State Estimation of Power System with Interline Power Flow Controller


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Now-a-days Flexible A.C. Transmission
System (FACTS) controllers are incorporated into the
power system network to control the power flow and
enhance system stability. Traditional state estimation
methods without integrating FACTS devices will not be
suitable for power systems embedded with FACTS
controller. Based on the conventional power system state
estimation model, a new method is proposed wherein an
IPFC based power injection model is incorporated in the
state estimation algorithm. Interline power flow controller
(IPFC) is one of the versatile FACTS device. The
proposed method is tested on Anderson and Fouad 9-bus
test system and the results are presented.

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State Estimation of Power System with Interline Power Flow Controller

  1. 1. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010State Estimation of Power System with Interline Power Flow Controller V.Gomathi1, C.Venkateshkumar2, and Dr.V.Ramachandran3 1, 2 College of Engineering Guindy, Anna University / Department of EEE, Chennai Tamilnadu, India. Email:, 3 College of Engineering Guindy, Anna University / Department of CSE, Chennai Tamilnadu, India Email: rama@annauniv.eduAbstract— Now-a-days Flexible A.C. Transmission devices have been utilized to meet a growing demandSystem (FACTS) controllers are incorporated into the of the transfer capabilities due to developing wheelingpower system network to control the power flow and transactions in the deregulation environment. Someenhance system stability. Traditional state estimation interesting applications of FACTS devices can bemethods without integrating FACTS devices will not besuitable for power systems embedded with FACTS found to economic dispatch(ED), AC/DC optimalcontroller. Based on the conventional power system state power flow (OPF), available transfer capability (ATC),estimation model, a new method is proposed wherein an contract path based electricity trading, and transmissionIPFC based power injection model is incorporated in the congestion management. [2]-[3].state estimation algorithm. Interline power flow controller The Interline Power Flow Controller (IPFC) concept(IPFC) is one of the versatile FACTS device. The provides a solution for the problem of compensating aproposed method is tested on Anderson and Fouad 9-bus number of transmission lines at a given substationtest system and the results are presented. while the UPFC is used as a powerful tool for the cost effective utilization of individual transmission lines by Index Terms— IPFC, Power Injection model, FACTS,State Estimation, WLS. facilitating the independent control both the real and reactive power flow. Any inverters within the IPFC are I. INTRODUCTION able to transfer real power to any other and thereby facilitate real power transfer among the lines, together Flexible ac transmission system (FACTS) devices with independently controllable reactive seriesenable secure operation of power systems which have compensation of each individual line. The mainto be otherwise upgraded in order to relieve load on objective of the IPFC is to optimize both real andcongested transmission lines or to optimize the system reactive power flow among multi-lines, transfer powerresources. As these devices start populating the from overloaded to underloaded lines. However, it cantransmission systems, monitoring of the system state also be utilized to compensate against reactive voltagewill require detailed models of these devices and their drops and the corresponding reactive line power, and tointegration into the existing power system applications. increase the effectiveness of the compensating systemOne of these applications with a critical role in system against dynamic disturbances [4]-[6]. Hence there hasmonitoring is the state estimator. This paper presents been increasing interest in the analysis of IPFC inthe formulation, solution and testing results for the power system.However; very limited efforts have beenproblem of state estimation of system containing made to study the impact of FACTS devices on powerinterline power-flow controller (IPFC). Due to the system state estimation. A new method is introduced toenlargement of interconnected electric power system incorporate IPFC devices into the power stateand the increasingly complexity of electric power estimation. This paper attempts to deduce the model ofsystem structure, hence energy management system state estimation with IPFC using the conventional(EMS) is critical for modern power system State power system state estimation model. A powerestimation plays an important role in EMS, which injection model that transfers the affect of IPFCprovides a reliable and consistent system data by towards the power flow to the transmission lines isprocessing real time redundant telemetered and pseudo presented. This method can be integrated to themeasurements. These measurements typically consist conventional state estimation program with theof bus voltage magnitudes, real and reactive line flows consideration of IPFC.and power injection. Processing these real time data,different kinds of advanced application software in II. THE STATE ESTIMATION PROBLEMEMS are derived, such as voltage stabilityanalysis, security constraint and transient stability A. Formulationanalysis et al. Since the concept of flexible AC WLS state estimation minimizes the weighted sum oftransmission systems (FACTS) was proposed by squares of the residuals.Hingorani in the 1860s,[1] many various FACTS 56© 2010 ACEEEDOI: 01.ijepe.01.02.11
  2. 2. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010Consider the set of measurements given by the vector z Vn is the voltage magnitude at bus n, where n= i,j.: Z = h(x) + e (1) δij is the difference between the voltage phase hT=[h1(x),h2(x),…,hm(x)] (2)hi(x) is the nonlinear function relating measurement i angles at buses i and j,to the state vector x.xT=[x1,x2,…,xn ] is the system state vector Gij+jBij is the ijth element of the complex bus admittance matrix,eT=[e1,e2,…,em] is the vector of measurement errors. gij+bij is the series admittance of the branchLet E(e) denote the expected value of e , with the connecting buses i and j,following assumptions:E(e)=0, i=1,2,…,E(eiej)=0 (3) gsi+bsi is the shunt admittance of the branchMeasurement errors are assumed to be independent and connecting buses i and j,their covariance matrix is given by a diagonal matrix R N is the number of buses in the system.:Cov(e)=E[e.eT]=R=diag{�12,�22,…,�m2} (4)The WLS estimator will minimize the followingobjective function: III. INTERLINE POWER FLOW CONTROLLER Min J(x) =(zi-hi(x))2/Rii= [z-h(x)]TR-1[z-h(x)] It is common that the Interline Power Flow (5) Controller employs a number of dc to ac inverters in The objective of weighting the squared differences in order to offer series compensation for each line. As aeq(5) is to provide a mathematical way of describing new concept for the compensation and effective powerthe accuracy of the meters. More precisely, the standard flow management, it addresses the target ofdeviation of a meter is a statistical value that describes compensating a number of transmission lines at a givenhow tightly the measurements taken are clustered substation.around the true value. Thus, if the standard deviation islarge, the measurement is relatively inaccurate; while a A. Configuration of Interline Power Flow Controllersmall standard deviation value indicates a small error Generally, the Interline Power Flow Controllerrange. (IPFC) is a combination of two or more independently controllable static synchronous series compensatorsB. Measurement Functions (SSSC) which are solid-state voltage source converters According to the previous discussion, the measured which inject an almost sinusoidal voltage at variablequantities are represented by the vector z, and h(x) magnitude and couples via a common DC link asrepresents a set of functions that depend on the values shown in Fig.1.Conventionally, series capacitivebeing estimated. These functions are used to calculate compensation fixed, thyristor controlled or SSSCthe estimated values corresponding to measured values based, is employed to increase the transmittable realz. For this study, only the bus voltage magnitudes, the power over a given line and to balance the loading of ainjected real and reactive powers, and the real and normally encountered multi-line transmission system.reactive branch power flows will be used as the They are controlled to provide a capability to directlyquantities being measured. With exception of the bus transfer independent real power between thevoltage magnitudes, the corresponding h(x) functions compensated lines while maintaining the desiredare nonlinear and are calculated as follows: distribution of reactive flow among the line. Real and reactive power injection at bus i: N (6) P =| Vi | ¥| V j |(Gij cos δij + Bij sin δij ) i j=1 N (7) Qi =| Vi | ¥| V j |(Gij sin δij − Bij cos δij ) j=1Real and reactive power flow from bus i to bus k Pij=Vi2 (gsi+gij)-|Vi|*|Vj|(gij cosδij+bij sinδij)(8) Qij=-Vi2 (bsi+bij)-|Vi|*|Vj|(gij sinδij-bij cosδij) Fig.1. Simplified Schematic of the IPFC model(9) Consider simplified schematic of IPFC model in Fig.1, each compensating inverters is linked together atwhere: their dc terminals. With this scheme, in addition to 57© 2010 ACEEEDOI: 01.ijepe.01.02.11
  3. 3. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010providing series reactive compensation, any inverter reactances of the two coupling transformers. Fig.4.can be controlled to supply real power to the common depicts a two voltage-source model of the IPFC. Thedc link from its own. two voltage sources, Vser are controllable in both magnitudes and phase angles. Vser should be defined as: Vser = r Vi ejγ (10) The values of r and γ are defined within specified limits given by equations. The variables r represents certain percent of the voltage magnitude Vi at bus i. 0 ≤ r ≤ rmax and 0 ≤ γ ≤ 2π Fig.2. Two-Inverter Interline Power Flow Controllertransmission line. Thus, an overall surplus power canbe transferred from the underutilized lines which canbe used by other lines for real power compensation.Evidently, this arrangement maintains the overallpower balance at the common dc terminal byappropriate control action. An elementary IPFC schemeconsisting of two back-to-back dc to ac inverters isused as a tool to compensate a transmission line by Fig.3. Representation of two series connected voltage sourcesseries voltage injection. Two synchronous voltagesources, with phasors V1pq and V2pq, in series with The steady state IPFC mathematical injection model istransmission line1 and 2 respectively, represent the two developed by replacing voltage source Vser by a currentback-to-back dc to ac inverters as illustrated in Fig2. source Iser parallel with a susceptance bser = 1/ Xser.B. IPFC Power Injection Model Therefore,the series current Iser is defined by: This section focuses on the steady-state Iser = ─ j bser Vser (11)modeling of IPFC for the implementation of the devicein the conventional power flow program using injection The current source Iser can be modeled by injectedpower flow IPFC model. The injection power flow power at the three buses i , j and k which the IPFC isIPFC model is based on the representation of IPFC in connected as shown in Fig.4. The current sources Isersteady-state conditions by two voltage sources each are corresponds to the injection powers Siser , Sjser and Skserin series with a certain reactance. A MATLAB where:conventional N-R power flow program has been Siser = 2Vi (─ Iser )*modified in order to incorporate the injection powerIPFC model in power flow program. Sjser = Vj ( Iser )* The simplest IPFC consists of two back-to- Skser = Vk ( Iser )* (12)back DC-to-AC converters, which in a substation areconnected in series with two transmission lines viatransformers and the DC terminals of the converters areconnected together via a common DC link as shown inFig.1. In the flowing section, a model for IPFC whichwill be referred as IPFC injection model is derived.This model is helpful in understanding the impact ofthe IPFC on the power system in steady state.Furthermore, the IPFC injection model can easily beincorporated in steady state power flow model. Since Fig.4. Representation of two series voltages sources by two currentsthe series voltage sources converters does the main sources.function of the IPFC. The injection powers Siser , Sjser and Skser are simplified to:C. IPFC Power Injection Model based on Two Voltage Siser = 2 Vi [ j bser r Vi ejγ]*Source Representation = ─2 bser r Vi2sin γ ─ j 2 bser r Vi2 cos γ Piser = ─2 bser r Vi2 sin γ An IPFC can be represented in steady-state Qiser = ─2 bser r Vi2cos γ (13)conditions by two voltage sources representing If we define θij = θi ─ θj and θik = θi ─ θk we have:fundamental components of output voltage waveforms Sjser = Vj [─ j bser r Vi ejγ]*of the two converters and impedances being the leakage 58© 2010 ACEEEDOI: 01.ijepe.01.02.11
  4. 4. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010= bser r Vi Vj sin (θij + γ ) + j bser r Vi Vj cos (θij + γ )Pjser = bser r Vi Vj sin (θij + γ ) (18)Qjser = bser r Vi Vj sin (θij + γ ) (14) Table.1. Modification of Jacobian matrix by injectionSkser = Vk [─ j bser r Vi ejγ ]* power flow IPFC model= bser r Vi Vk sin (θik + γ ) + j bser r Vi Vk cos (θik + γ )Pkser = bser r Vi Vk sin (θik + γ ) E (i,i) = Eo (i,i) F (i,i) = Fo (i,i)Qkser = bser r Vi Vk cos (θik + γ ) (15) E (i,j) = Eo (i,j) F (i,j) = Fo (i,j) E (i,k) = Eo (i,k) F (i,k) = Fo (i,k)Based on the explanation above, the injection model of E (j,j) = Eo (j,j) ─ F (j,j) = Fo (j,j) + Pjsertwo series connected voltages sources can be seen as Qjser F (j,i) = Fo (j,i) + Pjserthree dependent loads as shown in Fig.5. E (j,i) = Eo (j,i) + F (k,k) = Fo (k,k) + Qjser Pkser E (k,k) = Eo (k,k) ─ F (k,j) = Fo (k,j) + Qkser Pkser E (k,i) = Eo (k,i) + Qkser G(i,i) = Go (i,i) H (i,i) = Ho (i,i) + G(i,j) = Go (i,j) 4Qiser G(i,k) = Go (i,k) H(i,j) = Ho (i,j) G(j,j) = Go (j,j) + H(i,k) = Ho (i,k) Fig.5. IPFC model Pjser H(j,j) = Ho (j,j) + G(j,i) = Go (j,i) ─ QjserThe apparent power supplied by the two series voltages Pjser H(j,i) = Ho (j,i) +sources is calculated from: G(k,k) = Go (k,k) ─ Qjser Pkser H(k,k) = Ho (k,k) + G(k,i) = Go (k,i) + Qkser Pkser H(k,i) = Ho (k,i) + Qkser (16)Active power and reactive power supplied byconverters 1 and 2 are distinguished as: IV. CO-ORDINATION ALGORITHM FOR STATE ESTIMATION WITH INTERLINE POWER FLOWPser1 = r bser Vi Vj sin ( θij + γ ) ─ r bser Vi2 sin γ CONTROLLERQser1 = ─ r bser Vi Vj cos (θij + γ ) + r bser Vi2 cos γ + r2 bser Vi2 The detailed solution steps of the proposedQser2 = ─ r bser Vi Vk cos (θik + γ ) + r bser Vi2cos γ + algorithm can be summarized as follows: r2 bser Vi2According to the operating principle of the IPFC, the Step 1: Input system data and telemeteredoperating constraint representing the active power measurements load flow;exchange among the converters via the common DClink is given by Step 2: Set iteration count k = 0 Pser2 = ─ Pser1 (17)The equality above is valid when the losses are Step 3: calculate system measurementsneglected. Step4: Initialize the state vector v(0),e(0)D. Incorporating IPFC Power Injection ModelintoLoad Flow program Step 5: Compute Jacobin matrix H(x(k)) with IPFC The IPFC injection model can be incorporated in aload flow program. If a IPFC is located between nodes Step6: Obtain ΔV(k+1) AND Δ θ(k+1) .i, j and k in a power system, the admittance matrix is V(k+1)=ΔV(k)+ΔV(k+1) , θ(k+1)=Δ θ(k)+Δ θ(k+1)modified by adding a reactance equivalent to X serbetween node i and j and node i and k .The suffix o Step6: Check for convergence. Ifindicates without IPFC. The Jacobian matrix is modified by addition of max {|�v (k+1)| , |�θ(k+1)|} > € go to Step 4appropriate injection model powers.If we consider thelinearized load flow model as: Otherwise, set k = k + 1 and go to Step 7 Step 7: Print results. 59© 2010 ACEEEDOI: 01.ijepe.01.02.11
  5. 5. ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 2, July 2010 V. TEST SYSTEM AND RESULTS power system state estimation model, this paper introduces the model of state estimation embedded with In this section, Anderson and Fouad 9- bus IPFC. A power injection model that transfers the effecttest system has been used to validate the effectiveness of IPFC on the power flow between the interconnectedof the proposed method. The IPFC is incorporated in lines is presented. It is demonstrated that the algorithmthe buses 4, 5, and 6. The measurement data for testing retains good convergence property as the traditionalthe modified state estimation algorithm are obtained WLS method and it possess the main merit ofusing the results from power flow analysis. The results extending the state estimation algorithm including theof the proposed method are verified with the results effects of Interline Power Flow Controller.obtained from traditional state estimation method. Thesolution is found to be more accurate, the REFERENCEScomputational effort is reduced and there is animprovement in the voltage profile. The tolerance [1] SUN Guo-qiang ,WEI Zhi-nong “Power System Stateassumed for convergence is 10−4. Estimation with Unified Power Flow Controller” DRPT2008 6-9 April Nanjing China 2008. [2] Jun Zhang and Akihiko Yokoyama “A Comparison between the UPFC and the IPFC in Optimal Power Flow Control and Power Flow Regulation” IEEE 2006 [3] Nursyarizal Mohd and Ramiah Jegatheesan “WLS modification Power Systems State Estimation Embedded with FACTS Devices” Proceedings of the International Conference on Electrical Engineering and Informatics Institut Teknologi Bandung, Indonesia 2007. [4] Satish Kumar Singh, and Jaydev Sharma” A Hopfield Neural Network based Approach for State Estimation of Power Systems Embedded with FACTS Devices” vol.4 IEEE 2006. [5] Bei Xu and Ali Abur ,“State estimation of System With UPFCs Using the Interior Point Method”, IEEE Fig.6. Anderson Fouad 9-Bus with IPFC Transactions on Power Systems, vol.19, n 3, pp. 1635- 1641 ,August, 2004. Table. 2. STATE ESTIMATION RESULTS FOR [6] B. Xu, A. Abur, "State Estimation of Systems with Embedded FACTS Devices," in Proc. IEEE Power Tech 9- BUS SYSTEM Conf,vol.5 2003. WITHOUT IPFC WITH IPFC [7] A.J. Wood, B.F. Wollemberg, Power Generation, BUS Operation and Control, 2nd. Ed. (New York: Wiley, NO. V/pu δ(°) V/pu δ(°) 1996,453-513). 1 1.0400 0 1.0400 0 VII. BIOGRAPHIES 2 1.0250 9.280 1.0256 8.817 Gomathi Venugopal received the Bachelors degree from University of Madras, in 2002 and the Masters degree from College of Engineering, Anna University, Chennai in 2004. 3 1.0250 4.665 1.0250 4.043 She is presently working as a Lecturer in College of Engineering, Anna University; Chennai.Her fields of interest 4 1.0258 -2.217 1.0259 -2.217 include Power System control and operation, Service Oriented Architecture and Web Services. 5 0.9956 -3.989 0.9972 -4.306 Venkateshkumar Chandrasekaran received his 6 1.0127 -3.687 1.0129 -4.464 Bachelors degree from Anna University, Chennai, in 2006.He is presently pursuing his Masters in College of Engineering, 7 1.0258 3.720 1.0254 3.254 Anna University, Chennai.His fields of interest include Power System Operation and Control, FACTS and Power System 8 1.0159 0.728 1.0155 0.195 Planning. 9 1.0324 1.967 1.0321 1.345 Ramachandran Veilumuthu received his Masters degree and Ph.D in Electrical Engineering from College of Engineering, Anna University, Chennai, India. He is currently working as a Professor in the Department of Computer VI. CONCLUSION Science, College of Engineering, Anna University, Chennai. In the proposed method the state estimation of His research interests include power system reliability engineering, network security, soft computing and Webpower system embedded with Interline power flow technology.controller is presented. Based on the conventional 60© 2010 ACEEEDOI: 01.ijepe.01.02.11