220kv降壓變電所電氣一次系統(tǒng)設(shè)計(jì)275

220kv降壓變電所電氣一次系統(tǒng)設(shè)計(jì)275,kv,降壓,變電所,電氣,一次,系統(tǒng),設(shè)計(jì) for involves using linear functions to express the total cost function The developed model includes di erent electrical constraints such as voltage drops substation and transformer capacities power flow and radial flow constraints The proposed planning problem is formu lated as a Mixed Integer Linear Programming MILP problem to avoid the use of nonlinear programming and thus avoiding the pos is because it represents the main link between transmission system planning process 20 consider it a stage in distri stations equipment installation timing The site selection in Fig 1 The substation size and the service area are usu ally determined based on electrical considerations and con straints such as equipment capacities and feeders voltage drop constraints 1 2 Several distribution planning models have been devel oped that can be divided into four main categories 3 4 Corresponding author Tel 519 888 4567x7061 fax 519 746 3077 E mail address telfouly hivolt uwaterloo ca T H M El Fouly Available online at Electrical Power and Energy Systems and distribution system The available sites and sizes of substations result in definite constraints on both transmis sion and distribution systems planning process and thus substations design parameters have a great impact on feed ers routing Substations usually set limits on the overall economics of the distribution system planning although their cost represents a relatively small part of the total cost of distribution system Substations are the most involved component of distribution system when it comes to the planning of the system This stage is considered by 60 of utility planners as one of the stages in the transmission of the substation is not entirely based on electrical consid eration City plans and environmental restrictions are usu ally the main determining factors in this process In the best scenario the city will provide the planner with a set of available sites candidate sites to choose from It is possi ble that none of these sites will meet the optimal solution However the planner has to select the second best site In general the substation site selection process is considered as a screening process through which all possible site loca tions are investigated and classified into unsuitable candi date and future evaluation sites This process is illustrated sibility of getting trapped in local solutions A numerical example is presented to validate the e ectiveness of the developed model C211 2007 Elsevier Ltd All rights reserved Keywords Distribution system planning Distribution substation Optimization Radial distribution systems 1 Introduction Distribution substation planning is considered the most important step in the power system planning process This bution system planning while the rest 20 deals with it as a separate process 1 2 Substation planning involves substation site selection substation size and service areas determination and sub A new optimization model siting sizing T H M El Fouly a H H Zeineldin b a Department of Electrical and Computer Engineering University of Waterloo b Masdar Institute of Science and Technology P O Received 24 August 2006 received in revised form Abstract This paper presents a new planning optimization model for distribution 0142 0615 see front matter C211 2007 Elsevier Ltd All rights reserved doi 10 1016 j ijepes 2007 10 002 distribution substation and timing E F El Saadany a M M A Salama a 200 University Avenue West Waterloo Ontario Canada N2L 3G1 Box 45005 Abu Dhabi United Arab Emirates 4 September 2007 accepted 22 October 2007 substation siting sizing and timing The proposed model 30 2008 308 315 and Static Load Subsystem Models Determine the size and the location of either the distribution substation or pri mary feeders Static Load Total System Models Determine the opti mal substation location and size network routing load transfer among stations and feeders sizes Dynamic Load Subsystem Models Determine the size the location and timing of installing substations and its equipment or the optimal feeders routings Dynamic Load Total System Models Determine the size the location and the timing of installation of the distribution substations and primary feeders In 5 an approach to determine the sizing and timing of substations was proposed In this approach sizing and tim ing were e ectively decoupled by using the Pseudo Dynamic approach This approach requires sequential applications of the single time period static planning model Moreover in the proposed algorithm the question Fig 1 Substation siting selection process T H M El Fouly et al Electrical Power of whether or not to construct a substation is based com pletely on voltage drop considerations The major draw back of this method is that voltage forecasts which decide the possibility of constructing a substation are based on the assumption that load densities are uniform within a substation service area This is not true for most practical cases Moreover this model did not take into con sideration the equipment locations In 6 a transportation approach for solving the substation location sizing and service area problem was developed This approach assumed that the total demand is equal to the total supply and the objective was to determine a feasible flow pattern that minimizes the total transportation cost while satisfy ing all demands This approach did not include the equip ment costs in its objective function and also modeled all existing and potential substations as source nodes which leads to an optimal solution with all substations being uti lized even though some of them serve only a small amount of load Moreover this method did not consider any con straints such as voltage constraints in its solution In addi tion no voltage drop calculations were included In 7 a fixed charge transshipment model for the problem of choosing an optimal substation location was developed The objective function of the developed model included both the fixed and the variable cost components and was solved using an integer branch and bound technique However this developed model was a static model it did not consider any variation in the demands with time Moreover it did not include any constraints for voltage limits A fixed charge transshipment network procedure to solve the multi period distribution system planning problem was suggested 8 This technique was used for optimal distribution substation and primary feeders plan ning However this technique did not include any con straints for voltage limits In 9 and 10 a Heuristic Combinational Optimization algorithm was proposed to determine the optimum required substations capacities and then a Multi source Locating algorithm is used to allocate the substations by minimizing the cost of energy losses on the feeders This procedure does not require the selection of candidate sub station locations In 11 an adaptive mutation particle swarm optimization algorithm was developed to solve for the optimal substation location and sizing This approach does not require candidate substation location and it takes into account both the substation construction investment and the geographic information system GIS An optimal substation service area and feeder routing method based on minimum feeder loss was developed 12 In this method a GIS with distribution data base computer graphics and the minimal path and the load switch pattern algorithm were integrated to solve the planning problem The mini mal path algorithm was used to redistribute the load points Load between two switched were lumped and assigned to the switch at the farther end from the main transformer The load switch pattern was used to connect the feeder paths for the substation and to distribute the load points Constraints such as flow limits power flow and network radiations were taken into account Another substation expansion planning procedure was developed 13 It proposed a mathematical clustering technique to determine the feasible candidates while considering the substation capacities feeder capacities and voltage regula tions limitations After that a genetic algorithm is used to solve the optimization problem for expansion requirements for existing substations and new substation allocations and capacities determination These aforementioned proce dures 9 13 did not include any constraints for voltage lim its Moreover the problem formulations did not consider a time varying demand In 14 a probabilistic methodology for distribution sub station location selection was presented This methodology took into account the hourly or daily load cycle For dif ferent hourly load scenarios the load center locations are determined and weighted according to their load magni Energy Systems 30 2008 308 315 309 tude These locations are then used to develop a probability distribution that is used in determining the maximum prob ability perimeter of the area where the substation should be located The process also takes into account factors such as land availability and the cost of land A model developed non discrete functions for distribution substation sizing sitting and timing taking into account the di erent compo nents for the substations cost function and various con straints including voltage power flow radial flow and capacities constraints was presented 15 Moreover the model considered a time varying demand for the sectors under investigation However the main drawback in this model is that the optimization process is carried out for each planning interval independent on the results obtained for previous intervals This results in some feeders being installed at earlier periods then removed latter with new kWh The interest tax inflation and insurance rates are considered to be equal to 10 10 6 and 1 respec tively Transformer units are allowed to be loaded to 75 of its rated value It is also assumed that the maximum allowable voltage drop along each feeder is 275 V 2 5 of the system nominal voltage which is set to be 11 kV The transformer copper loss at rated power is assumed to be 127 kW 15 Nine feeders are available for each substa tion total available feeders are 27 feeders and each feeder is assumed to supply the sector demand directly without intermediate points as given in Table 3 This table also Table 1 Sector demands over studied periods D p n MVA Interval n Sector p 123456789 1 2 21 51 41 416 2 3 44 3 52 5547 3 5 55 4 53 757 4 6 66 4 553 767 5 7 67 5 53 767 Table 2 Table 3 Feeders variables and their available routes Variable Route sector number Variable Route sector number Variable Route sector number From To From To From To X 1 41X 10 61X 19 21 X 2 42X 11 62X 20 22 X 3 43X 12 63X 21 23 X 4 44X 13 64X 22 24 X 5 45X 14 65X 23 25 X 6 46X 15 66X 24 26 X 7 47X 16 67X 25 27 310 T H M El Fouly et al Electrical Power and Energy Systems 30 2008 308 315 feeders installed in the next periods which is practically infeasible Moreover the problem was formulated as a Mixed Integer Nonlinear Programming MINLP which could result in local optimal solutions due to nonlinearity This paper addresses these drawbacks This paper is organized as follows Section 2 presents the system under study The proposed problem formulation for the distribution substation siting sizing and timing optimization model is presented in Section 3 The proposed problem formulation was modeled and solved using the General Algebraic Modeling Software GAMS solvers 16 In Section 4 the results generated from the proposed optimization model are presented A modified problem for mulation to ensure preventing ine cient transmission of power is discussed in Section 5 This section also presents the generated results from the modified formulation Finally in Section 6 conclusions are presented 2 System under study The service area under investigation consists of 9 sectors as shown in Fig 2 The area of each sector is 0 44 km 2 and it is assumed that the proposed sectors for substation installation by the city are sectors 2 4 and 6 The planning period is set to be 10 years divided into 5 time intervals of 2 years each The sectors demand growth over the 10 year planning period 5 intervals is given in Table 1 15 Each Fig 2 Area under study indicating the proposed substation sites by the city substation is rated at 40 MVA and can be equipped with a maximum of two transformer units each rated at 20 MVA The units ratings proposed locations and assigned vari ables are given in details in Table 2 The substation fixed cost is assumed to be 200 000 while the transformer unit installation cost is assumed to be 150 and the cost of energy is assumed to be 0 17 Proposed units capacities and variables Unit number m Type Rating MVA Location Variable 1 Substation 40 Sector 4 xx 1 n 2 Substation 40 Sector 6 xx 2 n 3 Substation 40 Sector 2 xx 3 n 4 Transformer 20 Sector 4 xx 4 n 5 Transformer 20 Sector 4 xx 5 n 6 Transformer 20 Sector 6 xx 6 n 7 Transformer 20 Sector 6 xx 7 n 8 Transformer 20 Sector 2 xx 8 n 9 Transformer 20 Sector 2 xx 9 n X 8 48X 17 68X 26 28 X 9 49 18 69X 27 29 and presents the assigned variable for each available feeder and its available route 3 Problem formulation When planning to install a distribution system substa tion and its components the main objective is to minimize the overall cost of equipment installation and energy losses This cost depends on factors such as substation siting tim ing of equipment installation and equipment transformer loading Regarding the substation siting increasing the number of installed substations or improper proposed site selection could greatly increase the overall system cost Interest rates inflation rates taxes and insurance rates impact the timing of installation of equipment and hence the overall cost is a ected Since the amount of energy loss is dependent on the equipment loading an increase in load ing level will result in an increase in the overall cost More over previous planning models based on a one interval period could result in an impractical solution such as installing a feeder in an earlier period and then removing it in a latter period 15 In such cases human expertise is required to eliminate these impractical solutions To take into account all these factors the paper proposes a new problem formulation that minimizes the overall cost The problem was formulated over the whole planning period to avoid the necessity of human expertise and to accom plish the following targets 1 Determining the optimal time of equipment installation 2 Adequately determine the siting and sizing of the substations The main objective over the whole planning horizon can be written as follows cost X q n 1 R n b n C S1 C1 S 1 n C S2 C1 S 2 n C S3 C1 S 3 n C T11 C1 S 4 n C T12 C1 S 5 n C T21 C1 S 6 n C T22 C1 S 7 n C T31 C1 S 8 n C T32 C1 S 9 n C138 8760 C1 P cu C1 C H Tr C1 X 9 i 4 x i n 1 where q is equal to the number of design intervals within the 10 year planning period and is set equal to 5 Thus a two year period is chosen for each design interval to pro vide su cient time for equipment installation C S1 C S2 and C S3 are the fixed cost for substations 1 2 and 3 respectively C T11 C T12 are the cost of the two transformer units to be installed at substation 1 including the cost of the iron losses C T21 C T22 are the cost of the two trans former units to be installed at substation 2 including the cost of the iron losses C T31 C T32 are the cost of the two transformer units to be installed at substation 3 including T H M El Fouly et al Electrical Power the cost of the iron losses S i n is a binary variable indicat ing the installation of unit i at a given period n P cu is the transformer copper loss at rated power kW C is the cost of energy kWh H Tr is the transformer unit rating MVA x i n is the power delivered from unit transformer i at a given period n if this unit transformer is installed and it is set to zero if the unit transformer is not installed R n and b n are the fixed charge rate and the present worth factor for a given interval n respectively and are calculated as follows R n i t r r 1 r 2 q 1C0n C0 1 8 n where n 1 q 2 b n f C0 r 1 f 1 r C16C17 2 q 1C0n C0 1 C18C198 where n 1 q 3 where r t f i are the interest tax inflation and insurance rates respectively In this formulation transformers power losses are calcu lated as a percentage of the transformer loading This per centage is assumed equal to the ratio of the transformer copper loss at rated power P cu to the transformer unit rat ing H Tr The objective function is minimized subject to the following constraints 3 1 Additional constraints to overcome nonlinearity A decision variable y i n is used to determine whether or not a transformer is delivering power This was done by multiplying the variable xx i n power delivered by trans former by the binary variable y i n Unfortunately this will enforce nonlinearity in the problem In order to avoid this a variable x i n is introduced to replace the product of both variables and constraints are added as follows 0 6 x i n 6 xx i n 8 i where i 4 9and8 n where n 1 q 4 xx i n C0 M 1 C0 y i n 6 x i n 6 M C1 y i n 8 i where i 4 9 and 8 n where n 1 q 5 where M is a big number and was chosen to be equal to 10 000 to guarantee that the constraint shown in Eqs 4 and 5 will converge to indicate whether a transformer is used or not xx i n is the power delivered from unit trans former i at a given period n MVA and y i n is a binary variable indicating the dissipated power from unit i at a gi ven period n A value of y i n equal to 1 indicates that power is transferred through the transformer while a value of zero means that no power is transferred 3 2 Fixed cost constraints As mentioned earlier S ij represents a binary decision variable that determines the installation of a unit i in a cer tain year j The cost of a unit will vary depending on the Energy Systems 30 2008 308 315 311 year it is installed due to the change in both R and b A bin ary variable F was added which relates the amount of lighted in Eqs 8 and 9 Eqs 10 and 11 have been for mulated to force variableS to equal 1 once a unit i has variable indicating the existence of feeder j at a given per and ij been installed in period j and above 3 3 Capacity constraints Each substation and each transformer has a capacity of 40 MVA and 20 MVA respectively However they are allowed to be loaded to 75 of their rated capacity for maximum e ciency operation This results in capacity lim its of 30 MVA and 15 MVA for each substation and each transformer respectively Moreover the lower limits for the substations and transformers loading are set to zero This could be expressed as follows 0 6 xx i n 6 15y i n 8 i where i 4 9 and 8 n where n 1 q 12 0 6 xx l n 6 30 8 n and where l 1 2 and 3 13 3 4 Power flow constraints These constraints represent the law of conservation of energy where the total loading of each substation at a given time interval n is equal to the sum of loading of its individual transformers units and at the same time equals to the sum of the demands of the sectors supplied by this substation and the total copper loss of the substations units These constraints are expressed as follows xx 1 n X 9 z 1 X 9 p 1 D p n x z hi P cu 1000 xH Tr C1 x 4 n x 5 n 8 n where n 1 q 14 xx 2 n X 18 z 10 X 9 p 1 D p n x z hi P cu 1000 xH Tr C1 x 6 n x 7 n 8 n where n 1 q 15 xx 3 n X 27 z 19 X 9 p 1 D p n x z hi P cu 1000 xH C1 x 8 n x 9 n power supplied by a unit in two consecutive years to the decision variable S ij S i 1 6 Mx i 1 8 i 1 9 6 S i 1 P x i 1 30 8 i 1 9 7 F i j 6 Mx i j 8 i 1 9 and 8 j 2 5 8 F i j P x i j 30 9 S i j PC0Mx i jC01 F i j 8 i 1 9andj 2 5 10 S i j 6 C0 x i jC01 30 F i j 8 i 1 9 and j 2 5 11 The first two constraints focus on the installation of a unit in the first year If power is being delivered by a unit on the first year S i1 will equal 1 and thus indicating the operation of this unit The variable F ij indicates whether a unit has been installed starting from the second period as