Abstract
A computer algorithm for optimal voltage controlwith voltage regulators, suitable for large radial distribution networksis given in this paper. An objective function concerning thetotal cost of the voltage regulators (investment and maintenancecost) as well as the cost of losses of the examined networks is developedand constitutes the base of the algorithm. This algorithmmakes the initial selection, installation and tap setting of the voltageregulators, which provide a smooth voltage profile along the network,utilizing former algorithms suitably modified and optimized.Then it attempts to minimize the number of the initially selectedvoltage regulators as much as possible, by moving them in sucha way as to control the network voltage at the minimum possiblecost (maximization of the objective function). The algorithm is fast,efficient and reliable as its application to practical distribution networksshows.
Index Terms—Radial primary distribution networks, Voltagecontrol, Voltage regulators, Cost minimization.
I. INTRODUCTION
IF THE reinforcement of a network were required becauseof excessive voltage drop, any such reinforcement could bedeferred if the voltage drop could be sufficiently reduced bysome means, subject to economic as well as technical considerations.Various devices such as capacitors and voltage regulators(VR’s) can be installed to reduce the voltage drop, experiencedat critical points of medium voltage networks. Conductorreplacements at network segments can also be used to maintainthe voltage along the entire network.The papers [1], [2] propose reconductoring of currentlyoperating primary distribution networks in order to optimizethem technically as much as possible defraying the minimumcost. Representative papers dealing with the optimization ofmedium voltage networks operation by selecting (kind andsize), installing and controlling the appropriate number of capacitors,are [3]–[10]. Fewer papers deal with the determinationof the optimal locations and real-time control (tap positions)of a minimum VR number, in order to minimize the peakpower and energy losses and provide a smooth voltage profilealong a distribution network with lateral branches, under timevarying conditions. Recent papers of this kind are [3], [4], [5],[6]. Specifically an integrated method for the optimal reactivepower and voltage control of radial distribution networks byusing capacitors and VR’s is given in [3], [4], [5], which areparts of a complete study, as well as in [6]. All these papersdecouple the capacitor problem from the VR problem and propose VR’s for a network completely compensated withcapacitors.The network voltage is the criterion for the selection of theoptimal VR number, locations and tap positions in [3], [4], [5].An economic function, which estimates the power and energylosses, is given in retrospect but this function is not utilizedduring the main problem-solving process concerning the optimumVR placement and installation. The power flow at thenetwork segments is calculated by an approximate method (V-Pmodel, [11]).In [6], the voltage regulation is initially attempted bychanging the tap positions at the substation and solving againthe capacitor problem. If the desirable voltage regulation isnot achieved in this way, a VR is placed at the main feeder,next to the node where the subfeeder with the heaviest load isconnected and then the proper tap position of this VR is determined.Sometimes VR’s are placed at very long subfeedersto improve their voltage profile. Consequently in this paperthe VR positions are in a way predetermined and they are notindicated by the method.The present paper utilizes the basic philosophy of the algorithmof [3], [4], [5] only with regard to the initial VR selection,placement and tap setting. But even in this stage it differentiatesthe method of the above papers by calculating the currentsat the network segments by load flow analysis instead of an approximatemethod as these papers do. After the determination ofthe initial VR number and locations the optimization proceduredoes not finish in opposition to [3], [4], [5], because it is truethat the resultant solution solves the problem of the excessivevoltage drop technically but it is not surely the most economicalone. For this reason an objective function is developed inthe context of this paper, which includes the VR total cost andthe cost of losses of the examined network (evaluating the powerlosses for the peak load and the energy losses according to an approximateannual load curve consisting of twelve distinct meanmonthly load values). Based on this function a procedure investigatingthe possible reduction of the number of the initiallyselected VR’s is evolved so as the finally proposed solution willbe the most economical one.The application of the proposed method to a great number ofpractical radial primary distribution networks has proved thatthere are no restrictions according to the size of the examinednetworks as the method is easy to use, very fast and efficient.


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