THE STATE estimation (SE) is described as a process

Transcription

1 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. IEEE TRANSACTIONS ON SMART GRID 1 Three-Phase State Estimation Using Hybrid Partice Swarm Optimization Sara Nanchian, Student Member, IEEE, Ankur Majumdar, Student Member, IEEE, and Bikash C. Pa, Feow, IEEE Abstract This paper proposes a method for three-phase state estimation SE) in power distribution network incuding on-oad tap changers OLTC) for votage contro. The OLTC tap positions are essentiay discrete variabes from the SE point of view. Estimation of these variabes in SE presents a formidabe chaenge. The proposed methodoogy combines discrete and continuous state variabes votage magnitudes, anges, and tap positions). A hybrid partice swarm optimization HPSO) is appied to obtain the soution. The method is tested on standard IEEE 13- and 123-bus unbaanced test system modes. The proposed agorithm accuratey estimates the network bus votage magnitudes and anges, and discrete tap vaues. The HPSO-based tap estimation provides a more accurate estimation of osses in the network, which heps in fair aocation of cost of osses in arriving at overa cost of eectricity. Index Terms Hybrid partice swarm optimization HPSO), tap estimation, three-phase state estimation SE). I. INTRODUCTION THE STATE estimation SE) is described as a process of finding network votage magnitudes and anges so that a the other network quantities such as transformer, feeder oadings, etc. can be obtained from them. SE is a standard computationa task in supervisory contro and data acquisition SCADA) for transmission system. At transmission eve generaized framework 1] is we adopted for SE with emphasis on bad data anaysis incuding handing switch status error. There is aways an assumption of baanced system at transmission eve so singe-phase positive sequence network data are adequate. The distribution network is hardy baanced and symmetric so three-phase SE is necessary. Unti recenty it was not much important to have mandatory SE at distribution system. But with growing controabe devices and components, it is now important to have state estimator for efficient operation of the distribution network. Manuscript received Apri 14, 2015; accepted Apri 26, This work was supported in part by the Engineering and Physica Sciences Research Counci EPSRC) under Grant EP/F037686/1; in part by the Power Network Research Academy by EPSRC, U.K.; and in part by the Scottish and Southern Energy Networks, U.K. Paper no. TSG The authors are with the Department of Eectrica and Eectronics Engineering, Imperia Coege London, London SW7 2AZ, U.K. e-mai: s.nanchian11@imperia.ac.uk; ankur.majumdar@imperia.ac.uk; b.pa@imperia.ac.uk). Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier /TSG There have been growing iteratures in distribution system SE DSSE). Chen et a. 2] have provided a thorough mode of distribution transformer incuding core oss to obtain more accurate state estimates. Standard weighted east square WLS) is suggested. The quaity and adequacy of measurements being ess than required-severa papers focused on accuratey estimating the oads through additiona measurement pacements. References 3] 5] have proposed the concept of minimum additiona measurements for improving accuracy of the SE in WLS framework. Because of the radia nature of the distribution network it was found computationay much easier to formuate feeder current as state variabes 6], 7]. The resuts are very convincing and with sight modification in the form of incusion of constraints in the optimization objective, sma meshed network can aso be soved. Sma meshed network arises from cosing normay open point to extend the feed. Wang and Schuz 8] ater extended the branch current-based estimation to obtain set of ocations where pacement of meters provide maximum impact in terms of accuracy. References 9] 12] have demonstrated the impact of various degrees of unbaanced in the network oads and parameters and topoogica uncertainties on the accuracies of SE. Zero injection is taken as constraints in the nodes having no measurement. Meiopouos et a. 13] and Zhong and Abur 14] have demonstrated further the impact of inaccurate parameters, untransposed ines, ignored transformer vector groups etc. not ony on the accuracy of the estimated quantities but on the bad data rejection capabiity as we. This ed to the requirement of synchronized phasor measurements at the distribution eve. Recenty, Haughton and Heydt 15] proposed a inear state estimator for fu three-phase unbaanced distribution system. It assumes that synchronized phasor measurement unit PMU)-based measurement and other smart demand measurements are avaiabe. It is indicated smart meters may record and transmit active and reactive power, energy consumption over time intervas, e.g., 5, 15, and 60 min, so rea time SE is not possibe. Thukaram et a. 16] used graph theory approach to pace measurement to guarantee observabiity and then sove the node current injection equations to obtain node votage and ange which appears to work as robust approach to obtain the estimates. The radia nature of the distribution network is expoited by the backward forward sweep method proposed in 17] which is somewhat aong the ines of oad estimation as performed in radia distribution system power fow computation. It refines the pseudo measurement This work is icensed under a Creative Commons Attribution 3.0 License. For more information, see

2 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. 2 IEEE TRANSACTIONS ON SMART GRID by power summation at node. Reference 18] provides faster agorithm for estimating oads. The approach is to reduce the compexity of the network into severa oad estimation zones connected through physica measurements. None of the above references considered primary distribution transformer on oad tap changing position as estimated variabe. This excusion of transformer tap position as estimated variabe from the above references encouraged us to deveop a three-phase SE agorithm incuding the tap as discrete variabe and obtain the exact tap position which is not possibe by conventiona WLS method. Distribution network has aso other probem of rapid votage fuctuation because of the indeed from DG. The output from DG being not predictabe soar and wind) the votage variation in the network is very severe. So the votage contro is as important as feeder fow contro. On oad tap changing transformer in the primary substation is aso subjected to rapid contro actions. It is very important to incude tap position as an estimated variabe so that network contro can be performed more effectivey. There have not been much iterature in tap observabiity detection. Pires et a. 19] proposed a robust agorithm based on Givens rotation of the gain matrix to obtain the state and tap position under erroneous zero injection. The method is demonstrated to work we in Braziian system modes of varying compexity. Shiroie and Hosseini 20] used node votages, anges and tap position as state variabes under the assumption that the taps are continuous. However, in practice OLTC has discrete tap positions so inaccurate estimate produces inaccurate computed vaues of other network quantities such as feeder fows, osses, etc. So, the incorporation of the discrete tap variabes in SE is required for effective network contro. Commony, SE agorithm is deveoped based on the assumption of baanced network mode which assumes that ine parameters and oads are baanced. Based on this assumption the anaysis is appied on the singe-phase mode, simpy using the positive sequence network for estimation of the system states. However, in distribution networks the presence of singe and two-phase ateras, untransposed three-phase circuits and unbaanced oads affect the accuracy of the estimated states when assumption of baanced system is appied. This resuts in unexpected system performance or undesirabe operating situations. So, an appropriate three-phase estimator is required to accuratey obtain the states with taps as discrete variabes 7], 21]. The motivation of this paper came from the need of a comprehensive three-phase state estimator incuding tap as discrete variabe to obtain most accurate network noda votages and anges under unbaanced situation. SE is commony formuated as a WLS probem 22]. However, transformer tap positions make the probem a mixed integer noninear one. So, the soution of the probem through norma equation framework is not possibe as the objective function is not differentiabe 23]. Teixeira et a. 24] and Korres et a. 25] have assumed continuous taps instead of discrete and have incorporated rounding technique or sensitivity method to address the compexity of discrete vaues. However, this assumption reduces the accuracy of the SE and the soution does not represent the actua network taps positions. Therefore, the estimation of transformer tap positions has to be obtained from the soution of the mixed integer noninear optimization probem containing continuous and discrete vaues 26], 27]. There has been growing interest in the appication of heuristic agorithms such as neura networks, genetic agorithms GAs), honey bee mating optimization, and partice swarm optimization PSO) in recent years. To overcome the computationa difficuty of such compex optimization probem, these agorithms have been successfuy appied to wide range of optimization probem where they can hande mixed integer variabes of the objective functions as they do not need the function to be continuous and differentiabe 28]. PSO appears to be a very effective technique compared to GA and other evoutionary agorithms as it is simpe in concept and impementation. It has imited number of parameters in comparison to other heuristic optimization methods. It can be easiy appied to diverse issues where it can produce satisfactory soutions and stabe convergence characteristics 29]. However, PSO has weak form of seection that increases the amount of time to get to the effective area in the soution space. A hybrid form of PSO HPSO) is used to overcome this situation 30] combining the feature from PSO and GA. HPSO has been appied in baanced SE probem 31]. HPSO uses a seection method which is based on the evoution from generation to generation. Reference 31] considered a baanced three-phase distribution network mode without considering unbaanced nature of the system and discrete tap as state variabes. Our research proposes a fu three-phase state estimator incuding unbaanced oad, network mode and the discrete taps as additiona estimated variabes based on HPSO optimization technique in order to estimate the discrete vaue of the transformer taps. The contribution of our research ies in handing the compexity of the unbaanced system and correcty computing the discrete vaues of the tap. The performance of the proposed method has been tested on IEEE 13- and 123-bus test system modes and the resuts are presented. Like a the methods based on heuristic search, the HPSO method takes onger time tens of minutes) to converge in a reasonaby sized network mode. This apparenty weakens the case for HPSO for SE in rea time. It is important to note that SE in distribution SCADA is not done in rea time. Since the ife expectancy of the tap changing mechanism is infuenced by the number of operations of the taps, it is aso not aowed to have frequent tap operation when rapid changes and oads and generation take pace. HPSO can be appied for network computation used for operationa panning purposes such as hour ahead contingency anaysis and reactive power contro scheduing, oss estimation for dynamic pricing purpose. The HPSO-based soution in this way is sti attractive to operate the network with higher efficiency even though the cacuation is not done in rea time. This paper demonstrates the vaue of this concept through comprehensive modeing, computation and anaysis in this context. We have aso made severa modifications

3 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. NANCHIAN et a.: THREE-PHASE SE USING HPSO 3 of traditiona PSO and HPSO techniques to obtain soutions faster. This paper is organized as foows. Section II provides an overview of SE in distribution system. In Section III, the PSO soution method is described. Section IV provides an overview of HPSO. Section V presents the HPSO approach in the context of three-phase unbaanced SE for distribution network mode. Section VI demonstrates the resuts and discussions of the SE for IEEE 13- and 123-bus mode networks. Section VII concudes this paper. II. DISTRIBUTION SYSTEM STATE ESTIMATION The soution to DSSE probem is formuated as a minimization of the foowing objective function subject to satisfying severa equaity and inequaity constraints. The goa is to obtain the bus votage magnitudes, anges and tap positions that minimizes weighted square of the difference between the measured quantity and the estimated quantity which are functions of estimated states. It is expressed as min Jx) = m w ii ri 2 1) i=1 subject to: z i = h i x) + r i 2a) cx) = 0 2b) g min gx) g max 2c) where x state variabes such as votage magnitudes, anges, and tap positions; m number of measurements; w ii weighting factor of measurement variabe i, z = z a 1 z b 1 zc 1... za i z b i z c i... z a ] m zb m zc m ; z i measured vaue of ith measurement; h i ith measurement as a function of state x; r i ith measurement error. In three-phase system x = Vi k δi k ti k], where Vk i = Vi a Vi b Vi c] is the vector of three-phase votage magnitude at bus i, δi k = δi a δi b δi c] denotes the phase anges of bus i except the reference bus and ti k = ti a ti b ti c] is the transfomer s tap vector if present at ith bus. In three-phase mode, the power injected at bus i for phase k can be written as P k i = V k i Q k i = V k i 3 n =1 j=1 3 n =1 j=1 V j V j G k, G k, cos δi k δj ] + B k, B k, cos δi k δj 3) )] where G + jb is the system admittance matrix, n is number of buses and is the number of phases that can be singe-, two-, or three-phase. The power fow from buses i to j for phase k 4) can be written as foows: 3 P k = Vk i Vi cos δi k δi V k i Q k = Vk i where P k i, Qk i V k i =1 3 =1 3 =1 3 =1 G k, V j V i V j G k, G k, G k, cos δi k δj sin δi k δi ] + B k, sin δi k δi ] + B k, B k, cos δi k δi 5) )] ] B k, cos δi k δj 6) active and reactive power injection of phase k in bus i; P k, Qk active and reactive power fow of phase k from buses i to j; Vi votage magnitude of phase at bus i; δi ange of phase in bus i. A. Equaity Constraints cx) The equaity constraints are the set of equation corresponding to virtua measurements 3 n 0 = P k Gi Pk Di Vi k V j cos δi k δj =1 j=1 0 = Q k Gi Qk Di 3 n =1 j=1 V k i V j G k, ] + B k, G k, ] B k, cos δi k δj where P k Gi and Q k Gi are the rea and reactive power injected at bus i, respectivey, the oad demand at the same bus is represented by P k Di and Qk Di 32]. Indices n is number of buses and is the number of phases which can be singe-, two-, or three-phase. B. Inequaity Constraints These are the set of constraints of continuous and discrete variabes that represent the system operationa and security imits, such as setting upper and ower imits for contro variabes. These are as foows. 1) Bus Votage: Votage magnitudes at each bus in the network Vmin,i k Vk i Vmax,i k. 2) Bus Ange: The bus ange at each bus in the network δmin,i k δk i δmax,i k. 3) Transformer Taps: Transformer taps settings tmin,i k tk i tmax,i k. 7) 8)

4 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. 4 IEEE TRANSACTIONS ON SMART GRID III. PARTICLE SWARM OPTIMIZATION The PSO is a popuation-based optimization method first proposed by Kennedy and Eberhart 33], which is used to search the soution space of a given probem to find the candidate soution which can maximize or minimize a particuar objective function. Some of the attractive features of the PSO incude the ease of appication and the fact that no gradient information is required which aows the PSO to be used on functions where the gradient is either unavaiabe or computationay expensive to obtain. It generates high quaity soutions and has stabe convergence characteristic than other stochastic methods; so can be used to sove a wide array of optimization probems. It uses a number of partices that constitute a swarm. Each partice traverses the search space ooking for the goba minimum or maximum). During fight, each partice adjusts its position according to its own experience and the experience of neighboring partices, making use of the best position encountered by itsef pbest) and its neighbors gbest). Let X and V represent a partice position and its corresponding veocity in a search space, respectivey. The best previous position of a partice is recorded and represented as pbest. The index of the best partice amongst a the partices in the group is represented as gbest. The modified veocity and position of each partice are cacuated as foows 34]: V = WV 0 + C 1R 1 X pbest X 0 ) + C 2 R 2 X gbest X 0 9) X = X 0 + V 10) where i ith partice; j dimension of the veocity associated with partice i; V, X veocity and position of the partice at iteration j; W weighting function; C 1, C 2 weighting factors; R 1, R 2 random numbers between 0 and 1. In 9), X pbest is the pbest of partice and X gbest is the gbest of the group. A. Seection of Parameters for PSO and Simuation Condition The seection of key parameters to set up PSO such as W, C 1, C 2, and V max is an important task as they govern the rate of convergence. 1) Weighting Function: W is a weighting factor which is reated to the veocity of the partice during the previous iteration. It contros the amount of the previous veocity that partice takes in the next iteration. This vaue is equa to 1.0 for the origina PSO. The concept of veocity wi be ost if this vaue is set to zero. Shi and Eberhart 35] investigated the effect of W in the range 0.0, 1.4). The faster convergence is obtained by setting this vaue between 0.8, 1.2). However, setting of inertia weight that decreased from 0.9 to 0.4 generated satisfactory resut 34]. The weighting function is obtained as W = W ini W ini W fin ) iter 11) iter max where W ini and W fin are the initia and fina weight, respectivey, iter max is the maximum iteration number, and iter is the current iteration number. 2) Acceeration Coefficients C 1 and C 2 ): C 1 and C 2 affect the maximum step size of a partice in a singe iteration. C 1 reguates the maximum step size of a partice in the direction of the pbest whie C 2 reguates the maximum step size in the direction of the gbest 34] asshownin9). The partice veocity is imited by V max to minimize the possibiity of the partice escaping the search space. If the search space is defined by the bounds X min, X max ],thevaue of V max is typicay set to V max = K X max X min ) 12) where 0.1 K 1.0. Initiay, PSO has been performed severa times with different vaues of the key parameters of W, C 1, C 2, and V max to achieve the satisfactory resuts. B. Improving the Speed of Convergence We have made appropriate modification to update the position of the partice by changing the direction when reaching the search space boundary in order to improve the speed of convergence. The direction of the partice shoud be modified in such a way that it keeps the partice inside its range when the veocity takes the partice out of its boundary X min, X max ]. So the new position of the partice wi be updated-based on the foowing equation instead of 10): X = X 0 V 13) the optima soution be cose to the boundary the α factor heps to reach the soution faster X = X 0 αv 14) where α is an optimay chosen number between 0 and 1. We have discussed about a suitabe vaue of apha ater in the discussion section. C. Genera Agorithm for PSO The genera steps of PSO agorithm can be described as foows. 1) Generate initia popuation of partices with random veocities and positions. In this paper, these partices are bus votage magnitudes and anges and transformer tap positions. 2) These initia partices must be feasibe candidate soutions that satisfy the practica operation constraints. Set upper and ower imits for these partices v,δ,t). 3) For each partice of the popuation, cacuate the error based on 2a). 4) Obtain vaue of each partice in the popuation using the evauation function fitness function) and the penaty function. The vaue of fitness function is obtained as foows: 1 FFx) = 15) 1 + Jx) + Penatyx)

5 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. NANCHIAN et a.: THREE-PHASE SE USING HPSO 5 where Jx) comes from 1) and Penatyx) as foows: N Penatyx) = ρ x i x 0 ) 2 16) N number of penaized contro variabes; ρ scaar quadratic penaty weight; x 0 contro variabe current vaue p.u.); x i contro variabe penaty offset p.u.). 5) Compare each partices vaue with its pbest. The best vaue among the pbest is denoted as gbest. 6) Update the time counter t = t ) Update the inertia weight W given by 11). 8) Modify the veocity V of each partice according to 9). 9) Modify the position of each partice according to 10) and 14). If a partice vioates its position imits in any dimension, set its position at the proper imit according to 14). 10) Each partice is evauated according to its updated position. If the vaue of each partice is better than the previous pbest, the current vaue is set to be pbest. If the best pbest is better than gbest, this vaue is set to be gbest. 11) If the maximum of a variation of the state variabe x is smaer than and the iteration has reached maximum number of iteration specified go to step #12. Otherwise, go to step #6 unti the end criteria are satisfied. 12) The partice that generates the atest gbest is the optima vaue. IV. HYBRID PARTICLE SWARM OPTIMIZATION The PSO agorithm has a weak seection process which very much depends on pbest and gbest, therefore, the searching area is imited by pbest and gbest. This eads to increase in the amount of time that it takes to get to the effective area in the soution space. The HPSO method has been introduced based on tournament seection method of GA, in order to improve the weakness of PSO method in this area. The introduction of the tournament seection mechanism in PSO agorithm, the effect of pbest and gbest is graduay eiminated by the seection which can resut in the wider search area. The purpose of the seection in evoutionary agorithm is to infuence the execution of the agorithm on a specific region of search space; usuay one that deivered promising soutions in the recent past. Partice positions with ow vaues are repaced by those with high vaues using the tournament seection method 30]. Therefore, the number of highy evauated partices is increased whie the number of owy evauated partices is reduced at each iteration. It shoud be mentioned that athough, the partice position is substituted by another partice position, the information reated to each partice is reserved. Therefore, the intensive search in a current effective area and dependence on the past high evauation position are reaized 30]. V. DISTRIBUTION SYSTEM STATE ESTIMATION BY HPSO This section presents the appication of the HPSO agorithm for soving the DSSE probem. The set of tasks invove. i A. Network Configuration and Network Data The presence of unsymmetrica-network components and unbaanced-oad on unbaanced distribution system makes it essentia to consider the exact mode of the system components three-phase mode). It incudes the information about ine resistance, reactance, tap setting connectivity information, etc. Therefore, the foowing provides information regarding three-phase mode of various components of the network such as ine, transformers and switches 36]. 1) Line Mode: The distribution overhead ines and underground cabes are three-, two-, or singe-phase and are most often untransposed serving unbaanced oads. In addition, since the votage drops due to the mutua couping of the ines is paying important part in the anaysis of the distribution network, it is important to compute the impedance of the overhead and underground ine segment as accurate as possibe. Therefore, it is necessary to retain the sef and mutua impedance terms of the conductors and take into account the ground return path for the unbaanced currents 37]. A modified Carson s equation has been appied to mode the overhead ines and underground cabes ) / 1 Z ii = r i j0.121 Ln mie GMR i 17) Z = j0.121 Ln 1 ) / mie 18) D where Z ii sef-impedance of conductor i in /mie; Z mutua impedance between conductors i and j in /mie; r i resistance of conductor i in /mie; GMR i geometric mean radius of conductor i in feet; D distance between conductors i and j in feet. Whie using the modified Carson s equations there is no need to make any assumptions, such as transposition of the ines. By assuming an untransposed ine and incuding the actua phasing of the ine and correct spacing between conductors, the most accurate vaues of the phase impedances, sef and mutua, are determined. Whie appying modified Carson s equations 17) and 18) to a three-phase overhead or underground circuit which consists of n phases and neutra conductors the resuting impedance matrix wi be n n. For most appications, it is necessary to have the 3 3 phase impedance matrix. Therefore, the foowing Kron s reduction is appied in order to breakdown the impedance matrix into the 3 3 phase frame matrix. In this approach, a the ines wi be modeed by 3 3 phase impedance matrix and for two- and singe-phase ines the missing phases are modeed by setting the impedance eement to zero 37] Z = Z Z in Z nj Z nn. 19) 2) Transformer Mode: The three-phase transformer banks are commony used in the distribution network and provide the fina votage transformation to the customers oad. The conventiona transformer modes based on a baanced

6 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. 6 IEEE TRANSACTIONS ON SMART GRID three-phase assumption can no onger be used when system is unbaanced. Three-phase transformers are modeed by an admittance matrix which depends on the connection type. The admittance matrix of a transformer is sub-divided into sub-matrices for both sef and mutua admittances between the primary and secondary. In the anaysis of the distribution feeder, it is required to mode the various three-phase transformer connections correcty. The comprehensive cacuations of three-phase transformers and their various connections can be found in 37]. 3) Switch Mode: Switches are modeed as branches with zero impedance when the switch is cosed or as branches with zero admittance when it is open. The operationa constraints imposed by the open or cosed status of the switching branches wi be as foows. 1) When the switch between buses i and j is cosed for branch i j, the votages and anges for buses i and j for a the three phases are equa V i V j = 0 δ i δ j = 0. 2) When the switch is open between buses i and j, the active and reactive power fow to the switch wi be zero P = 0 Q = 0. These have been incuded as equaity constraints in the SE formuation and a weighted quadratic penaty function defined in 16) is appied to sove the above equaity constraint probem in which a penaty factor is added to the objective function moment any constraint vioation occurs. 4) Load Mode: The oads on distribution network are generay unbaanced and can be connected in a grounded wye configuration or an ungrounded deta configuration. It is aso possibe to have three-, two-, or singe-phase oads with varying degree of unbaance. The oads are commony indicated by compex power consumed per phase and supposed to be ine-to-neutra for wye oad and ine-to-ine for deta oad 37]. In this paper, oads are modeed as constant impedance, constant current and constant compex power or any combination of the three. Typicay, the oad vaues are given as nomina power deivered to the oad and must be converted into the appropriate constant mode parameters. The genera form of ZIP mode is as foows 38]: V P L = P n c P 1 + cp 2 V n Q L = Q n c Q V 1 + cq 2 V n ) V + c P 3 ) + c Q 3 ) ] 2 20) V n ] V 2. 21) The two- and singe-phase oads are modeed by setting the vaues of the compex power to zero for the nonexistent phases for both wye and deta connected oads 37]. V n Fig. 1. Setting up of HPSO. B. Power Fow Cacuation Three-phase power fow program suitabe for distribution system has been set up with network information and oad data to generate measurement data as an input to the state estimator. The normay distributed noise component has been added to these measurements to produce input for state estimator. Usuay, 1% 3% error is associated with true measurements whie the error for pseudo measurements oad data) is considered to vary between 20% and 50%. C. State Estimation Based on HPSO Agorithm The foowing steps have been foowed to estimate the state by HPSO estimator. 1) Set up a set of HPSOs parameters such as number of partices N, weighting function W, acceeration coefficients C 1 and C 2, and maximum number of iterations. 2) Generate an initia popuation of the state variabes V, δ, and t) with random veocities and positions in the soution space. 3) Set upper and ower imits for state variabes V, δ, and t).

7 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. NANCHIAN et a.: THREE-PHASE SE USING HPSO 7 Fig. 4. Proposed penaty function. Fig. 2. IEEE 13-bus distribution system. Fig. 5. True and estimated phase votage a for IEEE 13 bus system. Fig. 3. IEEE 123-bus distribution system. 4) For each state variabe, if the variabe is within the set imits, go to the foowing step. Otherwise, that variabe is infeasibe. 5) The state has been cacuated based on the minimization between measurements and cacuated vaue based on HPSO agorithm. Fig. 1 iustrates the DSSE using HPSO agorithm. VI. RESULTS AND DISCUSSION A. Case Studies The proposed modified HPSO approach was impemented in MATLAB by Inte Xeon processor at 2.40 GHz with 12.0 GB of RAM and has been tested on IEEE 13- and 123-bus test systems to vaidate the proposed agorithms. The network parameters and oad data are obtained from 39] and 40]. The topoogies of the test systems are shown in Figs. 2 and 3. The systems consist of both overhead ines and underground cabes. The overhead ines and underground cabes have been modeed with modified Carson s equations. There are both three- and singe-phase oads. The three-phase oads are either star or deta connected. The oads in the system have been modeed in ZIP-mode. A three-phase transformer is modeed as three individua singe-phase transformers. Measurements were generated using three-phase power fow program with addition of normay distributed noise component to generate noisy measurements. The error of true measurement was assumed 3% whie the error in pseudomeasurement oad data) was considered 20%. Severa trias are performed for appropriate parameter vaue seection. Appropriate combination of W ini, W fin, C 1, C 2 have been appied. The foowing vaues have been chosen for HPSO estimator; W ini = 0.9, W fin = 0.4, C 1 = C 2 = The vaues are very cose to those recommended by Naka et a. 31] and van den Bergh 34]. In order to choose the best vaue for apha, the agorithm was run for different vaues of apha between 0 and 1 in step of 0.1 in order to obtain the vaue with the east convergence time. It is found that α = 0.2 produces the best convergence speed for this exampe system. The number of partices and the number of iterations are 200 and 1000, respectivey. The ower and upper imits of contro variabes corresponding to the coding on the HPSO is set in such a way that the inequaity constraints of the contro variabes are satisfied as isted in 22a). The shape of the proposed penaty function is dispayed in Fig p.u. Vi a, Vb i, Vc i 1.05 p.u. 22a) 30 δi a, δb i, δc i b) 0.9 ti a, tb i, tc i c) The tap ratio of transformer is specified in the range of in steps of The zero injections, votages, and anges across the cosed switch and votage at the reguator bus have been taken as equaity constraints in the SE formuation. A weighted quadratic penaty function is added to the objective function to take care of each of these equaity constraints. The switch between buses 9 and 10 is assumed to be cosed for 13-bus test system. Figs. 5 7 show the rea and estimated vector of votages and Tabe I shows the rea and estimated vector of anges at different phases of the IEEE 13-bus mode

8 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. 8 IEEE TRANSACTIONS ON SMART GRID Fig. 6. True and estimated phase votage b for IEEE 13 bus system. Fig. 8. True and estimated phase votage a for IEEE 123 bus system. Fig. 9. True and estimated phase votage b for IEEE 123 bus system. Fig. 7. True and estimated phase votage c for IEEE 13 bus system. TABLE I TRUE AND ESTIMATED ANGLE Fig. 10. True and estimated phase votage c for IEEE 123 bus system. TABLE II TRUE AND ESTIMATED TAP POSITION FOR 13-BUS SYSTEM AT BUS 6 distribution network. There are five switches in the 123-bus system. The switch between buses 121 and 123 is assumed to be open whie other switches are assumed to be cosed for this network. Figs show the rea and estimated vector of votages of the IEEE 123-bus mode distribution network. In Figs. 5 10, the vaue of votage has been taken as 1 where there is no phase avaiabe for the given bus on the graphs. Aso, in Tabe I, the dashes show that there is no phase avaiabe for the given bus. The obtained resuts are found to be very satisfactory within the aowabe error range. The main advantage of the HPSO-based method is in correct estimation of the transformer taps as it is shown in Tabe II for 13-bus test system and Tabe III for 123-bus system, which is the most important findings from this research reported here. TABLE III TRUE AND ESTIMATED TAP POSITION FOR 123-BUS SYSTEM B. Discussions We have appied both PSO and HPSO to obtain tap position estimates. Both methods have been tested on IEEE 13- and 123-bus test systems. PSO takes on an average of 6 7 h to

9 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. NANCHIAN et a.: THREE-PHASE SE USING HPSO 9 Fig. 11. True and estimated phase votage a for reduced mode of IEEE 123 bus system. Fig. 13. True and estimated phase votage b for reduced mode of IEEE 123 bus system. Fig. 12. Convergence characteristic of HPSO and PSO. obtain the soution on 13-bus test system. We have modified the partice position update equation for improving the speed of convergence as given in 14). Therefore, the execution time reduced to 2 3 h. HPSO on the other hand takes min to converge for 13-bus test system. The convergence characteristic of HPSO and improved PSO with correction are shown in Fig. 12 for 13-bus test system. As can be seen from convergence characteristic, HPSO method is much faster than PSO method. In the idea smart grid environment in principe the state estimator in distribution system shoud be running in rea time. There are severa practica imitations to reaize this in practice. Even the data from modern smart meters are communicated to distribution SCADA every few hours. The most automated distribution network in the U.K. does not transmit data more than twice a day. The teecommunication infrastructure in most automated distribution network is such that it is not possibe to transmit haf houry measured and stored smart meter data more than twice a day to the contro center. Samarakoon et a. 41] have documented in detais the standard and practice of data transmission from smart meters in various countries across the word. Given this situation, one obvious question arises: is there any possibiity for rea time SE in power distribution system in the forcibe future? The frequency of tap operation is aso another practica consideration. Considering the operating ife of transformer, after 3000 operations, it requires maintenance and after operations the Fig. 14. True and estimated phase votage c for reduced mode of IEEE 123 bus system. transformer tap changing mechanism shoud be repaced with a new one. In that case changing the tap position every few seconds wi damagingy resut in shortening the transformer operating ife. So it is convincing that unike transmission system the SE in distribution system wi not run every 2 5 s. Aso, the HPSO method with correction for improving the speed has been appied to IEEE 123-bus test system mode. It takes on an average of 4 h to obtain the soution. However, by identifying and considering ony those buses where votage and anges are affected significanty by changing the tap changer position the execution time has reduced to 90 min as a resut of the reduction in the number of state variabes. Those buses have been encosed through a dashed ine in Fig. 3 and the resuts are shown in Figs. 11, 13, and 14. Oneway to improve the speed of convergence of HPSO is to paraeize the agorithm. In the context of computation in power

10 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. 10 IEEE TRANSACTIONS ON SMART GRID the computed network osses are noticeaby different which is very usefu outcome of this proposed methodoogy. Fig. 15. Fig. 16. KW osses for HPSO and WLS. KVAr osses for HPSO and WLS. transmission, it has been expored to obtain improvement in speed of computation. Jeong et a. 42] have achieved 4.8 times faster than norma PSO for transmission system SE. Because of the simiarity of the structure of the equations and between the inter-reationship between variabes it is possibe to achieve simiar resuts based on the appication of parae PSO for the given network in this paper. This is not pursued further because of the ack of access to parae computing custer. The comparison of the resuts of tap estimation from WLS and HPSO reveas that estimation of the continuous vaues of tap changer may resut in an inaccurate tap position since it is based on the rounding technique whie HPSO provides the exact position of transformer taps by estimating the discrete vaues of transformer tap positions. So HPSO output provides more accurate votage and ange estimates thus heps in obtaining better estimate of ine and transformer oading and osses. This is very usefu in dynamic price setting for efficient eectricity market operation and aso for optimum scheduing of votage and var contro VVC) resources. The power osses in the ines for 123 node system have been computed and the resuts are shown in Figs. 15 and 16. It is ceary seen that HPSO-based technique provides more accurate oss figures. Given the customer has to bear the cost of the osses HPSO-based estimated votage and anges and tap positions when used to cacuate operationa osses for pricing, they wi resut in more fairer vaue. This ceary justifies the novety and benefit of this research contribution. One network operator Scottish and Southern Energy) in the U.K. has aready found this approach usefu for network oss cacuation in their 33/11 kv network. Compared to WLS-based approach VII. CONCLUSION The technique proposed in this paper has addressed the transformer taps estimation in the context of distribution SE. It has, for the first time, appied HPSO method to estimate transformer tap positions without any assumption and aso in unbaanced three-phase distribution system. The simuation resuts on IEEE 13- and 123-bus standard system modes showed that the HPSO method can generate reiabe estimate for transformer taps with discrete variabes in distribution network whie minimizing the objective function. It is aso demonstrated that it performs better when compared to PSO. This paper aso contributes to nove strategies to expedite soution from PSO and HPSO. The soution from HPSO is accurate and is very usefu for computation of various quantities accuratey used in the operationa panning time scae, i.e., VVC and pricing in short term market. Moreover, operationa osses from HPSO is much accurate in this case ower than WLS method. In that sense this method is better than WLS method as it provides higher accuracy. Such ower osses wi hep owering the overa cost of eectricity. In a distribution network where about 6% of eectricity generated is ost, accurate estimation of that has huge technica and commercia benefits. The technique proposed in this paper definitey wi hep to reaize those benefits. No gross error is assumed in tap measurement, the tap position measured can be corrupted whie being teemetered. A further work continues for bad tap error detection in a arge practica power distribution network mode. Aso, our immediate future pan is to expore mixed integer noninear optimization sover for distribution SE probem. REFERENCES 1] O. Asac, N. Vempati, B. Stott, and A. Monticei, Generaized state estimation power systems], in Proc. 20th Int. Conf. Power Ind. Comput. App., Coumbus, OH, USA, May 1997, pp ] T.-H. Chen, M.-S. Chen, T. Inoue, P. Kotas, and E. Chebi, Three-phase cogenerator and transformer modes for distribution system anaysis, IEEE Trans. Power De., vo. 6, no. 4, pp , Oct ] I. Royteman and S. Shahidehpour, State estimation for eectric power distribution systems in quasi rea-time conditions, IEEE Trans. Power De., vo. 8, no. 4, pp , Oct ] A. S. Meiopouos and F. Zhang, Mutiphase power fow and state estimation for power distribution systems, IEEE Trans. Power Syst., vo. 11, no. 2, pp , May ] K. Li, State estimation for power distribution system and measurement impacts, IEEE Trans. Power Syst., vo. 11, no. 2, pp , May ] C. Lu, J. Teng, and W.-H. Liu, Distribution system state estimation, IEEE Trans. Power Syst., vo. 10, no. 1, pp , Feb ] M. Baran and A. Keey, State estimation for rea-time monitoring of distribution systems, IEEE Trans. Power Syst., vo. 9, no. 3, pp , Aug ] H. Wang and N. Schuz, A revised branch current-based distribution system state estimation agorithm and meter pacement impact, IEEE Trans. Power Syst., vo. 19, no. 1, pp , Feb ] C. Hansen and A. Debs, Power system state estimation using threephase modes, IEEE Trans. Power Syst., vo. 10, no. 2, pp , May ] A. Rankovi, B. M. Maksimovi, and A. T. Sari, A three-phase state estimation in active distribution networks, Int. J. Eect. Power Energy Syst., vo. 54, pp , Jan

11 This artice has been accepted for incusion in a future issue of this journa. Content is fina as presented, with the exception of pagination. NANCHIAN et a.: THREE-PHASE SE USING HPSO 11 11] C. Muscas, S. Suis, A. Angioni, F. Ponci, and A. Monti, Impact of different uncertainty sources on a three-phase state estimator for distribution networks, IEEE Trans. Instrum. Meas., vo. 63, no. 9, pp , Sep ] P. P. Barbeiro, H. Teixeira, J. Krstuovic, J. Pereira, and F. Soares, Expoiting autoencoders for three-phase state estimation in unbaanced distributions grids, Eect. Power Syst. Res., vo. 123, pp , Jun ] A. Meiopouos, B. Fardanesh, and S. Zeingher, Power system state estimation: Modeing error effects and impact on system operation, in Proc. 34th Annu. Hawaii Int. Conf. Syst. Sci., Maui, HI, USA, Jan. 2001, pp ] S. Zhong and A. Abur, Effects of nontransposed ines and unbaanced oads on state estimation, in Proc. IEEE Power Eng. Soc. Winter Meeting, vo. 2. New York, NY, USA, 2002, pp ] D. Haughton and G. Heydt, A inear state estimation formuation for smart distribution systems, IEEE Trans. Power Syst., vo. 28, no. 2, pp , May ] D. Thukaram, J. Jerome, and C. Surapong, A robust three-phase state estimation agorithm for distribution networks, Eect. Power Syst. Res., vo. 55, no. 3, pp , ] M. F. M. Júnior, M. A. Ameida, M. C. Cruz, R. V. Monteiro, and A. B. Oiveira, A three-phase agorithm for state estimation in power distribution feeders based on the powers summation oad fow method, Eect. Power Syst. Res., vo. 123, pp , Jun ] I. Dzafic, D. Abakovic, and S. Hensemeyer, Rea-time three-phase state estimation for radia distribution networks, in Proc. IEEE Power Energy Soc. Gen. Meeting, San Diego, CA, USA, Ju. 2012, pp ] R. Pires, L. Mii, and F. Lemos, Constrained robust estimation of power system state variabes and transformer tap positions under erroneous zero-injections, IEEE Trans. Power Syst., vo. 29, no. 3, pp , May ] M. Shiroie and S. Hosseini, Observabiity and estimation of transformer tap setting with minima PMU pacement, in Proc. IEEE Power Energy Soc. Gen. Meeting Convers. De. Eect. Energy 21st Century, Pittsburgh, PA, USA, Ju. 2008, pp ] S. Wang, X. Cui, Z. Li, and M. Shahidehpour, An improved branch current-based three-phase state estimation agorithm for distribution systems with DGs, in Proc. IEEE Innov. Smart Grid Techno. Asia ISGT Asia), Tianjin, China, May 2012, pp ] A. Abur and A. Gomez-Exposito, Power System State Estimation: Theory and Impementation. New York, NY, USA: Marce Dekker, ] Y. Fukuyama, State estimation and optima setting of votage reguator in distribution systems, in Proc. IEEE Power Eng. Soc. Winter Meeting, vo. 2. Coumbus, OH, USA, 2001, pp ] P. Teixeira, S. R. Brammer, W. L. Rutz, W. C. Merritt, and J. L. Samonsen, State estimation of votage and phase-shift transformer tap settings, in Proc. Conf. Power Ind. Comput. App. Conf., Batimore, MD, USA, May 1991, pp ] G. Korres, P. J. Katsikas, and G. C. Contaxis, Transformer tap setting observabiity in state estimation, IEEE Trans. Power Syst., vo.19,no.2, pp , May ] H. Maaouf, R. A. Jabra, and M. Awada, Mixed-integer quadratic programming based rounding technique for power system state estimation with discrete and continuous variabes, Eect. Power Compon. Syst., vo. 41, no. 5, pp , ] M. Liu, S. K. Tso, and Y. Cheng, An extended noninear prima-dua interior-point agorithm for reactive-power optimization of arge-scae power systems with discrete contro variabes, IEEE Trans. Power Syst., vo. 17, no. 4, pp , Nov ] A. Arefi, M. R. Haghifam, and S. H. Fathi, Distribution harmonic state estimation based on a modified PSO considering parameters uncertainty, in Proc. IEEE Trondheim PowerTech, Trondheim, Norway, Jun. 2011, pp ] K. Lee and J. Park, Appication of partice swarm optimization to economic dispatch probem: Advantages and disadvantages, in Proc. IEEE PES Power Syst. Conf. Expo. PSCE), Atanta, GA, USA, Oct. 2006, pp ] P. Angeine, Using seection to improve partice swarm optimization, in Proc. IEEE Int. Conf. Evo. Comput. Proc. IEEE Word Congr. Comput. Inte., Anchorage, AK, USA, May 1998, pp ] S. Naka, T. Genji, T. Yura, and Y. Fukuyama, A hybrid partice swarm optimization for distribution state estimation, IEEE Trans. Power Syst., vo. 18, no. 1, pp , Feb ] M. R. ARashidi, M. F. AHajri, and M. E. E-Hawary, Enhanced partice swarm optimization approach for soving the non-convex optima power fow, Word Acad. Sci. Eng. Techno., vo. 4, no. 2, pp , ] J. Kennedy and R. Eberhart, Partice swarm optimization, in Proc. IEEE Int. Conf. Neura Netw., vo. 4. Perth, WA, Austraia, Nov. 1995, pp ] F. van den Bergh, An anaysis of partice swarm optimizers, Ph.D. dissertation, Dept. Comput. Sci., Univ. Pretoria, Pretoria, South Africa, Nov ] Y. Shi and R. Eberhart, A modified partice swarm optimizer, in Proc. IEEE Int. Conf. Evo. Comput. Word Congr. Comput. Inte., Anchorage, AK, USA, May 1998, pp ] A.-R. Ghasemi, R. Ebrahimi, A. Babaee, and M. Hoseynpoor, A modified Newton Raphson agorithm of three-phase power fow anaysis in unsymmetrica distribution networks with distributed generation, J. Basic App. Sci. Res., vo. 3, no. 9, pp , Sep ] W. H. Kersting, Distribution System Modeing and Anaysis. Boca Raton, FL, USA: CRC Press, ] K. Wang et a., Research on time-sharing ZIP oad modeing based on inear BP network, in Proc. 5th Int. Conf. Inte. Human Mach. Syst. Cybern. IHMSC), vo. 1. Hangzhou, China, pp , Aug ] W. Kersting, Radia distribution test feeders, in Proc. IEEE Power Eng. Soc. Winter Meeting, vo. 2. Coumbus, OH, USA, 2001, pp ] W. H. Kersting, Radia distribution test feeders, IEEE PES Distrib. Syst. Ana. Subcommit., Tech. Rep. 975, ] K. Samarakoon, J. Wu, J. Ekanayake, and N. Jenkins, Use of deayed smart meter measurements for distribution state estimation, in Proc. IEEE Power Energy Soc. Gen. Meeting, San Diego, CA, USA, Ju. 2011, pp ] H.-M. Jeong, H.-S. Lee, and J.-H. Park, Appication of parae partice swarm optimization on power system state estimation, in Proc. Asia Pac. Transmiss. Distrib. Conf. Expo., Oct. 2009, pp Sara Nanchian S 12) received the M.Sc. degree in eectrica power engineering from the University of Manchester, Manchester, U.K., in She is currenty pursuing the Ph.D. degree with the Department of Eectrica and Eectronic Engineering, Imperia Coege London, London, U.K. Her current research interests incude state estimation for active distribution network. Ankur Majumdar S 12) received the B.E.E. Hons.) degree in eectrica engineering from Jadavpur University, Kokata, India, in 2009, and the M.Tech. degree in eectric power systems from the Indian Institute of Technoogy Dehi, New Dehi, India, in He is currenty pursuing the Ph.D. degree with the Department of Eectrica and Eectronic Engineering, Imperia Coege London, London, U.K. He is currenty a Research Assistant with the Department of Eectrica and Eectronic Engineering, Imperia Coege London. His current research interests incude state estimation, smart grid security, and power system anaysis. Bikash C. Pa M 00 SM 02 F 13) received the B.E.E. Hons.) degree from Jadavpur University, Kokata, India, in 1990; the M.E. degree from the Indian Institute of Science, Bengauru, India, in 1992; and the Ph.D. degree from Imperia Coege London, London, U.K, in 1999, a in eectrica engineering. He is currenty a Professor with the Department of Eectrica and Eectronic Engineering, Imperia Coege London. His current research interests incude state estimation, power system dynamics, and fexibe ac transmission system controers. Dr. Pa is the Editor-in-Chief of the IEEE TRANSACTIONS ON SUSTAINABLE ENERGY.