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A Real Application of Measurement-Based Load Modeling in Large-Scale Power Grids and its Validation Dong Han, Student Member, IEEE, Jin Ma, Ren-mu He, and Zhao-yang Dong, Senior Member, IEEE
Abstract—Load model is one of the most important elements in power system simulation and control. Based on more than 20 years of practice using load characteristic recorders in the measurementbased load modeling, this paper proposes the Expectation Composite Load Model to predict unseen data. The methods for load bus classification and parameter identification are also provided. The generalization capability of the proposed load modeling is validated by the measured load dynamics and system dynamics during two three-phase short circuit tests of the NE power grid in China. In order to evaluate the measurement-based load model, the Probabilistic Collocation Method (PCM) is applied to quantitatively analyze uncertainties of the simulation responses raised by the parameters. Index Terms—Composite load model, field measurement, power system stability, Probabilistic Collocation Method, uncertainty analysis.
I. INTRODUCTION
L
OAD model is one of the most important electric components in power system simulation and control [1], [2]. However, it has been observed that different load models have different, even opposite impacts on simulation results for dynamic stability and voltage collapse [3]–[8]. For instance, when using the standard Western Electricity Coordinating Council (WECC) dynamic database to simulate the 1996 WECC blackout, the simulation did not agree with the disturbance recordings. After modifying load models from constant current load model to a combination of induction motor and various static loads, the oscillatory disturbance in the actual system was reproduced [9]. Currently, load modeling [10]–[18] and parameter identifiability [19]–[21] based on the field measurement are the commonly used approaches in power system analysis. However, one of the most difficult problems is yet unsolved, i.e., what is the ideal number of load models suitable for dynamic simulation? Manuscript received June 13, 2008; revised February 20, 2009. First published September 09, 2009; current version published October 21, 2009. This work was supported in part by the Chinese National Key Basic Research Special Fund (No.2004CB217901), in part by NSFC (No.50707009), in part by the Ministry of Education (20070079014), in part by the BeiJing Nova Program, and in part by “111” project (B08013). Paper no. TPWRS-00476-2008. D. Han, J. Ma, and R.-M. He are with the Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control of Ministry of Education, North China Electric Power University, 102206 Beijing, China (e-mail:
[email protected]). Z. Y. Dong is with the Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong. Digital Object Identifier 10.1109/TPWRS.2009.2030298
Both a single load model and load modeling for all load buses in dynamic simulation are inappropriate and impractical options. In addition, there are related questions that remain unanswered. For example, how is load modeling on power system dynamics validated? Does the measurement-based load model have good generalization capability? Without answers to these questions, it is hard for the measurement-based load modeling to be widely applied in large-scale power grids. To address these questions, the Expectation Composite Load Model (ECLM) is proposed here for transient and dynamic stability, based on our over 20 years of practice of measurementbased load modeling in China. To date, 14 load characteristic recorders have been installed to observe load dynamics in power grids of China. They have provided thousands of records of measured load dynamics. The data have been accumulated and analyzed using principles and techniques summarized in this paper as a guideline for the application of measurement-based load modeling in large-scale power grids. Moreover, the applications of measurement-based load modeling in the NE power grid of China are also introduced. The NE power grid, one of major power grids in China with a generation capacity of more than 45 000 MW, is interconnected with several other large-scale power grids. Because the load center is in the South of the grid while the main energy producers lie in the North, large amounts of energy have to be transferred from the North to the South. Simulations show that different load models and parameters have significant effects on the available transfer capability (ATC) of the major transmission corridors in the NE power grid. Load modeling is often validated using measured load dynamics obtained from a certain substation (in substation sense) [11]–[18]. However, the veracity of system dynamic simulation is hard to be evaluated due to a lack of data on the dynamic behavior of the whole system, not to mention the effect of load modeling on system dynamics (in power grid sense) [3], [6], [7], [9], [10]. Thanks to the three-phase short circuit disturbances performed on the 500-kV transmission network artificially in the NE power grid in 2004 and 2005, respectively, the valuable measured data of load dynamics and system dynamics are provided for this research. Using these unique data sets, the application of our measurement-based load modeling in large-scale power grids is validated in both substation sense and power grid sense. The remainder of this paper is organized as follows. Section II introduces principles and techniques to guide the application of measurement-based load modeling in large-scale power grids.
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Section III validates the measurement-based load modeling proposed in Section II through the three-phase short circuit tests in substation sense and in power grid sense. Section IV quantitatively analyzes the uncertainty of key parameters in the measurement-based load model, based on the Probabilistic Collocation Method (PCM). Section V concludes the whole paper.
Too low voltage levels, such as 10 kV or voltage lower than 10 kV, including relatively exhaustive but large number of load buses, will make the network structure of dynamic simulation too complex and load modeling too difficult. Moreover, it requires much more effort to survey the proportions of load classes at every load bus. Usually, in a 500-kV transmission network, the loads connecting at 220 kV/110 kV or 220 kV/66 kV step-down transformers can meet this requirement. should not be too P3) The optimal clustering number large or too small for the engineering application. , the maximum optimal clustering Before computing should be set to satisfy . number satisfies Usually the rule-of-thumb is that , where is the number of clustered data [23], [24]. P4) The load bus close to the cluster center in each cluster group should be chosen as the typical load bus. Through the steps of surveying on the load classes from dispatchers via questionnaire, calculating the proportions according to actual transmission power of typical day, the load buses can be clustered [25]. After clustering, there will be a cluster center in each cluster group, and then the load bus close to the cluster center can be chosen for the installation of load characteristic recorder. According to the proposed principles, the following four steps were carried out in classifying and clustering load buses in the NE power grid. S1) Select clustering indices. Load buses basically comprise five load classes (industrial, agricultural, commercial, residential, and other loads) in the NE power grid. After taking into account the influence of seasonal changes on loads, ten clustering indices were adopted. Namely, maximum summer and maximum winter load proportion of the five load classes. S2) Select the appropriate voltage level of load buses. In the NE power grid, load in power system dynamic simulation represents the total active power and reactive power at the 220 KV/66 KV substation step-down side. Therefore, 234 load buses at 66-kV voltage level are included in the clustering data set. . S3) Determine the bound of , , satisfies . Because Then the optimal clustering number falls into the bound 15]. [2 S4) Choose a substation in each cluster group. The 234 load buses were classified into seven groups after fuzzy cluster analysis finally. In each group, a typical substation near the cluster center was chosen to install the load characteristic recorder. The substations are HaXi, QingBei, JiXi, XiJiao, YuShu, ChengXi, and HuShiTai. The load dynamics of these seven groups were recorded from normal disturbances and three-phase short circuit tests in 2004 and 2005.
II. MEASUREMENT-BASED LOAD MODELING IN LARGE-SCALE POWER GRIDS A. Guide and Practice on Load Classification and Clustering Using one single load model is obviously inappropriate in large-scale power grid, since sometimes load characteristics are very different. It seems more reasonable to build its own load model at each load bus from measured data. But it is impractical for a large-scale power grid that comprises too many load buses. If the load characteristic recorder is installed at each load bus, it would require immense investment and cause difficulties in updating and maintaining the parameter database of the load model. In fact, different load buses may share some common features, such as similar load class proportions, similar changes in load, load location, and so on. Thus, if load buses can be classified and clustered into several groups by some criteria and only one typical substation in each group is chosen to install the load characteristic recorder, the load model identified from measured load dynamics can be used at all the load buses in the same group. In this way, the number of load models for dynamic simulation can be significantly reduced while the main characteristics of loads in a real system can also be maintained. Based on fuzzy cluster analysis [22]–[25], there are several stages to cluster load buses. Firstly, determine the clustering indices for clustering, i.e., the common and representative features of loads. Secondly, choose the voltage level at which load buses are clustered. Thirdly, after combining the above two stages, and cluster the compute the optimal clustering number load buses. Finally, select one substation among each clustering group. Based on our practice in the NE power grid, four principles to be used in load classification and clustering are proposed. P1) The clustering indices should not be too complex or too simple. It should reflect the fundamental and essential features of loads. A too complex clustering index will increase the difficulty to extract representative features of each cluster group, while a too simple one tends to reduce the reliability of clustering results. Because the proportion of each load class can reflect load changes, such as the load classes of industrial, agricultural, commercial, and residential [25], [26], it can be chosen as one of the clustering indices. Some load classes can be subdivided if more detailed characteristics need to be taken account into, for example, industrial load class can be further divided into light industry, heavy industry, etc. Moreover, regarding load has time-variant characteristic, the clustering indices can take into account the seasonal and time changes. P2) Voltage level at which the load buses are clustered should not be too low. Both the precision of measurement-based load modeling and the best-cost performance should be taken into consideration.
B. Multi-Curve Identification The induction motor parallel with ZIP load model is used in this paper, as shown in Fig. 1, and details about model structure and equivalence can be found in [17] and [18].
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and where is the sampling points of this measurement; are, respectively, the model output of active load and reand are the measured active load at the th step; active load and reactive load at the th step; and and are weighting vectors for active and reactive load. Equations (3) and (4) are absolute fitting errors. Since the load value may vary in a wide range among the measurements, the relative error is better to reflect the accuracy of the fitting, which , : can be defined as
Fig. 1. Equivalent circuit of the composite load model.
There are 14 parameters in this composite load model to be identified, i.e.,
(5) (6)
where, is stator winding resistance of motor; is stator is magnetizing reactance of leakage reactance of motor; is rotor resistance of motor; is rotor leakage remotor; is rotor inertia constant; is torque coactance of motor; efficient in proportion to the square of speed; is torque cois the initial active power efficient in proportion to speed; proportion of the equivalent motor in the composite load model; is used to specify the capacity base of the equivalent motor; and are the proportional coefficients of the constant and impedance and constant power in static active load; and are the proportional coefficients of the constant impedance and constant reactive power in static reactive load. and are defined as (1) and (2): Herein (1) where is the active load in the steady state before the disis the initial active load of the equivalent turbance, and motor: (2) where is the chosen voltage base, and is the bus voltage in the steady state before the disturbance. It has been shown that the load model identified from multiple data sets is more accurate than a model built from a single test sample [14]. Load characteristic recorders at the substations in the NE power grid have been in operation for more than four years, and each substation has accumulated tens to thousands of load records. To take full advantage of these records, the multi-curve identification technique is introduced into our measurement-based load modeling. recorded data available, then for the th Assume there are data, the root-mean-squared error of active power and reactive power between the model output and the field measurement, and , can be formulated as defined as
where
represent the average active load and reactive load for the th data. Thus, the loss function for multi-curve identification can be formulated as (7) are the weighting coefficients for different measurewhere ments. Minimizing objective (7) generates a load model which is a best fit of all the measurements, and we call it the Expectation Composite Load Model (ECLM), which is applied at bulk system level. The multi-curve load modeling process is here formulated as a nonlinear optimization problem to be solved for the parameter set, minimizing the objective functions (7). Based on our practice on multi-curve identification process, a hybrid algorithm combining the genetic algorithm and Simplex Search Method is proposed [17]. Herein, the genetic algorithm is first applied to find regions that the optimum may lie in, and then the Simplex Search Method is run to find the optimum. All load records in one substation are collected into one database to identify an ECLM. Usually the measured data are collected every half year or every year to update this database of parameters in our practice. Before parameters are re-identified, the statistical characteristics of the measured data are first studied to find the common laws of loads [18]. Then according to these statistical laws, the measurement-based load model is built, and the new identified parameters can be obtained to replace the old ones. They can be used for dynamic simulations subsequently. III. VALIDATION OF MEASUREMENT-BASED LOAD MODELING A. Validation in Substation Sense
(3)
(4)
To simulate load dynamics of the artificial three-phase short circuit disturbances in 2004 and 2005, two load models are built. The first load model, called ECLM I, is built upon the measured data collected before the first test on March 25, 2004. The second load model, called ECLM II, is built upon the measured
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TABLE I IDENTIFIED PARAMETERS OF ECLMS I AND II
Fig. 2. Outputs of ECLM I and the measurements on 9:26:41, March 25, 2004 at HaXi Substation.
data collected before the second test on March 29, 2005 (including the measured data on March 25, 2004). Table I shows the identified parameters of ECLM I and ECLM II of the seven substations, which have been put into practice. The values of these identified parameters in Table I are given in per unit. Model outputs (dashed lines) at HaXi and YuShu substations are shown in Figs. 2 and 3, respectively. Solid lines represent the measured load dynamics. The voltage dips of the measured data were usually less than 0.2 p.u. when normal disturbances occurred. In contrast, during the three-phase short circuit disturbances on March 25, 2004 and March 29, 2005, the voltage dips of the seven substations were greater than 0.25 p.u., and even reached more than 0.4 p.u. at some substations. In Figs. 2 and 3, it is clear that the load model built upon the measured data under normal disturbances can well describe the load dynamics under the three-phase short circuit disturbances. It demonstrates good generalization capability of the two Expectation Composite Load Models.
Fig. 3. Outputs of ECLM II and the measurements on 13:30:52, March 29, 2005 at Qingbei Substation.
TABLE II MSE OF ECLM I AND II IN SUBSTATION SENSE
Table II shows output errors of ECLM I and II under the two disturbances in 2004 and 2005 at seven load substations, respectively. The mean squared error (MSE) between model outputs
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and the measured data are used as the error criteria. Smaller MSE indicates better accuracy in describing the load dynamics:
(8)
where is the number of sample points; is the measured is the output of the idendata at the th sampling point; and tified load model at the th sampling point. Table II clearly shows that load modeling based on historical measured data at seven substations can well describe the load dynamics under the three-phase short circuit disturbances. That is, the load model built upon normal disturbances has the ability to predict unseen load characteristics under major disturbances. Therefore, the measurement-based load modeling further exhibits good generalization capability in substation sense.
Fig. 4. Bus voltage angle and amplitude of the simulated results and the measured data at LY 500-kV bus.
B. Validation in Power Grid Sense Although the measurement-based load modeling shows good generalization capability in substation sense, further investigation is needed to know whether simulations using such load modeling can reflect system dynamics in the real system. During disturbances in 2004 and 2005, PMUs recorded dynamic behaviors at 500-kV buses, short-circuit capacity and the fault process, etc.; meanwhile, Energy Management System (EMS) recorded the steady-state data and system topological structure at the same time. In order to observe the effect of load model on dynamic simulation, the topological structure, steady-state data, fault process, other models, and parameters keep fixed, only the load model structures or parameters are changed. Figs. 4–6 show simulated results of the simulations and the measurements at 500-kV buses in 2004 and 2005, respectively. Two other load models are applied to compare the simulated results. The one is 40% constant impedance parallel with 60% constant power static load model, which takes no account of the effect of induction motor in simulations. The other is the Synthesis Load Model (SLM), and the model structure is induction motor parallel with static load model. Using the measured data of the first disturbance test in 2004, parameters of the SLM were obtained through modifications based on trials and errors to fit the measurements. In other word, the closeness between the simulated results using the SLM and the measured data is achieved only depending on modifications of the loads. It is appropriate to compare a load model with the SLM, since the discrepancies between simulations and measurements arise from many factors, which cannot be removed by only modifying load models, such as parameters of generators, excitation systems and algorithm error, etc. It can be seen clearly from Figs. 4–6 that simulated results of ECLMs I and II reflect system dynamics much better than the static load model does, especially the dynamics during the first swing after the disturbance was cleared. Furthermore, the simulated results of ECLMs I and II are very close to those of the SLM, and sometimes with even better approximation toward the measured data.
Fig. 5. Active power of the simulated results and the measured data at SL side of Line LY-SL.
Fig. 6. Bus voltage angle and amplitude of the simulated results and the measured data at DF 500-kV bus.
The MSEs of ECLM I, II and the SLM are listed in Table III, which shows the errors in the Expectation Composite Load Models are smaller. It demonstrates that clustering the 234 load buses into seven groups in the NE power grid is
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TABLE III MSES OF ECLM I, II AND THE SLM IN POWER GRID SENSE
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However, how do we quantitatively analyze the parameter uncertainty of load model in dynamic stability? Traditional methods requiring repeated simulations and intensive computation time, e.g., Monte Carlo method, are inapplicable to power system dynamic simulations because of high-dimensionality and strong nonlinearity. In this paper, the Probabilistic Collocation Method (PCM) is adopted. It can be used to efficiently analyze the quantitative parameter uncertainty with fewer simulations at a very low computational cost. IV. UNCERTAINTY ANALYSIS OF THE EXPECTATION COMPOSITE LOAD MODEL A. Probabilistic Collocation Method
Fig. 7. Model outputs of ECLM II with 500-kV bus.
K = 1 and K = 0:1 at HX
The basic idea of the PCM is to approximate the model response as a polynomial function of uncertain parameters, based on the probability density functions of the uncertain parameters [27], [28]. Once this simple approximation is found, the influence of uncertain parameters can be quickly estimated. Suppose the response is a function of the uncertain param. The goal of the PCM is to approximate eter , i.e., the estimated value of : (9)
reasonable and valid. The idea of classifying load buses and applying multiple parameter sets in a large-scale power grid is proved to be practical. In addition, ECLMs I and II show good generalization capability in power grid sense. Therefore, the proposed methodology of measurement-based load modeling is proved to be efficient and practical for large-scale power grids. However, during the simulations, it is found that the ECLMs I have distinct impact on dynamic staand II with different bilities [21]. Fig. 7 displays the simulated results of ECLM II and . The larger is, the more with optimistic the simulated results are. To a great extent, Figs. 4–7 also imply that load model does have a large impact on available transfer capability calculation, and that variations in the important parameters of a load model directly affects the results of dynamic simulation. On the other hand, the dynamic equations of load models are multi-valued, i.e., quite different models and parameters may produce similar simulation results. When the parameters with high sensitivity vary in some intervals, how to evaluate the composite load model need to be further studied. For instance, whether the simulated results or the measurements can fall in the confidence intervals, where the key regions or which the key parameters are that have great impact on dynamic stabilities, how the simulation uncertainties are under the critical state, and so on. Therefore, it is necessary to quantitatively estimate the uncertainty in simulation outputs resulting from uncertainties in model inputs and parameters. A detailed analysis of parameter uncertainty will identify the key sources of uncertainty that merit further research. It will also provide useful information and guidance for the modification and calibration of measurement-based load modeling and dynamic simulation.
are constant, and are the orthogonal polynomial functions of parameter . If the probability density function of is , then the excan be written as the function in form pectation value of of the Gaussian Quadrature equations, as shown in (10) [29]: where
(10) Assuming that
is expressed as the linear model of , i.e., , and , are known, and can be solved by running the model only twice to obtain the real outputs of the response . The definition of orthogonal polynomials is (11)
where
.
and are orthogonal polynomials of order and of , respectively, and is some weighting function. For any , the set of orthogonal polynoprobability density function as the mials for that distribution can be derived by using weighting function. Also, set , . has a uniform probability For example, suppose that distribution from 0.1 to 1.0. To find the first-order orthogonal , (12) is substituted for (11): polynomial (12)
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TABLE IV AND ERRORS IN THE FIRST- TO APPROXIMATION MODELS
FOURTH-ORDER
Fig. 9. Voltage angle uncertainty at DF 500-kV bus raising from the sending ends.
Fig. 8. Uncertainty of voltage angle at HX 500-kV bus using second-order approximation model.
Once is known, it can be used recursively to find and so on. of are in (13). Since the Gaussian Quadrature technique is borrowed in the are orthogonal polynoPCM and mials, it is easy to get the probability distribution information of the estimation , such as the expectation value and the standard deviation, etc. See (13) at the bottom of the page. Regarding the approximation models, the sum of MSE for each input set is used to measure the overall error. Namely, (14) where is the number of values in each approximation model. varies simultaneously and identically at seven Assume substations in the NE power grid. Taking the major disturbance in 2005 as an example, Table IV lists the input values of and errors in the first- to fourth-order approximation models of the bus voltage angle at HX 500-kV bus. The results show that good approximation is achieved by using the PCM. Fig. 8 shows expectation values and the confidence interval standard deviations of voltage angle at HX 500-kV bus of using the second-order approximation model. In addition, the measured data and the simulated result of ECLM II are also displayed. It can be observed from Fig. 8 that the simulated results
Fig. 10. Voltage angle uncertainty at DF 500-kV bus raising from the receiving ends.
of ECLM II are very close to the expectation values and fall into the confidence interval. Furthermore, the measured data also fall into the confidence interval except at several individual sampling points. B. Uncertainty Analysis of the Measurement-Based Load Model The validity of the PCM in dynamic simulation of power systems had been proved [28], [30]. This subsection describes the application of the second-order approximation model to analyze in the measurement-based load model. the uncertainty of Since load buses in HaXi, QingBei, and JiXi cluster groups are near the fault point and are sending ends of the NE power grid (called sending ends), while those in XiJiao, YuShu, ChengXi, and HuShiTai are far from the fault point and are receiving ends (called receiving ends), the uncertainty of at sending ends and receiving ends are studied, respectively, to find the key loads or key regions. Figs. 9 and 10 show their uncertainties of voltage angle at DF 500-kV bus. From Figs. 9 and 10, it demonstrates that the uncertainty of in HaXi, QingBei, and JiXi cluster groups is very large,
(13)
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Fig. 11. Active power uncertainty at BJ side in YY-BJ 500-kV line raising from the sending ends.
Fig. 12. Active power uncertainty at BJ side in YY-BJ 500-kV line raising from the receiving ends.
especially the first swing after the disturbance was cleared, and consequently has significant impacts on simulation responses. In addition, the measured data at most of the sampling points are included in the confidence interval (the sampling points from 2.2 s to 3.36 s are outside the confidence interval). In contrast, the uncertainty of other four cluster groups is much smaller, and the confidence interval fails to include the measured data. In addition, it can be seen that the simulated outputs of ECLM II are close to the expectation values both in sending ends and receiving ends, which accord with the conception of the proposed Expectation Composite Load Model. Moreover, through uncertainty analysis, the key regions that have large impact on dynamic simulations and system stabilities are identified; and they are HaXi, QingBei, and JiXi cluster groups. It is useful for model and simulation calibration. Once a disturbance occurs, the key load groups can be quickly located using the PCM. Then the study of load influences on system dynamics can focus on these groups. Hence, the number of loads which need further study can be significantly reduced. If the disturbance is cleared at the limiting operation time, a small variation in vital parameters may raise a large uncertainty or make the system unstable, and the same parameters from different load groups may have different uncertainty. The duration of the limiting operation time is from 1 s to 1.14 s. standard deviaFig. 11 shows the expectation values and tions of active power at BJ side in YY-BJ 500-kV line, when varies at HaXi, QingBei, and JiXi cluster groups. It is clear from Fig. 11 that the uncertainty of is also very standard deviations large. The maximum difference of the is 418.75 MW at 1.82 s. In contrast, the uncertainties of XiJiao, YuShu, ChengXi, and HuShiTai cluster groups are much smaller. Fig. 12 shows the uncertainties, and the maximum difstandard deviations is 62.14 MW at 3.44 s. ference of When the NE power grid is operating at the critical state, the uncertainties would raise rapidly in the key regions. Since there are a large number of load buses in a real system, if only a single load model is adopted in the whole system, it is difficult to locate key loads or key region, and further impede analyzing the effect of loads on system dynamics. To address this issue, we divide a large power grid into several groups according to the load classes and features of each load bus. Thus, the influence of each load group can be further studied, and then different load models or parameter sets can be applied to different load groups.
V. CONCLUSION This paper proposes the Expectation Composite Load Model for transient stability using the measured data to predict unseen data. Moreover, to apply the proposed load model in a large-scale power grid, the principles and techniques are also introduced based on our more than 20 years of experience in load modeling. The measurement-based load modeling is validated using the measured load dynamics and system dynamics under the artificial three-phase short circuit disturbances in NE power grid in 2004 and 2005. Case studies show the validity and good generalization capability of the proposed measurementbased load modeling. In addition, the disturbances also verify our practice in the large-scale power grids. Finally, to evaluate the measurement-based load modeling, the Probabilistic Collocation Method is introduced to quantitatively analyze the pahas large uncerrameter uncertainty. Analysis shows that tainty in simulation responses, especially the first swing after the disturbances. The simulated results are close to the expec, and the key cluster groups are also found tation values of that will provide useful information for model and parameter calibration. Associating with other error location technology, future studies will focus on multi-parameter uncertainty analysis, model and parameter evaluation, model calibration taken account into the uncertainty, and so on. ACKNOWLEDGMENT The authors would like to thank the Dispatch and Communication Center of the NE power grid in China, who provided all the measured data of PMU and the simulation database (including network topology, power flow data, dynamic simulation data, etc.). REFERENCES [1] IEEE Task Force on Load Representation for Dynamic Performance, “Load representation for dynamic performance analysis”,” IEEE Trans. Power Syst., vol. 8, no. 2, pp. 472–482, May 1993. [2] P. Kundur, Power System Stability and Control. New York: McGrawHill, 1993. [3] J. V. Milanovic and A. Hiskens, “Effects of load dynamics on power system damping,” IEEE Trans Power Syst., vol. 10, no. 2, pp. 1022–1028, May 1995. [4] I. A. Hiskens and J. V. Milanovic, “Load modeling in studies of power system damping,” IEEE Trans. Power Syst., vol. 10, no. 4, pp. 1781–1788, Nov. 1995.
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Dong Han (S’06) received the B.S. degree from Shandong University, Jinan, China, in 1997 and the M.S. degree from North China Electric Power University, Beijing, China, in 2005, both in electrical engineering. Currently, she is pursuing the Ph.D. degree at North China Electric Power University, Beijing. Her main research interests are dynamic simulation assessment, load modeling, and dynamic power system.
Jin Ma received the B.S. and M.S. degrees from Zhejiang University, Hangzhou, China, in 1997 and 2000, respectively, and the Ph.D. degree from Tsinghua University, Beijing, China, in 2004, all in electrical engineering. Currently, he is an Associate Professor with North China Electric Power University, Beijing. His main research interests are load modeling, nonlinear system control, dynamic power system, and power system economics.
Ren-mu He received the B.S. degree from Tsinghua University, Beijing, China, in 1967 and the Ph.D. degree in electrical engineering from Lausanne Institute of Science and Technology (EPFL), Lausanne, Switzerland, in 1985. Currently, she is a Professor with North China Electric Power University, Beijing. Her main research interests are power system dynamics, simulation veracity, dynamic load modeling, deregulation, software engineering, and wide area measurements.
Zhaoyang Dong (M’99–SM’06) the Ph.D. degree from The University of Sydney, Sydney, Australia, in 1999. He is currently with Hong Kong Polytechnic University. He previously held academic positions at The University of Queensland, Brisbane, Australia, and National University of Singapore. He also holds industrial positions with Powerlink Queensland, and Transend Networks, Tasmania, Australia (both are transmission network service providers in the corresponding states). His research interest includes power system planning, power system security assessment, power system stability and control, electricity market, and computational intelligence and its application in power engineering.
