A STATE ESTIMATION ALGORITHM OF POWER SYSTEM BASED ON THE MIXED MEASUREMENT

1、A state estimation Algorithm of power system based on the mixed measurementZhang HengInstitute of Electrical Engineering, HoHai University, Nanjing (210098)E-mail：Zhangheng_626163 AbstractAt present, the measurement s of the wide area measurement system (WAMS) and supervisory control and data acquis

2、ition (SCADA) are both available in power systems, but the measuring accuracy of the WAMS is much better than that of SCADA. Hence, a linear dynamic state estimation algorithm is proposed to deal with this problem. The measurements of the active and reactive power flow and power injections at the no

3、des of the SCADA system are transformed into the equivalent current phases by measurement transformation, so that these measurements can be combined with those of WAMS and form a mixed measuring system. The algorithm proposed is denoted by rectangular coordinates and the linear exponential smoothing

4、 technique and linear time-invariant Kalman filtering method are used to implement the forecasting and estimation. Since the proposed algorithm has a constant Jacobin matrix, the calculating time can be significantly reduced and the calculating accuracy ensured. Simulations are carried out in an IEE

5、E14-bus test system to demonstrate the validity and advantages of the algorithm proposed.Keywords: state estimation, wide area measurement system, measurement transformation, phase measurement unit, power systems1. IntroductionDynamic state estimation is a branch of the research for state estimation

6、. Since the electric power system is a dynamic system and the state variables are changing continuously, the dynamic state estimation is more close to the hypostasis of the electric power system than static estimation. Besides, dynamic estimation has pre-estimate function, which can provide informat

7、ion faster than real time for system analysis and control module, the function can increase observables analysis, unhealthy data identification and topology error identification function in state estimation, therefore, dynamic state estimation is all long regard to be an important problem by interna

8、tional academia. However, since the Kalman filtering method for dynamic state estimation is extracted in 70y of 20century, dynamic state estimation is still to be the research stage, there are no reports for practical application. The main reason is: predictive model is hard to be built, wave filter

9、ing process is complex, and calculation is very huge.WAMS has become an important tendency of the power system development, whos PMU can supply abundant and high precision information that provide a very powerful tool for power system state estimation 2-10. The main feature of PMU is as flowering: m

10、illisecond hierarchies update cycle that has a slow state change in a short period, so PMU would be good for the insufficiency of dynamic state prediction; direct measure of state dates of electric network. Under the rectangular coordinate system, the measured data (contain voltage and current phase

11、 measure) and state data has a linear relationship, and it would reduce the calculate quantity of Kalman filtering.Thus, we can foresee that the appearance of PMU will release the 2 aspect difficulties of dynamic state estimation predict precision and calculation work quantity. Literature 7-8 has tr

12、ied putting PMU measurement into dynamic state estimation. Literature 7 has explored linear dynamic state estimation Algorithm at the assumption of totally using the PMU measurement; the algorithm has a strict demand to the configuration of PMU which is hard to implementation in a long time. Conside

13、ring of it, literature 8 has done an improvement on the basis, and brought forward the linear dynamic state estimation algorithm which implement predictable linear dynamic state estimation mixed algorithm, but it just brings out the admixture in algorithm without combining linear dynamic estimation

14、by utilizing mixedmeasurement data.Because of the research status of state estimation this paper extract linear dynamic state estimation algorithm on the base of mixed measurement. The algorithm uses measure transfer technology 11 to change branch power measurement and node point filling power measu

15、rement of SCADA system into equivalent current phase measurement to build up a mixed measurement system with PMU phase measurement, which makes the mixed measurement and the state variables to be the linear relationship. On the foundation we bring forward the linear dynamic state estimation algorith

16、m under rectangular coordinate system. The algorithm has a constant Jacobin matrix which improves the estimation speed greatly, assurances its calculated precision. So the algorithm contains theory gist and practical value.2. The formation of mixed measuration2.1 The disposal of WAMS measureWAMS mea

17、sure function is done by PMU which mainly measure the amplitude and phase angle of the voltage and the amplitude and phase angle of the branch current.Under the rectangular coordinate system, the branch current phase measure is:I W = I W cos W + jI W sin cos W(1)LLLLLThe bus voltage phase measure is

18、:V W = VW cosW + jVW sin cos W(2)Where I W and WNNNNNare individual the branch current amplitude and phase angle measurementLLNmeasured by PMU of WAMS; VNW and Ware individual the bus voltage amplitude and phase anglemeasure.Form the equation (1) and (2), we can see that the real part and the imagin

19、ary part of the branch current phase and the bus voltage phase will be the indirect measurement; the corresponding measure variance can be got by adopting indirect measurement transfer equation. (The concrete equation can be found in literature 9).2.2 The disposal of SCADA measurementFor the branch

20、without WAMS, this paper use the measure transforms technology to change the brunch power measure P mea and Q mea into the equivalent branch current phase measure:ijijP mea e + Q mea fP mea f Q mea eIijmeareqv =ijiiji + je 2 + f 2ijiijie 2 + f 2(3)ijWhere I meareqviiiiexpress the equivalent branch c

21、urrent phase measure of brunch i j ; ei and fiare the real part and imaginary part of i sides node voltage.There are vast node filling power measures in SCADA system, to adequately utilize these data; rise the redundancy, this paper adopts the measurement transform technology to change the brunch po

22、wer measure into the equivalent branch current phase measure:meameameameaiI mear eqv = Piei + Qie 2 + f 2fi + j Pifi Qieie 2 + f 2(4)iiiiIn the formula: I mear eqv is the equivalent node filling current of the node i ; Pmea and Q mea areiiithe filling measure power of the node i .We can see from equ

23、ation (3) and (4) that: the equivalent current measure is also indirectly and the corresponding measure variance can be got from indirect measurement transfer theory (the concreteequation can be found in literature 11), According to the homolog measure variance, we can get the weight coefficient of

24、the homolog measure data. Thus the mixed measure system would be constituted by WAMS measure and equivalent current measure, the mixed measure system is expressed by zeqv .3The linear dynamic state estimation algorithm3.1 The mathematic model of the linear dynamic state estimationThe mixed measure s

25、ystem containing equivalent branch current phase measure, equivalent filling current phase measure and equivalent the real part and imaginary part of voltage measure is formed through the above measure transformation. On the condition of the unaltered of the network-topological structure, it can be

26、known that the relationship of mixed measure phase and the state variance is numerous. The dynamic state estimation problem in mixed measure system can be express from using the n dimension random linear system and the m dimension random measure system as following:xk +1 = Fk xk + Gk + keqv(5)Zk= Hx

27、k + vkeqv(6)Where xk is the n 1 dimension in the k hour; Zkis the m 1 dimension in the k hour; H isthe linear measure function;Fk andGk are the dynamic model parameter matrix;Fk is the statetransform matrix, Gkis the control phase; k is the system model inaccuracy which is assumed to bethe classical

28、 smooth flat noise sequence as k N (0, Qk ) , Qkis the variance of the modelinaccuracy;vk is the measure inaccuracy which is regard as random flat noise submitting normaldistribution as vk N (0, Rk ) , Rk is the variance of measure inaccuracy.We suppose that we have surveyed these vectors z1 , z2 .z

29、k , and seek the k hours estimated statevector xk1k ,after we measure the zk +1 in k + 1 hour, we are requested to get the state vector estimatedvaluexk +11k +1 ,the guide rule of the estimation is take the estimated inaccuracy variance matrixPk +11k +1 of the state vector as the minimal function:Tm

30、in J k +1 = min Ex (ek +1 k +1ek +1 k +1 )(7)Where ek +1 k +1 = xk +1 k +1 xk +1 , and xk +1 is the truth value of the k+1 hour state variable; Ex (.) isthe expectation value of statistical regularity.3.2 The linear dynamic state estimation algorithmTo satisfy the need of the dynamic state estimatio

31、n, the parameter Fk and Gk in formula (5) must be got on line. The algorithm adopts HOLT two parameters linear exponential smooth technology to calculate Fk and Gk , the specific formula deduce detailed see in literature 12.The linear dynamic state estimation forecast steps is as following:xk +1 k =

32、 ak + bk(8)P= F P F T + Q(9)k +1 kk k k kkWhereak is the level component,ak = xk k + (1 ) xk k 1 ; bk is the oblique component,bk = (ak ak 1 ) + (1 )bk 1 ; and are the two different smooth parameters, satisfying , 0,1 ;xk +1 k is the forecast value of the k + 1 hour; Pk k is the k hours estimate cov

33、ariancematrix, P= E (e eT ) ; e= x x, x is the k hours real value of state variable; Pisk kk k k k k kk kkkk +1 kTthe homolog forecast covariance matrix, Pk +1 k = E (ek +1 k ek +1 k) , ek +1 k = xk +1 k xk +1 .After we get the forecast valuexk +1 k of the k+1 hours state variable, according to the

34、linearvariance estimate method, through recipe we get a group of optimal recursive formulas of Kalman filtering, we can get the calculate formulas of the linear dynamic state estimation filtering associating the recursive formulas of the system state equation, the concrete Inferential reasoning proc

35、ess are seen in literature 13.The formulas are as following:xk +1 k +1 = xk +1 k + Kk +1 ( zk +1 Hxk +1 k )(10)Kk +1 = Pk +1 k H( HPH1TTk +1 k+ Rk +1 )(11)Pk +1 k +1 = (1 Kk +1 H )Pk +1 kWhere Kk +1 are the k + 1 hour Kalman filling gain matrix.The characters of the algorithm are:(12)1) After measur

36、e transformation, Jacobi matrix H is sparse constant matrix which only related to nets topological structure. At the presupposition of the unchanged of the nets topological structure, the recursion formula of x and k , P are totally uncoupled, they can calculated alone, thus ,we can advance calculat

37、e the value of k and P ,the left is to state forecast and the calculation of recursion formula of x , the calculation speed is very fast.2)The algorithm can simultaneity supply system state estimate value and forecast value which is very important to the running analysis and control of the power sys

38、tem.3) On the condition of power system stability operating, when the time interval is very short andthe node load filling is unchanged, the equationxk +1 k = xk +1 k +1 is satisfied, we can see that thealgorithm will change into the tracking dynamic state estimation.The process of the algorithm is

39、shown as follows.startRead the initial conditionUpdate matrix F kand vector GkForecast data baseCalculate forecast value xk+1kand homolog covariance matrix Pk+1k through Equation (8) and (9)Form Jacobi matrix J by net topological structureK=k+1ZZk +1 Measuringtransformeqvk +1Calculate gain matrixKk+

40、1 by equation(11)Calculate filtering value xk+1k+1 and homolog covariance matrix Pk +1 k +1 by equation (10)and(11)Real-time data baseFigure.1 Procedure of the proposed method4Computational Issues4.1 Computational Issues descriptionThe example adopts IEEE 14 node system to emulate. The testing progr

41、am runs on the PC compatible machine with 2.0GHZ dominant frequency and 256MB memory. With the system tidal current as real value in the emulation, considering that the measure system data are easy to be disturbed by GAOSS flat noise, the measure data are formed by superimposing homolog normal distr

42、ibution random measure inaccuracy on the basis of testing system tidal current.On the basis that the important electric power plant and electric substation need to install PMU, this paper install PMU on the generator bus 1,2,3,6,8and electric substation bus 4,5 of the IEEE 14node system.The load cur

43、ve data come from a dispatching center load data recording by one day, the system estimated every 10min, current load adopt 144 points sampling in the whole day, and the peak responsibility is 3.8277MW, after normalizing according to the peak responsibility, the curve shows as following in Figure.2.

44、4.2 The result of the emulationThis paper implements the algorithm on the MATLAB6.5, and compares with minimal weighting square law and normal procedure dynamic state estimation algorithm. Figure.3 supplies the tracing curve of the 13 bus voltage swing value and phase angle, from which we can see th

45、at the algorithm can estimate the system state, especially when the load change smoothly.Figure.2 Curve of the load(a)Phase angle(b)Amplitude of voltageFigure.3 State tracing results of bus 13In order to understand the capability of the algorithm easily, this paper adopts the average and the max val

46、ue of the absolute error as the calculate capability index, the capability index calculate formula are as following: (k ) =1Nbus e (k ) t (k ) Nbus iii =1Nbus(14)i v(k ) =1Nbusiii =1V e (k ) V t (k )iIn the formula: e (k ) is the estimate value of the voltage phase angle on the k hour of node i ;V e

47、 (k ) is the estimate value of the voltage wing value on the k hour of node i ;number of the system; t is the homolog real value.Nbus is the nodeTable.1 compares the capability and calculate time of this papers algorithm and the WLS estimate algorithm, WLS adopts classic method to deal with the PMU

48、measure in literature6.From the table ,we can see that because the Jacobi matrix in my algorithm are sparse constant matrix, it calculates very fast. Although this paper adopts measure formulation technology, its calculate precision is better than WLS method. The reason is that the dynamic state est

49、imation contains the forecast step reducing the influence of state estimation precision because of the measure transformation, which shows the superiority of the linear dynamic state estimation algorithm.Table 1: Precision comparison of the proposed method and WLS methodAlgorithmAverage calculate ti

50、me/msAverage valueMax valueAverage valueMax valueproposed method0.00750.04090.00370.024620.68WLS method0.01010.08330.01360.065580.18The paper adopts the norm of filtering step covariance matrixPk +1 k +1to express theconvergence property and stability of the method, and compares with the conventiona

51、l based on extended KALMAN dynamic state estimation algorithm described in literature14, the compare result is shown in Figure.4.From the curve we can see that the proposed method and the conventional dynamic state estimation algorithm all have preferable convergence, but the convergence of the prop

52、osed method is better than the other.Figure.4 Convergence comparison of different algorithmIn order to future check the capability of the proposed method, this paper does 3 groups of experiment on the test system, they are containing one PMU, three and five. The first experiment installs the PMU on

53、node 1; the second install on node 1, 3, 6; the third on 2,3,6,8. The result shown in Table 2.From the Table 2 we can see that when the number of PMU installed increase, the advantage of the proposed method will be more obviously.Table 2: Results of numerical testNumber of PMUAverage valueMax valueA

54、verage valueMax value10.01530.09650.01460.084320.01120.06350.00970.048630.00980.05230.00610.03125ConclusionThe measure precision of PMU is much preferable, it can improve the systems observables and the precision of dynamic state estimation, the more the PMU is installed, and the advantage of the pr

55、oposed method will be more obviously. The power system linear dynamic state estimation algorithm based on mixed measurement presented by this paper has no strict request on the disposal of PMU which is suit for the develop status of PMU in our country. The above example indicates that the proposed m

56、ethod is better than other algorithms on calculate speed and precision supplying the practical theoretical gist for linear dynamic state estimation. The next work need to deeply research the influence on bad data checked and identification, observables analyses and power system parameter identificat

57、ion of state estimation brought by PMU to promote the utility of the linear dynamic state estimation.References1 DEBS A, LARSON R. A dynamic estimation for t racking t he state of a power system. IEEE Trans on PowerSystems, 1970, 89 (7): 167-168.2 DING Junce, CAI Zexiang, WANG Keying. An overview of state estimation based on wide2area measurement system. Automation of Electric Power Systems, 2006, 30 (7): 98-103.3 ZHAO Hongga, XUE Yusheng, WANG Dexing, et al. State estimati