuous basis is an insurmountable task • temporal variation in loads from hour-to-hour, day-today, and season-to-season and thus there cannot be an “all purpose” load model Despite some significant research done in the 70s, 80s and 90s, up to several years ago many utilities used very simplistic load models that comprise mainly of voltage dependant static polynomial load representation – that is essentially a combination of constant impedance (Z), constant current (I) and constant power (P) loads (commonly referred to as ZIP load models). These models are certainly not true representation of the system, particularly in light of the high penetration of induction motor loads (e.g. residential air conditioners). More recently, many utilities have used more

II. LOAD IDENTIFICATION USING MEASUREMENT DATA The measurement-based load modeling approach uses advanced optimization algorithms to estimate appropriate parameters and load compositions for a suitable load model structure. The overall procedure (shown in Fig. 1) used in this work is summarized as follows: •

Acquire the measurement data (timestamp, time-domain voltages and currents for each phase)

•

Use a post-processing technique to screen events suited for load model parameter estimation

•

Use a DFT-based signal processing algorithm to convert three-phase voltages and currents into positive sequence per-unit voltage, active power, and reactive power

•

Select a load model structure

•

Identify which parameters can be estimated reliably from the available measurements

•

Estimate distribution feeder impedance (R and X) based user-defined performance criteria

2

•

Obtain a best estimate for the desired parameters using the optimization algorithm

•

Validate the derived load model using commercially available software packages like PSS/ETM

Data Collection

Event Selection

Data Processing

Load Model Structure

Parameter Derivation for the Load Model Structure

Criteria (3) and (4) would ensure that motor dynamic response will be pronounced in the event. The event selection process has been automated so that the user does not have to manually analyze each event recorded by the monitor. A DFT based sliding window algorithm was developed to convert three-phase voltages and currents into positive sequence, per unit voltage, current, real power , and reactive power. Sixteen samples per cycle were found to be sufficient for the optimization algorithm. Note that the sliding window algorithm inherently results in filtering in the input data; no explicit filter was implemented in the algorithm. B. Load Model Structures Identified for this Study In order to make sure that the developed physical load models can be conveniently integrated into the system planning tools such as Siemens PTI PSS/ETM and GE PSLFTM, two load model structures were considered in this phase of the project. These two load model structures incorporate both static and dynamic characteristics of the loads. 1) Single Machine Structure

Model Validation

Fig. 1. System Identification Process

A. Data Collection and Processing As part of the first phase of the project, different commercially available data acquisition devices (PQ monitors, digital fault recorders (DFRs), digital relays etc.) were identified that can be used for collecting data suitable for load modeling. The field data used for this project was collected using PQ monitors and digital fault recorders. The ideal location for collecting data is on the secondary side of substation distribution transformer (low-voltage side). Either a single feeder or multiple feeders (using totalized current) can be monitored. A set of filtering criteria was developed to filter out the events suitable for load modeling parameter estimation. The main criteria for selecting an event are: 1.

The algorithm needs response of loads to balanced 3phase disturbances. An unbalance of up to 10% is acceptable. The fault should preferably be an upstream transmission fault or on an adjacent feeder. Downstream faults on the feeder being monitored cannot be used because that will contain fault current and not response of loads.

2.

The event should not be a momentary interruption because the optimization algorithm cannot handle discontinuity. By the same token, the event should not have large discontinuities such as load drop in real and reactive power response.

3.

The event should have significant (15-20%) drop in voltage from the pre-disturbance value.

4.

The event should be at least 4 cycles in duration.

5.

The event should have a few cycles of pre-event data to initialize the state variables.

The first structure, referred to as the “1-machine” structure, was built upon the structure developed in the first phase of the project (see Fig. 2) [4]. Optimized parameters are those which are optimized during the non-linear optimization process. For these parameters, the user has to provide an initial estimate. Derived parameters are those which are calculated either based on user input or during the optimization process, but are not optimized. The measurement data is available on the low voltage side of the distribution transformer (“metering point”) while the loads are connected at the load bus. The key elements of this model are summarized below: Initial Estimates and Bounds – An extensive literature review was performed to come up with different sets of machine and static parameters that have been used in previous load modeling efforts. Feeder Impedance – Feeder impedance is represented explicitly and derived based on a user defined X/R ratio and voltage drop of the feeder. Load Bus Capacitor – The capacitor B2 (in Fig. 2) represents the net effect of distribution (e.g. pole top) capacitor banks. Its value is calculated to ensure that the net reactive power at the metering point matches the initial measurement. Induction Motor Model – The dynamics of the load is represented by an equivalent (represented using a 3rd order model) induction motor. Two options for representing mechanical torque characteristics for the motor load were implemented, namely constant and polynomial torque representation. Kp (optimized parameter) is the percentage of the real power component of motor load. Lower and upper bounds on Kp of 0.2 and 0.8 respectively were considered. Note that, this range is reasonably broad and should be narrowed down if better load information is available. The machine power factor (optimized parameter) is used to calculate the steady state reactive power of the induction motor in the load structures. Most of the induction motors in

3

practice will have a full load power factor between 0.85-0.88, and thus an initial estimate of 0.87 was used in most cases. In some cases, 0.87 power factor did not give a good. Based on the events tested so far, the initial power factor may have to be reduced to as low as 0.6 to get a reasonable fit. This can be explained by the fact that in our load structure we are using a single motor (or two motors) to represent the aggregated effect of a large number of motors, all of which are not running necessarily at rated load and power factor. Static Model – The static load is represented in terms of a polynomial expression (ZIP). The default bounds on the static coefficients are 0 and 1. However, in some cases a lower bound of -1 on the static parameters can give a better fit. The static load power factor is an input parameter that can be changed by the user. The default value used is 0.9. For some static loads the power factor can be as high as, or higher than, 0.95. However, because we are trying to model the static load at the substation bus value of 0.9 is more realistic to take into account reactive losses as we go down in voltage (i.e. transformation that is not explicitly modeled).

heavier) industrial motors loads from typically smaller (and much lighter inertia) residential motor loads such as residential air conditioners. The two motors are referred to as the “large motor” and “small motor” in this paper. In another project (see [11] and [12]) we have used this model structure to represent residential air conditioners and have augmented the model with additional features to facilitate modeling the stalling characteristics of residential air conditioning load – modeling stalling behavior was not within the scope of work of this project. Load Bus

Transmission bus 230, 115, 69- kV

Rfeeder : Derived Xfeeder : Derived

Feeder Equivalent Rfdr, Xfdr

LTC

Derived Data Vmag_load Pm_load Qm_load

Input Data time stamp Vmag Pm Qm Vang

Rfeeder : Derived Xfeeder : Derived

Feeder Equivalent Rfdr, Xfdr

B2

M Induction Motor Optimized Param: xls,xlr,rr,rs,xm,H

Large Induction Motor

Optimized Param: xls,xlr,rr,rs,xm,H

M

Small Induction Motor

ZIP

Load Bus

Transmission bus 230, 115, 69- kV

M

Load Capacitance

Optimized Param: ap,bp,cp (Z,I,P coefficients of real power) aq,bq,cq (Z,I,P coefficients of reactive power)

Derived Param: Xcapacitor

Derived Param: Tm(=Te)

Fig. 3. Two Machine Structure with Distribution Feeder

LTC

Derived Data Vmag_load Pm_load Qm_load

Input Data time stamp Vmag Pm Qm Vang

Additional elements of this model which are different from the single machine model are summarized below: ZIP Optimized Param : ap,bp,cp (Z,I,P coefficients of real power) aq,bq,cq (Z,I,P coefficients of reactive power)

B2

Load Capacitance

Derived Param: Xcapacitor Optimized Parameters Induction Motor

Measured Data For each time step: Time Voltage magnitude Voltage angle Real power Reactive power

kp

% of Dynamic Machine Real Power

ap

Z coefficient of Real Power

xls

Stator Reactance

bp

I coefficient of Real Power

xlr

Rotor Reactance

cp

P coefficient of Real Power

rs

Stator Resistance

aq

Z coefficient of Reactive Power

rr

Rotor Resistance

bq

I coefficient of Reactive Power

Magnetizing Reactance

cq

P coefficient of Reactive Power

xm

LMPD Algorithm

User Input Voltage drop Feeder X/R Machine power factor Static load power factor Initial guesses Bounds of parameters

Static

H

Inertia Constant

pf

Machine Power Factor

Calculated Parameters Rfeeder

Distribution Feeder Resistance

Xfeeder

Distribution Feeder Reactance

Kq

% of Dynamic Machine Reactive Power

Tm0

Steady-state Machine Torque

Xcap

Capacitance at the load Bus

Fig. 2. Single Machine Structure with Distribution Feeder

2) Two Machine Structure The two-machine structure (shown in Fig. 3) is an extension of one machine structure. The purpose of adding the second machine is to be able to separate out typically large (and

Machine Inertia Constant – The lower and upper bounds for the small motor were considered to be between 0.03 and 0.3, respectively. The lower and upper bounds for the large motor were considered to be between 0.5 and 1.5, respectively. The lower bound of 0.03 for the small machine is based on the lab tests performed on rotors of residential air conditioners [12]. Percentage of Dynamic Real Power (Kp) – For the two machine structures there are two percentages of dynamic real power: Kp _l =

Re al power consumptio n of the l arg e motor Total real power measured at the load bus

Kp _s =

Re al power consumptio n of the small motor Total real power measured at the load bus

(4) (5)

The default bounds on Kp_l are set to 0.2 and 0.8 (same as the 1-machine structure). Kp_s has bounds of 0.1 and 0.3. However, these bounds could be changed as needed. C. Load Model Parameter Estimation Once the load model configuration is defined, the load model parameters can be determined based on field measurement data and modern state-of-the-art parameter identification approaches [3, 4]. The aim of parameter estimation techniques is to find the set of model parameters that results in the best fit between the measurement samples and model predictions. In this work, a non-linear least-square algorithm available in the MATLAB® Optimization Toolbox was used [13].

4

The non-linear parameter estimation is an iterative process. In successive iterations the sum of squared errors between simulated and measured output signals is calculated. Based on this, the parameters are updated through the optimization algorithm. The iterative process will stop if the sum of squared errors is within the specified tolerance or if the parameter changes are small enough.

Event 1 Chickamauga - Measured Positive Sequence Voltage Vpos 1.2 1

Voltage(pu)

The objective function is set to the mean squared error of measured and simulated active and reactive power at each time step. A Runga-Kutta numerical integration technique was used to perform the numerical integration of the load model state equations.

0.8 0.6 0.4 0.2 0 0

0.02

0.04

0.06

0.08

0.12

0.14

0.16

0.18

0.2

Event 1 Chickamauga - Measured Positive Sequence Real and Reactive Powers Ppos

5

III. ACTUAL RESULTS

Qpos

4

A. Event Description The simplified on-line diagram in Fig. 4 shows the region close to a monitoring point from a utility in the southern part of the United States. Four events were obtained from this site. However, model development and validation results (in PSS/ETM) for only one event is shown here. A three-phase transmission fault (shown in Fig. 4) occurred on the 161KV system and voltages and powers were recorded on the 13 kV bus at a substation (substation #2) downstream from the fault. The positive sequence data for this event is shown in Fig. 5. 161kV Bus 161kV transmission line

B1

26/13kV line Fault

B6

B5

3 Per Unit P and Q

Twelve cases were studied, using field measurements from either a PQ monitor or a DFR from three utilities. Here we will discuss one of these events.

B2

0.1 Time(s)

2 1 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-1 -2 Time(s)

Fig. 5 Positive Sequence V, P, and Q Recorded at Substation #2 (12/04/05, 2:04am) – Data per Unitized on 1MVA 13.2KV Base

B. Model Development The proposed method was applied to find the parameters of the load model. The converged parameters are shown in Table 1. Responses of real and reactive power, obtained using these derived parameters, were then compared with the response of real and reactive power that was generated from simulation. Responses obtained from the 1-machine structure are shown in Fig. 6. Similar results were obtained from the 2- machine structure as shown in Table 1. Plots of real and reactive power are however not shown for brevity. C. Load Model Validation in PSS/ETM

#1 #2 #3 Switching Station B3

161/26 kV

#1 B4

#2 26/13 kV

Substation2 Feeders

Fig. 4 Simplified One-Line Diagram of the Utility System

To illustrate the use of the models this event was simulated in Siemens PTI PSS/ETM. For creating a tuned case for this event, a summer planning case was obtained from the utility. The generation dispatch, status of main capacitor banks and loading in this case was modified based on the state estimator data provided by the utility. The parameters obtained from the algorithm were used to simulate the load response in this full system model obtained from the utility. The simulated response was compared with the measured response (shown in Fig. 7). A good match between measured and simulated response indicates that the load model is reasonable enough to represent the actual loads attached to the bus, for this event.

5 Table 1. Converged Parameters Obtained for One Machine and Two Machine Structure

Structure 1

Structure 2

the summer months leading to greater small motor load content. 3.

In general, it seems that for events at the same substation and roughly the same time of day and season the load model parameters do not vary by much.

4.

In general, there does seem to be a tendency for the motor load content in the load to be higher as we get into the afternoon hours on a summer day.

The results from the measurement case shown here clearly show the ability of the proposed optimization approach to derive load model parameters for the two load model structures. Similar results were obtained for the other events. Pmeasured Vs.Pevaluated: Krause 4.5 Pmeasured Pcalculated Pmeasured versus Pevaluated (pu)

4

3.5

3

2.5

2

1.5

1.

Primarily, the study has reinforced the fact that a purely static load model for system studies is certainly not appropriate for capturing true load response.

2.

In general the percentage of motor load tends to be higher in the summer months, than in the winter months and for the 2-machine structure, the percentage of small motor tends to be higher in the summer. This is all expected since generally air conditioners are more predominant in

0.02

0.04

0.06

0.08 0.1 0.12 Time (sec)

0.14

0.16

0.18

0.2

Qmeasured Vs. Qevaluated: Krause

IV. SUMMARY AND FUTURE WORK

2 Qmeasured Qcalculated

1.5 Qmeasured versus Qevaluated (pu)

The overall objective of this multi-year research was aimed at developing a measurement-based approach that can be easily used by utilities to develop load models for operation and planning studies. As a result, a set of guidelines for selecting monitoring locations and system events was developed. Two load model structures that can be easily implemented in bulk system stability programs were also developed. An improved nonlinear least-square estimation was used for identifying parameters of the load two load models. In general the work under phase-1 and 2 of this multiyear program has provided much value and understanding of the load modeling process. Twelve events from three different utilities were used to test the entire method. The results obtained so far are very promising. Some of the general conclusions as a result of this project are summarized as follows:

0

1

0.5

0

-0.5

-1

-1.5 0

0.02

0.04

0.06

0.08 0.1 0.12 Time (sec)

0.14

0.16

0.18

0.2

Fig. 6 Comparison of Measured and Calculated (Using Converged Parameters) Real and Reactive Power – Single Machine Structure (V.D. – 1%)

6

V. ACKNOWLEDGEMENT

Real Power: Measured Vs. Simulated Pmeasured

Psimulated

4.5 4

Real Power(pu)

3.5 3 2.5 2 1.5 1 0.5 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Time(sec)

In addition, all the authors wish to thank and acknowledge the contributions of Mr. J. Smith, Mr. W. Kook towards model validation and Mr. W. Sunderman for developing and automating the filtering methodology.

Reactive Power: Measured Vs. Simulated Qmeasured

Qsimulated

3

We would like to also grateful acknowledge the co-sponsors of this research, TVA, CenterPoint, Oncor, ERCOT, AEP, FirstEnergy, Consolidated Edison, and Long Island Power Authority.

2.5 2 Reactive Power(pu)

The authors wish to acknowledge the support of David Mercado of CenterPoint, Dejim Lowe of TVA, and Roy Boyer of Oncor for providing the measurement data, tuned power flow cases, and other additional information regarding the events and system during the course of this project. In particular, we would like to thank Tom Cain of TVA for his insightful thoughts, and technical guidance through the second phase of this program. We appreciate Jose Conte of ERCOT for providing valuable comments during the course of this work.

1.5 1 0.5 0 -0.5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-1

VI. REFERENCES [1]

-1.5 Time(sec)

[2] Fig. 7 Comparison of Measured and Simulated (in PSS/ETM) Real and Reactive Power – Single Machine Structure (V.D. – 1%)

As might be expected for any optimization algorithm, multiple solutions for the load model parameter can be found in each case due to multiple local minimum of the mathematical function. Therefore, it is extremely important that engineering judgment be applied during the selection of initial estimates and bounds for individual parameters. The type of system (weak versus strong), approximate location where the fault occurred, a sense of loading on the feeders, season and time of day, amount of shunt capacitors on the distribution feeder , and when the event occurred should all be factored into the selection of initial estimates and bounds of individual parameters. There is still a critical need to perform sensitivity studies to understand the variability in load model parameters due to variations in load due to regional and temporal (time of day, season etc.) changes. Due to limited measurement data available for deriving load model parameters, additional effort is required to determine how to apply measurement-derived parameters from one bus at a specific point in time to systemwide models at potentially different time periods. To achieve this, the next step in EPRI’s load modeling effort is based on integrating the measurement-based approach discussed here with the learning from the component based approach (i.e. testing and characterizing load components e.g. the work in [12]) and to look at how sensitivity analysis may be used in a systematic way in power system studies to deal with the variations in load behavior.

[3]

[4]

[5]

[6] [7]

[8]

[9]

[10]

[11]

[12]

[13]

L. Pereira, D. Kosterev, P. Mackin, D. Davies, J. Undrill and W. Zhu, “An Interim Dynamic Induction Motor Model for Stability Studies in the WSCC,” IEEE Transactions on Power Systems, November 2002 IEEE Task Force Report, “Standard Load Models for Power Flow and Dynamic Performance Simulation,” IEEE Transactions on Power Systems, Vol. 10, No. 3, pp. 1302-1313, August 1995 V. Knyazkin, C. A. Canizares, L.H. Soder, “On the parameter estimation and modeling of aggregate power system loads Power Systems,” IEEE Transactions on Volume 19, Issue 2, May 2004 A. Maitra, A. Gaikwad, P. Zhang, M. Ingram, D. L. Mercado and W. D. Woitt, “Using System Disturbance Measurement Data to Develop Improved Load Models” Proceedings of the IEEE Power Systems Conference and Exposition, 2006. IEEE Task Force on Load Representation for Dynamic Performance “Load representation for dynamic performance analysis (of power systems),” IEEE Trans. Power Syst., vol. 8, pp. 472–482, May 1993 “Bibliography on load models for power flow and dynamic performance simulation,” IEEE Trans. Power Syst., vol. 10, pp. 523–538, Feb. 1995. R. H. Craven, T. George, G. B. Price, P. O. Wright, and I. A. Hiskens, “Validation of dynamic modeling methods against power system response to small and large disturbances,” in Proceedings of CIGRÉ General Session, Paris, Aug. 1994. P. Pourbeik, D. Wang and K. Hoang, “Load Modeling in Voltage Stability Studies”, Proceedings of the IEEE PES General Meeting, June 2005, San Francisco. R. J. Koessler, W. Qiu, M. Patel and H. K. Clark, “Voltage Stability Study of the PJM System Following Extreme Disturbances”, IEEE Trans. PWRS, Vol. 22, Issue 1, Feb. 2007, pp:285 – 293. J. A. Diaz De Leon and B. Kehrli, “The Modeling Requirements for Short-Term Voltage Stability Studies” Proceedings of the IEEE Power Systems Conference and Exposition, 2006. P. Pourbeik and B. Agrawal, “A Hybrid Model for Representing AirConditioner Compressor Motor Behavior in Power System Studies”, Proceedings of the IEEE PES GM 2008. A. M. Gaikwad, R. Bravo, D. Kosterev, A. Maitra, P. Pourbeik, B. Agrawal and D. Brooks, “Results of Residential Air Conditioner Testing in WECC”, Proceedings of the IEEE PES GM 2008. MATLAB® Optimization Toolbox Version 3.0.4, Mathworks Inc. 2006.

VII. BIOGRAPHIES Arindam Maitra (M’1995) received his BSEE, MS, and Ph.D. degrees from R.E.C. Nagpur and Mississippi State University in 1995, 1997 and 2002, respectively. He is currently a senior project manager in System Studies

7 Group at EPRI where he is responsible for conducting and managing activities associated with distribution and transmissions studies. His research interests are in the areas of modeling and simulation techniques for power system harmonics, power system transients, distribution reliability, load modeling, computer applications in power systems, and power system control and protection. He has authored and co-authored numerous technical papers on such topics. Anish M. Gaikwad (M’2000) received his BSEE, and MS degrees from R.E.C. Nagpur and Mississippi State University in 1997, and 2002, respectively. He is currently a senior engineer in System Studies Group at EPRI in Knoxville, Tennessee. He has worked on various topics related to distribution and transmission studies including load modeling, power system transients, distribution reliability, and in general computer applications in power systems. He has written various technical papers and articles. Pouyan Pourbeik (M’1993, SM’2002) received his BE and PhD in Electrical Engineering from the University of Adelaide, Australia in 1993 and 1997, respectively. From 1997 to 2000 he was with GE Power Systems. From 2000 to 2006 he was with ABB Inc. In June 2006 he joined EPRI Solutions Inc. In 2007 EPRI Solutions Inc. became part of EPRI. At EPRI he is presently a Technical Executive. Throughout his career he has been involved in and led studies related to all aspects of power systems modeling, dynamics and control. He is presently chairman of the CIGRE WG C4.601 on Power System Security Assessment and is the Chairman of the Power System Stability Subcommittee of the IEEE PES. He is a registered professional engineer in North Carolina. Daniel Brooks (M’92, SM 2007) received his B.S. and M.S. degrees in electrical engineering from Mississippi State University and his M.B.A. degree from University of Tennessee-Martin. He manages the systems analysis and studies group at EPRI (previously EPRI Solutions), Knoxville, TN, where he manages and conducts power systems engineering analytical studies spanning transmission, distribution, generation, and system operations. Before joining EPRI, he worked for over nine years with Electrotek Concepts managing and conducting similar studies. Mr. Brooks is a registered professional engineer in the state of Tennessee and is a member of the IEEE Power Engineering Society.