Static Voltage Stability Enhancement Using FACTS Controller

Static Voltage Stability Enhancement Using FACTSControllerIsaiah G. Adebayo1 , Adisa A. Jimoh 2 , Adedayo A. Yusuff 3 , C. Subramani 41,2,3Department of Electrical Engineering, Tshwane University of Technology, Pretoria, South Africa.4Department of Electrical and Electronics Engineering, SRM University, Kanchipuram, India1 isaiahadebayo@, 2Jimohaa@tut.ac.za, 3Yusuffaa@tut.ac.za, 4csmsrm@Abstract— The modern day power system is faced with challenges of voltage instability and has become a great concern to the power system industries. In this work, we proposed a technique of the Network structural Characteristics Participation Factor (NSCPF) to identify the most critical node where reactive power compensator can be placed for voltage stability enhancement. The approach is based on the use of eigenvalue decomposition technique on the submatrix of the partitioned bus admittance matrix. Conventional power flow based approach of voltage stability index (L-Index) and the modal analysis methods are used as benchmarks to the proposed approach to determine its effectiveness. The STATCOM FACTS controller is in turn installed at the critical bus as identified by both techniques. Simulation results obtained show that, the suggested approach saves time and is more advantageous in identifying the suitable bus for the placement of STATCOM.Keywords— Power flow, Power electronics, Voltage stability indices, Network Structural characteristics, Modal AnalysisI.INTRODUCTIONPower system voltage stability is a complex matter that has been challenging the power system utilities in the past two decades [1],[2]. The continuous increase in power demand and more interconnections with limited transmission expansion has been a demanding task to operate the power system in an efficient way [3]. The consequence of the occurrence of voltage instability in power systems may be very catastrophic as this could lead to voltage collapse [4]. This incident is characterized by a slow variation in the system operating point, as a result of increase in loads, in such a manner that voltage magnitudes gradually decrease until a sharp, accelerated change occurs [5].A number of major blackouts throughout the world have been directly related with this phenomenon, for example, the blackout experienced in 2003 in North America, and later in Europe, New Zealand, France, Iran, Belgium, Japan and so on [6]. Thus, it has become a major threat and concern to the power system operators and has been considered as an active area of research in the recent year. Over the years, considerable attempts have been made by several researchers to curb the occurrence of voltage collapse in power systems. The use of PV and QV curves have gained much attention since the incident of voltage collapse in Tokyo and are well documented in the literature [7],[8]. These techniques are computationally demanding and are time consuming, especially for large and complex networks. Other voltage instability and voltage collapse prediction techniques reported in the literature [9] include continuation power flow (CPF) method [10], modal analysis [11], the minimum singular value of the power flow Jacobian [12], voltage instability proximity indicator [13].The use of these methods, however, is time consuming and laborious, particularly for a large power system network as it involves performing a power flow solution before a collapse point is detected. Most recently, considerable stability indices have been introduced and developed in the literatures to assess the condition of system voltage stability. These indices include, among others voltage stability index (L-index), voltage collapse proximity index (VCPI), Line stability index, Line stability factor (LPQ) and Fast Voltage stability index (FVSI) [1], [14]-[16]. Although, the use of these indices has helped system operators a lot, especially to determine the bus that is susceptible to collapse. However, the process is always too tedious and time consuming as it requires performing a multiple power flow before the point is detected. Thus, there is a need for a reliable and fast tool for voltage collapse point detection in power system.Although a considerable effort has been made by the author of [17] in detecting nodes suitable for optimal location of reactive power compensators for voltage stability enhancement, however, the best nodes identified by the authors for the placement of compensators may not be the most critical, as their work did not capture the bus which participate (contribute) most to the smallest eigenvalue (critical mode) identified. FACTS devices are mostly used to provide power flow and voltage control in many utilities. The use of FACTS controller devices such as UPFC, STATCOM, SVC, GUPFC, TCSC, IPFC among others, for voltage control is well documented in the open literatures [11],[18],[19].In this paper, we suggest an approach based on the network topological characteristics of power system which makes use of the critical mode and the associated eigenvectors978-1-5090-3751-3/16/$31.00 ©2016 IEEEto compute the weak nodes where reactive power compensator can be placed. Comparative analysis of this approach is done with the existing power flow based L-index. All the techniques presented are tested on the IEEE 5 bus and the practical 26-bus test systems. The STATCOM FACTS deviceis used as a reactive compensator device for voltage stabilityenhancement in this paper. The remaining of this paper isorganized as follows: Section II gives the mathematical formulation of the suggested approach of the NSCPF and a brief note on the conventional power flow based L-Index technique, while a brief description of the STATCOM used is presented in Section III. Section IV present result and discussion of the work and the conclusion of the work is presented in Section V. II. PROBLEM FORMULATIONSMathematical formulations of NSCTPF start from thebasic law of circuit theory. It is derived by partitioning the Y-admittance matrix into four regions as shown in (1)»¼º«¬ª»¼º«¬ª=»¼º«¬ªL G LL LG GL GG L G V V Y Y Y Y I I (1) »¼º«¬ª=LL LG GL GG Y Y Y Y Y (2)If we further expand (1) and manipulate the resulting algebraic equations, we have;»¼º«¬ª»¼º«¬ª=»¼º«¬ªL G LL LG GL GG L G V I D W H Z I V (3) where[][]1−=GG GG Y Z[][][]GL GG GL Y Y H 1−−= [][][]1−=GG LG LG Y Y W[][][][][]GL GG LG LL LL Y Z Y Y D −=The eigenvalue decomposition of matrix LL D is given by *1*i ini i LL f f F F D ξξ¦===(4)whereF is an orthonormal matrix with eigenvectors i f and ξis a diagonal matrix with eigenvalues i ξ.Expanding (3) also results in:[][][][]{}G LG L LLL I W I D V −=−1(5)Substitution of (21) in (22)[][][][]{}G LG L n i i i i L I W I v V −¼º«¬ª=¦=1*ξν (6)From (5) and (6), it can be seen that large values of iξdepicts small changes in the load voltage. However, as thesystem is stressed, the value of i ξ becomes smaller and theload voltage becomes weaker. If the magnitude of i ξis equal to zero, the corresponding load voltage collapses. The weak load bus is surrounded by lines with high impedances. The extent of whether the reactive elements are not enough or sufficient in power system is solely depends on the participation between network buses observable from the eigenvectors of the matrix F. In some occasions, the criticalbus, which is associated to the smallest eigenvalue may not be a more critical load bus.Thus, this present work digs deep to further explore theconcept of structural based participation factor to determinethe most critical load bus, which contributes most to thesmallest eigenvalue as identified using (4) for voltage stabilityenhancement. We termed this Network Structural Characteristics Theory-Participation Factor (NSCTPF) in this work. This is done by identifying the elements contributingmost in these modes. The bus participation factor measuring the contribution of the th i bus to the thj mode is the product of right and left eigenvectors defined in (7) and it is given asji ij ij f f NSCTPF =(7)It follows that, the bus, which has large participation factorscorresponds to the most critical system buses which are liable to voltage collapse.L-index proposed by [20] and the modal analysis of the reduced Jacobian matrix [11] are used in this work as benchmarks to test the effectiveness of the proposed approach of NSCTPF. With these techniques, the suitable locations for the STATCOM FACTS device are determined. Details of the mathematical formulations of the L-Index and the modal analysis techniques are reported in [20] and [11] respectively. The L index varies in a range between 0 (no load) and 1 (voltage collapse). The maximum of these indices gives the proximity of the system voltage collapse. For the modal analysis, the bus with the highest value of the Modal Analysis Participation Factor (MAPF) is usually considered the critical bus.II STATCOM FACTS CONTROLLERSTATCOM is a shunt-connected device, which regulates the voltage at the connected bus to the reference value by controlling the voltage and angle of internal voltage source. The resulting STATCOM can inject or absorb reactive power to or from the bus to which it is connected and thus control the bus voltage magnitude. The STATCOM has the capacity to either inject or absorb the reactive power of the system, depending on the voltage magnitude to which it is connected into. When system voltage is low, the STATCOM injectsreactive power (STATCOM capacitive). When system voltage is high, it absorbs reactive power (STATCOM inductive). There are two major models of STATCOM reported in the literatures. These models have been well tested in power systems. Namely, the Current Injection Model (CIM) and the Power Injection Model (PIM) [21],[22]. In the CIM, STATCOM has a current source connected in shunt to the bus for voltage magnitude control. The PIM model of the STATCOM is a shunt voltage source behind an equivalent reactance or impedance, which is also referred to as a voltage source model (VSM). This steady state power injection model of STATCOM has proved to be reliable when incorporated in power systems. Details formulation of the power injection model is well reported in [23].IV SIMULATION RESULTS AND DISCUSSIONThe effectiveness of all the approaches presented is tested on both IEEE 5 bus and the practical 26-bus power systems. The IEEE 5 bus test system consists of two generators, three load buses seven transmission lines . On the other hand, the 26 bus practical power system consists of six generator buses, twenty load buses and forty six transmission lines. All the data used for the 26-bus system is taken from [24]. In this paper, the generator and load buses are arranged sequentially. Load buses 24, 25, 21, 19 and 17 of the 26 bus power system are selected at random for voltage stability analysis. MATLAB 2014b are used as simulation tools in this work. Results and discussions of the IEEE 5 bus and the 26 bus test systems, respectively are presented in this section.A.The IEEE 5 bus test systemFor the proposed NSCPF, first, we applied the eigenvalues decomposition on the matrix of (4) to identify the critical mode of the system. This matrix shows the electrical interconnection between the load buses in the power system network. It is based on the admittance matrix of the system. The associated network structural based eigenvectors are then used to compute the values of the Network Structural Characteristics Participation Factor (NSCPF) of each load bus. The results of the eigenvalues of each load bus, with the corresponding mode, NSCPF and the total computational time obtained for the IEEE 5 test systems are as presented in Table I.Load bus 4 which corresponds to the mode 2 of the IEEE 5 bus system has the highest value of the NSCPF (0.4468) , thus it is considered as the weak bus of the network where reactive power compensator may be placed for voltage stability enhancement.The traditional power flow based results of the modal analysis and the L-index techniques for the IEEE 5 bus system are as shown in Table II and III respectively. It could be seen that the results of the modal analysis obtained are in agreement with that obtained for the proposed NSCPF. This is as shown in Table II. Bus 4 has the maximum value of MAPF (0.3749) and corresponds to mode 2 of the system. Thus, this bus is considered as the weakest of all the load buses of the IEEE 5 bus system. Worth-noting is the similarity between the proposed NSCPF and the MAPF. The difference between the two approaches, however, is obvious. The formal depends on the network structural interconnections of buses in power system and are non-iterative in nature. They are captured by the admittance matrix of the system.On the other hand, the MAPF is power flow based and are iterative. It depends solely on the active and reactive power loads of the system and the Jacobian matrices. With the L-Index approach, bus 5 is found to have the least allowable loads of 260MVar and maximum values of L-Index (1.0102), with the least voltage magnitude (0.5321). Thus, based on this approach, bus 5 is identified as the bus suitable for the injection of reactive power. It must be stated, however, that it only takes just a single computational step to attain a solution with the proposed method of NSCPF (1.207473), whereas, it takes longer period of time for the power flow based approaches, with the exception of the modal analysis.B.The 26 – bus practical power systemSimilar procedures as presented for the case of IEEE 5 bus system are also followed here. The results of the NSCPF-Eigenvalues for each load bus of the 26-bus system are as presented in Figure 1. Also presented in Table IV are the results of simulations obtained for the conventional power flow based L-Index approach and the proposed NSCPF. The results of voltage magnitude obtained with the computational time at each reactive power load variation for the selected load buses 17, 19, 21, 24 and 25 are also shown in Table IV. The results of the MAPF of each selected load buses of the 26-bus system are also represented in Table V.Fig. 1: NSCPF Eigenvalues of 26-bus systemWith the suggested technique based on the network topological structure of power systems, of the five weak load buses 17,19,21,24 and 25 selected, bus 24 is found to have the maximum value of NSCPF (0.4238) and also correspond to mode 10 of the 26 – bus practical power system as shown in Table IV and Figure 1 respectively. Similar results are also obtained for the conventional power flow based approaches, except that bus 25 is ranked as the weakest bus of the 26-bus power system with the modal analysis method.C. Voltage Stability Enhancement with STATCOM FACTSDevicePresented in this section are the results obtained when the STATCOM is placed on the weak buses identified by the approaches considered for both the IEEE 5 bus and the 26 bus power systems. STATCOM is placed at the load buses randomly selected for the 26 bus power system and at the three load buses of the IEEE 5 bus system. The result of the voltage magnitude improvement obtained for the IEEE 5 bus and the 26 bus power systems when STATCOM is placed at buses 3,4 and 5 of the IEEE 5 bus system and load buses 17, 19 , 21, 24 and 25 of the 26 bus systems are as presented in the figures 2 to 4 and figures 5 to 9 respectively.TABLE IResults of the proposed NSCPF for the IEEE 5 bus test systemTABLE IIResults of the MAPF obtained for the IEEE 5 bus systemTABLE IIIResults of the L-Index obtained for the IEEE 5 bus systemTable IVResults of the L-Index and NSCTPFTABLE VResults of the MAPF for the 26-bus power systemsWhen STATCOM is placed on load buses 3,4 and 5 of the IEEE 5 bus system, one after the other, there is a considerable improvement in the voltage profile of the system.However, it could be observed that the voltage profile Improvement of the load buses is more obvious when STATCOM is located at bus 4, being the weakest load bus identified by both the proposed NSCPF and the modal analysis of the reduced Jacobian techniques. This is as shown in Figure 6. For instance, the basecase voltage magnitude of bus 4 is 0.9664p.u. With the injection of reactive power through the placement of STATCOM FACTS device, the voltage profile increases to 1.0405 p.u. Similarly, for the 26-bus power system, with the placement of STATCOM on load bus 24, the voltage magnitude of the entire buses also increases.RankBusNo BasecaseVoltagemag(p.u)NSCPF-EigenvaluesModes NSCPF ComputationalTime (secs)2nd 3 0.9652 3.6483 1 0.41901st 4 0.9664 8.9915 2 0.4468 1.207473 3rd 5 0.9656 72.4611 3 0.1342Rank BusNo Eigenvalues Mode MAPF ComputationalTime(secs)2nd 3 73.5592 1 0.34201st 4 7.2398 2 0.3749 2.672109 3rd 5 13.5385 3 0.2831Ranking order BusNoQmax(MVar)L-IndexVoltageMag. (p.u)ComputationalTime (secs)3rd 3 350 1.0003 0.5573 10.208304 2nd 4 345 1.0068 0.5382 6.903298 1st 5 260 1.0102 0.5321 5.609871Bus No Qmax VoltageMag(p.u)L-index Computationaltime (secs)ProposedNSCTPFComputationaltime (secs)21430 0.5666 0.8661 13.340921 0.170624 237 0.5574 0.9223 8.023498 0.423825 238 0.5616 0.8940 10.983421 0.0171 4.908761 19550 0.5858 0.8461 23.023145 0.109117520 0.5796 0.7801 20.210987 0.0631Rank BusNo Eigenvalues MAPF ComputationalTime (secs)5th 17 5.0278 0.00173rd 19 45.0131 0.1065 5.672109 4th21 39.5662 0.06302nd24 25.9740 0.18571st25 28.3753 0.2554For example, there is a drastic voltage drop (basecase) at bus 24 as shown in Figure 8 the basecase voltage magnitude of bus 24. However, with the incorporation of STATCOM at bus 24, the voltage magnitude of targeted bus increases rapidly and so also are the voltage magnitude of other load buses. Similar trend of voltage profile improvement can be observed when STATCOM is placed at buses 17, 19, 21 and 25 as shown in Figures 5, 6, 7 and 9 respectively.Fig. 2. STATCOM at bus 3Fig.3. STATCOM at bus 4 Fig. 4. STATCOM at bus 5 Fig. 5. STATCOM at bus 17Fig. 6. STATCOM at bus 19Fig. 7. STATCOM at bus 21V CONCLUSIONA new approach based on the network structural properties of power system is presented in this paper. The effectiveness of this approach and the conventional power flow based techniques presented is tested on both the IEEE 5 bus and the 26-bus practical power systems. The main aim is to ensure voltage stability enhancement through the incorporation of the STATCOM FACTS device. The weakest bus of the IEEE 5 bus and the 26-bus practical power systems are first identified through the techniques presented. This bus is taken as the best location for the reactive power compensator. The result obtained shows that, bus, suitable for the placement of STATCOM is better identified through the proposed NSCPF compared with the conventional approaches. The suggested technique saves time and requires less computational effort before the weakest bus is identified. This is a great advantage when considering the present Smart Grid system and will also go a long way to aid the power utilities in the operation and planning of the power system.ACKNOWLEDGMENTThe authors acknowledge the financial support received from the Tshwane University of Technology and Rand Water, Pretoria, South AfricaFig. 8. STATCOM at bus 24Fig. 9. STATCOM at bus 25REFERENCES[1] V. Balamourougan, T.S. Sidhu & M.S. Sachdev. “Technique for onlinePrediction of voltage collapse”, IEEE Proc. Gener. Transm. Distr. Vol.151, No 4, Pp. 453-460, 2004 [2] M. Begovic, J. Bright, T. Domin, S. Easterday-McPadden, A. G. Girgis,W. Hartmann, C.Henville, M. Ibrahim, K. Kozminski, R.Marttila, M. K. 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