Optimal DG placement in deregulated electricity market

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1 Electric Power Systems Research 77 (2007) Optimal DG placement in deregulated electricity market Durga Gautam, Nadarajah Mithulananthan Electric Power System Management, Energy Field of Study, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand Received 19 August 2006; received in revised form 14 November 2006; accepted 16 November 2006 Available online 29 December 2006 Abstract This paper presents two new methodologies for optimal placement of distributed generation (DG) in an optimal power flow (OPF) based wholesale electricity market. DG is assumed to participate in real time wholesale electricity market. The problem of optimal placement, including size, is formulated for two different objectives, namely, social welfare maximization and profit maximization. The candidate locations for DG placement are identified on the basis of locational marginal price (LMP). Obtained as lagrangian multiplier associated with active power flow equation for each node, LMP gives the short run marginal cost (SRMC) of electricity. Consumer payment, evaluated as a product of LMP and load at each load bus, is proposed as another ranking to identify candidate nodes for DG placement. The proposed rankings bridges engineering aspects of system operation and economic aspects of market operation and act as good indicators for the placement of DG, especially in a market environment. In order to provide a scenario of variety of DGs available in the market, several cost characteristics are assumed. For each DG cost characteristic, an optimal placement and size is identified for each of the objectives. The proposed methodology is tested in a modified IEEE 14 bus test system Elsevier B.V. All rights reserved. Keywords: Distributed generation; Locational marginal price; Optimal power flow; Electricity market; Social welfare 1. Introduction DGs are considered as small power generators that complement central power stations by providing incremental capacity to power system. Although DGs may never replace the central power stations, these can be an attractive option when constraints in transmission network prevent economic, or least expensive, supply of energy reaching demand. However, penetration and viability of DG at a particular location is influenced by technical as well as economic factors. The technical merits of DG implementation include voltage support, energy-loss reduction, release of system capacity, and improve utility system reliability [1]. Economical merit, on the other hand, encompasses hedge against high electricity price. This incentive is enhanced with vertical unbundling of utilities and market mechanisms such as real time pricing. By supplying loads during peak load periods, where the cost of electricity is high, DG can best serve as a price hedging mechanism. DG can have a great value in a highly congested area where LMPs are higher than elsewhere. In such situation, it can serve Corresponding author. Tel.: ; fax: address: mithulan@ait.ac.th (N. Mithulananthan). the local load and effectively reduce the load. The placement of DG, however, should be carried out with due consideration to its size and location. The placement should be optimal in order for the maximum benefit of DG implemented in the network. Improper placement in some situations can reduce benefits and even jeopardize the system operation. Numerous techniques are proposed so far to address the viability of DGs in power system. Capacity investment planning of distributed generation under competitive electricity market from the perspective of a distribution company is proposed in Ref. [2]. An approach for optimal design of grid connected DG systems in relation to its size and type to satisfy on-site reliability and environmental requirements is presented in Ref. [3]. Besides, several optimization tools, including artificial intelligence techniques, such as genetic algorithm (GA), tabu search, etc., are also proposed for achieving the optimal placement of DG. An optimization approach using GA for minimizing the cost of network investment and losses for a defined planning horizon is presented in Ref. [4]. GA has been used to obtain penetration level of DG for minimizing the total cost of operation including fixed and variable cost in Ref. [5]. The method for optimal placement of DG for minimizing real power losses in power distribution system using GA is proposed in Ref. [6]. The gradient and second order methods to determine the optimal location for /$ see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.epsr

2 1628 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) the minimization of losses or line loading is employed in Ref. [7]. An iterative method that provides an approximation for the optimal placement of DG for loss minimization is demonstrated in Ref. [8]. Analytical methods for determining optimal location of DG with the aim of minimizing power loss are proposed in Ref. [9]. Placement and penetration of distributed generation under LMP based standard market design with the objective of generation cost minimization is proposed in Ref. [10]. Optimal placement of DG with Langrangian based approach using traditional pool based OPF and voltage stability constrained OPF formulations is proposed in Ref. [11]. Present study encompasses the placement of DG in a pool based wholesale electricity market with centralized dispatch. DG is considered as a negative load. The placement problem is formulated for the two different objectives, namely, maximizing social welfare and maximizing the profit of DG owner. The paper is organized in five sections. Section 2 sets out the OPF formulation dealing with social welfare maximization problem. Section 3 presents the methodology adopted to evaluate the placement of DG wherein the rankings used to identify the candidate nodes for the placement are also discussed. The OPF results and inferences drawn from the same are covered in Section 4. Several cases have been considered to depict possible scenarios and results have been shown in graphical and tabular format. The conclusions that can be drawn from the analysis are presented in Section Problem formulation The problem is formulated with two distinct objective functions, namely, social welfare maximization and profit maximization. Social welfare is defined as the difference between total benefit to consumers minus total cost of production [12]. It is the sum of producers surplus and consumers surplus as shown in Fig. 1. In general term, it represents the surplus to society and is maximum when the market price is equal to the marginal cost of producing the last unit of electricity [12]. The traditional OPF algorithm for cost minimization is modified to incorporate the demand bids, in addition to the generation bids. LMP is determined as the lagrangian multiplier of the power balance equation in OPF. The generator and customer bids are taken as inputs to OPF. The base case OPF based on social welfare maximizing algorithm evaluates the generation dispatch, demands and prices at each of the nodes. The nodal prices so obtained are indicator for identifying candidate nodes for DG placement. The placement is intended to meet the demand at a lower price by changing the dispatch scenario. The profit maximization problem is viewed from the perspective of DG owner, who chooses to place DG at the load nodes. In order for them to achieve maximum revenue out of the dispatched power, placement and size of DG chosen should reduce the LMP to a value that maximizes the profit. As higher LMP value might considerably lower the revenue making the profit negative Social welfare maximization The objective function is formulated as quadratic benefit curve submitted by the buyer (DISCO) minus quadratic bid curve supplied by seller (GENCO) minus the quadratic cost function supplied by DG owner. N max (B i (P Di ) C i (P )) C(P D ) (1) i=1 Alternatively, the maximization problem (1) can be formulated as a minimization problem with multiplying the objective function by 1. N min (C i (P ) B i (P Di )) + C(P D ) (2) i=1 subject to 2.2. Equality constraints The network for the transmission of electric energy is modeled via the power balance equation at each node in the network. The sum of power flows, active and reactive, injected into a node minus the power flows extracted from the node has to be zero. N P i = P + P D P Di = v i [v j {G ij cos(δ i δ j ) j=1 +B ij sin(δ i δ j }] (3) N Q i = Q Q Di = v i [v j {G ij sin(δ i δ j ) j=1 B ij cos(δ i δ j }] (4) 2.3. Inequality constraints Fig. 1. Social surplus with quadratic supply and demand curves. Generation limits: The generating plants have a maximum and minimum generating capacity beyond which it is not feasible to generate due

3 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) to technical or economic reasons. Generating limits are specified as upper and lower limits for the real and reactive power outputs. Real power generation limits: P min P P max Reactive power generation limits: Q min Q Q max Line flow limit: The line flow limit specifies the maximum power that a given transmission line is capable of transmitting under given conditions. The limit can be based on thermal or stability considerations. Thermal limits are usually considered for shorter lines. The following constraint checks for the absolute power flow both at sending and receiving ends of particular line to be within the upper limit of the line. S ij S max ij S ji S max ji Bus voltage limit: Voltage limits refer to bus voltage to remain within an allowable narrow range of levels. v min i v i v max i where N denotes the total number of buses in the system; P denotes real power generated at bus i; P Di denotes real power demand at bus i; P D denotes the power supplied by the DG at bus i. B i (P Di )=a Di + b Di P Di c Di (P Di ) 2, denotes purchaser benefit functions at bus i; C i =(P )a + b P + c (P ) 2, denotes the producer offer (bid) price at bus i; C(P D )=a D + b D P D + c D (P D ) 2, denote the cost characteristic of DG at bus i; v i denotes the voltage at bus i; δ i denotes the power angle at bus i; B ij denotes the susceptance of the line ij; G ij denotes the conductance of the line ij; Q denotes reactive power generated at bus i; P max and P min denotes upper and lower real power generation limits of generator at bus i; Q max and Q min denote upper and lower reactive power generation limits of generator at bus i; v max i and v min i denote upper and lower limits of voltage at bus i; S ij denotes the complex power transfer from bus i to bus j; S ji denotes the complex power transfer from bus j to bus i; Sij max and Sji max denote the complex power flow limit for line ij and line ji. For base case OPF, P D = 0 For load bus, P = 0 For generator bus, P Di = 0 P D = Profit maximization The profit maximization formulation constitutes two nested blocks. The inner block is handled by the independent system operator (ISO). In order to achieve the short-run economic optimum, ISO collects the electric power bids from suppliers, consumers and DG placement and size from DG owner. The DG owner being one of the market participants, lies outside the block and submits the DG size they are willing to penetrate in the market. ISO then runs OPF taking into consideration the network constraints. The objective of this OPF is to minimize the total costs. This block allows overall control and coordination of generation and transmission. The LMP obtained from the OPF is used by the DG owner in order to calculate the profit which is evaluated as revenue minus cost for the particular DG. The process is iterative as LMP is also a function of DG penetration. The profit with DG placement at each of the node is evaluated as: Profit i = λ i P D C(P D ) (5) where P D denotes the DG size at node i; λ i denotes the LMP at node i after placing DG; C(P D )=a D + b D P D + c D (P D ) 2 denotes the cost characteristic of DG at node i. The optimization process will identify the node and corresponding optimal DG size that will bring maximum profit to the DG owner. 3. Methodology For a specific combination of supplier and demand bid curves, the base case OPF first calculates different electricity prices for different nodes in the network. The nodal prices are obtained from the lagrangian multipliers of the non-linear equality constraints. The increasing functions for supplier bids and decreasing functions for the consumer bids are treated as the marginal cost or benefits of the bidder. The difference in prices results from active line constraints and losses in the transmission system. To identify candidate nodes for the placement of DG, two rankings are defined, namely, LMP based ranking and consumer payment (CP) based ranking Locational marginal price (LMP) based ranking LMP is the lagrangian multipliers associated with the active power flow equations for each bus in the system. LMP at any node in the system is the dual variable for the equality constraint at that node [13]. LMP is generally composed of three components, a marginal energy component (same for all buses),

4 1630 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) a marginal loss component and a congestion component. Considering the case of real power spot price at bus i, LMP is given by: LMP i = λ + λ P N L L P ij + μ Lij (6) P i P ij=1 LMP i = λ + λ L,i + λ C,i (7) where λ is the marginal energy component at the reference bus which is same for all buses, λ L,i = λ( P L / P i ) is the marginal loss component and λ C,i = μ Lij ( P ij / P i ) is the congestion component. Thus, the spot price at each bus is location specific and differs by the loss component and the congestion component. Theoretically, this location-based price equals the economically efficient market value of electricity at that point, factoring into account constraints everywhere in the system. Higher LMP implies a greater effect of active power flow equations of the node on total social welfare of the system. In other words, higher LMP implies higher the generation pressed by demand at that node. It thus provides indication that for the objective of social welfare maximization, injection of active power at that node will improve the net social welfare. As the DG is assumed to inject real power at a node, the node with highest LMP will have first priority for DG placement. Accordingly, the load buses are ranked in descending order of LMPs with the first node in the order as the best candidate for DG placement as shown below. LMP 1 LMP 2 LMP = LMP 3 (8). LMP n where n is the number of load locations. Best location = index {max(lmp)} (9) 3.2. Consumer payment based ranking CP calculated as the product of LMP and capacity of load is considered as another criterion to segregate candidate nodes for DG placement. Thus, the CP evaluated at the load bus i is the product of LMP and load at bus i. CP 1 CP 2 CP = LMP i Load i = CP 3 (10). CP 4 Best location = index {max(cp)} (11) CP i reflects the total amount the consumer at node i need to pay for the electricity. The ranking is influenced from the fact that market for DG placement can be viewed from two standpoints. One scenario might be where price is high but load is relatively small, while in the other, price is relatively low but load is high. The ranking based on consumer payment is intended to focus on the later scenario wherein total nodal payment is given the priority rather than the high price. The ranking will have overall effect of reducing dominant loads in the system. In effect, LMP goes down and the dominant customer would be better off, as the amount they need to pay would be less compared to no DG case. The candidate nodes are iteratively selected for the placement. The placement is carried out with several cost characteristics assumed for DG. As the placement technique is intended to bring down the LMP, DG with operating cost higher than LMP will find no incentive for placement. The DG with operating cost lower than those bided by supplier is expected to have higher penetration while the one with higher cost is expected to have smaller penetration. 4. Simulation results and discussion The effects of DG penetration under the two scenarios, namely, social welfare maximization and profit maximization, are discussed in detail. The analysis is extended for the various cost characteristics assumed for the DG Cost characteristics used for DG Wide varieties of DG technologies with varying operating characteristics are available in the market. To depict the variation, assumptions are made for the cost characteristics. CHP units, due to their heat recovery system can deliver power at much cheaper price than the central generation. The technologies such as fuel cells are characterized by their high cost while technologies such as reciprocating engines and gas turbines lie somewhere in the middle. In order to accommodate the varieties of DG units, assumptions are made on the basis of the cost characteristics of central generation. Table 1 shows the cost characteristics of DGs considered in this work. The cost comparison among the various units is made as per the incremental cost. Incremental cost is a function of power output of the unit where slope indicates cost to produce incremental quantity and intercept indicates no load cost. Other conditions remaining the same, the lesser the slope, the lower the incremental cost and higher the penetration. The crossing over of two different incremental cost characteristics reveals that operational cost effectiveness depends on power output. The crossing over is determined by no load cost and slope of the curve. The Table 1 Distributed generation data DG ID a DG b DG c DG DG DG DG DG DG DG DG Note: a DG, b DG, c DG are quadratic cost coefficient of DG.

5 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) Table 2 Ranking based on LMP Rank Bus P D (MW) LMP ($/MWh) Fig. 2. Cost characteristic of various DG. unit cheaper due to lower no load cost can prove to be expensive beyond certain power output if the slope is large and vice versa. The cost characteristic of DG units considered in modified IEEE 14 bus test system is shown in Fig. 2. The cost characteristics considered have wide variety of slopes and accordingly, intersection at several points. Hence, the comparative study of operational cost among the units relies on power output. The incremental cost characteristics of various DGs considered in this study is shown in Fig. 3. As the quadratic component of DG1 and DG2 is very small, their incremental cost is almost constant for the entire range of output. Same is the case with the DG6 and DG7. However, DG3, DG4 and DG5 show monotonically increasing incremental cost with crossover at several points Base case analysis The social welfare maximization problem encompasses the welfare of consumers as well as producers. The analysis is extended for various cost characteristics assumed for the DG. The system used in this study, modified IEEE 14 bus test system, consists of 9 load buses and 5 generators. The loads are assumed to be elastic with power factor of 0.91 (lagging). The maximum social welfare is found to be $/h. The total real power loss in the system is MW. The generation, load and LMP corresponding to the maximum social welfare for the base case are determined at each node. Results revealed that generator buses have lower values of LMP compared to the load buses Candidate nodes for DG placement The system has a maximum load of MW at node 4. Contrary to the node with maximum load, the highest LMP of $/MWh is recorded at node 14 as shown in Table 2. This shows high LMP should not necessarily be at the node with high load. Load exceeding the transmission capacity at a particular location might lead to high LMP. However, due to the loop flow, loads at other nodes and overall network configuration do play a role in determining LMP. The ranking of the load buses according to LMP and consumer payment are shown in Tables 2 and 3, respectively DG placement for social welfare maximization The optimal DG size for each of the load bus is determined from the social welfare maximizing problem. Results revealed that there is an optimal DG size at each of the load bus for which the net social welfare is maximum. However, the max- Table 3 Ranking based on consumer payment Rank Bus P D (MW) LMP ($/MWh) Consumer payment ($/h) Fig. 3. Incremental cost characteristics of various DG

6 1632 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) imum net social welfare obtained from these optimal sizes is different from one load bus to another. Another worth noticeable point is that the placement as well as penetration of DG is found to vary with the cost characteristics used. Even for the same load bus, different optimal sizes are obtained when different cost characteristics are used. The cheaper the unit the higher the penetration and so is the net social welfare. This shows DG penetration as well as social welfare is a function of DG cost characteristics. The study has been carried out to identify the optimal placement and penetration when the DG is cheaper or expensive than the existing central generation. The results associated with two expensive DGs, namely, DG6 and DG7 are presented as sample results. However, summary of the results for all DGs are given in the end of this section Placement of DG6 The maximum net social welfare that can be achieved when the placement of DG6 is carried out at different load buses is shown in Fig. 4. The corresponding optimal DG size at each of the load bus is also shown in Fig. 5. For instance, if placement is to be carried out at node 14, optimal size of DG for the social welfare of $/h is MW. Similarly, for placement at bus 11 the optimal size giving the social welfare of $/h is MW and so on. It is interesting to note that net social welfare is maximized for the case of DG at node 14. Hence, the optimal placement of DG6 is node 14 with the optimal size of MW. The social welfare maximization is found to capture the first candidate node of LMP ranking given in Table 2. Moreover, the ranking is found to capture first four candidate nodes accurately in the same order. The variation of net social welfare with respect to DG size for node 14 is shown in Fig. 6. As apparent from the figure, beyond the optimal size there is a reduction in net social welfare. For non-optimal size same social welfare can be obtained for two different sizes of DG. However, maximum net social welfare is obtained only for the optimal DG size. Fig. 5. Optimal DG size at respective nodes with DG Placement of DG7 The maximum net social welfare that can be achieved when the placement of DG7 is carried out each of the load buses is shown in Fig. 7. The maximum net social welfare of $/h is obtained when the placement is made at node 14. Corresponding optimal DG size is found to be MW. The smaller optimal size compared to the placement of DG6 can be attributed to higher incremental cost of DG7. The optimal size of DG after placing DG7 at each of these buses is shown in Fig. 8. From the figure it is revealed that no DG is selected for node 5. As apparent from Table 2, node5is the last candidate node for DG placement. Hence, the placement is found to follow the ranking based on LMP. The variation of net social welfare with respect to DG size for the placement of DG7 at node 14 is shown in Fig. 9. Results revealed that placements as well as sizes vary with the cost characteristics. The summary of results corresponding to the placement of all the seven DGs considered in the study is given in Table 4. Fig. 4. Net social welfare at respective nodes with DG6. Fig. 6. Social welfare vs. DG size for the placement of DG6 at node 14.

7 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) Table 4 Result summary for the placement of DG with different cost characteristics DG Best location Optimal DG size (MW) Social welfare ($/h) Remarks DG1 Bus CP based ranking DG2 Bus CP based ranking DG3 Bus DG4 Bus LMP based ranking DG5 Bus LMP based ranking DG6 Bus LMP based ranking DG7 Bus LMP based ranking Fig. 7. Net social welfare at respective nodes with DG7. the penetration and so is the net social welfare. Hence, the lower incremental cost followed by higher penetration is found to favor consumer payment based ranking given in Table DG placement for profit maximization The present discussion encompasses the placement of the same DG characteristics as the one considered for social welfare maximization Placement of DG6 Fig. 8. Optimal DG size at respective nodes with DG7. Interestingly, it is observed that for the placement of DG1 and DG2, social welfare is maximized when placement is made at node 4. In other words, the placement is found to track first candidate node of consumer payment based ranking rather than LMP ranking. Furthermore, as shown in Table 4 the penetration of DG1 and DG2 is higher compared to that of DG6 and DG7. The higher penetration can be attributed to the lower incremental cost as is apparent from Fig. 3. The cheaper the unit, the higher Fig. 10 shows the corresponding maximum profit at each load bus after the placement of DG6. Fig. 11 shows the optimal DG size corresponding to the maximum profit at each of the load bus. The maximum profit of $/h is found for the placement at node 14. The corresponding optimal DG size is MW which is less than the value obtained for social welfare maximization shown in Fig. 5. The variation of profit with the penetration of DG6 at load bus 14 is shown in Fig. 12. The maximum profit is found for the optimal size as shown in Fig. 11. As the penetration increases, LMP at a node will reduce. If the LMP reduces to a value making the consumer payment lower than the operating cost of DG, profit for DG owner would be negative. This is apparent from Fig. 12 which shows that beyond the optimal DG size, profit will decrease and can even be negative if the penetration reaches a higher value. Fig. 9. Social welfare vs. DG size for the placement of DG7 at node 14. Fig. 10. Maximum profit at respective nodes with DG6.

8 1634 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) Table 5 Result summary for the placement of DG with different cost characteristic DG Best location Optimal DG size (MW) Profit ($/h) Remarks DG1 Bus CP based ranking DG2 Bus CP based ranking DG3 Bus DG4 Bus DG5 Bus DG6 Bus LMP based ranking DG7 Bus LMP based ranking Fig. 11. Optimal DG size at respective nodes with DG6. Fig. 14. Optimal DG size at respective nodes with DG7. Fig. 12. Profit vs. DG size for placement of DG6 at node Placement of DG7 The profit that can be achieved to DG owner with the placement of DG7 and corresponding optimal sizes at each of the load buses is shown in Figs. 13 and 14, respectively. The variation of profit with the penetration of DG7 at load bus 14 is shown in Fig. 15. Profit maximization results reveal that there is no profit for DG owner when the placement is carried out at bus 5. Results show that even for the DG with same cost characteristic, profit maximization comes up with the lower optimal size compared to social welfare maximization as can be seen from Tables 4 and Comparison between social welfare and profit maximization Tables 6 and 7 show the comparative study of results obtained from two placement techniques. The placement of DG6 and DG7 Fig. 13. Maximum profit at respective nodes with DG7. Fig. 15. Profit vs. DG size for placement of DG7 at node 14.

9 Table 6 Comparison of results for placement of DG6 D. Gautam, N. Mithulananthan / Electric Power Systems Research 77 (2007) DG Bus Social welfare maximization Profit maximization Social welfare ($/h) LMP ($/MWh) P DG (MW) Profit ($/h) LMP ($/MWh) P DG (MW) Table 7 Comparison of results for placement of DG7 DG Bus Social welfare maximization Profit maximization Social welfare ($/h) LMP ($/MWh) P DG (MW) Profit ($/h) LMP ($/MWh) P DG (MW) is observed for social welfare as well as profit maximization problem. The corresponding values of LMP at each of the nodes after placing the optimal size of DG are tabulated. 5. Conclusions The paper proposes two new methodologies of DG placement in an OPF based wholesale electricity market. Optimal placement and size is identified for social welfare as well as profit maximization problem. For each DG cost characteristics, there is an optimal location and size for which the net social welfare is becoming maximum. The same condition is found to hold true for profit maximization, as well. For the DG placement at a node, social welfare maximization ends up with lower LMP value compared to profit maximization. Accordingly, optimal DG size for profit maximization is lower than that for social welfare maximization. This is due to the fact that social welfare is concerned with consumer as well as producers surpluses; however, profit is concerned only with the surplus to producers which will acquire high value as the price increases. The high LMP results in higher consumer payment with a consequent increase in the revenue to DG owner. DG penetration is found to reduce the dispatch of central generation. The optimal placement and penetration is found to depend on the cost characteristics of DG as well as those of central generations. The DG with incremental cost lower than the central generation is found to have a higher penetration in the system, and similarly, the one with higher incremental cost, the lower penetration. Considerable reduction in central generation dispatch is observed with high DG penetration. LMP and consumer payment have been identified as tools for screening candidate nodes for DG placement. The DGs with lower incremental cost compared to central generating stations have a higher penetration and is found to follow the ranking made on the basis of consumer payment. On the other hand, the DGs with higher incremental cost have lower penetration and is found to follow the ranking made on the basis of LMP. It has also been observed that a high penetration of DG can also lead to negative profit for the DG owner. The situation is found to prevail when LMP reduces considerably due to high DG penetration. If the LMP reduces to a value making the consumer payment lower than the operating cost of DG, profit for DG owner would be negative. Under such scenario, DG owner will find no incentive for placement. References [1] P.P. Barker, Determining the impact of distributed generation on power systems: Part 1 radial distribution systems, in: Proceedings of IEEE Power Engineering Society Summer Meeting, 2000, pp [2] W.E. Khattam, K. Bhattacharya, Y. Hegazy, M.M.A. Salama, Optimal investment planning for distributed generation in a competitive electricity market, IEEE Trans. Power Syst. 19 (August (3)) (2004) [3] M. Pipattanasomporn, M. Willingham, S. Rahman, Implications of onsite distributed generation for commercial/industrial facilities, IEEE Trans. Power Syst. 20 (February (1)) (2005)

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