Electrical Power and Energy Systems 45 (2013) 152–158

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Electrical Power and Energy Systems

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A new coordinated approach to state estimation in integrated power systems

Ali Reza Abbasi, Ali Reza Seifi ⇑School of Electrical and Computer Engineering, Shiraz University, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 May 2009Received in revised form 25 August 2012Accepted 29 August 2012Available online 11 October 2012

Keywords:Mixed state estimation (MSE)Integrated power systemEnergy management system (EMS)Distribution management system (DMS)

0142-0615/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijepes.2012.08.058

⇑ Corresponding author. Tel.: +98 711 2303081; faxE-mail address: seifi@shirazu.ac.ir (A.R. Seifi).

Many large cities have their hybrid transmission and distribution networks, while traditionally, transmis-sion and distribution state estimators are studied and developed separately. In order to achieve a globalconsistent state estimation solution, the balance transmission and unbalance distribution networks arestudied as a whole in this paper. A novel master–slave-splitting (MSS) iterative method is developedfor calculating large-scale and mixed state estimation (MSE) problem. In the MSS method, with introduc-ing the boundary fictitious measurement, the MSE problem of large scale is split into a balanced trans-mission state estimation and many unbalanced distribution state estimation sub-problems of smallscale. In order to fit the different features between balanced transmission and unbalanced distributionnetworks, each sub-problem can be solved with different algorithm. Several case studies are carriedout, and the accuracy, convergence, efficiency and reliability of the proposed method are validated.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Today, state estimation is an essential part in almost every en-ergy management system throughout the world and telemeterdata (real-time measurement) in power systems contain errorsand state estimation is used to clean up the erroneous data. Stateestimation is indeed a systematic procedure to process the set ofreal-time measurements to come up with the best estimate ofthe current state of the system. The result of state estimation pro-vides the real time database for other application, such as securityassessment, control and economic dispatch and power quality.

Interconnected power system, the number of power transac-tions taking place over large distances, which involves many con-trol areas has increased and are expected to grow in the futureas well. In this situation, the operators in control areas are forcedto monitor the grid on a large scale to operate it reliably. In energycontrol centers the raw measurements obtained through the SCA-DA system from the grid are processed by the state estimator,which provides the estimate of the operating state of the system.In order to monitor the large scale power transactions taking placeover many areas, a wide area state estimator is required.

Traditionally, the transmission and distribution networks areusually operated by separate departments even in a single utility.But in fact, a real power system is an integration of transmissionand distribution networks; therefore, the interaction between thetransmission and distribution systems should be considered inoperation, and great benefit can be derived from global coordi-nated control between transmission and distribution systems,

ll rights reserved.

: +98 711 6287294.

especially with the rapid development of distributed generationin the distribution network [1]. In order to implement a globalcoordinated operation and control, mixed state estimation (MSE)aiming to build a consistent real-time model for the whole trans-mission and distribution networks should be studied at first.

Traditionally, the transmission and distribution state estimatorsare studied and developed separately [2–14]. The distribution sys-tems are treated as equivalent loads in transmission systems, whilethe transmission systems are treated as equivalent power supplysources in the distribution systems. As a result, due to the differentdata source of measurement set with different accuracy and redun-dancy, remarkable power and voltage mismatches will arise at theboundary nodes and the consistent solution of MSE cannot be got.Two shortcomings of traditional method are listed as follows:

(1) The voltage angle differences between the root nodes of dif-ferent radial feeders cannot be estimated only by separatedistribution estimator. As a result, even though the voltagemagnitudes for the root nodes of different feeders can beestimated accurately, the power flow study with fictitiousclosed loops among feeders cannot be done. Moreover, it isdifficult to implement network reconfiguration withunknown root node voltages [15].

(2) Since the solution is not consistent in the whole network, itis difficult to implement the global optimization amongtransmission and distribution controllable resources, whichimpairs the security and economy of integrated power sys-tem operation. One example is that for the transmission sys-tems, the correctness of voltage stability analysis cannotbeen assured if operation of the OLTC installed in distribu-tion system is ignored in load modeling [16].

A.R. Abbasi, A.R. Seifi / Electrical Power and Energy Systems 45 (2013) 152–158 153

The idea to solve the MSE problem for whole transmission anddistribution networks was not feasible several years ago. It is dis-cussed as follows:

(1) Utilities generally paid almost all attention to transmissionnetworks, while the distribution systems were simplifiedas equivalent loads in transmission networks. So, it was lackof motivation to study MSE problem several years ago.

(2) Despite state estimation had been widely applied to trans-mission networks, it was not feasible in distribution net-works for serious lack of remote measurements severalyears ago.

(3) Transmission and distribution networks are usually man-aged by separate departments even in a single utility. In alarge city or region, there generally exist one transmissioncontrol center and several distribution control centers withgeographically distributed locations. Their computer sys-tems were usually developed by different vendors. So itwas difficult to exchange information among these differentcomputer systems for solving MSE problem.

The idea to solve the MSE problem for whole transmission anddistribution networks is feasible now as follows:

(1) With the wide application of automation technology to dis-tribution systems, the situation in observability of primarydistribution networks is improving now. Meanwhile, manyresearchers have addressed the topic of distribution stateestimation for many years, and some valid methods havebeen proposed for distribution state estimation by now.

(2) Almost all the transmission control centers are equippedwith EMS [17–19], and many distribution control centersare also equipped with DMS [20]. In these computer sys-tems, transmission and distribution networks have alreadybeen modeled in detail, and state estimations can be donefor transmission and distribution systems respectively evenunder real time environment.

(3) WAN-based communication technology is widely applied topower systems and is available for the rapid communicationbetween EMS and DMS. Meanwhile, control center applica-tion program interface (CCAPI) [21] provides the standardfor information exchange between EMS and DMS developedby different vendors. It becomes more and more feasible toachieve a consistent MSE solution by exchanging littleboundary information between existing EMS and DMS.

Here we orient to a more general MSE problem, of which theimportant characteristics are listed as follows:

(1) The size of the integrated power system is tremendous. For atypical medium size system, for example, the number of230 kV nodes of a transmission network is 300, including200 load nodes. If each load node has 20 medium voltagefeeders and each feeder has 20 distribution nodes on aver-age, then the total number of nodes in the integrated powersystem will reach over 80,000.

(2) The transmission and distribution systems differ in voltagelevel, network topology structure, parameter of element,modeling, accuracy and redundancy of measurement. Eachof them needs its own suitable algorithm. For instance, fastdecoupled state estimation (FDSE) algorithm is fit for balancedtransmission systems [2], while branch current basedalgorithm is fit for radial unbalanced distribution systems[5]. If a single algorithm is adopted to solve the MSE, forthe remarkable diversity between the transmission and

distribution systems, it is difficult to ensure simultaneouslythe numerical stability and computational efficiency [6].Therefore, a hybrid method for MSE is needed to satisfysimultaneously both the requirements of the transmissionand distribution systems.

(3) The models for transmission and distribution networks arealways built and maintained in geographically distributedEMS and DMS respectively, which requires the algorithmsupporting geographically distributed computation. In orderto develop an efficient algorithm for the distributed comput-ing, communication and computing should be fast enough.On the other hand, the proposed algorithm should be com-patible with state estimation program in existing EMS andDMS.

(4) The transmission systems are three-phase balanced, so thesingle phase equivalent system is used. While the distribu-tion systems are three-phase unbalanced, the state estima-tion in distribution systems should be three-phase, whichshould be also considered in the MSE.

According to the above characteristics of the MSE, a generalmethod to deal with the large scale MSE problem should be a split-ting method to support distributed or parallel computation. Histor-ically, several splitting methods have ever been proposed for stateestimation of large-scale interconnected system [22–26]. However,these methods were oriented to pure transmission systems (or dis-tribution systems) with equilibrium partitions (with same voltagelevels), and do not meet well the special requirements of the hy-brid MSE problem described above. Therefore, based on the mas-ter–slave-typed physical feature of the integrated power system,a novel master–slave-splitting (MSS) method with rigorous math-ematical foundation is developed to solve the MSE problem in thispaper.

2. Problem formulation

In an integrated power system including transmission and dis-tribution networks, Z denotes the integrated measurement vector,and the measurement equation is

Z ¼ hðxÞ þ m ð1Þ

where x, h(x) and m denote state, measurement function and mea-surement error, respectively. Then, the MSE problem can be formu-lated as a weighted least squares (WLSs) problem as

Minx JðxÞ ¼ ½Z � hðxÞ�T W½Z � hðxÞ� ð2Þ

where W 2 RM�M is integrated weight matrix and M is the totalnumber of measurements in the integrated power system. Differ-ing from the traditional separated transmission and distributionstate estimations, MSE are here covering the whole electrical net-work by the global WLS objective function described in Eq. (2).Furthermore, the optimal condition of the WLS problem (see Eq.(2)), which is called as the MSE equations in this paper, can bewritten as

HTðxÞW½Z � hðxÞ� ¼ 0 ð3Þ

where H(x) = @h(x)/@x is the Jacobian matrix. In this paper, a moregeneral method oriented to the original MSE problem described inEq. (2) is studied. Here, power networks in a large city or regionare generally managed by a transmission control center and severaldistribution control centers, meanwhile, the situation in observabil-ity of primary distribution network is improving.

Fig. 2. Illustration for the fictitious boundary injection measurements.

154 A.R. Abbasi, A.R. Seifi / Electrical Power and Energy Systems 45 (2013) 152–158

3. Master slave splitting method for mixed state estimation

3.1. Mixed state estimation equations in master slave splitting form

As shown in Fig. 1, the integrated power system is a typicalmaster–slave-typed system. Here the balanced transmission sys-tem is the master system with a detailed structure of the ‘‘general-ized power supply’’ seen from the unbalanced distribution system,while the unbalanced distribution system is the slave system witha detailed structure of the ‘‘generalized load’’ seen from the bal-anced transmission system.

In Fig. 1, the load nodes in the balanced transmission system aretaken as root nodes of the unbalanced distribution feeders, whichmake up the node set of the boundary system B, CB; the rest nodesof the balanced transmission system make up the node set CM; therest nodes of unbalanced distribution system make up the node setCS. Then x and Z of the integrated power system can be decom-posed into:

x ¼ ½ xM xB xS � ð4Þ

Z ¼ ½ ZM ZB ZS � ð5Þ

where xM, xB and xS denote the transmission state, boundary stateand distribution state, respectively; ZM and ZS correspond to themeasurement sets used by the traditional separated transmissionand distribution state estimators, respectively; ZB denote the zeroinjection measurements at boundary nodes (see Fig. 1). Supposethe measurements telemetered by different control centers areindependent, then the weight matrix in Eq. (3) is block diagonal as:

W ¼WM 0 0

0 WB 00 0 WS

264

375 ð6Þ

where WM, WB and WS are the corresponding diagonal blocks of theweight matrix. Thus, Eq. (3) can be rewritten as:

HTMMðxM; xBÞ HT

BMðxM; xBÞ 0

HTMBðxM; xBÞ H0TBBðxM � xBÞ þ H00TBBðxB; xSÞ HT

SBðxB; xSÞ0 HT

BSðxB; xSÞ HT

SSðxB; xSÞ

2664

3775

WM ½ZM � hMðxM; xBÞ�WB½ZB � h0BðxM; xBÞ � h00BðxB; xSÞ�

WS½ZS � hSðxB; xSÞ�

264

375 ¼ 0

ð7Þ

where HMM, HMB, HBM ;HBS , HSB and HSS are the corresponding blocksof the Jacobian matrix H; hM and hS are the measurement functionsof ZM and ZS, respectively; h0B and h00B are the power flows throughfrom the boundary nodes to the balanced transmission systemand the unbalanced distribution system, respectively; H0BB and H00BB

are the Jacobian matrices of h0B and h00B with respect to xB, respec-tively. As shown in Fig. 2, we introduce fictitious boundary injectionmeasurements Z0B and Z00B as:

Fig. 1. Integrated power system with master–slave-type feature.

Z0B ¼ ZB � h00BðxB; xSÞZ00B ¼ ZB � h0BðxB; xSÞ

(ð8Þ

In a real-life balanced transmission system, the line voltage andthree-phase power are usually telemetered. If we suppose thatthe root node voltage of distribution system is of three-phase bal-ance approximately, then the balanced line voltage of the root nodecan be naturally adopted as the boundary state xB. Furthermore, ifwe let the fictitious measurements Z0B and Z00B be both representedin accumulation of three phase powers, then it is easy to implementthe data exchange between the balanced transmission and unbal-anced distribution state estimators.

Eq. (7) can be decomposed by Eq. (8) into the following form:

HTMMðxM; xBÞ HT

BMðxM ; xBÞ 0

HTMBðxM ; xBÞ H0TBBðxM � xBÞ 0

0 0 0

264

375 WM½ZM � hMðxM; xBÞ�

WB½Z0B � h0BðxM; xBÞ�WS½ZS � hSðxB; xSÞ�

24

35

þ0 0 00 H00TBBðxB; xSÞ HT

SBðxB; xSÞ0 0 0

24

35 WM ½ZM � hMðxM; xBÞ�

WB½Z00B � h00BðxB; xSÞ�WS½ZS � hSðxB; xSÞ�

24

35

þ0 0 00 0 00 HT

BSðxB; xSÞ HT

SSðxB; xSÞ

24

35 WM ½ZM � hMðxM ; xBÞ�

WB½Z00B � h00BðxB; xSÞ�WS½ZS � hSðxB; xSÞ�

24

35

¼ 0 ð9Þ

Eqs. (10) and (11) in boundary nodes for the balanced transmissionand unbalanced distribution systems can be described into the fol-lowing form:

Z0BM¼X3

U¼1

Z0BU ð10Þ

h0BM¼X3

U¼1

h0BU ð11Þ

By Eqs. (8)–(11), Eq. (7) can be transformed into the following form:

HTMMðxM; xBÞ HT

BMðxM; xBÞ

HTMBðxM; xBÞ H0TBBðxM; xBÞ

" #WM½ZM � hMðxM; xBÞ�WB½Z0BM

� h0BNðxM; xBÞ�

" #¼

0yBMðxM ;xBÞ

" #

ð12Þ

HTBSðxB; xSÞ HT

SSðxB; xSÞh i WB Z00B � h00BðxB; xSÞ

� �WS½ZS � hSðxB; xSÞ�

" #¼ 0 ð13Þ

where

yBðxB; xSÞ ¼ �H00TBBðxB; xSÞWB Z00B � h00BðxB; xSÞ� �

� HTSBðxB; xSÞWS½ZS

� hSðxB; xSÞ� ¼ 0 ð14Þ

yBMðxB; xSÞ ¼

X3

U¼1

yBUðxB; xSÞ ð15Þ

VBS ¼ VBM � ½1\0 1\� 120 1\120 � ð16Þ

Here, Eqs. (12) and (13) are called as transmission and distributionstate estimation equations, respectively, where yB and yBM

are

A.R. Abbasi, A.R. Seifi / Electrical Power and Energy Systems 45 (2013) 152–158 155

introduced as the intermediate variable and reflect the effect of themeasurement residual of the unbalanced distribution system on thebalanced transmission state estimation. As illustrated in Fig. 2, theintroduced fictitious boundary injection measurements have clearlyphysical meaning, i.e. Z0BM

is the fictitious measurement of the ‘‘gen-eralized single phase load’’ seen from the balanced transmissionsystem, while Z00B is the fictitious measurement of the ‘‘generalizedthree phase power supply’’ seen from the unbalanced distributionsystem. Although the fictitious measurements are introduced, obvi-ously the solution of Eqs. (12) and (13) are equal to that of Eq. (7).Furthermore, from Eqs. (8)–(13), it can be found that HBM and H0BB

are just the Jacobian matrices of Z0B with respect to xM and xB,respectively, while H00BB and HBS are just the Jacobian matrices ofZ0B with respect to xB and xS, respectively. Then it is naturally to con-struct all of the blocks of the Jacobian matrix in Eqs. (12)–(14),where the fictitious measurement Z0BM

is incorporated with ZM inthe balanced transmission state estimator and the fictitious mea-surement Z00B is incorporated with ZS in the unbalanced distributionstate estimator. As a result, the transmission and distribution stateestimations are decoupled naturally.

Fig. 3. The distributed structure for online MSE.

3.2. MSS method with discussions

Here, the node voltage and branch current are selected as thestate variable of the MSE. Based on the MSE Eqs. (12) and (13),an MSS iterative method is presented as follows:

Step 1. Initialize the boundary voltage V ð0ÞBSand fictitious mea-

surement Z00ð0ÞB ; k ¼ 0, where k is the iteration counter.Step 2. With the fictitious measurement Z00ðkÞB specified, let V ðkÞBS

bethe reference voltage and estimate the distribution voltageV ðkþ1Þ

S by solving Eq. (13), and then by Eqs. (8) and (15), calculatethe fictitious measurement Z0ðkþ1Þ

B and intermediate variableyðkþ1Þ

B from V ðkÞBS, Z00ðkÞB and V ðkþ1Þ

S just obtained.Step 3. By Eqs. (10) and (15) calculate the fictitious measure-ment Z0ðkþ1Þ

BMand intermediate variable yðkþ1Þ

BM.

Step 4. With the fictitious measurement Z0ðkþ1ÞBM

specified, substi-

tute yðkþ1ÞBM

into Eq. (12) and solve it to estimate the transmission

voltage V ðkþ1ÞM V ðkþ1Þ

BM

h iT, and then by Eq. (8) calculate fictitious

measurement Z00ðkþ1ÞB from V ðkþ1Þ

M V ðkþ1ÞBM

h iTjust obtained.

Step 5. If the norm of update vector V ðkþ1ÞB � V ðkÞB

��� ��� is less thanthe tolerance e, the convergence is got, otherwise k = k + 1 andby Eq. (16), calculate the boundary voltage V ðkÞBS

and then turnto Step 2.

Several discussions on above MSS method are done as follows:

(1) The MSS method is also a type of splitting method, wherethe MSE problem of large scale is decoupled naturallyinto the balanced transmission and unbalanced distributionstate estimation sub-problems. But it is distinguished fromthe traditional splitting ones equally partitioned in capacityand voltage level [22–26]. In transmission state estimation,Z0B and yB are specified, which appropriately reflects thecomparatively weak effect of the distribution system onthe transmission system. While in the distribution state esti-mation, in addition to Z00B being specified, VBS is considered asreference voltages in the distribution system, which reflectsthe determinative effect of the state of the transmission sys-tem on that of the distribution system. Such a special itera-tive scheme reflects the different physical positions betweenthe transmission and distribution systems, which is of greatbenefit to the convergence.

(2) The MSS method for MSE can be described in a comprehen-sible way, i.e. in implementing the distribution state estima-tion, the voltage of root node of distribution system and thefictitious injection measurement Z00B are got from the result ofthe transmission state estimation and fixed, while in imple-menting the transmission state estimation, the intermediatevariable yBM

and fictitious injection measurement Z0BMare got

from the result of distribution state estimation and fixed.These two parts of state estimations are alternated andrepeated until convergence is achieved. Obviously, theproposed method is compatible with the existing WLS-basedstate estimation software, since no specific technique isrequired for solving the transmission and distribution stateestimation equations. As a result, we can take suitable algo-rithm for each of them, which are regarded as an importantcharacteristic of the MSE problem presented above. Here,per unit quantities, are used for data exchange between sin-gle-phase transmission system and three-phase distributionsystem to meet the needs of the MPF for different per unitbases.

(3) Distribution state estimation Eq. (13) is yet of large scale,and can be split further into numerous state estimationsub-problems for independent distribution sub-systems as:

HTBiSiðxBi

; xSiÞ HT

SiSiðxBi

; xSiÞ

h i WBiZ00Bi� h00Bi

ðxBi; xSiÞ

h iWSi½ZSi� hSi

ðxBi; xSiÞ�

24

35

¼ 0 i ¼ 1; . . . ;nf

ð17Þ

Hence, based on the MSS method, a MSE problem of large scale issplit into a balanced transmission state estimation and many unbal-anced distribution state estimation sub-problems of small scale,which supports parallel or distributed computation efficiently.

(4) It is important for convergence to determine a goodinitial value of the fictitious measurement Z00B. In real-timeenvironment, the power injection into the root node of thedistribution system and the equivalent load power inthe transmission system are always telemetered by the dis-tribution and transmission control centers, respectively. It isa good idea to adopt one of these two real-time measure-ments as the initial value of Z00B. Especially in the onlinetracking mode, high precision of the initial value of Z00B canbe ensured and thus the local convergence of the proposedMSS method can be ensured.

(5) In the proposed MSE method, common state estimationtechniques are used in transmission [2] and distribution[5] networks, therefore, convergence of the proposedmethod is guaranteed in iterating back and forth betweenmaster and slave problems by reasons the convergence ofthe mentioned state estimation methods.

156 A.R. Abbasi, A.R. Seifi / Electrical Power and

3.3. Online distributed computation

There generally exist a transmission control center and severaldistribution control centers in a large city or region. Due to geo-graphically distributed location of these control centers, onlineMSE calculation should support such a geographically distributedcomputation. Such a distributed structure for online MSE calcula-tion can be explained by Fig. 3, where TSE and DSE denote the bal-anced transmission and unbalanced distribution state estimators,respectively.

In Fig. 3, the solutions for TSE and DSEs are performed in EMSand DMSs respectively, and EMS communicates with DMSsthrough wide area network (WAN) in each MSS iteration step. Inthe iterative process, EMS transfers the voltage and injectionpower at root nodes of distribution system to correspondingDMS, while each DMS transfers the intermediate variable and loadpower of transmission system to EMS. The global convergence ofthe MSE is judged by EMS.

Such a proposed distributed structure is compatible with anyexisting EMS and DMS with minor code modification. As a result,EMS and DMSs are combined in a unit by the online MSE, whichprovides a consistent real-time model for the whole transmissionand distribution networks.

3.4. Detailed iterative schemes

In fact, the MSS method for MSE described above is just an out-line method, nonlinearity of transmission and distribution stateestimation equations have to be considered. In order to solve theMSE equations completely, inner sub-iteration needs to be intro-duced, and two types of detailed iterative schemes are constructedas follows:

(1) Multi-step alternating iterative (MAI) scheme: at each MSSiteration step, each of the TSE and DSE is solved by severalinner sub-iterations manually controlled, and the numberof sub-iterations can be different for each of TSE and DSE.

(2) Convergence alternating iterative (CAI) scheme: at each MSSiteration step, converged TSEs and DSEs are solved, wherethe convergence tolerance can be controlled.

The two schemes described above are the same in outline withsome details different. Besides the number of sub-iterations, theconvergence criterions for these two schemes are different as well.The global convergence criterions of the MAI scheme can be takenas:

(1) TSE converges,(2) DSE converges, and(3) kVkþ1

B � VkBk is less than the tolerance e.

Fig. 4. Flow-chart of num

However, the global convergence of the CAI scheme requiresonly the third condition listed above, since the convergence of

Energy Systems 45 (2013) 152–158

the transmission and distribution state estimation has beenachieved at each MSS iteration step. By comparison, the twoschemes above are different in CPU time and in communicationtime. Having a less total number of sub-iterations and more inter-action between TSE and DSE, the MAI scheme needs much morecommunication and is therefore more suitable for the parallel com-putation with a communication speedy enough. On the other hand,having a less number of MSS iterations and more inner iterations inTSE and DSE, the CAI scheme needs less communication and ismore practical for geographically distributed computation. Thecomparative results are reported in Section 4.

4. Test results

The proposed MSS method for MSE is implemented here. In or-der to simulate online distributed structure as shown in Fig. 3, aMSE program developed with MATLAB is separated into two parts,one is the balanced transmission state estimator and the other isthe unbalanced distribution one. For all of the tests reported inthe following text, the convergent tolerance is e = 0.0001 pu.

The flow chart of numerical test for MSE is illustrated in Fig. 4,where all of the data prepared for MSE, including network param-eter and measurement data, etc., are separated into two parts withrespect to the balanced transmission and unbalanced distributionsystems. In Fig. 4, the integrated power flow calculator (MPF),which provides a unified power flow solution for a integratedpower system, is also split into the balanced transmission andunbalanced distribution power flow calculator based on the MSSmethod [27]. The solution of the MPF is taken as the true valueof measurement, random error of which is generated by the mixedmeasurement simulator (MMS) consisting of two independentparts with respect to the balanced transmission and unbalanceddistribution systems. Finally, data communication between thebalanced transmission and unbalanced distribution state estima-tors is carried out in each MSS iteration step and repeated until aconsistent MSE solution is got.

In order to study the performance of the MSS method for MSE,five test integrated power systems, named as 5A, 11B, 14B, 30C,30D are constructed here. In these test systems, four IEEE standardsystems, including IEEE 5-, 11-, 14- and 30-bus systems are adoptedas the transmission parts, while four radial distribution systems,including 19-bus system [28] and IEEE 13-, 34-, 37-bus systemsnamed as A, B, C and D are connected into transmission systems asthe partial loads of the transmission systems. For example, the testsystem 5A is the combination of the transmission system IEEE 5-bus and the distribution system A (The distribution system A is con-nected into the bus number 4 of transmission system IEEE 5-bus). Inorder to show the value of the MSE study, the MSS method with the

erical test for MSE.

Table 2Comparison between the results of the traditional and MSE methods of Table 2.

Method jDVBM j (pu) DhBM (�) DPBM (kw) DQBM(kvar)

Traditional 0.039 7.392 198.7 87.3MPF <0.0001 <0.001 0.1 0.2

Table 3Comparison on performance between the CAI and MAI iterative schemes for 14B testsystem.

Scheme NMSS NT ND

CAI 2 5 5MAI 4 4 3

Table 1Summary of results state estimation for the test system 5A.

Method |VB| (pu) hB (�) PB (Mw) QB (Mvar)

Traditional Trans. 0.961 �7.392 1.5123 0.9497Dist. Ph.1 Ph.2 Ph.3 Ph.1 Ph.1 Ph.2 Ph.3 Ph.1 Ph.1 Ph.2 Ph.3 Ph.1

1 1 1 0 �120 120 0.572 0.568 0.571 0.351 0.333 0.353MSE Trans. 0.94 �8.9912 1.7441 1.051

Dist. 0.94 0.94 0.94 �8.99 �128.99 111.01 0.591 0.5631 0.59 0.361 0.332 0.358

Trans. = transmission, Dist. = distribution and Ph. = phase.

A.R. Abbasi, A.R. Seifi / Electrical Power and Energy Systems 45 (2013) 152–158 157

CAI scheme is compared with the traditional separated state esti-mation method for the 5A test system and the results are shownin Table 1.

In order to show the value of the MSE study, the MSS methodwith the CAI scheme is compared with the traditional separatedstate estimation method for the 5A test system. Table 1 showssummary of results state estimation for the test system 5A.

Table 2 shows Comparison between the results of the tradi-tional and MSE methods of Table 1 (In Tables 1 and 2, the resultsare given for traditional method worked by others). In the table,DVBM ;DhBM ;DPBM and DQ BM

denote the maximum boundary mis-matches of voltage magnitude, voltage angle, active power andreactive power, respectively. NMSS denotes the number of MSS iter-ation. NT and ND denote the numbers of sub-iterations for balancedtransmission and unbalanced distribution state estimators sub-iteration for distribution system respectively. In Table 1 and thefollowing text, the FDSE [2] and branch current based algorithms[5] are adopted for the balanced transmission and unbalanced dis-tribution state estimations respectively. Thus, each sub-iterationfor transmission system includes a P–h iteration and a Q–V itera-tion of FDSE algorithm, and a sub-iteration for distribution systemis an iteration of forward/backward sweep algorithm. Here, thereal-life situation with lack of real time measurement is consid-ered, and accuracy of the measurement simulated for the distribu-tion system is lower than that for the transmission system.

In Table 2, for the traditional method, since there is no commonreference voltage between the transmission and distribution sys-tems, the boundary mismatch of voltage angle is large and valuedof 7.392�, and due to the different accuracy and redundancy ofmeasurement sets, the boundary power mismatch is also remark-able and valued of 198.7 kw + 87.3 kvar. However, consistent solu-tion of MSE with good accuracy can be achieved by the MSSmethod.

Performances of the two proposed iterative schemes of the MSSmethod _CAI and MAI_ are compared in Table 3. The number ofMSS iterations for the CAI scheme is less than that for the MAIone. In Table 3, for the MAI scheme, the NT and ND are less a bitthan that of the CAI scheme. Because of less communication be-tween M and S (less NMSS in Table 3), it is suggested that CAI

scheme be adopted if online geographically distributed computa-tion is needed. While for the MAI scheme, with assignment of lessnumber of sub-iterations for the transmission and distribution sys-tems at each MSS iteration step, the total number of sub-iterationsis less than that of the CAI scheme. It means the MAI scheme isusually more efficient for parallel computation with enough spee-dy communication.

5. Conclusions and future studies

In order to achieve a global consistent state estimation solution,the balanced transmission and unbalanced distribution networksare studied as a whole in this paper. Based upon the master–slave-typed feature of integrated power system, a novel MSS meth-od for calculating large-scale and hybrid MSE problem isdeveloped.

In the MSS method, with introducing the boundary fictitiousmeasurement, the MSE problem of large scale is split into a bal-anced transmission state estimation and many unbalanced distri-bution state estimation sub-problems of small scale. Differentstate estimation algorithm and base of per-unit power can beadopted to fit the different features between the transmissionand distribution systems. The geographically distributed structurefor online MSE computation is presented. Based on the MSS meth-od, two types of detailed iterative schemes with different charac-teristics, namely MAI and CAI, are constructed. Several casestudies are carried out. From the numerical results, the global con-sistent solution of MSE can be got by the MSS method, and theaccuracy, convergence, efficiency and reliability of the MSS methodare validated.

In order to implement global optimized control between trans-mission and distribution systems, future studies needs to do, suchas

(1) Implementation of MSE by intelligent state estimators.(2) Var optimization for integrated power systems, where

besides the traditional controllable variables, var output ofdistributed generator can also be included.

(3) Voltage stability evaluation for integrated power systems.

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