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Dynamic sub-transmission system expansion planning incorporating distributed generation using hybrid DCGA and LP technique
Electrical Power and Energy Systems 48 (2013) 111–122
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Dynamic sub-transmission system expansion planning incorporating distributed generation using hybrid DCGA and LP technique H. Shayeghi a,⇑, A. Bagheri b a b
Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil, Iran Department of Electrical Engineering, Islamic Azad University, Abhar Branch, Abhar, Iran
a r t i c l e
i n f o
Article history: Received 14 August 2012 Received in revised form 9 November 2012 Accepted 25 November 2012
Keywords: Expansion planning Dynamic expansion Sub-transmission system Distributed generation DCGA LP
a b s t r a c t Since the emerging of distributed generation (DG) technologies, their penetration into power systems has provided new options in the design and operation of electric networks. In this paper, DG units are considered as a novel alternative for supplying the load of sub-transmission system. Thus, the mathematical model of considering DG on the expansion planning of sub-transmission system is developed. Fix and variable costs of the plan and the related constraints are formulated in the proposed model. The proposed objective function and its constraint are converted to an optimization problem where the hybrid decimal codification genetic algorithm (DCGA) and linear programming (LP) technique are employed to solve it. Solution of the proposed method gives the optimal capacity of substations; optimal location and capacity of DGs as well as optimal configuration of the sub-transmission lines. To demonstrate the effectiveness of the proposed approach, it is applied on a realistic sub-transmission system of Zanjan Regional Electrical Company, Iran, and the results are evaluated. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Sub-transmission system is an intermediate network between transmission and distribution networks, where the energy is injected from transmission substations and delivered to distribution substations. With consumption growth of the loads, the existing sub-transmission network must be able to reliably feed the distribution substations. If not, the existing network loses its adequacy and needs to be expanded [1,2]. The aim of the sub-transmission system expansion planning (SSEP) is to propose and decide network reinforcements and new installations that minimize the expected total network cost with adequate reliability [1]. In expansion planning, it is determined which type of equipment, when and with how much capacity should be added to the existing network, so that the system regain its required adequacy and the exposed cost is minimum. Such an optimization problem with the mentioned purpose and its related constraints is solved within a specified time interval. It is obvious that the network must be adequate at any time for supplying the load of customers. Altering the load demand of customers cause that this problem cannot be solved regardless of time effect. On the other hand, introducing the time variable to the set of equations manifolds the problem dimension. If the time is regarded in ⇑ Corresponding author. Address: Daneshgah Street, P.O. Box: 179, Ardabil, Iran. Tel.: +98 451 5519262; fax: +98 451 5512904. E-mail address: [email protected] (H. Shayeghi). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.11.029
the planning studies, the planning study is called dynamic, otherwise it is named static [1]. In the conventional methods, SSEP implements by installation of new substations and lines or by upgrading of existing ones. Until now, several researches have been represented on the expansion planning of substations. In [3] a multistage procedure and genetic algorithm was used for locating the substations and feeder’s routing. In this study, considering constraints such as voltage drop, feeder’s capacity and radial configuration of network, the minimum expansion cost has been obtained. Haghifam and Shahabi [4] represented genetic algorithm (GA) method to choose new substations among the candidate ones and to upgrade the existing substations; voltage drop limit was considered for allocation of the loads. The loads regarded as fuzzy to model the uncertainty of load forecast and for the sake of longterm planning, pseudo-dynamic method was used. This study is about the sub-transmission substations and the sub-transmission lines have not been included in the problem. Transmission and sub-transmission network’s structures are similar. However, in expansion planning studies, the size of subtransmission networks is, in general, smaller than the size of the transmission ones and in sub-transmission systems, the number of connected generators is fewer [2]. In the literature, different methods for finding the optimal solution of lines expansion planning have been reported (see Ref. [5] for more details). An extended and meticulous analysis of appropriate methods to deal with the sub-transmission and distribution expansion problem using tree search technique was reported in [6]. In [7] a heuristic
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optimization approach guided by marginal nodal prices was suggested for the transmission planning. Other methods like Benders decomposition [8], linear programming [9], branch and bound algorithm [10], GA [11], Tabu search algorithm [12], and simulated annealing [13] have been suggested in order to reach a feasible and optimal solution. By introduction of distributed generation sources into power system, which are the results of deregulation and advances in technology, new options have been appeared in the design and planning of networks [14–16]. Beside, with respect to the site constraints in the installation of lines and substations, consideration of DG in the design and planning of electric networks has been of great attractiveness. Hence, the design of networks considering DG, as a new alternative, should be regarded and the related problem must be formulated. In recent years, different studies have been reported on the allocation of distributed generations in distribution networks. In most of them, given an existing network, optimal location and size of DGs for installation on different buses of network are determined to achieve different goals such as: reduction of losses [17,18], improving the voltage profile [19,20] and improvement of reliability indices [21,22]. Khalesi et al. [23] proposed multi-objective function to determine the optimal locations to place DGs in distribution system for minimizing power loss of the system and enhance reliability improvement and voltage profile. Time varying load was applied in this optimization to reach pragmatic results meanwhile all of the study and their requirement are based on cost/benefit forms. A novel approach was employed based on dynamic programming to solve this multi-objective problem. Distributed generation has also been used in distribution systems capacity problems. In [24], a framework has been reported to solve the problem of multistage distribution system expansion planning in which installation and/or reinforcement of substations, feeders and distributed generation units are taken into consideration as possible solutions for system capacity expansion. It was shown that the use of DG can defer reinforcements and installations to have minimum cost [25,26]. Few researches have been reported on expansion planning of subtranmission system considering distributed generation. In 2001, for the first time, a successive elimination algorithm (SEA) for expansion of sub-transmission system, considering the use of DG on the substations, was suggested [27]. Here, by assuming that the load of each substation was known, the optimal capacity of substations, the location and size of DGs, and the sub-transmission lines expansion were investigated and the effects of using the DG on reduction of total expansion costs was discussed. The same problem was solved using GA and the results were compared with those of SEA by Feng et al. [28]. In these methods, the fitness function includes the cost of installed substations, the cost of transformers added to the existing substations and capital cost of DG units. However, the annual variation of load and operational costs of DGs have not been considered in the problem solution. Also, the loss of the substations and lines have not been taken into account, whereas consideration of energy losses in expansion planning makes the plan more profitable in long term and imposes less loss cost to the network [29]. However, the problem has been modeled as a static expansion plan not as dynamic one. This paper presents the dynamic sub-transmission system expansion planning considering the use of distributed generation from the viewpoint of regional electrical companies. Countries like Iran are at the beginning of restructuring. In Iran, there are several regional electrical companies which they own different parts of network and DG units, and they are responsible for providing the electric energy of consumers, and for design and operation of sub-transmission system. In the proposed fitness function, fixed and variable costs, the losses of substations and lines, and also,
the constraints related to the network and operation of substations and DGs have been considered. The optimal capacity of DG units and generated power of substations in each year of study, the generated power of DGs in each year of study at each load level, and finally the optimal configuration of sub-transmission lines are determined year by year. These parameters are optimized with minimizing total expansion cost and energy loss to supply the load of sub-transmission system. Thus, the problem of dynamic SSEP is formulated as an optimization problem with considering DG and the system constraints. To solve this optimization problem, the hybrid decimal codification genetic algorithm (DCGA) and linear programming (LP) technique is proposed. This newly developed strategy combines the advantage of the GA and LP technique to provide robust performance for the solution of the complex dynamic SSEP problem. The main contributions of this paper are: modeling the dynamic SSEP in the presence of DG, considering a comprehensive objective function for the problem, employing a hybrid DCGA and LP technique to the problem solution, and applying the proposed method on a real and practical network. The effectiveness of the proposed method is demonstrated by its application on a real sub-transmission system of Zanjan Regional Electrical Company, Iran, and the results are compared with the expansion planning of the same system without considering DG. The results evaluation verifies that considering DG in dynamic sub-transmission system expansion planning problem leads to the considerable reduction of total expansion cost of network (expansion and operational costs) and therefore DG provides more economical network plans. In addition, from the technical point of view, the different components of network loss is reduced.
2. Problem statement 2.1. Cost components In sub-transmission system expansion planning problem with considering DG, the purpose is to determine the time, location and capacity of equipment which must be installed to serve the load of sub-transmission system by minimum investment and operational cost, satisfying the related constraints. Problem unknowns include the time and amount of substations’ capacity expansion; the time, location, and capacity of new lines; and the time, location, and capacity of new DG units to be installed. In addition, in this paper, the generated power by DG units in different years of study and load levels are determined. Expansion costs can be divided into two parts: investment (fixed) costs and variable (operation) ones. Fixed costs are one-time costs that are spent during construction and installation of substations, lines and DG units; they do not depend on the intended loading level to be served after operation. But, the variable costs exist as the system is in service and depend on the loading required [30]. The fixed costs include:
Cost of new substations installation. Cost of existing substations expansion. Cost of new lines construction. Cost of DG units installation. No load loss cost of substation’s transformers.
The variable costs of plan are as follows: Cost of DG unit’s operation. Cost of purchased power from the upward grid (transmission network). Load loss cost of substations’ transformers. Loss cost of the power passing through the lines.
H. Shayeghi, A. Bagheri / Electrical Power and Energy Systems 48 (2013) 111–122
As will be explained in the next parts, some unknowns of problems such as number of lines and DG units will be determined by GA, and some others by solving LP technique for each configuration proposed by GA method. In Section 3, the mathematical model of dynamic expansion costs and their combination as the fitness function are given.
113
Minimize F ¼ SIC þ SEC þ DGIC þ LCC þ DGOC þ EC þ SLC þ LLC
ð1Þ
In the above cost function, economic evaluation is based on the present-worth cost of the plans; namely, the costs are considered as their present-worth value. The proposed fitness function includes eight parts which are described in details as follows.
2.2. Model of sub-transmission substation’s load In addition to transmission network, which supplies the load of sub-transmission system, DG units, as an alternative, can serve some part of the load. Thus, further to the installation time, location and size of DG units, their way of operation must be determined. Thus, modeling of the substation’s loads by their peak value is not sufficient, but the annual load variation must be considered. In this paper, the loads of substations have been modeled as three-level approximation of Load Duration Curve (LDC) according to Fig. 1 [31]. This curve can be obtained from power consumption history of substations in the load forecasting studies [32].
3.2.1. Substations installation cost (SIC) This part of fitness function is the cost of new substations installation as Eq. (2):
SIC ¼
nn X T X bt C s;i ðPts;i Þ
ð2Þ
i¼1 t¼1
where Cs,i is the installation cost of ith new substation having the capacity of Pts;i in year t ($), Pts;i is the capacity of ith substation installed in year t (MW), bt is the present-worth factor in year t, 1 and b ¼ 1þd ; where d is the discount rate, T is the number of planning years, t is Index for year and nn is the number of new substations.
3. Mathematical modeling In this section, mathematical modeling for the dynamic subtransmission system expansion planning including distributed generation is described. In this paper, and in the network under study, the regional electrical company is the owner of network and DG units, and is responsible for providing the electric energy of consumers and for design and operation of sub-transmission system, as it is in Iran.
3.2.2. Substation expansion cost (SEC) This part is the cost of new added transformers for increasing the capacity of existing substations and is expressed as follows:
SEC ¼
ne X T X bt Ct i nt ti
ð3Þ
i¼1 t¼1
3.1. Problem variables
where Cti is the cost of transformer installed on ith substation ($), ntti is the number of transformers installed on ith substation in year t and ne is the number of existing sub-transmission substations.
The decision variables of dynamic sub-transmission system expansion planning considering distributed generation can be described as follows:
3.2.3. Distributed generations installation cost (DGIC) The cost of DG units forms this part of fitness function is given by:
Installation time, location and size of DG units. Amount of supplied power by transmission network and DG units in each year and level of LDC. Installation time, number and the route of new subtransmission lines. 3.2. Fitness function It should be noted that choice of the properly objective function is very important in synthesis procedure for achieving the desired level of system performance. Thus, the mathematical model of the proposed fitness function is defined as follows:
neþnn T XX
bt C DG SDG it
ð4Þ
i¼1 t¼1
where CDG is the DGs’ installation cost ($/MW), SDG it is the capacity of DG installed on ith substation in year t (MW) and DG units are installed in modules of particular capacities, e.g. 10 MW. 3.2.4. Lines construction cost (LCC) Cost of lines constructed between sub-transmission substations and also between sub-transmission substations and transmission ones composes LCC according to Eq. (5):
LCC ¼
ns X T X bt clij ntij
ð5Þ
i;j¼1 t¼1
where clij is the cost of line constructed at corridor i–j which is dependent on line’s type and length ($), ntij is the number of new constructed circuits of line at corridor i–j in year t and ns is the number of sub-transmission and transmission substations, i.e. ns = ne + nn + ng.
P1
Load (MW)
DGIC ¼
3.2.5. DGs’ operation cost (DGOC) The power generation in DG units requires expending on providing of their input energy (fuel cost), and on their repairing and maintenance cost. The present-worth cost of DGs operation cost is calculated as follows [22]:
P2
P3
T1
T2
T3
Time (h) Fig. 1. Load–Duration Curve of substations’ loads.
DGOC ¼
neþnn T XX
bt
i¼1 t¼1
nld X PDG itd T d K DG
ð6Þ
d¼1
where PDG itd is the generated power of DG units installed on ith substation in year t and in dth level of LDC (MW), Td is the duration
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of dth level of LDC (h), KDG is the operational cost of DG ($/MW h) and nld is the number of levels of LDC (three levels in this paper). 3.2.6. Electricity cost (EC) Electric companies must pay for the electric energy, which they receive from the transmission network. Moreover, the cost of active power can be differing in different levels of LDC. Usually, it is high in the peak hours and is low in other times. The presentworth cost of providing the energy of sub-transmission system from the transmission network is given by
EC ¼
ng X T nld X X bt PGitd T d K Gd i¼1 t¼1
ð7Þ
Fig. 3. Structure of the proposed particle.
LLC ¼ lc3
ns X T nld X X bt rtij P2ij;td T d i¼1 t¼1
d¼1
ð11Þ
d¼1
where PGitd is the imported power into sub-transmission system from ith transmission substation in year t and in dth level of LDC (MW), K Gd is the electricity price of the transmission system in level d of LDC ($/MW h) and ng is the number of transmission substations.
where r iij is the resistance of corridor i–j in year t (ohm), Pij,td is the flowing power at corridor i–j, in year t and in level d of LDC (MW) and lc3 is the coefficient of lines losses cost ($/MW h volt2).
3.2.7. Substation’s loss cost (SLC) The loss of substation’s transformers consist of two parts: load and no load losses as given by Eq. (8). The load losses is the resistive losses which is dependent on the amount of transformers loading, but the no load losses is the iron core losses which has a constant value and is imposed to the network as long as the transformer is switched on [1]. The cost arisen from the energy losses of transformers should be taken into account in SSEP [29]. The cost of load and no load energy losses can be calculated with respect to the transformer type and the amount of resistive and core losses of the transformer using Eqs. (9) and (10):
To complete the model of dynamic sub-transmission system expansion planning problem including DG, which its fitness
SLC ¼ SLC1 þ SLC2 bt
i¼1 t¼1 neþnn T XX
bt
i¼1 t¼1
Defining the fitness function and coding of chromosomes regarding the problem unknowns and tuning the related variables of DCGA
ð8Þ
neþnn T XX
SLC2 ¼ lc2
Start
nld X Knli nt ti T d
Creating the initial population
ð9Þ
Decoding the chromosomes and calculation of DGIC and LCC for all of the planning years
d¼1 nld X Kli nt ti Pt2itd T d
ð10Þ
d¼1
where SLC is the substation’s total loss cost ($), SLC1 is the substation’s’ no load loss cost ($), SLC2 is the substation’s load loss cost ($), Knli is the no load loss of the transformer of ith substation (MW), Kli is the load loss coefficient of the transformer of ith substation (1/ MW), ntti is the number of transformers of ith substation in year t, Ptitd is the power passing through the transformer of ith substation in year t and in dth level of LDC (MW), lc1 is the substations no load loss cost ($/MW h), and lc2 is the substations load loss cost ($/ MW h).
Applying the reproduction operator of GA
SLC1 ¼ lc1
3.3. Problem constraints
Performing the LP technique, determining the power generation of DGs, power purchased from the transmission system and lines’ flows; calculation of SIC, SEC, DGOC, EC, SLC and LLC for all of the planning years based on the chromosome proposed by GA Calculating the objective function Applying the cross-over operator of GA with the rate of Pc
3.2.8. Lines losses cost (LLC) The lines loss is a function of the lines resistance and the amount of power flowing through them. The considered model in this study for the power flow calculations is DC load flow. The lines losses is inserted into the fitness function as follows:
Applying the mutation operator of GA with the rate of Pm
No
Is the stop condition satisfied? Yes Introducing the best chromosome
End Fig. 2. Different arrangements of parallel transformers on substations.
Fig. 4. Flowchart of the proposed approach.
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Fig. 5. Single-line diagram of the test network.
Table 1 Technical and economic data for the study. Parameter
Value
Electricity price in the first level of LDC ($/MW h) [34,39] Electricity price in the second level of LDC ($/MW h) Electricity price in the third level of LDC ($/MW h) Installation cost of DG units ($/MW) [34,39] Operational cost of DG units ($/MW h) [34,39] Number of planning years Discount rate (%)
50 30 20 200,000 25 5 12
Table 2 Parameters of DCGA used in simulation. Parameter
Value
Problem dimension Number of chromosomes Number of iterations PC Pm
415 20 2000 0.7 0.05
where Ps,it is the Loading of ith substation in year t (MW), rfsi is the reserve factor for ith substation and Xit is the set of installable capacities on ith substation in year t. Although, considering the reserve factor for the substations somehow guarantees the reliability of substations, but in some cases, e.g. when there is only one transformer installed on the substation, considering the reserve factor is ineffective. In this case, if that one transformer is out of service, the substation’s load will not be supplied. Thus, in this paper, the possibility of single contingency on the transformers of substations has been regarded for choosing the substation’s capacity. In this way, in the case of single contingency on a transformer of a substation, other transformers of that substation must not be overloaded. In this research, concerning the paralleling concept of transformers, the paralleled transformers (Fig. 2) on the substations are similar. 3.3.2. Operational constraint of DG units The generation of DG units must be less than their capacity. Thus, we have: DG 0 6 P DG itd 6 Sit
i ¼ 1; 2; . . .
; ne þ nc
d ¼ 1; 2; . . . ; nld
t ¼ 1; 2; . . . ; T function as given by Eq. (1), it is necessary to consider the following constraints in the proposed model: 3.3.1. Limitation on substations loading Conventionally, to consider the reliability of substations, a loading limit is considered such that the loading of each substation must be lower than that limit [4]. This constraint is defined as follows:
0 6 Ps;it 6 ð1 rfsi ÞSs;i ¼ 1; 2; . . . ; T
i ¼ 1; 2; . . . ; ne þ nn t
Ss;i 2 Xit
ð12Þ
where PDG itd is the generated power of DGs of ith substation in year t year and in dth level of LDC (MW). 3.3.3. Limitation of feeding the load by DG units In the design of distribution networks in presence of distributed generation, it is tried to provide the majority of the needed energy from transmission network via sub-transmission system not from DG units [33,34]. Therefore, in this study, the maximum amount of power generated by DGs is considered according to Eq. (14):
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Table 3 Results of substations expansion in two cases. Substation number
Installed or expanded capacity of substation in each year (MVA) Case 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
neþnn X
PDG itd 6 0:35Dtd
Case 2
1
2
3
4
5
1
2
3
4
5
3 30 3 30 2 30 3 30 3 30 3 15 3 30 3 15 3 15 3 7.5 3 30 3 30 2 30 3 30 2 24 3 30 2 30 3 30 3 15 3 15 3 15 3 30 4 30 3 30 2 30 3 15 3 15 3 30 3 15 2 30 4 15 3 15 3 15 3 15
3 30 3 30 2 30 3 30 3 30 4 15 3 30 4 15 3 15 3 7.5 3 30 3 30 2 30 3 30 2 24 4 30 2 30 3 30 3 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 3 15 3 15 3 15
3 30 3 30 3 30 3 30 4 30 4 15 4 30 4 15 3 15 3 7.5 4 30 3 30 2 30 3 30 2 24 4 30 2 30 4 30 4 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 3 15 3 15 3 15
4 30 3 30 3 30 3 30 4 30 4 15 4 30 4 15 3 15 3 7.5 4 30 4 30 2 30 3 30 3 24 4 30 3 30 4 30 4 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 4 15 3 15 3 15
4 30 3 30 3 30 3 30 4 30 4 15 4 30 4 15 3 15 3 7.5 4 30 4 30 2 30 3 30 3 24 4 30 3 30 4 30 4 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 4 15 3 15 3 15
3 30 2 30 2 30 2 30 3 30 3 15 3 30 2 15 2 15 2 7.5 3 30 3 30 2 30 3 30 2 24 3 30 2 30 3 30 2 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 2 30 2 15 2 30 2 15 2 15 2 15 2 15
3 30 2 30 2 30 2 30 3 30 3 15 3 30 2 15 2 15 2 7.5 3 30 3 30 2 30 3 30 2 24 4 30 2 30 3 30 2 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 2 30 2 15 3 30 3 15 3 15 2 15 2 15
3 30 2 30 2 30 2 30 3 30 3 15 3 30 3 15 2 15 2 7.5 3 30 3 30 2 30 3 30 2 24 4 30 2 30 3 30 2 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 2 30 2 15 3 30 3 15 3 15 3 15 2 15
3 30 2 30 2 30 3 30 3 30 3 15 3 30 3 15 2 15 2 7.5 3 30 4 30 2 30 3 30 2 24 4 30 2 30 3 30 3 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 3 30 2 15 3 30 3 15 3 15 3 15 3 15
3 30 2 30 2 30 3 30 4 30 3 15 3 30 3 15 2 15 2 7.5 3 30 4 30 2 30 4 30 2 24 4 30 2 30 3 30 3 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 3 30 2 15 3 30 3 15 3 15 3 15 3 15
ði ¼ 1; 2; . . . ; ne þ nc
0 6 nijt þ n0ij 6 nmax ij
t ¼ 1; 2; . . . ; T
i¼1
d ¼ 1; 2; . . . ; nldÞ
ð14Þ
where Dtd is the total load of sub-transmission system in year t and in dth level of LDC (MW). 3.3.4. Capacity limitation of new installed substations and existing expanded substations Usually, there is a limitation on installing the new substations or expanding the existing ones, such that we cannot install or expand a substation more than a specific capacity due to technical and site constraints. This limitation is given by:
0 6 Ss;it 6 Smax s;it
; i ¼ 1; 2; . . . ; ne þ nn t ¼ 1; 2; . . . ; T
ð15Þ
Smax s;it is the maximum installable capacity on ith substation in year t. Despite that DG units need small site area, however, there is a limitation for installing DG units, which can be regarded as follows: DG 0 6 nDG it 6 ni max
i ¼ 1; 2; . . . ; ne þ nn t ¼ 1; 2; . . . ; T
ð16Þ
where nDG ti is the number of DG units on ith substation in year t and nDG i max is the maximum number of installable DG units on ith substation. 3.3.5. Maximum constructible circuits for the sub-transmission lines This constraint is given by Eq. (17) and states that the constructed circuits at each corridor must be fewer than the maximum constructible circuits at that corridor.
i; j ¼ 1; 2; . . . ; ns
ð17Þ
where n0ij is the number of existing circuits at corridor i–j, nijt is the number of new circuits at corridor i–j in yeart t, and nmax is the maxij imum number of constructible circuits at corridor i–j. 3.3.6. Loading limit of sub-transmission lines In this paper, the reliability of sub-transmission lines has been considered as reserve factor [27]. Loading of the lines in different levels of LDC must be less than maximum loading limit as given by:
jP ij;td j 6 ð1 rflÞjPmax ijt j
ð18Þ
where rfl is the reserve factor for the lines. The reserve factor is considered to make sure that the lines are not overloaded in the case of single contingency on the other lines or on DG units. Moreover, for prevention of substations islanding in single contingencies of lines, at least two lines must be connected to each substation [35]. 3.4. DCGA and chromosome structure of the problem Standard genetic algorithm is a random search method that can be used to solve nonlinear system of equations and optimize complex problems. The base of this algorithm is the selection of individuals. It does not need a good initial estimation for the sake of problem solution. In other words, the solution of a complex problem can be started from weak initial estimations and then be corrected in evolutionary process of fitness. The genetic algorithm manipulates the strings that may be the solutions of the problem
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H. Shayeghi, A. Bagheri / Electrical Power and Energy Systems 48 (2013) 111–122 Table 4 Generated power of DG units in case 2. Substation number
Generated power of DG units in each year and each load level in MW (T1 = 1000 h, T2 = 5260 h, T3 = 2500 h) 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
2
3
4
5
T1
T2
T3
T1
T2
T3
T1
T2
T3
T1
T2
T3
T1
T2
T3
10 20 10 10 10 10 0 20 10 10 10 0 0 0 10 0 0 10 20 0 0 10 20 10 0 20 10 10 10 0 20 10 10 10
8.86 15.07 8.71 8.82 8.83 8.65 0 15.01 8.77 8.80 9.07 0 0 0 8.93 0 0 8.89 15.17 0 0 8.96 15.78 8.93 0 15.33 8.74 8.63 8.64 0 14.66 8.90 8.94 8.45
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 10 20 10 10 10 0 0 0 10 0 0 20 20 10 0 10 20 10 10 20 10 10 20 0 20 10 10 10
8.65 12.08 8.7417 12.15 8.63 11.79 8.35 11.92 8.57 8.61 8.66 0 0 0 8.7429 0 0 12.30 12.12 8.69 0 8.7993 12.55 8.76 8.71 12.33 8.58 8.38 11.36 0 11.42 8.7315 8.76 8.59
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 10 20 10 10 10 0 0 0 10 10 0 20 20 10 0 10 20 20 10 20 10 10 20 0 20 10 10 10
8.98 12.13 8.98 12.19 8.97 11.92 8.76 12.03 8.92 8.95 8.96 0 0 0 9.1013 9.07 0 12.33 12.25 9.03 0 9.12 12.45 12.31 9.05 12.21 8.94 8.73 11.58 0 11.64 9.05 9.10 8.94
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 10 20 10 10 10 0 0 0 10 10 10 20 20 10 0 10 30 20 10 20 10 10 20 0 20 10 20 10
9.28 11.92 9.27 11.88 9.29 11.61 9.06 11.73 9.24 9.28 9.27 0 0 0 9.38 9.35 9.32 11.94 11.84 9.32 0 9.39 18.8 11.91 9.31 11.86 9.27 8.99 11.33 0 11.35 9.33 11.91 9.22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 20 20 10 10 10 0 0 0 10 10 10 20 20 10 0 10 30 20 10 20 10 20 20 10 20 10 20 20
9.58 12.02 9.59 11.87 9.61 11.59 11.64 11.71 9.55 9.56 9.59 0 0 0 9.77 9.70 9.67 12.44 12.37 9.66 0 9.72 16.38 12.07 9.64 11.89 9.57 11.37 11.37 9.58 11.37 9.68 12.04 12.46
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[36,37]. This algorithm has been used to solve many practical problems such as transmission and sub-transmission network expansion planning [31]. The genetic algorithm generally includes three fundamental genetic operators of reproduction, crossover and mutation. These operators conduct the chromosomes toward better fitness. There are three methods for coding of problems based on genetic algorithm method: real codification, binary codification and decimal codification [36,38]. Due to that the parameters used in this study are of integer type, thus the third method, i.e. decimal codification genetic algorithm is employed. To code the information in the present work, the chromosome shown in Fig. 3 is considered. The proposed chromosome is generally composed of T parts, equal to the number of planning years. Each part is in turn divided into two sections. In the first section, the value of ith gene expresses the number of DG units that are installed on the ith substation in the related year. The number of added sub-transmission lines to each corridor of network in each year is represented by the value of second section. The number of genes of first section is equal to the number of existing and new sub-transmission substations (ne + nn); the number of genes of second section equals to the number of candidate corridors for construction.
3.5. Chromosome decoding and calculation of fitness function components With respect to the proposed chromosome, the cost of installed DGs is calculated with decoding Section 1 of the chromosome in each year. The cost of lines also is calculated by decoding Section 2.
Now, it is turn to determine the optimal power generation of DG units and the power purchased from the transmission network in each year and each level of LDC, to determine the other components of fitness function. The proposed method for this aim is explained as follows. 3.6. Performing the linear programming Providing the needed energy of sub-transmission system from the transmission network imposes an expense for the electric companies. In addition, supplying the whole load of sub-transmission system only by DGs is not economical. Thus, the participation degree of transmission system and DG units in providing the needed energy of sub-transmission system must be determined. For a given chromosome (the number of DG units on each substation and also the number of lines at different corridors are known), a subsidiary optimization, in each iteration of DCGA, is performed using linear programming to find the optimal power generated by DG units and also the optimal amount of power provided from the transmission system in each year and at each level of LDC. The fitness function optimized by LP technique is the sum of DGs operation cost and electricity cost of purchased power from the transmission network as given by:
Minimize F LP ¼ DGOC þ EC ¼
neþnn T XX
bt
i¼1 t¼1
ng X nld T nld X X X PDG bt PGitd T d K Gd itd T d K DG þ d¼1
i¼1 t¼1
ð19Þ
d¼1
The equality and inequality constraints used in the above problem solution by LP technique is described by Eqs.(20)–(24):
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Table 5 The results of lines expansion in two cases. From bus
To bus
Number of constructed line circuits in each year Case 1
1 2 3 3 4 5 5 6 6 6 7 7 8 9 9 11 11 12 13 13 14 14 14 15 16 17 18 18 18 19 19 20 21 22 22 23 24 25 26 27 28 29 30 31 21 32 22 33 34
HV1 HV1 HV1 HV2 HV1 HV1 HV2 7 HV1 HV5 8 HV4 9 10 HV1 HV1 HV2 HV2 14 HV 15 HV2 17 18 HV3 HV3 19 HV3 HV6 HV3 HV6 HV3 HV3 23 HV3 HV3 HV3 HV2 HV2 HV1 HV5 HV5 HV4 HV5 32 HV3 33 HV3 HV6
PGitd PDitd
Case 2
1
2
3
4
5
1
2
3
4
5
0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 2 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0
1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 2 1 0
1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1
1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0
0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 2 0 0 0 1 1 0 1 1 1 1 0 1 0
0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 2 0 0
1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 2 0 1 0 0 0 0 1 0 0 1 2 1 0 0 0 1 0
1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 2 2 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1
1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 2 0 0 1 0
1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0
ns X Pij;td ¼ 0
ð20Þ
j¼1
hitd hjtd X ij;t
ð21Þ
jPij;td j 6 ð1 rflÞjPmax ijt j
ð22Þ
DG 0 6 PDG itd 6 Sit
ð23Þ
Pij;td ¼
neþnn X
PDG itd 6 0:35Dtd
ði ¼ 1; 2; . . . ; ne þ nc
t ¼ 1; 2; . . . ; T
in year t and level d of LDC (MW), hitd is the voltage angle of ith substation in year t and level d of LDC (rad), Pmax is the capacity of corijt ridor i–j in year t (MW) and Xijt is the reactance of corridor i–j in year t (ohm). Eqs. (20) and (21) are the relations of DC load flow [29,35]. By performing the LP approach, the generated power of DG units and the power purchased from the transmission network in each year and at each level of LDC are determined. Consequently, the loading of lines and substations are found out and the related components of fitness function calculated. With these explanations, we can summarize the proposed method using the flowchart illustrated in Fig. 4.
d
i¼1
¼ 1; 2; . . . ; nldÞ
ð24Þ
where PDG itd is the generated power of DGs on ith substation in year t and level d of LDC (MW), PDitd is the load demand of ith substation
4. Numerical study To evaluate the effectiveness of the proposed method, it is applied to the real sub-transmission system of Zanjan Regional
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
Number of installed DG units in each year (capacity of each unit is 10 MW) 1
2
3
4
5
1 2 1 1 1 1 0 2 1 1 1 0 0 0 1 0 0 1 2 0 0 1 2 1 0 2 1 1 1 0 2 1 1 1
0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1
With DG Without DG
300 250 200 150 100
1
2
3
4
5
Year Fig. 6. Total expansion cost during the planning years.
Accumulative cost (M$)
Substation number
total expansion cost in each year (M$)
Table 6 The installed DG units on substations in case 2.
With DG Without DG
1027.06 871.26 704.53 530.43 331.93
1
2
3
4
5
Year Fig. 7. Accumulative total expansion cost during the planning years.
each substation is 4. The number of study years is 5, starting from now to 5 years ahead. Other required parameters are given in Table 1. Also, the parameters of DCGA used for simulation are presented in Table 2. It should be noted that these parameters have been selected in a way that the algorithm obtains the best results. To study the effects of distributed generation, as a new option for supplying the load of the system, considering the input data, the problem is solved in two cases:
Electrical Company, located in northwest of Iran. This system is consisted of 34 63/20 kV substations; eleven of them are newly installed substations, which must be connected to the network. The new substations are installed and operated at the beginning of planning. The 63/20 kV substations are fed by six 400/63 kV or 230/63 kV or 400/230/63 kV transmission substations. The singeline diagram of the test network is depicted in Fig. 5 and its details are given in the Appendix. The substation’s load value in second and third levels is considered 0.4 and 0.7 times of their peak value, respectively; the annual load growth in all levels of LDC is 7%. All the corridors between existing substation’s and the dashed ones are candidates for construction. The lines have the capacity of 40 MW, and the related cost is 80 k$/km [34,39]. The reserve factor for the lines is considered 30%; and the maximum constructible circuits of lines at the corridors are 4. Each DG unit has the size of 10 MW; and the maximum number of installable DG units on
Case 1: there are no installed DG units on the substations and the whole load of the sub-transmission system is provided from the transmission network. Case 2: DG units can be installed on the sub-transmission substations and participate in supplying the load of system. The results of the test, including the capacities of expanded or installed substations in each year, the constructed lines between substations in each year, the location and size of DG and their
Table 7 Cost components of two cases during the planning years. Present-worth cost (M$)
Experiment Case 1
Substations installation and expansion cost Lines construction cost DGs installation cost DGs operation cost Cost of purchased power from the transmission network Total cost Accumulative total cost
Case 2
1
2
3
4
5
1
2
3
4
5
65.03 78.44 0 0 183.79 327.26 327.26
1.16 32.66 0 0 175.58 209.4 536.66
0.92 40.08 0 0 167.75 208.75 745.41
0.78 20.97 0 0 160.26 182.01 927.42
0.26 21.57 0 0 153.1 174.93 1102.35
46.88 52.83 60 43.08 129.36 331.93 331.93
0.58 24.38 12.5 39.6 121.43 198.5 530.43
0.12 16.8 3.19 37.72 116.27 174.1 704.53
0.46 14.94 4.27 36.06 110.98 166.73 871.26
0.57 9.79 5.08 34.68 105.68 155.8 1027.06
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Table 8 Loss components of two cases during the planning years. Present-worth cost (M$)
Experiment Case 1
Lines loss Substations no-load loss Substations load loss
Case 2
1
2
3
4
5
1
2
3
4
5
84,842 198,021 94,945
115,326 211,163 102,437
178,492 222,994 109,458
138,057 234,292 119,347
138,164 238,235 134,205
39,022 169,776 61,164
29,885 176,347 63,380
55,423 177,658 71,765
29,228 184,223 78,234
113,888 193,421 84,122
4
x 10
Lines Loss (MW-hr)
With DG Without DG
11.3888
5.5423 3.9022 2.9338
1
2
3
4
5
Year Fig. 8. Lines loss during the planning years.
Substations no loas loss (MW-hr)
5
x 10
With DG Without DG
2.1116 1.9342
1.6978
1
2
3
4
generated power in each year and each level of LDC are listed in Tables 3–6. As it can be seen, the installation of DGs has decreased the expanded and installed capacities, such that the substations exist in the plan with the lower capacities and costs. Considering the DG units has also decreased the need for more lines and high capacity lines; consequently, the cost of lines construction is reduced. Table 4 shows that in the levels of LDC which the electricity cost of transmission system is high, some part of the system’s needed energy is generated by DG units. Also, in the levels of LDC that the operational cost of DG units is high, most of the system’s energy is injected from the transmission network into sub-transmission system to reduce the total operational cost. The cost components (the cost in each year and the accumulative cost) of the two experiments are given in Table 7 and Figs. 6 and 7. In the first year of study, due to installation of considerable number of DG units, the total cost in case 2 is more than case 1. However, this relatively high primary investment cost is compensated in the next years by low construction cost of lines, low expansion cost of substations and operational cost. The losses components with and without of DG are compared in Table 8 and Figs. 8–10. According to Table 8 and Fig. 8, the lines losses in the presence of DG, due to the lower loading of lines is less than that without the use of DG. In addition, installation of DGs on the substations has decreased the number of needed new transformers. Because of this, the no load loss of substations has been reduced as shown in Fig. 9. Similarly, the load loss of substations is decreased. Considering the total cost of the plan and the energy losses, the dynamic expansion planning of sub-transmission system by using distributed generation is more economical and it imposes less loss to the system.
5
Year
5. Conclusion
Fig. 9. Substations no-load loss during the planning years.
4
Substations load loss
x 10
With DG Without DG
9.4945 8.4122 7.8234 7.1765 6.338 1
2
3
4
Year Fig. 10. Substations load loss during the planning years.
5
Emerging of distributed generations has provided new options in the design and planning of power systems. The novelty of this paper is formulation of dynamic SSEP problem in the presence of DG units and solution of it by a developed hybrid DCGA and LP technique. The developed method uses both the computational capability of GA and advantage of mixed integer LP technique for achieving the high solution quality and accuracy. The proposed model with all system constraints is expressed as an optimization problem, where the objective function is comprehensive and includes different cost components. The other feature of this study is that the DG’s generated power at different load levels and the operational costs are determined. To demonstrate the effectiveness of the proposed method, it is applied on a real test system in two cases: one with considering DG units and another without them. Evaluating the results show that the installation of DGs has decreased the expanded and installed capacities. In addition, it was shown that considering DG units significantly reduced the expansion and operational costs of plan and different components of network loss. In general, it can be concluded that considering DG in dynamic SSEP problem is able
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H. Shayeghi, A. Bagheri / Electrical Power and Energy Systems 48 (2013) 111–122 Table 9 Specification of substations. Substation (bus) number
Substation name
Peak of load in base year (MW)
Existing capacity (MVA)
Expandable or installable capacity (MVA)
Voltage level (kV)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 HV1 HV2 HV3 HV4 HV5 HV6
Zanjan1 Ideloo Azadeghan Koshkan Sangshahr Saeedabad Dandi Mahneshan Soltanabad Zanjanrood Khamseh Sorboruy Bonab Soltanieh Simanzanjan Abhar3 Saeenghaleh Gheidar Garmab Zobahan Tolombekhaneh Hidaj Abhar1 Irankhodro Chavarzagh Gholshahr Shahrara Petroshimi Gholaber Maadenrui Simankhamseh Abhar4 Khorramdareh Zarrinabad Zanjan Qayati Abhar Dandi Ijrood Gheydar
61 38 42 48 65 41 65 41 19 13 63 61 19 56 24 69 29 63 33 22 20 54 74 37 35 20 21 40 25 35 38 30 28 25 – – – – – –
2 30 2 30 2 30 2 30 2 30 2 15 2 30 2 15 2 15 1 7.5 2 30 3 30 2 30 2 30 1 24 2 30 2 30 2 30 2 15 2 15 2 15 2 30 2 30 2 30 0 0 0 0 0 0 0 0 0 0 250 250 375 250 200 200
4 30 4 30 4 30 4 30 4 30 4 15 4 30 4 15 4 15 4 7.5 4 30 4 30 4 30 4 30 4 24 4 30 4 30 4 30 4 15 4 15 4 15 4 30 4 30 4 30 3 30 3 15 4 15 3 30 4 15 3 30 4 15 4 15 4 15 4 15 – – – – – –
63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 230/63 400/230/63 230/63 230/63 400/63 400/63
Table 10 Specification of lines. Corridor
Length (km)
Capacity (MVA)
Corridor
Length (km)
Capacity (MVA)
1-HV1 2-HV1 3-HV1 3-HV2 4-HV1 5-HV1 5-HV2 6–7 6-HV1 6-HV5 7–8 7–38 8–9 9–10 9-HV1 11-HV1 11-HV2 12-HV2 13–14 13-HV2 14–15 14–17 14-HV2 15–18 16-HV3 17-HV3 18–19
0 47 2.3 10 9 11 20 51 56 30 20 0 84 34 35 7 8 6 30 12 30 28 15 13 0 34 51
2 50 2 25 1 25 1 25 2 25 1 50 1 50 2 50 2 50 1 25 2 50 2 50 2 50 2 50 2 50 1 50 1 50 2 50 2 50 2 50 2 50 2 50 2 50 1 50 2 50 2 50 250
18–37 18-HV6 19-HV3 19-HV6 20-HV3 21-HV3 22–23 22-HV3 23-HV3 24-HV3 25-HV2 26-HV2 27-HV1 28-HV5 29-HV5 30–38 31-HV5 21–32 32-HV3 22–33 33-HV3 34-HV6
70 10 117 70 2 5 17 23 13 24 43 5 4 10 20 10 13 5 10 10 15 51
2 50 1 50 2 50 1 2 25 2 60 1 25 2 50 1 50 2 25 0 0 0 0 0 0 0 0 0 0 0 0
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to make the plan more optimal from the economic and technical points of view.
Appendix A. Test system data See Tables 9 and 10.
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Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Dynamic sub-transmission system expansion planning incorporating distributed generation using hybrid DCGA and LP technique H. Shayeghi a,⇑, A. Bagheri b a b
Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil, Iran Department of Electrical Engineering, Islamic Azad University, Abhar Branch, Abhar, Iran
a r t i c l e
i n f o
Article history: Received 14 August 2012 Received in revised form 9 November 2012 Accepted 25 November 2012
Keywords: Expansion planning Dynamic expansion Sub-transmission system Distributed generation DCGA LP
a b s t r a c t Since the emerging of distributed generation (DG) technologies, their penetration into power systems has provided new options in the design and operation of electric networks. In this paper, DG units are considered as a novel alternative for supplying the load of sub-transmission system. Thus, the mathematical model of considering DG on the expansion planning of sub-transmission system is developed. Fix and variable costs of the plan and the related constraints are formulated in the proposed model. The proposed objective function and its constraint are converted to an optimization problem where the hybrid decimal codification genetic algorithm (DCGA) and linear programming (LP) technique are employed to solve it. Solution of the proposed method gives the optimal capacity of substations; optimal location and capacity of DGs as well as optimal configuration of the sub-transmission lines. To demonstrate the effectiveness of the proposed approach, it is applied on a realistic sub-transmission system of Zanjan Regional Electrical Company, Iran, and the results are evaluated. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Sub-transmission system is an intermediate network between transmission and distribution networks, where the energy is injected from transmission substations and delivered to distribution substations. With consumption growth of the loads, the existing sub-transmission network must be able to reliably feed the distribution substations. If not, the existing network loses its adequacy and needs to be expanded [1,2]. The aim of the sub-transmission system expansion planning (SSEP) is to propose and decide network reinforcements and new installations that minimize the expected total network cost with adequate reliability [1]. In expansion planning, it is determined which type of equipment, when and with how much capacity should be added to the existing network, so that the system regain its required adequacy and the exposed cost is minimum. Such an optimization problem with the mentioned purpose and its related constraints is solved within a specified time interval. It is obvious that the network must be adequate at any time for supplying the load of customers. Altering the load demand of customers cause that this problem cannot be solved regardless of time effect. On the other hand, introducing the time variable to the set of equations manifolds the problem dimension. If the time is regarded in ⇑ Corresponding author. Address: Daneshgah Street, P.O. Box: 179, Ardabil, Iran. Tel.: +98 451 5519262; fax: +98 451 5512904. E-mail address: [email protected] (H. Shayeghi). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.11.029
the planning studies, the planning study is called dynamic, otherwise it is named static [1]. In the conventional methods, SSEP implements by installation of new substations and lines or by upgrading of existing ones. Until now, several researches have been represented on the expansion planning of substations. In [3] a multistage procedure and genetic algorithm was used for locating the substations and feeder’s routing. In this study, considering constraints such as voltage drop, feeder’s capacity and radial configuration of network, the minimum expansion cost has been obtained. Haghifam and Shahabi [4] represented genetic algorithm (GA) method to choose new substations among the candidate ones and to upgrade the existing substations; voltage drop limit was considered for allocation of the loads. The loads regarded as fuzzy to model the uncertainty of load forecast and for the sake of longterm planning, pseudo-dynamic method was used. This study is about the sub-transmission substations and the sub-transmission lines have not been included in the problem. Transmission and sub-transmission network’s structures are similar. However, in expansion planning studies, the size of subtransmission networks is, in general, smaller than the size of the transmission ones and in sub-transmission systems, the number of connected generators is fewer [2]. In the literature, different methods for finding the optimal solution of lines expansion planning have been reported (see Ref. [5] for more details). An extended and meticulous analysis of appropriate methods to deal with the sub-transmission and distribution expansion problem using tree search technique was reported in [6]. In [7] a heuristic
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optimization approach guided by marginal nodal prices was suggested for the transmission planning. Other methods like Benders decomposition [8], linear programming [9], branch and bound algorithm [10], GA [11], Tabu search algorithm [12], and simulated annealing [13] have been suggested in order to reach a feasible and optimal solution. By introduction of distributed generation sources into power system, which are the results of deregulation and advances in technology, new options have been appeared in the design and planning of networks [14–16]. Beside, with respect to the site constraints in the installation of lines and substations, consideration of DG in the design and planning of electric networks has been of great attractiveness. Hence, the design of networks considering DG, as a new alternative, should be regarded and the related problem must be formulated. In recent years, different studies have been reported on the allocation of distributed generations in distribution networks. In most of them, given an existing network, optimal location and size of DGs for installation on different buses of network are determined to achieve different goals such as: reduction of losses [17,18], improving the voltage profile [19,20] and improvement of reliability indices [21,22]. Khalesi et al. [23] proposed multi-objective function to determine the optimal locations to place DGs in distribution system for minimizing power loss of the system and enhance reliability improvement and voltage profile. Time varying load was applied in this optimization to reach pragmatic results meanwhile all of the study and their requirement are based on cost/benefit forms. A novel approach was employed based on dynamic programming to solve this multi-objective problem. Distributed generation has also been used in distribution systems capacity problems. In [24], a framework has been reported to solve the problem of multistage distribution system expansion planning in which installation and/or reinforcement of substations, feeders and distributed generation units are taken into consideration as possible solutions for system capacity expansion. It was shown that the use of DG can defer reinforcements and installations to have minimum cost [25,26]. Few researches have been reported on expansion planning of subtranmission system considering distributed generation. In 2001, for the first time, a successive elimination algorithm (SEA) for expansion of sub-transmission system, considering the use of DG on the substations, was suggested [27]. Here, by assuming that the load of each substation was known, the optimal capacity of substations, the location and size of DGs, and the sub-transmission lines expansion were investigated and the effects of using the DG on reduction of total expansion costs was discussed. The same problem was solved using GA and the results were compared with those of SEA by Feng et al. [28]. In these methods, the fitness function includes the cost of installed substations, the cost of transformers added to the existing substations and capital cost of DG units. However, the annual variation of load and operational costs of DGs have not been considered in the problem solution. Also, the loss of the substations and lines have not been taken into account, whereas consideration of energy losses in expansion planning makes the plan more profitable in long term and imposes less loss cost to the network [29]. However, the problem has been modeled as a static expansion plan not as dynamic one. This paper presents the dynamic sub-transmission system expansion planning considering the use of distributed generation from the viewpoint of regional electrical companies. Countries like Iran are at the beginning of restructuring. In Iran, there are several regional electrical companies which they own different parts of network and DG units, and they are responsible for providing the electric energy of consumers, and for design and operation of sub-transmission system. In the proposed fitness function, fixed and variable costs, the losses of substations and lines, and also,
the constraints related to the network and operation of substations and DGs have been considered. The optimal capacity of DG units and generated power of substations in each year of study, the generated power of DGs in each year of study at each load level, and finally the optimal configuration of sub-transmission lines are determined year by year. These parameters are optimized with minimizing total expansion cost and energy loss to supply the load of sub-transmission system. Thus, the problem of dynamic SSEP is formulated as an optimization problem with considering DG and the system constraints. To solve this optimization problem, the hybrid decimal codification genetic algorithm (DCGA) and linear programming (LP) technique is proposed. This newly developed strategy combines the advantage of the GA and LP technique to provide robust performance for the solution of the complex dynamic SSEP problem. The main contributions of this paper are: modeling the dynamic SSEP in the presence of DG, considering a comprehensive objective function for the problem, employing a hybrid DCGA and LP technique to the problem solution, and applying the proposed method on a real and practical network. The effectiveness of the proposed method is demonstrated by its application on a real sub-transmission system of Zanjan Regional Electrical Company, Iran, and the results are compared with the expansion planning of the same system without considering DG. The results evaluation verifies that considering DG in dynamic sub-transmission system expansion planning problem leads to the considerable reduction of total expansion cost of network (expansion and operational costs) and therefore DG provides more economical network plans. In addition, from the technical point of view, the different components of network loss is reduced.
2. Problem statement 2.1. Cost components In sub-transmission system expansion planning problem with considering DG, the purpose is to determine the time, location and capacity of equipment which must be installed to serve the load of sub-transmission system by minimum investment and operational cost, satisfying the related constraints. Problem unknowns include the time and amount of substations’ capacity expansion; the time, location, and capacity of new lines; and the time, location, and capacity of new DG units to be installed. In addition, in this paper, the generated power by DG units in different years of study and load levels are determined. Expansion costs can be divided into two parts: investment (fixed) costs and variable (operation) ones. Fixed costs are one-time costs that are spent during construction and installation of substations, lines and DG units; they do not depend on the intended loading level to be served after operation. But, the variable costs exist as the system is in service and depend on the loading required [30]. The fixed costs include:
Cost of new substations installation. Cost of existing substations expansion. Cost of new lines construction. Cost of DG units installation. No load loss cost of substation’s transformers.
The variable costs of plan are as follows: Cost of DG unit’s operation. Cost of purchased power from the upward grid (transmission network). Load loss cost of substations’ transformers. Loss cost of the power passing through the lines.
H. Shayeghi, A. Bagheri / Electrical Power and Energy Systems 48 (2013) 111–122
As will be explained in the next parts, some unknowns of problems such as number of lines and DG units will be determined by GA, and some others by solving LP technique for each configuration proposed by GA method. In Section 3, the mathematical model of dynamic expansion costs and their combination as the fitness function are given.
113
Minimize F ¼ SIC þ SEC þ DGIC þ LCC þ DGOC þ EC þ SLC þ LLC
ð1Þ
In the above cost function, economic evaluation is based on the present-worth cost of the plans; namely, the costs are considered as their present-worth value. The proposed fitness function includes eight parts which are described in details as follows.
2.2. Model of sub-transmission substation’s load In addition to transmission network, which supplies the load of sub-transmission system, DG units, as an alternative, can serve some part of the load. Thus, further to the installation time, location and size of DG units, their way of operation must be determined. Thus, modeling of the substation’s loads by their peak value is not sufficient, but the annual load variation must be considered. In this paper, the loads of substations have been modeled as three-level approximation of Load Duration Curve (LDC) according to Fig. 1 [31]. This curve can be obtained from power consumption history of substations in the load forecasting studies [32].
3.2.1. Substations installation cost (SIC) This part of fitness function is the cost of new substations installation as Eq. (2):
SIC ¼
nn X T X bt C s;i ðPts;i Þ
ð2Þ
i¼1 t¼1
where Cs,i is the installation cost of ith new substation having the capacity of Pts;i in year t ($), Pts;i is the capacity of ith substation installed in year t (MW), bt is the present-worth factor in year t, 1 and b ¼ 1þd ; where d is the discount rate, T is the number of planning years, t is Index for year and nn is the number of new substations.
3. Mathematical modeling In this section, mathematical modeling for the dynamic subtransmission system expansion planning including distributed generation is described. In this paper, and in the network under study, the regional electrical company is the owner of network and DG units, and is responsible for providing the electric energy of consumers and for design and operation of sub-transmission system, as it is in Iran.
3.2.2. Substation expansion cost (SEC) This part is the cost of new added transformers for increasing the capacity of existing substations and is expressed as follows:
SEC ¼
ne X T X bt Ct i nt ti
ð3Þ
i¼1 t¼1
3.1. Problem variables
where Cti is the cost of transformer installed on ith substation ($), ntti is the number of transformers installed on ith substation in year t and ne is the number of existing sub-transmission substations.
The decision variables of dynamic sub-transmission system expansion planning considering distributed generation can be described as follows:
3.2.3. Distributed generations installation cost (DGIC) The cost of DG units forms this part of fitness function is given by:
Installation time, location and size of DG units. Amount of supplied power by transmission network and DG units in each year and level of LDC. Installation time, number and the route of new subtransmission lines. 3.2. Fitness function It should be noted that choice of the properly objective function is very important in synthesis procedure for achieving the desired level of system performance. Thus, the mathematical model of the proposed fitness function is defined as follows:
neþnn T XX
bt C DG SDG it
ð4Þ
i¼1 t¼1
where CDG is the DGs’ installation cost ($/MW), SDG it is the capacity of DG installed on ith substation in year t (MW) and DG units are installed in modules of particular capacities, e.g. 10 MW. 3.2.4. Lines construction cost (LCC) Cost of lines constructed between sub-transmission substations and also between sub-transmission substations and transmission ones composes LCC according to Eq. (5):
LCC ¼
ns X T X bt clij ntij
ð5Þ
i;j¼1 t¼1
where clij is the cost of line constructed at corridor i–j which is dependent on line’s type and length ($), ntij is the number of new constructed circuits of line at corridor i–j in year t and ns is the number of sub-transmission and transmission substations, i.e. ns = ne + nn + ng.
P1
Load (MW)
DGIC ¼
3.2.5. DGs’ operation cost (DGOC) The power generation in DG units requires expending on providing of their input energy (fuel cost), and on their repairing and maintenance cost. The present-worth cost of DGs operation cost is calculated as follows [22]:
P2
P3
T1
T2
T3
Time (h) Fig. 1. Load–Duration Curve of substations’ loads.
DGOC ¼
neþnn T XX
bt
i¼1 t¼1
nld X PDG itd T d K DG
ð6Þ
d¼1
where PDG itd is the generated power of DG units installed on ith substation in year t and in dth level of LDC (MW), Td is the duration
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of dth level of LDC (h), KDG is the operational cost of DG ($/MW h) and nld is the number of levels of LDC (three levels in this paper). 3.2.6. Electricity cost (EC) Electric companies must pay for the electric energy, which they receive from the transmission network. Moreover, the cost of active power can be differing in different levels of LDC. Usually, it is high in the peak hours and is low in other times. The presentworth cost of providing the energy of sub-transmission system from the transmission network is given by
EC ¼
ng X T nld X X bt PGitd T d K Gd i¼1 t¼1
ð7Þ
Fig. 3. Structure of the proposed particle.
LLC ¼ lc3
ns X T nld X X bt rtij P2ij;td T d i¼1 t¼1
d¼1
ð11Þ
d¼1
where PGitd is the imported power into sub-transmission system from ith transmission substation in year t and in dth level of LDC (MW), K Gd is the electricity price of the transmission system in level d of LDC ($/MW h) and ng is the number of transmission substations.
where r iij is the resistance of corridor i–j in year t (ohm), Pij,td is the flowing power at corridor i–j, in year t and in level d of LDC (MW) and lc3 is the coefficient of lines losses cost ($/MW h volt2).
3.2.7. Substation’s loss cost (SLC) The loss of substation’s transformers consist of two parts: load and no load losses as given by Eq. (8). The load losses is the resistive losses which is dependent on the amount of transformers loading, but the no load losses is the iron core losses which has a constant value and is imposed to the network as long as the transformer is switched on [1]. The cost arisen from the energy losses of transformers should be taken into account in SSEP [29]. The cost of load and no load energy losses can be calculated with respect to the transformer type and the amount of resistive and core losses of the transformer using Eqs. (9) and (10):
To complete the model of dynamic sub-transmission system expansion planning problem including DG, which its fitness
SLC ¼ SLC1 þ SLC2 bt
i¼1 t¼1 neþnn T XX
bt
i¼1 t¼1
Defining the fitness function and coding of chromosomes regarding the problem unknowns and tuning the related variables of DCGA
ð8Þ
neþnn T XX
SLC2 ¼ lc2
Start
nld X Knli nt ti T d
Creating the initial population
ð9Þ
Decoding the chromosomes and calculation of DGIC and LCC for all of the planning years
d¼1 nld X Kli nt ti Pt2itd T d
ð10Þ
d¼1
where SLC is the substation’s total loss cost ($), SLC1 is the substation’s’ no load loss cost ($), SLC2 is the substation’s load loss cost ($), Knli is the no load loss of the transformer of ith substation (MW), Kli is the load loss coefficient of the transformer of ith substation (1/ MW), ntti is the number of transformers of ith substation in year t, Ptitd is the power passing through the transformer of ith substation in year t and in dth level of LDC (MW), lc1 is the substations no load loss cost ($/MW h), and lc2 is the substations load loss cost ($/ MW h).
Applying the reproduction operator of GA
SLC1 ¼ lc1
3.3. Problem constraints
Performing the LP technique, determining the power generation of DGs, power purchased from the transmission system and lines’ flows; calculation of SIC, SEC, DGOC, EC, SLC and LLC for all of the planning years based on the chromosome proposed by GA Calculating the objective function Applying the cross-over operator of GA with the rate of Pc
3.2.8. Lines losses cost (LLC) The lines loss is a function of the lines resistance and the amount of power flowing through them. The considered model in this study for the power flow calculations is DC load flow. The lines losses is inserted into the fitness function as follows:
Applying the mutation operator of GA with the rate of Pm
No
Is the stop condition satisfied? Yes Introducing the best chromosome
End Fig. 2. Different arrangements of parallel transformers on substations.
Fig. 4. Flowchart of the proposed approach.
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Fig. 5. Single-line diagram of the test network.
Table 1 Technical and economic data for the study. Parameter
Value
Electricity price in the first level of LDC ($/MW h) [34,39] Electricity price in the second level of LDC ($/MW h) Electricity price in the third level of LDC ($/MW h) Installation cost of DG units ($/MW) [34,39] Operational cost of DG units ($/MW h) [34,39] Number of planning years Discount rate (%)
50 30 20 200,000 25 5 12
Table 2 Parameters of DCGA used in simulation. Parameter
Value
Problem dimension Number of chromosomes Number of iterations PC Pm
415 20 2000 0.7 0.05
where Ps,it is the Loading of ith substation in year t (MW), rfsi is the reserve factor for ith substation and Xit is the set of installable capacities on ith substation in year t. Although, considering the reserve factor for the substations somehow guarantees the reliability of substations, but in some cases, e.g. when there is only one transformer installed on the substation, considering the reserve factor is ineffective. In this case, if that one transformer is out of service, the substation’s load will not be supplied. Thus, in this paper, the possibility of single contingency on the transformers of substations has been regarded for choosing the substation’s capacity. In this way, in the case of single contingency on a transformer of a substation, other transformers of that substation must not be overloaded. In this research, concerning the paralleling concept of transformers, the paralleled transformers (Fig. 2) on the substations are similar. 3.3.2. Operational constraint of DG units The generation of DG units must be less than their capacity. Thus, we have: DG 0 6 P DG itd 6 Sit
i ¼ 1; 2; . . .
; ne þ nc
d ¼ 1; 2; . . . ; nld
t ¼ 1; 2; . . . ; T function as given by Eq. (1), it is necessary to consider the following constraints in the proposed model: 3.3.1. Limitation on substations loading Conventionally, to consider the reliability of substations, a loading limit is considered such that the loading of each substation must be lower than that limit [4]. This constraint is defined as follows:
0 6 Ps;it 6 ð1 rfsi ÞSs;i ¼ 1; 2; . . . ; T
i ¼ 1; 2; . . . ; ne þ nn t
Ss;i 2 Xit
ð12Þ
where PDG itd is the generated power of DGs of ith substation in year t year and in dth level of LDC (MW). 3.3.3. Limitation of feeding the load by DG units In the design of distribution networks in presence of distributed generation, it is tried to provide the majority of the needed energy from transmission network via sub-transmission system not from DG units [33,34]. Therefore, in this study, the maximum amount of power generated by DGs is considered according to Eq. (14):
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Table 3 Results of substations expansion in two cases. Substation number
Installed or expanded capacity of substation in each year (MVA) Case 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
neþnn X
PDG itd 6 0:35Dtd
Case 2
1
2
3
4
5
1
2
3
4
5
3 30 3 30 2 30 3 30 3 30 3 15 3 30 3 15 3 15 3 7.5 3 30 3 30 2 30 3 30 2 24 3 30 2 30 3 30 3 15 3 15 3 15 3 30 4 30 3 30 2 30 3 15 3 15 3 30 3 15 2 30 4 15 3 15 3 15 3 15
3 30 3 30 2 30 3 30 3 30 4 15 3 30 4 15 3 15 3 7.5 3 30 3 30 2 30 3 30 2 24 4 30 2 30 3 30 3 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 3 15 3 15 3 15
3 30 3 30 3 30 3 30 4 30 4 15 4 30 4 15 3 15 3 7.5 4 30 3 30 2 30 3 30 2 24 4 30 2 30 4 30 4 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 3 15 3 15 3 15
4 30 3 30 3 30 3 30 4 30 4 15 4 30 4 15 3 15 3 7.5 4 30 4 30 2 30 3 30 3 24 4 30 3 30 4 30 4 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 4 15 3 15 3 15
4 30 3 30 3 30 3 30 4 30 4 15 4 30 4 15 3 15 3 7.5 4 30 4 30 2 30 3 30 3 24 4 30 3 30 4 30 4 15 3 15 3 15 3 30 4 30 3 30 3 30 3 15 3 15 3 30 3 15 3 30 4 15 4 15 3 15 3 15
3 30 2 30 2 30 2 30 3 30 3 15 3 30 2 15 2 15 2 7.5 3 30 3 30 2 30 3 30 2 24 3 30 2 30 3 30 2 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 2 30 2 15 2 30 2 15 2 15 2 15 2 15
3 30 2 30 2 30 2 30 3 30 3 15 3 30 2 15 2 15 2 7.5 3 30 3 30 2 30 3 30 2 24 4 30 2 30 3 30 2 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 2 30 2 15 3 30 3 15 3 15 2 15 2 15
3 30 2 30 2 30 2 30 3 30 3 15 3 30 3 15 2 15 2 7.5 3 30 3 30 2 30 3 30 2 24 4 30 2 30 3 30 2 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 2 30 2 15 3 30 3 15 3 15 3 15 2 15
3 30 2 30 2 30 3 30 3 30 3 15 3 30 3 15 2 15 2 7.5 3 30 4 30 2 30 3 30 2 24 4 30 2 30 3 30 3 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 3 30 2 15 3 30 3 15 3 15 3 15 3 15
3 30 2 30 2 30 3 30 4 30 3 15 3 30 3 15 2 15 2 7.5 3 30 4 30 2 30 4 30 2 24 4 30 2 30 3 30 3 15 3 15 3 15 3 30 3 30 2 30 2 30 2 15 2 15 3 30 2 15 3 30 3 15 3 15 3 15 3 15
ði ¼ 1; 2; . . . ; ne þ nc
0 6 nijt þ n0ij 6 nmax ij
t ¼ 1; 2; . . . ; T
i¼1
d ¼ 1; 2; . . . ; nldÞ
ð14Þ
where Dtd is the total load of sub-transmission system in year t and in dth level of LDC (MW). 3.3.4. Capacity limitation of new installed substations and existing expanded substations Usually, there is a limitation on installing the new substations or expanding the existing ones, such that we cannot install or expand a substation more than a specific capacity due to technical and site constraints. This limitation is given by:
0 6 Ss;it 6 Smax s;it
; i ¼ 1; 2; . . . ; ne þ nn t ¼ 1; 2; . . . ; T
ð15Þ
Smax s;it is the maximum installable capacity on ith substation in year t. Despite that DG units need small site area, however, there is a limitation for installing DG units, which can be regarded as follows: DG 0 6 nDG it 6 ni max
i ¼ 1; 2; . . . ; ne þ nn t ¼ 1; 2; . . . ; T
ð16Þ
where nDG ti is the number of DG units on ith substation in year t and nDG i max is the maximum number of installable DG units on ith substation. 3.3.5. Maximum constructible circuits for the sub-transmission lines This constraint is given by Eq. (17) and states that the constructed circuits at each corridor must be fewer than the maximum constructible circuits at that corridor.
i; j ¼ 1; 2; . . . ; ns
ð17Þ
where n0ij is the number of existing circuits at corridor i–j, nijt is the number of new circuits at corridor i–j in yeart t, and nmax is the maxij imum number of constructible circuits at corridor i–j. 3.3.6. Loading limit of sub-transmission lines In this paper, the reliability of sub-transmission lines has been considered as reserve factor [27]. Loading of the lines in different levels of LDC must be less than maximum loading limit as given by:
jP ij;td j 6 ð1 rflÞjPmax ijt j
ð18Þ
where rfl is the reserve factor for the lines. The reserve factor is considered to make sure that the lines are not overloaded in the case of single contingency on the other lines or on DG units. Moreover, for prevention of substations islanding in single contingencies of lines, at least two lines must be connected to each substation [35]. 3.4. DCGA and chromosome structure of the problem Standard genetic algorithm is a random search method that can be used to solve nonlinear system of equations and optimize complex problems. The base of this algorithm is the selection of individuals. It does not need a good initial estimation for the sake of problem solution. In other words, the solution of a complex problem can be started from weak initial estimations and then be corrected in evolutionary process of fitness. The genetic algorithm manipulates the strings that may be the solutions of the problem
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H. Shayeghi, A. Bagheri / Electrical Power and Energy Systems 48 (2013) 111–122 Table 4 Generated power of DG units in case 2. Substation number
Generated power of DG units in each year and each load level in MW (T1 = 1000 h, T2 = 5260 h, T3 = 2500 h) 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
2
3
4
5
T1
T2
T3
T1
T2
T3
T1
T2
T3
T1
T2
T3
T1
T2
T3
10 20 10 10 10 10 0 20 10 10 10 0 0 0 10 0 0 10 20 0 0 10 20 10 0 20 10 10 10 0 20 10 10 10
8.86 15.07 8.71 8.82 8.83 8.65 0 15.01 8.77 8.80 9.07 0 0 0 8.93 0 0 8.89 15.17 0 0 8.96 15.78 8.93 0 15.33 8.74 8.63 8.64 0 14.66 8.90 8.94 8.45
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 10 20 10 10 10 0 0 0 10 0 0 20 20 10 0 10 20 10 10 20 10 10 20 0 20 10 10 10
8.65 12.08 8.7417 12.15 8.63 11.79 8.35 11.92 8.57 8.61 8.66 0 0 0 8.7429 0 0 12.30 12.12 8.69 0 8.7993 12.55 8.76 8.71 12.33 8.58 8.38 11.36 0 11.42 8.7315 8.76 8.59
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 10 20 10 10 10 0 0 0 10 10 0 20 20 10 0 10 20 20 10 20 10 10 20 0 20 10 10 10
8.98 12.13 8.98 12.19 8.97 11.92 8.76 12.03 8.92 8.95 8.96 0 0 0 9.1013 9.07 0 12.33 12.25 9.03 0 9.12 12.45 12.31 9.05 12.21 8.94 8.73 11.58 0 11.64 9.05 9.10 8.94
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 10 20 10 10 10 0 0 0 10 10 10 20 20 10 0 10 30 20 10 20 10 10 20 0 20 10 20 10
9.28 11.92 9.27 11.88 9.29 11.61 9.06 11.73 9.24 9.28 9.27 0 0 0 9.38 9.35 9.32 11.94 11.84 9.32 0 9.39 18.8 11.91 9.31 11.86 9.27 8.99 11.33 0 11.35 9.33 11.91 9.22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 20 10 20 10 20 20 20 10 10 10 0 0 0 10 10 10 20 20 10 0 10 30 20 10 20 10 20 20 10 20 10 20 20
9.58 12.02 9.59 11.87 9.61 11.59 11.64 11.71 9.55 9.56 9.59 0 0 0 9.77 9.70 9.67 12.44 12.37 9.66 0 9.72 16.38 12.07 9.64 11.89 9.57 11.37 11.37 9.58 11.37 9.68 12.04 12.46
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[36,37]. This algorithm has been used to solve many practical problems such as transmission and sub-transmission network expansion planning [31]. The genetic algorithm generally includes three fundamental genetic operators of reproduction, crossover and mutation. These operators conduct the chromosomes toward better fitness. There are three methods for coding of problems based on genetic algorithm method: real codification, binary codification and decimal codification [36,38]. Due to that the parameters used in this study are of integer type, thus the third method, i.e. decimal codification genetic algorithm is employed. To code the information in the present work, the chromosome shown in Fig. 3 is considered. The proposed chromosome is generally composed of T parts, equal to the number of planning years. Each part is in turn divided into two sections. In the first section, the value of ith gene expresses the number of DG units that are installed on the ith substation in the related year. The number of added sub-transmission lines to each corridor of network in each year is represented by the value of second section. The number of genes of first section is equal to the number of existing and new sub-transmission substations (ne + nn); the number of genes of second section equals to the number of candidate corridors for construction.
3.5. Chromosome decoding and calculation of fitness function components With respect to the proposed chromosome, the cost of installed DGs is calculated with decoding Section 1 of the chromosome in each year. The cost of lines also is calculated by decoding Section 2.
Now, it is turn to determine the optimal power generation of DG units and the power purchased from the transmission network in each year and each level of LDC, to determine the other components of fitness function. The proposed method for this aim is explained as follows. 3.6. Performing the linear programming Providing the needed energy of sub-transmission system from the transmission network imposes an expense for the electric companies. In addition, supplying the whole load of sub-transmission system only by DGs is not economical. Thus, the participation degree of transmission system and DG units in providing the needed energy of sub-transmission system must be determined. For a given chromosome (the number of DG units on each substation and also the number of lines at different corridors are known), a subsidiary optimization, in each iteration of DCGA, is performed using linear programming to find the optimal power generated by DG units and also the optimal amount of power provided from the transmission system in each year and at each level of LDC. The fitness function optimized by LP technique is the sum of DGs operation cost and electricity cost of purchased power from the transmission network as given by:
Minimize F LP ¼ DGOC þ EC ¼
neþnn T XX
bt
i¼1 t¼1
ng X nld T nld X X X PDG bt PGitd T d K Gd itd T d K DG þ d¼1
i¼1 t¼1
ð19Þ
d¼1
The equality and inequality constraints used in the above problem solution by LP technique is described by Eqs.(20)–(24):
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Table 5 The results of lines expansion in two cases. From bus
To bus
Number of constructed line circuits in each year Case 1
1 2 3 3 4 5 5 6 6 6 7 7 8 9 9 11 11 12 13 13 14 14 14 15 16 17 18 18 18 19 19 20 21 22 22 23 24 25 26 27 28 29 30 31 21 32 22 33 34
HV1 HV1 HV1 HV2 HV1 HV1 HV2 7 HV1 HV5 8 HV4 9 10 HV1 HV1 HV2 HV2 14 HV 15 HV2 17 18 HV3 HV3 19 HV3 HV6 HV3 HV6 HV3 HV3 23 HV3 HV3 HV3 HV2 HV2 HV1 HV5 HV5 HV4 HV5 32 HV3 33 HV3 HV6
PGitd PDitd
Case 2
1
2
3
4
5
1
2
3
4
5
0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 2 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0
1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 2 1 0
1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1
1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0
0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 2 0 0 0 1 1 0 1 1 1 1 0 1 0
0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 2 0 0
1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 2 0 1 0 0 0 0 1 0 0 1 2 1 0 0 0 1 0
1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 2 2 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1
1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 2 0 0 1 0
1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0
ns X Pij;td ¼ 0
ð20Þ
j¼1
hitd hjtd X ij;t
ð21Þ
jPij;td j 6 ð1 rflÞjPmax ijt j
ð22Þ
DG 0 6 PDG itd 6 Sit
ð23Þ
Pij;td ¼
neþnn X
PDG itd 6 0:35Dtd
ði ¼ 1; 2; . . . ; ne þ nc
t ¼ 1; 2; . . . ; T
in year t and level d of LDC (MW), hitd is the voltage angle of ith substation in year t and level d of LDC (rad), Pmax is the capacity of corijt ridor i–j in year t (MW) and Xijt is the reactance of corridor i–j in year t (ohm). Eqs. (20) and (21) are the relations of DC load flow [29,35]. By performing the LP approach, the generated power of DG units and the power purchased from the transmission network in each year and at each level of LDC are determined. Consequently, the loading of lines and substations are found out and the related components of fitness function calculated. With these explanations, we can summarize the proposed method using the flowchart illustrated in Fig. 4.
d
i¼1
¼ 1; 2; . . . ; nldÞ
ð24Þ
where PDG itd is the generated power of DGs on ith substation in year t and level d of LDC (MW), PDitd is the load demand of ith substation
4. Numerical study To evaluate the effectiveness of the proposed method, it is applied to the real sub-transmission system of Zanjan Regional
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
Number of installed DG units in each year (capacity of each unit is 10 MW) 1
2
3
4
5
1 2 1 1 1 1 0 2 1 1 1 0 0 0 1 0 0 1 2 0 0 1 2 1 0 2 1 1 1 0 2 1 1 1
0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1
With DG Without DG
300 250 200 150 100
1
2
3
4
5
Year Fig. 6. Total expansion cost during the planning years.
Accumulative cost (M$)
Substation number
total expansion cost in each year (M$)
Table 6 The installed DG units on substations in case 2.
With DG Without DG
1027.06 871.26 704.53 530.43 331.93
1
2
3
4
5
Year Fig. 7. Accumulative total expansion cost during the planning years.
each substation is 4. The number of study years is 5, starting from now to 5 years ahead. Other required parameters are given in Table 1. Also, the parameters of DCGA used for simulation are presented in Table 2. It should be noted that these parameters have been selected in a way that the algorithm obtains the best results. To study the effects of distributed generation, as a new option for supplying the load of the system, considering the input data, the problem is solved in two cases:
Electrical Company, located in northwest of Iran. This system is consisted of 34 63/20 kV substations; eleven of them are newly installed substations, which must be connected to the network. The new substations are installed and operated at the beginning of planning. The 63/20 kV substations are fed by six 400/63 kV or 230/63 kV or 400/230/63 kV transmission substations. The singeline diagram of the test network is depicted in Fig. 5 and its details are given in the Appendix. The substation’s load value in second and third levels is considered 0.4 and 0.7 times of their peak value, respectively; the annual load growth in all levels of LDC is 7%. All the corridors between existing substation’s and the dashed ones are candidates for construction. The lines have the capacity of 40 MW, and the related cost is 80 k$/km [34,39]. The reserve factor for the lines is considered 30%; and the maximum constructible circuits of lines at the corridors are 4. Each DG unit has the size of 10 MW; and the maximum number of installable DG units on
Case 1: there are no installed DG units on the substations and the whole load of the sub-transmission system is provided from the transmission network. Case 2: DG units can be installed on the sub-transmission substations and participate in supplying the load of system. The results of the test, including the capacities of expanded or installed substations in each year, the constructed lines between substations in each year, the location and size of DG and their
Table 7 Cost components of two cases during the planning years. Present-worth cost (M$)
Experiment Case 1
Substations installation and expansion cost Lines construction cost DGs installation cost DGs operation cost Cost of purchased power from the transmission network Total cost Accumulative total cost
Case 2
1
2
3
4
5
1
2
3
4
5
65.03 78.44 0 0 183.79 327.26 327.26
1.16 32.66 0 0 175.58 209.4 536.66
0.92 40.08 0 0 167.75 208.75 745.41
0.78 20.97 0 0 160.26 182.01 927.42
0.26 21.57 0 0 153.1 174.93 1102.35
46.88 52.83 60 43.08 129.36 331.93 331.93
0.58 24.38 12.5 39.6 121.43 198.5 530.43
0.12 16.8 3.19 37.72 116.27 174.1 704.53
0.46 14.94 4.27 36.06 110.98 166.73 871.26
0.57 9.79 5.08 34.68 105.68 155.8 1027.06
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Table 8 Loss components of two cases during the planning years. Present-worth cost (M$)
Experiment Case 1
Lines loss Substations no-load loss Substations load loss
Case 2
1
2
3
4
5
1
2
3
4
5
84,842 198,021 94,945
115,326 211,163 102,437
178,492 222,994 109,458
138,057 234,292 119,347
138,164 238,235 134,205
39,022 169,776 61,164
29,885 176,347 63,380
55,423 177,658 71,765
29,228 184,223 78,234
113,888 193,421 84,122
4
x 10
Lines Loss (MW-hr)
With DG Without DG
11.3888
5.5423 3.9022 2.9338
1
2
3
4
5
Year Fig. 8. Lines loss during the planning years.
Substations no loas loss (MW-hr)
5
x 10
With DG Without DG
2.1116 1.9342
1.6978
1
2
3
4
generated power in each year and each level of LDC are listed in Tables 3–6. As it can be seen, the installation of DGs has decreased the expanded and installed capacities, such that the substations exist in the plan with the lower capacities and costs. Considering the DG units has also decreased the need for more lines and high capacity lines; consequently, the cost of lines construction is reduced. Table 4 shows that in the levels of LDC which the electricity cost of transmission system is high, some part of the system’s needed energy is generated by DG units. Also, in the levels of LDC that the operational cost of DG units is high, most of the system’s energy is injected from the transmission network into sub-transmission system to reduce the total operational cost. The cost components (the cost in each year and the accumulative cost) of the two experiments are given in Table 7 and Figs. 6 and 7. In the first year of study, due to installation of considerable number of DG units, the total cost in case 2 is more than case 1. However, this relatively high primary investment cost is compensated in the next years by low construction cost of lines, low expansion cost of substations and operational cost. The losses components with and without of DG are compared in Table 8 and Figs. 8–10. According to Table 8 and Fig. 8, the lines losses in the presence of DG, due to the lower loading of lines is less than that without the use of DG. In addition, installation of DGs on the substations has decreased the number of needed new transformers. Because of this, the no load loss of substations has been reduced as shown in Fig. 9. Similarly, the load loss of substations is decreased. Considering the total cost of the plan and the energy losses, the dynamic expansion planning of sub-transmission system by using distributed generation is more economical and it imposes less loss to the system.
5
Year
5. Conclusion
Fig. 9. Substations no-load loss during the planning years.
4
Substations load loss
x 10
With DG Without DG
9.4945 8.4122 7.8234 7.1765 6.338 1
2
3
4
Year Fig. 10. Substations load loss during the planning years.
5
Emerging of distributed generations has provided new options in the design and planning of power systems. The novelty of this paper is formulation of dynamic SSEP problem in the presence of DG units and solution of it by a developed hybrid DCGA and LP technique. The developed method uses both the computational capability of GA and advantage of mixed integer LP technique for achieving the high solution quality and accuracy. The proposed model with all system constraints is expressed as an optimization problem, where the objective function is comprehensive and includes different cost components. The other feature of this study is that the DG’s generated power at different load levels and the operational costs are determined. To demonstrate the effectiveness of the proposed method, it is applied on a real test system in two cases: one with considering DG units and another without them. Evaluating the results show that the installation of DGs has decreased the expanded and installed capacities. In addition, it was shown that considering DG units significantly reduced the expansion and operational costs of plan and different components of network loss. In general, it can be concluded that considering DG in dynamic SSEP problem is able
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H. Shayeghi, A. Bagheri / Electrical Power and Energy Systems 48 (2013) 111–122 Table 9 Specification of substations. Substation (bus) number
Substation name
Peak of load in base year (MW)
Existing capacity (MVA)
Expandable or installable capacity (MVA)
Voltage level (kV)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 HV1 HV2 HV3 HV4 HV5 HV6
Zanjan1 Ideloo Azadeghan Koshkan Sangshahr Saeedabad Dandi Mahneshan Soltanabad Zanjanrood Khamseh Sorboruy Bonab Soltanieh Simanzanjan Abhar3 Saeenghaleh Gheidar Garmab Zobahan Tolombekhaneh Hidaj Abhar1 Irankhodro Chavarzagh Gholshahr Shahrara Petroshimi Gholaber Maadenrui Simankhamseh Abhar4 Khorramdareh Zarrinabad Zanjan Qayati Abhar Dandi Ijrood Gheydar
61 38 42 48 65 41 65 41 19 13 63 61 19 56 24 69 29 63 33 22 20 54 74 37 35 20 21 40 25 35 38 30 28 25 – – – – – –
2 30 2 30 2 30 2 30 2 30 2 15 2 30 2 15 2 15 1 7.5 2 30 3 30 2 30 2 30 1 24 2 30 2 30 2 30 2 15 2 15 2 15 2 30 2 30 2 30 0 0 0 0 0 0 0 0 0 0 250 250 375 250 200 200
4 30 4 30 4 30 4 30 4 30 4 15 4 30 4 15 4 15 4 7.5 4 30 4 30 4 30 4 30 4 24 4 30 4 30 4 30 4 15 4 15 4 15 4 30 4 30 4 30 3 30 3 15 4 15 3 30 4 15 3 30 4 15 4 15 4 15 4 15 – – – – – –
63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 63/20 230/63 400/230/63 230/63 230/63 400/63 400/63
Table 10 Specification of lines. Corridor
Length (km)
Capacity (MVA)
Corridor
Length (km)
Capacity (MVA)
1-HV1 2-HV1 3-HV1 3-HV2 4-HV1 5-HV1 5-HV2 6–7 6-HV1 6-HV5 7–8 7–38 8–9 9–10 9-HV1 11-HV1 11-HV2 12-HV2 13–14 13-HV2 14–15 14–17 14-HV2 15–18 16-HV3 17-HV3 18–19
0 47 2.3 10 9 11 20 51 56 30 20 0 84 34 35 7 8 6 30 12 30 28 15 13 0 34 51
2 50 2 25 1 25 1 25 2 25 1 50 1 50 2 50 2 50 1 25 2 50 2 50 2 50 2 50 2 50 1 50 1 50 2 50 2 50 2 50 2 50 2 50 2 50 1 50 2 50 2 50 250
18–37 18-HV6 19-HV3 19-HV6 20-HV3 21-HV3 22–23 22-HV3 23-HV3 24-HV3 25-HV2 26-HV2 27-HV1 28-HV5 29-HV5 30–38 31-HV5 21–32 32-HV3 22–33 33-HV3 34-HV6
70 10 117 70 2 5 17 23 13 24 43 5 4 10 20 10 13 5 10 10 15 51
2 50 1 50 2 50 1 2 25 2 60 1 25 2 50 1 50 2 25 0 0 0 0 0 0 0 0 0 0 0 0
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to make the plan more optimal from the economic and technical points of view.
Appendix A. Test system data See Tables 9 and 10.
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