Optimal Allocation of Distributed Generations and

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Optimal Allocation of Distributed Generations and Remote Controllable Switches to Improve the Network Performance Considering Operation Strategy of Distributed Generations a

Mahdi Raoofat & Ahmad Reza Malekpour a

b

Faculty of Engineering, Shiraz University, Shiraz, Iran

b

Young Researchers Club, Zarghan Branch, Islamic Azad University, Zarghan, Iran Available online: 31 Oct 2011

To cite this article: Mahdi Raoofat & Ahmad Reza Malekpour (2011): Optimal Allocation of Distributed Generations and Remote Controllable Switches to Improve the Network Performance Considering Operation Strategy of Distributed Generations, Electric Power Components and Systems, 39:16, 1809-1827 To link to this article: http://dx.doi.org/10.1080/15325008.2011.615799

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Electric Power Components and Systems, 39:1809–1827, 2011 Copyright © Taylor & Francis Group, LLC ISSN: 1532-5008 print/1532-5016 online DOI: 10.1080/15325008.2011.615799

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Optimal Allocation of Distributed Generations and Remote Controllable Switches to Improve the Network Performance Considering Operation Strategy of Distributed Generations MAHDI RAOOFAT 1 and AHMAD REZA MALEKPOUR 2 1 2

Faculty of Engineering, Shiraz University, Shiraz, Iran Young Researchers Club, Zarghan Branch, Islamic Azad University, Zarghan, Iran Abstract This article proposes a new generation worth index for each load level to evaluate whether or not the distributed generation in that load level is worthwhile. The proposed index regards the impact of a distributed generation operation strategy on generation cost and reliability of the network. Based on the proposed generation worth index, the annual optimal operation strategy of distributed generation can also be estimated. Obviously, there is a mutual impact between the optimal operation strategy and the optimal site and size of distributed generations in the network. Hence, in the second part of the article, the proposed generation worth index and annual distributed generation operation strategy are utilized to determine the optimal size and location of distributed generations and the optimal location of remote controllable switches. The generation worth index is calculated to reduce the network energy loss, energy cost, and expected energy not supplied. The annual load is considered to be multilevel, and a genetic algorithm based method is developed for this optimization. Numerical results on a 33-bus distribution test network show the benefits of the proposed approach. Keywords generation worth index, distributed generation, genetic algorithm, remote controllable switch, optimal allocation, expected energy not supplied

1. Introduction Distributed generation (DG) is a promising approach for providing electric power in the heart of a distribution system. DGs are small generators that can operate in stand-alone mode or in connection with distribution networks [1, 2]. From an operational point of view, DGs can reduce the electrical network loss because they produce power in the proximity of load. Hence, it is better to allocate DG units in places where they can provide a higher loss reduction. Since DGs are so expensive, loss reduction is a very important and usual object for allocation of DGs [3, 4]. The other important effect of DGs on distribution networks is the improvement of network reliability. They can reduce the amount of required load shedding, the amount of interrupted load during faults, and the restoration time [5]. In islanding mode, it is Received 22 March 2011; accepted 16 August 2011. Address correspondence to Mr. Ahmad Reza Malekpour, Young Researchers Club, Zarghan Branch, Islamic Azad University, Zarghan 71896-37963, Iran. E-mail: malekpour_ahmad@ yahoo.com

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M. Raoofat and A. R. Malekpour

necessary that DGs maintain the voltage and frequency within their standard permissible levels, follow the load changes, and stay stable in large load switching events [6]. When allowed to operate in islanding mode, remote controllable switches (RCSs) are the most important tools to isolate islands. Therefore, they have significant effects on DG allocation, and simultaneous allocation of DGs and RCSs can conclude the optimal system reliability [7]. On the other hand, it is evident that the size of DGs has a significant role in both loss reduction and reliability improvement. As a result, the size of a DG must be optimized in the allocation stage. Optimal DG allocation to reduce the energy loss was proposed in [3, 4]. Simultaneous loss reduction and reliability improvement is another objective function for DG allocation [8, 9]. Optimal DG and recloser allocation was proposed to improve reliability in [10]. Simultaneous DG and RCS allocation in order to reduce the energy loss and improve the network reliability was proposed in [6]. Some useful algorithms have been proposed to solve the DG or RCS allocation problem. Voltage and loss sensitivity analysis [10] and the genetic algorithm (GA) [3, 6, 9] are some methods that have been used so far. In some other works, the GA was proposed for allocation of RCSs and manual switches to optimize system reliability [11]. The GA is also used for simultaneous allocation of switches and protective devices [12]. The immune algorithm [13], linear programming [14], ant colony [15], particle swarm [16], and simulated annealing [17] are some other methods that have been proposed to find the optimal locations for switches. Because of previously mentioned impacts of DGs on network performance, there are some different strategies for DG operation. To enhance the rate of return of investment, many DGs are operated with full capacity, while their operation cost is lower than the utility energy cost. On the other side, some DGs remain in standby mode to increase their availability and improve the reliability indices of the network. In [18], an hourly reliability worth (HRW) index was proposed to compare these strategies for each load level and determine the optimal schedule for DGs to work in standby or generation mode. The HRW index considered both reliability and energy cost aspects. Obviously, there is a mutual impact between DG operation strategy and DG optimal size and location. Therefore, this article suggests considering optimal DG operation strategy in the stage of DG allocation and network planning. In this article, two different modes are defined for operation of each DG at each load level: needed and not-needed modes. The first mode indicates that DG is needed to generate energy, and the latter denotes that DG is not needed to run at that load level but should be ready to start up in situations where the upstream system is interrupted [19]. In the next step, the article proposes a new generation worth index (GWI) for each DG at each load level, which considers advantages and disadvantages of generation of DG to determine which mode is better at which time. Based on the proposed GWI for each load level, the annual optimal operation strategy of the DG can be estimated, which has a significant influence on the revenue and performance of the DG. Considering this effect, the proposed algorithm uses a GWI and operating strategy of DGs, in addition to some other information and constraints, to determine the optimal size and location of DGs and the optimal location of RCSs. The objective function of this optimization is the reduction of the network loss and total energy cost and improvement of the reliability. A GA-based algorithm is developed to solve the problem. Numerical studies on a 33-bus test network show the capabilities of the proposed algorithm.

Optimal Allocation of DGs and RCSs

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2. Problem Definition In deregulated power systems, distribution companies and consumers can choose the supplier of their electrical energy, and utility and non-utility DGs are suitable choices for this purpose. On the other hand, DGs are expensive devices and their return of investment is very important for investors. Thus, usually it is accepted that each DG produces and sells the energy, while its generation cost is less than the market energy cost. Two main other results of using DGs may be loss reduction and reliability improvement. Only those DGs have considerable impact on improvement of the network reliability that can operate in islanding mode. Besides, RCSs have a major effect on the network reliability. Hence, simultaneous allocation of DGs and RCSs is better for assessing rather than sequential approaches [6]. Therefore, the main problem in this article is to find the optimal size and location of DGs and optimal location of RCSs in the network in order to reduce the energy bill and energy loss and also increase the reliability and the revenue of DGs. It is obvious that the optimal operation strategy of any DG during its lifetime affects its revenues and, thus, its optimal size and site. Vice versa, its location and size has a significant impact on its optimal strategy and its revenue. To regard this interaction, this article proposes a novel index, the GWI, which can be used to estimate the operational aspects of DG in the stage of planning. The index is useful to compromise between the benefits of continuous generation of DG and its role in the network reliability. It is noticeable that the continuous generation of DG may reduce its availability with a negative impact on reliability of the network. Two operation modes are supposed for each DG at each load level: needed and not needed. In the needed mode, the DG generates energy, and in the not-needed mode, it remains in the standby situation and is ready to start up when needed. The GWI can be used to decide which mode is better for each load level. Modeling the annual load curve by a multi-level load model, the optimal annual operation strategy of each DG can be determined. In a GA-based method, many different plans are proposed as populations of chromosomes. Each chromosome defines the size and location of some DGs and some RCSs in the network. Using the GWI, the annual operation strategy of each DG can be deduced. Finally, each chromosome is evaluated, and the optimal plan is concluded.

3. Reliability Assessment and Markov Process Modeling The distribution network of Figure 1 shows the location of DG and three RCSs in a typical network to describe the reliability aspects of the problem. This network is partitioned into four distinguishable parts. IS indicates the corresponding island of DG and US depicts the upstream system of the island. LS and DS are the lateral and downstream subsystems. To evaluate the reliability of the network with emphasis on the island, in the first step, considering all components of the island to be perfect, the reliability indices are calculated for the remaining system. The average interruption frequency (AIF) and average interruption duration (AID) of all buses are also calculated in this step using the algorithm of [20]. The calculated expected energy not supplied (EENS) of the remaining system is called EENSR . In Figure 1, the AIF and AID of bus 4 are the failure rate () and repair rate () of the upstream system of the island, and they are named US and US , respectively. It should be noted that the DG strategy does not have any influence on EENS of the other parts of the network.


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Figure 1. Typical distribution system with one DG and three RCSs. (color figure available online)

In the next step, the reliability of the island is assessed for both the needed and notneeded modes. Two complete state-space diagrams of Figures 2 and 3 are developed for needed and not-needed modes, and the Markov process is utilized to calculate the EENSxIS of the island in both modes. Then, total EENS of the network is calculated as follows: EENS D

NI XS

EENSxIS C EENSR ;

(1)

i D1

where x denotes the DG mode, and EENSR is the EENS of the remaining system. The results of this stage are the determinant in the decision on which mode is better. The above procedure is executed for each load level, separately. Figures 2 and 3 demonstrate the state-space diagrams of the two mentioned modes of DG. In these diagrams, and mention the failure and repair rates, respectively. The subscripts of and may be DG, US , and IS , which mean DG, upstream system, and island system, respectively. I S and I S can be calculated as below based on method of [20]: I S D

Nb X

i ;

(2)

Nb X

i :ri ;

(3)

i D1

UI S D

i D1

rI S D I S D

UI S ; I S 1 rI S

;

(4) (5)

where N b is the number of branches of the island and i and i are the failure and repair rates of the i th branch of the island, respectively. In the above diagram, the upstream system is modeled with two possible up and down states, while the island states are defined as F (failure) and S (success). In the S state, all branches of the island are healthy, but it does not mean that the island is



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Figure 2. State-space diagram when DG is needed.

energized. The DG model is similar to the island, but there is another state when the DG is successful but is deficient to supply the load of the island. This mode is notated with SD (supply deficiency). The deficiency of the DG capacity is modeled with the variable I , which is defined by Eq. (6): ( 1 if DG capacity island demand I D : (6) 0 if DG capacity < island demand When the DG is required to start up, e.g., in transition from state 8 to state 3, it may fail to run with the probability of PS . In state 1 of Figure 2, the needed DG is available and is running, and the upstream system and island are also completely successful. If the upstream system fails, the new state depends on DG capacity. If DG is deficient at that load level, a transition occurs to state 4, where the island and DG are successful but DG is deficient to supply the island. If the DG capacity is enough to supply the island, the next state will be state 3. In state 5, the island is successfulm but because there is no available power source, the island is interrupted. In state 8, the upstream system is down, and the island is also failed. After repair of the island, the possible states are 3, 5, or 4, according to the situation. In state 6, the upstream system and DG are available, but because the island is


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Figure 3. State-space diagram when DG is not needed.

in failure mode, it is interrupted. After repair of the island, it will be reconnected to the upstream system, and some minutes later, the DG will be started. If the DG fails to start, the next state will be state 2, and in success startup, the next state is 1. Figure 3 depicts the state-space diagram of the system when DG is scheduled as not needed. The state-space diagram is very similar to previous diagram with some differences. For example, when the system is in state 1, DG is successful but not needed; therefore, it is down. If the upstream system is failed, DG should be started up, and one of the states 3, 4, and 5 will be the next state, according to the conditions. Contrary to Figure 2, there is no transition from state 4 to 2 and from state 8 to 5. This is because DG is not needed, and no start up occurs. For both state-space diagrams, which are depicted in Figures 2 and 3, the limiting states can be calculated using the Markov process technique. The probability of i th state for needed and not-needed modes are notated with RiN and RiNN , respectively.

4. Calculating GWI The GWI is defined based on the reliability indices and financial aspects of each strategy. Hence, in this part of the paper, both reliability and financial aspects of these strategies are formulated to be used in GWI.


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In both needed and not-needed modes, states 1, 2, and 3 represent the up state for the island, and the island is energized, but the other states represent the down state, and the island is interrupted. Therefore, the island availability and unavailability for both modes are calculated by Eqs. (7) and (8) for each load level, respectively: AxIS D

3 X

Rix ;

(7)

Rix ;

(8)

i D1

UIxS

D

9 X


i D4

where Rix is the probability of state i and superscript x is N or NN, indicating the needed or not-needed modes, respectively. EENS and the expected total interruption cost (ETIC) of the island are calculated by Eqs. (9) and (10), respectively, for both DG operation modes: EENSxIS D UIxS :LI S :8760;

(9)

ETIC xIS D EENSxIS :CIC;

(10)

where CIC is the customer interruption cost ($/MWh), and LI S is the island load (MW), respectively. The other aspect of DG operation that should be regarded in the GWI is the influence of DG on the energy cost. Equations (11)–(15) calculate the energy cost of the island for states 1 to 3, in which the island is energized. ECiX is the energy cost of the island in operation mode of X and in state i . It is considered that DG can export or sell the energy to the upstream system when it is possible and worthwhile; EC1N D ŒLI S :CDG :I

Œ.LDG

C ŒLDG :CDG C .LI S

LI S /:.CU LDG /:CU :.1

CDG /:I:H (11)

I /:H;

EC1NN D LI S :CU ; H D

(

(12)

1 if DG production cost < utility energy cost 0 if DG production cost > utility energy cost

:

(13)

According to Eq. (11), in the needed mode of DG operation, when the DG capacity is sufficient to supply the island load (I D 1), the energy cost consists of the cost of supplying the island load using the DG (the first term) minus revenue from the energy exported to the United States while H D 1 (the second term). The third term of Eq. (10) represents the energy cost of the island when the DG is deficient to provide the whole island load (I D 0) and supplies a portion of the load related to its capacity. The remainder of the island load is served by the utility. In states 2 and 3, the energy cost formals are the same for both modes: EC2X D LI S :CU ;

(14)

EC3X D LDG :CDG ;

(15)

1816


where X is N or NN, LDG is the DG capacity (MW), LI S is the island load (MW), CDG is the DG generation cost ($/MWh), and CU is the utility energy cost ($/MWh). The expected total energy cost (ETEC) of the island for needed and not-needed modes are


ETEC N IS D

3 X

PiN :ECiN ;

(16)

PiNN :ECiNN ;

(17)

i D1

ETEC NN IS D

3 X i D1

The GWI is proposed to determine the optimal operation mode of DGs: ˚ N GWI D ETEC N I S C ETIC I S

˚

NN : ETEC NN I S C ETIC I S

(18)

For each load level, the GWI indicates whether or not the DG and running is worthwhile. In the case of a positive GWI, the not-needed mode is worthwhile; when it is negative, the best mode is needed. Figure 4 depicts a flowchart of the proposed procedure. In the next section, a multi level load is proposed to model hourly load variation, and the GWI is calculated for each load level separately.

5. Optimization Problem Formulation The main object of the proposed problem is to find the optimal location of DGs and RCSs in distribution networks. The optimal number of DGs and RCSs to be installed and the suitable size of each DG will be determined during the optimization problem. The estimated load duration curve (LDC) is used to obtain a more accurate load model and more optimal plan. In this article, a similar LDC is considered for all loads, but it is possible to use different LDCs for different load points. A GA-based algorithm is used to find the optimal plan [6]. As described in Section 6, each chromosome is a possible plan for location and size of DGs and location of RCSs. The first step in the evaluation of each chromosome is calculating the GWI for each proposed DG at each load level. Then the fitness function is calculated in the next step.

5.1.

Objective Function

In the proposed fitness or objective function, the installation cost of DGs and RCSs, their operation and maintenance cost, revenues from DG generation, reduced energy loss, and the total customer interruption cost of the network are considered. The multi-level load model is used, and the GWI is evaluated for all load levels for each DG. The proposed objective function, which is formulated by Eq. (19), considers interest rate, inflation rate,

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Figure 4. Flowchart to calculate the EENS of the network using GWI (NI S is the total number of islands, and LL is the load level). (color figure available online)

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load growth rate, and economic lifetime of equipment: 0 1 NDG NS X X A min.J / D @ CostDG CostRCS i ns;i C i ns;j i D1

0

C@


C

j D1

NDG X i D1

LL X

CostDG om;i C

NS X

CostRCS om;j

j D1

LL X

Ki :

i D1

NDG X

i Egen;j C

j D1

LL X i D1

ENSi :CICCPV2 ; i

1CPV1

Ki :Eloss;j A

(19)

i D1

where CICi is the customer interruption cost at the i th load level ($/MWhr), CostDG i ns;i is the installation cost of the i th DG, CostRCS om;j is the operation and maintenance cost of the i th DG, RCS Costi ns;j is the installation cost of the j th RCS, CostRCS om;j is the operation and maintenance cost of the j th RCS, Egen;j is the energy produced by the j th DG, Eloss;i is the energy loss during the i th load level, Ki is the cost of energy ($/kWh) in load level i , LL is the number of load levels, NDG is the total number of DGs installed in the system, and N s is the total number of RCSs installed in the system. The cumulative present value (CPV) method [21, 22] has been applied to evaluate the total costs and benefits of proposed plan during the economic lifecycle of equipment. The method of the time value of money or the CPV method is based on the premise that an investor prefers to receive a payment of a fixed amount of money today rather than an equal amount in the future. This method converts all costs and benefits of the plan during the lifecycle to the first year of operation. The following equations describe the concept: PV1 D CPV1 D PV 2 D CPV2 D

1 C Ii nf ; 1 C Ii nt .1

P V 1/EL ; 1 PV1

.1 C Ii nf /.1 C Lg/ ; 1 C Ii nt .1

P V 2/EL ; 1 PV2

where EL Ii nt Ii nf LG

is the economic lifetime of equipment, is the interest rate, is the inflation rate, and is the load growth rate.

(20) (21) (22) (23)

Optimal Allocation of DGs and RCSs 5.2.

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Constraints

Active and reactive power flow (Eqs. (24) and (25)) are equality constraints that should be met at all nodes of the network for all load levels. Bus voltage limits (Eq. (26)) and the maximum permissible loading of lines (Eq. (27)) are inequality constraints that should be considered: Pi D Vi

N X

Vj Yij cos.ıi

ıj

ij /;

(24)

ıj

ij /;

(25)

j D 1 W NN ;

(26)

j D1


Qi D Vi

N X

Vj Yij sin.ıi

j D1

Vmin Vj Vmax ; Ii Imax ;

i D 1 W NBR ;

(27)

where Ii is the current of the i th transmission line, NBR is the number of branches, Pi , Qi are the injected active and reactive power at the i th bus, Vi ∠ıi is the voltage phasor of the i th bus, and Yij ∠ ij is the ij th element of Y bus. In island operation, DGs should be able to supply the required power. Thus, in each load level, the reliability assessment will consider only those DGs that can supply the total load of the corresponding island; (28)

LI S LDG :

The maximum capacity of DGs that can be installed in the network is restricted by DG penetration rate: NDG X i D1

LiDG Kp :

X

Pload ;

(29)

where KP is the maximum acceptable DG penetration.

6. Proposed GA One of the most important steps in any GA optimization is defining suitable chromosomes. In the proposed GA, each chromosome consists of two strings. The first binary string indicates the location of the RCSs, and the second part that is an integer string determines the existence of DGs in system nodes and relative sizes. The length of each part is equal to the number of candidate locations for RCSs and DGs, respectively. The value of 1 for any bits of the RCS string shows the optimality of the RCS on that candidate location. The integer number in any bits of DG strings proposes the size of DG that is installed at the corresponding location. If any bit is zero, it means that no kind of DG is installed at that candidate location. Figure 5 illustrates the proposed chromosome.

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Figure 5. Proposed chromosome.

NSW is the number of candidate locations for RCS installation, and NDG is the number of candidate nodes for DG installation. The fitness function is described in Section 5. In proposed algorithm, a multi-point crossover operator is used. The chromosome includes two separated strings, and the second string defines the location and size of DGs. Therefore, three different mutation operators are defined for location of RCSs, location of DGs, and size of DGs. The operators are described completely in [7].

7. Numerical Studies In order to show the capability of proposed algorithm, two numerical examples are studied and compared with the base case (before placing any DG or RCS). In the first case, the algorithm is used to find the best locations for DGs and RCSs in the network based on cost privilege. The optimal operation strategy of each DG, in this case, is considered to be continuous operation, while the DG production cost is less than the utility energy cost. The availability of DG is also regarded [7]. The second case uses the GWI to determine the annual optimal operation strategy of DG in the procedure of allocating DGs and RCSs. A 33-bus distribution network, shown in Figure 6, is used as a usual distribution test network [23]. The parameters of lines and loads are presented in the Appendix. The candidate locations for RCSs and DGs are also shown in Figure 6. The total number of possible RCSs in the network is limited to six switches. Interest rate, inflation rate, and load growth rate are assumed to be 0.05, 0.08, and 0.025, respectively. Economic lifecycle is considered to be 15 years. The maximum acceptable DG penetration (Kp) is considered to be 35%. The annual load curve is broken down to three load levels with different load values and duration, which are defined in Table 1. The costs of energy, EENS, DG generation cost, and utility energy cost are also shown in Table 1 for different load levels. The installation and maintenance cost of RCSs are assumed to be 18,000 and 2000 ($/yr) respectively. The mean time to failure (MTTF) and mean time to repair (MTTR) of DGs are 550 and 75 hr, respectively. Table 2 defines the size and capital cost of available DGs [10]. The GA described in Section 6 is utilized with 100 initial populations. Crossover and mutation factors are 0.7 and 0.2, respectively, and 10% of each new generation is produced randomly. Once the best solution has no improvement after ten generations, the mutation and random population factors are increased to prevent the algorithm ending up in local minimum. The best solution is determined by 200 runs of the algorithm. The penalty method is used when constraint is violated. As mentioned previously, to show the main contribution of this article, two cases are studied and compared with the base case.



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Figure 6. Thirty-three-bus network with RCS candidate locations and location of protective fuses.

Table 1 Cost of energy and EENS for different load levels

Load level

Hour

Load value

Loss cost ($/MWh)

EENS cost ($/KWh)

Utility energy cost ($/MWh)

Peak Medium Base

1400 4440 2920

1 0.4 0.3

70 70 70

200 200 200

110 79 49

DG generation cost ($/MWh) 43 43 43

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Table 2 Candidate nodes, size, capital cost and operation and maintenance cost of DGs Size

DG specification

1 2 Candidate nodes


7.1.

Installation cost ($)

500-kW micro-turbine 330,980 1-MW micro-turbine 551,640 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33

Base Case

For the base case without any RCS or DG, EENS and energy loss are calculated at 13,237,509.33 and 81,106.29 MWh/yr, respectively. The fitness function for this case is $444,133,159.062. 7.2.

Case 1

In this case, the operation strategy of DGs is based only on cost privilege. Based on Table 1, all over the year, DG generation cost is less than the utility energy cost. Therefore, the DG strategy is needed, all through the year, with an availability of 0.88. Figure 7 and Table 3 completely illustrate the proposed plan. 7.3.

Case 2

In this case, RCSs and DGs are allocated simultaneously based on GWI calculated for each load level. The RCSs and DGs locations are shown in Figure 8, and the results are tabulated in Table 4. Although the number of RCSs and DGs, and the total capacity of DGs, are the same as Case 1, the optimal operation strategies of some DGs are different. Table 3 Proposed locations, sizes, and operation mode of DGs for Case 1 Island number

Island load

DG capacity (MW)

DG node

1

1.38

1

20

2

0.675

1

24

3

0.405

1

30

4

1.395

1

13

Load level Base Medium Peak Base Medium Peak Base Medium Peak Base Medium Peak

DG mode N N N N N N N N N N N N



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Figure 7. RCSs and DGs allocated for Case 1.

So, the optimal location of DGs and RCSs are affected and changed. In both cases, DGs are allocated in laterals. This is because, in laterals, DGs can provide higher loss reduction. Table 4 demonstrates the calculated values for ETEC, ETIC, and GWI of each island in addition to demand of all islands and the size of proposed DGs. As shown in Table 4, contrary to Case 1, the operation modes of DG in the base load have been changed from the needed to the not-needed mode for islands 3 and 4. According to expectations, the ETEC value in the needed mode is less than in the notneeded mode in all load levels, and the ETIC value of the not-needed mode is better than the case of the needed mode. Only in those cases, the not-needed mode is selected when the ETIC in the not-needed mode outweighs the ETEC advantages of the needed mode. Table 5 shows the EENS, loss, fitness values, and the DG benefits for both cases.


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Figure 8. RCSs and DGs allocated for Case 2.

As Table 5 shows, in Case 1, the existence of DGs and RCSs has reduced EENS, loss, and fitness function. It reveals that in comparison to the base case, the revenue from installation of these DGs and RCSs compensate the investment cost. In Case 2, using the proposed GWI and considering the optimal operation strategy of DGs in each load level, the location of DGs and RCSs is changed, as shown in Figure 2. Although the maximum allowable RCSs are utilized in both cases, the EENS of Case 2 is decreased with regard to change in the location of RCSs. As the proposed method considers reliability cost aspects, the location of RCSs has changed from candidate locations 12 and 13 to 3 and 5, which is because of the high failure rate of the lower lateral as well as its long distance. Also, the DG installed at node 30 covers a larger island in comparison to Case 1. This leads to a reduction in the ETIC of the other islands, while the ETIC of this island increased. As a result, the EENS of the network decreased, while the loss cost of the network increased,


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Table 4 Proposed locations, sizes, and operation mode of DGs and RCSs for Case 2 Island number

Island load (MW)

DG capacity (MW)

DG node

0.675

1

14

0.405

1

20

1.395

1

24

1.38

1

30

1


2

3

4

Load level

DG mode

Base Medium Peak Base Medium Peak Base Medium Peak Base Medium Peak

N N N N N N NN N N NN N N

ETEC N IS

N ETEC N IS

ETIC N IS

N ETIC N IS

GWI

6.401 8.582 17.048 2.435 17.099 12.623 16.985 14.166 96.165 16.76 13.689 94.494

9.920 21.322 74.218 5.952 12.791 44.520 20.503 44.063 153.323 20.278 43.579 151.64

10.843 14.457 36.142 4.957 6.609 16.522 15.012 20.017 230.196 33.743 44.991 290.638

9.943 13.257 33.144 3.472 4.630 11.574 10.990 14.653 230.196 29.767 39.689 290.638

2.619 28.705 54.172 2.033 27.911 52.195 0.504 24.534 57.158 0.459 24.589 57.147

Table 5 EENS, loss, and fitness values and the DG benefits for both cases

EENS (MWh/yr) Loss (MWh/yr) Benefit ($) Fitness function ($)

Base case

Case 1

Case 2

13,237,509.33 81,106.29 0 444,133,159.062

2,237,555.09 46,086.07 892,812.8 58,566,694.65

1,914,028.61 58,589.4 930,326.4 47,206,620.17

as shown in Table 5. Overall, using the proposed method, the fitness function of network decreased.

8. Conclusion DGs may be utilized in the needed or not-needed mode at each load level. To estimate the optimal operation strategy of DG in a time-variant load model, this article proposed a novel GWI that determines which mode of operation is more beneficial for DG at each load level. In the next step, a comprehensive algorithm was proposed in this article to find the optimal places of RCSs and DGs to minimize EENS, energy loss, and energy cost of network. As the main contribution, the proposed DG allocation algorithm considers the mutual impact of optimal operation strategy and optimal site and size of DGs in the planning phase. Contrary to what is commonly believed, the DG does not necessarily run during hours that the DG generation cost is smaller than the utility energy cost.

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Appendix A1. Network line data From

To

R1 ()

X1 ()

f (yr)

r (hr)

From

To

R1 ()

X1 ()

f (yr)

r (hr)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.0922 0.493 0.366 0.3811 0.819 0.1872 1.7114 1.03 1.044 0.1966 0.3744 1.468 0.5416 0.591 0.7463 1.289

0.047 0.2511 0.1864 0.1941 0.707 0.6188 1.2351 0.74 0.74 0.065 0.1238 1.155 0.7129 0.526 0.545 1.721

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.6 0.3 0.3 0.3 0.3

4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6

17 2 19 20 21 3 23 24 6 26 27 28 29 30 31 32

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

0.732 0.164 1.5042 0.4095 0.7089 0.4512 0.898 0.896 0.203 0.2842 1.059 0.8042 0.5075 0.9744 0.3105 0.341

0.574 0.1565 1.3554 0.4784 0.9373 0.3083 0.7091 0.7011 0.1034 0.1447 0.9337 0.7006 0.2585 0.963 0.3619 0.5302

0.3 0.6 0.3 0.3 0.3 0.6 0.3 0.3 0.6 0.3 0.3 0.3 0.3 0.3 0.3 0.3

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

Appendix A2. Network peak load data Bus

P (MW)

Q (Mvar)

Bus

P (MW)

Q (Mvar)

Bus

P (MW)

Q (Mvar)

Bus

P (MW)

Q (Mvar)

2 3 4 5 6 7 8 9

0.15 0.135 0.18 0.09 0.09 0.3 0.3 0.09

0.09 0.06 0.12 0.045 0.03 0.15 0.15 0.03

10 11 12 13 14 15 16 17

0.09 0.0675 0.09 0.09 0.18 0.09 0.09 0.09

0.03 0.045 0.0525 0.0525 0.12 0.015 0.03 0.03

18 19 20 21 22 23 24 25

0.135 0.135 0.135 0.135 0.135 0.135 0.63 0.63

0.06 0.06 0.06 0.06 0.06 0.075 0.3 0.3

26 27 28 29 30 31 32 33

0.09 0.09 0.09 0.18 0.3 0.225 0.315 0.09

0.0375 0.0375 0.03 0.105 0.9 0.105 0.15 0.06