孫晗畢業(yè)設(shè)計(jì)英文翻譯

1、外文翻譯（原文）山東理工大學(xué) 畢業(yè)設(shè)計(jì)（外文翻譯材料）學(xué) 院：專 業(yè)：學(xué)生姓名：指導(dǎo)教師：電氣與電子工程學(xué)院電氣工程及其自動(dòng)化 孫晗姜殿波Low-order dynamic equivalent estimation of power systems using data of phasor measurement unitsAbstractThis paper utilizes data measured by phasor measurement units (PMUs) to extract a low-order dynamic equivalent model for power s

2、ystem stability studies. The estimated model is a 2-order model for synchronous machines. This model has the advantage of simplicity of classical model and considerably reduces the oversimplifying error of classical model. This method offers an alternative approach to analytical model reduction tech

3、niques based on the detailed system models. The proposed method uses the synchronized bus voltage and current phasors measured by PMUs. Using post disturbance data, electrical and mechanical parameters of the equivalent generator are estimated sequentially. Furthermore, a new approach for estimation

4、 of two-machine and single machine infinite bus (SMIB) equivalent systems are presented for analysis of electromechanical oscillations. To evaluate the performance of the proposed approach, simulations are performed on a two area 13-bus test system and real measured PMU data. Simulation results show

5、 that the estimated model can represent the dynamic behavior of the studied system with good approximation.Keywords Phasor measurement unit; Model estimation; Power system model reduction; Power system oscillationsIntroductionWith the development of electrical industry, the scales of power systems h

6、ave become larger than ever. Owing to the dimension of interconnected power systems, it is often impractical to represent the entire system model in detail. Therefore, reduced order dynamic equivalents are used to represent groups of generators or external systems1.Many efforts are devoted to reduce

7、 power system model using analytical approach1,2,3and4. Analytical approaches based on the concept of coherency have the benefit of saving power system structure. However, these approaches need detailed parameters of all power system machines and elements. Due to continuous variation of system param

8、eters and changing environment of nowadays power system, analytical approach may not be a good choice for model reduction. To overcome this shortcoming and take system structure and parameters changes into account, measurement based approaches have been proposed5and6.Measurement-based methods use dy

9、namic responses of system disturbance to estimate dynamic equivalent parameters. The unknown parameters of the dynamic equivalent model can be determined using identification and parameter estimation methods7. The main drawback of measurement based approach is their need for fast dynamic response of

10、 power system. Fortunately, modern power systems use wide area measurement system (WAMS)8and9that utilize phasor measurement unit (PMU) as a basis for data gathering system. PMUs measure phasors of voltage, current and frequency with a time stamp in the time interval down to 20ms. A review of applic

11、ation of PMUs to power system operation and PMU placement methods has been provided in10. Therefore from organization point of view, there would be no concern about gathering fast dynamic response of power system. In5and11, a new method for parameter estimation using neural network has been presente

12、d. Wavelet transform is used in12for identification of inter-area oscillations using measured data by PMU. Third-order synchronous generator model estimation is presented in13and14. In these methods, transfer function of the machine is calculated by linearizing its equations about the operating poin

13、t and estimating the parameters. These methods have limited accuracy because of linearization error. Power system Thevenin model estimation for use in voltage stability evaluation is performed in6. This method uses continuously changing operating data in power system for parameter estimation. Refere

14、nce15equivalences two sides of a tie line by two classical machines and estimates their parameters by neglecting the damping effect. This approach uses the inter-area oscillation components in the bus voltages resulting from disturbances. The main attributes of measurement based methods are the abil

15、ity to aggregate several coherent or non-coherent groups of generators without requiring a large data set.In this paper, a new measurement based method using synchronized phasor measurements is presented. Dynamic equivalent of the external system viewed from the measured bus is identified in the for

16、m of classical or second-order model of synchronous generator. Estimation of the model parameters is done in two simple steps. At the first step, electrical parameters of equivalent machine are estimated. Mechanical parameters are estimated in the next step. Estimation of electrical parameters is ca

17、rried out by two methods. In one method, using non-linear least square, electrical parameters of the machine and its internal voltage angle are estimated together. In the other method, electrical parameters are estimated without estimation of the internal angle, which is calculated after estimation

18、of the transient reactance. The latter method is faster, while the former yields more accurate results. Machine modelling is then extended to model the prevailing tie-line oscillations using SMIB and two-area equivalent.The remainder of the paper is organized as follows. In Section The equivalent ma

19、chine parameter estimation, estimation of the classical model is formulated and presented with two methods. Section Illustration using the SMIB system and Section Estimation of external power system dynamics for a two-area system provide simulation results of these methods on the SMIB and two-area s

20、ystems. In Section Estimation of external power system dynamics for a two-area system, it is also shown how to identify a two-machine or SMIB equivalent model to investigate tie-line inter-area oscillations. The application of estimation approach on the real data is presented in Section Application

21、on the real PMU data. Conclusions are given in Section Conclusion.The equivalent machine parameter estimationThe classical or the second-order model of synchronous machine is the simplest model that can be used in electromechanical dynamics analysis. This model offers considerable computational simp

22、licity; it allows the transient electrical performance of a machine to be represented by a simple voltage source with fixed magnitude behind an effective transient reactance as shown inFig. 116. This model has good performance in determining the first swing stability17. When the system is subjected

23、to a disturbance, parameters of the classical model can be estimated using post disturbance data. The electrical parameters of the model to be estimated are the generator internal voltage (E ), transient reactance () and the variable rotor phase angle ( ). The mechanical parameters to be estimated a

24、re damping coefficientKdand inertia constant (H). As stated above, the generator internal voltage is assumed to be constant but the rotor phase angle varies from one sample to the other.Fig. 1.Circuit diagram of a classical model of a synchronous generator.Estimation of the classical model can be di

25、vided into two steps: estimation of the electrical parameters and estimation of the mechanical parameters.Estimation of electrical parametersIn this work, two different formulations for estimation of electrical part of classical model are presented.Nonlinear Least Square-1 (NLS1)According to Fig. 1,

26、 relationship between the internal voltage and the terminal voltage can be stated as follows:where,UandIare the generator terminal voltage and current phasors. By separating real and imaginary parts,(1)is divided into two equations as presented in the following.where,andIjare real and imaginary part

27、s of terminal voltage and current, respectively. Considering the lastmsamples, the above equations can be rewritten as following.With2mequations in(4)and(5)onlym+2variables, i.e.E,Xdandi,i=1,mare unknown. Ifm2then the set of equations will be over determined and can be calculated using the following

28、 nonlinear least square optimization:In(6)a suitable choice for initial conditions can beand. In the above least square formulation, withm sets of measurements, the Jacobian matrix has the size of(m+2)(m+2). Therefore, by increasing the number of measurement sets, computational effort will increase

29、progressively.Nonlinear Least Square-2 (NLS2)n the least square formulation of (6)with m sets of measurements, m unknowns are the generator internal angle corresponding to the individual samples. The following formulation removes these variables from the optimization problem. By assuming the termina

30、l voltage phasor as the angle reference,(1)By decomposing the current term (I) into real and imaginary parts, Eq.(7)can be written as follows:whereIrandIjare the real and imaginary part ifI. By calculating squared absolute value of the two sides of above equation, the following equation can be obtai

31、ned.where,Q is the generator reactive power output (Q=-UIj) andI is the magnitude of generator output current.Withmsets of measurements, there will bemequations with only two unknown variablesE and. Therefore, two measurement samples would be sufficient to solve the equations. For more accurate esti

32、mation of parameters usingm samples (m2), the following least square error optimization should be solved:The next step is to calculate the angle difference between the internal voltage and the terminal voltage.By adding the terminal voltage angle (measured by PMU) tothe internal rotor angle will be

33、obtained as=+; where is the angle of terminal bus voltage i.e.,=U. In the NLS2 formulation, the size of Jacobean matrix is22, i.e. this formulation is independent of the number of sample sets. Therefore, by increasing the number of measurement sets, the surplus calculation time will be minimal. On t

34、he other hand, unlike to NLS1 method, simultaneous estimation ofis not included in NLS2 method. Hence, the NLS1 method has a better performance on the description of machine or external system dynamic behavior.After estimation of the equivalent internal angle, mechanical parameters of the equivalent

35、 machine can be estimated.Estimation of mechanical parametersThe swing equation of synchronous machine is used to describe variations of the rotor angleduring disturbance.where,PmechandPelecare the mechanical power input and electrical power output of machine, respectively.Kdis damping coefficient a

36、ndH is inertia constant. Using the estimated internal angle () from NLS1 or NLS2 method,(12)can be used to estimateH andKd. Before then, however(12)should be transformed to a discrete form using the Bilinear or Tustin method18. In this method the operatoris substituted with, wherezis operator ofztra

37、nsform andTis sampling period. The discrete form of(12)is:where,Pais the acceleration power and is equal toPmech-Pelec. Withm set of measurement (m4) the parametersH andKdcan be estimated using the following linear least square optimization:where,It should be mentioned that in the classical represen

38、tation of synchronous machine,Pmechis assumed to be constant, i.e. the governor control is not taken to account. The steady-state or pre-disturbance value ofPeleccan be used forPmechto satisfy the equality ofPelecandPmechin pre-disturbance time window. In practice, the steady state value ofPelecis n

39、ot constant and changes continuously. In this case the moving average value of pre-disturbancePeleccan be used for determination ofPmech. Another solution for this problem is to assumePmechas an unknown variable and to modify the least square formulation of(14)to includePmechas an unknown variable t

40、o be estimated.Illustration using the SMIB systemIn this section, simulation results on the SMIB system are sampled and taken as the measurement data to estimate its machine parameters using the proposed algorithms. All the simulations are carried out using the Power System Toolbox19. At first, to v

41、alidate the accuracy of the proposed methods, the machine in the SMIB system is simulated with classical model. The system parameters are given in Appendix SMIB system parameters. To simulate a disturbance on the system, a three phase fault with duration of 0.05s is applied on the line connecting th

42、e machine to infinite bus. NLS1 and NLS2 methods are implemented on the post disturbance generator terminal voltage and current phasors.To simulate PMU data flow, the sampling time interval is selected to be 30 sample/s. It should be noted that the sampling rate of currently installed PMUs is varyin

43、g from 12 sample/s to 60 sample/s. The sensitivity of estimation method is investigated by changing the sampling time. It is observed that the estimation performance has negligible sensitivity to change of sampling rate in this range. Therefore, the sampling interval is selected to be 30 sample/s in

44、 the simulated test cases. From the large number of simulations, it is observed that selecting data window equal or greater than 3 times than the smallest system oscillation frequency is enough for estimation approach. In the SMIB test system, data window is selected to be 3.3s or 100 samples.In thi

45、s test case, the estimated model and original system have the same order and it is expected that the estimated parameters be equal to the original simulated machine parameters.Table 1shows the estimation results for this case. As it can be observed from this table, the estimation error is negligible

46、. The little error is due to the effect of Tustin linearisation error.Table 1.Parameter estimation results for classical and detailed generator model for SMIB test case.Parameters(pu)HKdOriginal Value0.36.52Classic ModelEstimated value (NLS1)0.36.48011.9905Estimation error (NLS1) %00.3060.2502Estima

47、ted value (NLS2)0.36.49222.002Estimation error (NLS2) %00.120.1Detailed ModelEstimated value (NLS1)0.26047.314.152Estimated value (NLS2)0.17458.04415.388In the second test, the machine is simulated with detailed model. The purpose of this test is to investigate the results of the proposed methods on

48、 a more realistic system. Detailed model can represent the actual behavior of the generators with less error. By applying a fault on the SMIB system, the resulting current and voltage phasors are considered as PMU data and used to estimate classical model parameters. The estimated parameters are sho

49、wn inTable 1. The results show that, the estimated parameters of NLS1 and NLS2 are different from each other and from the original classical model parameters. It should be mentioned that the estimated model is a classic model while the original model is a detailed machine model with order of 6. The

50、difference between estimated and original model accounts the effect of higher order dynamics.In order to validate the estimation results, similar disturbance is applied on the SMIB system with detailed model, with the original second-order model, and with the second-order NLS1 and NLS2 estimated mod

51、els. Active power and speed a oscillations of generator are shown inFig. 2andFig. 3, respectively.Fig. 2.Generator active power oscillations.Fig. 3.Generator speed oscillations.FromFig. 2andFig. 3one can observe that NLS1 and NLS2 estimated parameters are better approximations of the detailed genera

52、tor model with respect to the original classical model, and yield oscillations very close to the oscillations of detailed model. In other words, the estimated parameters are changed in such direction to compensate the difference between the second-order model and the detailed model, and represent th

53、e effect of higher order dynamics on the oscillatory mode. Characteristics of the oscillatory modes with different models of the SMIB system are shown inTable 2. These modes are extracted by applying Prony method in the time response of 0 to 5 s on the post-disturbance oscillations of active power20

54、. As shown in theTable 3, damping ratios (DR) of NLS1 and NLS2 models are approximately equal, but the oscillation damping frequency (DF) in the NLS1 model is more accurate than the other.Table 2.Oscillatory mode for different models of SMIB system.ModelDR error (%)DF error (%)Detailed-0.4355.784jCl

55、assic-0.0865.916j80.672.282NLS1-0.4975.779j16.670.086NLS2-0.4935.828j12.40.761Table 3.Parameters of the estimated equivalent machine from Bus 3, Bus 13 and SMIB of Buses 3&13, at three levels of loadingParametersEstimated values of detailed model150MW300MW450MWReduced from Bus 31.07240.59040.4504H5.

56、06098.987410.8035Kd1.50653.02214.7076Reduced from Bus 130.03410.03540.0372H7.486112.75111.714Kd2.31913.59843.1138Reduced from 3&13, SMIB1.21650.73580.5976H6.5468.219810.6673Kd1.39522.17782.7576Estimation of external power system dynamics for a two-area systemIn this section, the algorithm presented

57、in Section The equivalent machine parameter estimation is extended to estimate the external power system dynamics for a two-area system.Fig. 4shows the single-line diagram of the two-area system. This system consists of two identical areas connected through a relatively weak tie20. Each area includes two generating units that are strongly connected together (G1, G2 and G3, G4). As a result, G1 and G2 form a coherent group and G3 and G4 form another coherent group. When exposed to an