Multiple Distributed Generator Placement in Primary Distribution ...

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Multiple Distributed Generator Placement in Primary Distribution Networks for Loss Reduction Duong Quoc Hung, Student Member, IEEE, and Nadarajah Mithulananthan, Senior Member, IEEE

Abstract—This paper investigates the problem of multiple distributed generator (DG units) placement to achieve a high loss reduction in large-scale primary distribution networks. An improved analytical (IA) method is proposed in this paper. This method is based on IA expressions to calculate the optimal size of four different DG types and a methodology to identify the best location for DG allocation. A technique to get the optimal power factor is presented for DG capable of delivering real and reactive power. Moreover, loss sensitivity factor (LSF) and exhaustive load flow (ELF) methods are also introduced. IA method was tested and validated on three distribution test systems with varying sizes and complexity. Results show that IA method is effective as compared with LSF and ELF solutions. Some interesting results are also discussed in this paper. Index Terms—Analytical expression, loss reduction, loss sensitivity factor (LSF), multiple DG, optimal location, optimal power factor, optimal size.

I. I NTRODUCTION

I

N RECENT YEARS, the penetration of distributed generator (DG) into distribution systems has been increasing rapidly in many parts of the world. The main reasons for the increase in penetration are the liberalization of electricity markets, constraints on building new transmission and distribution lines, and environmental concerns [1]–[3]. Technological advances in small generators, power electronics, and energy storage devices for transient backup have also accelerated the penetration of DG into electric power generation plants [4]. At present, there are several technologies used for DG applications that range from traditional to nontraditional technologies. The former is nonrenewable technologies such as internal combustion engines, combined cycles, combustion turbines, and microturbines. The latter is renewable technologies such as solar, photovoltaic, wind, geothermal, ocean, and fuel cell. The main advantages of using renewable-energy-based DG sources are the elimination of harmful emissions and inexhaustible resources of the primary energy. However, the main disadvantages are relative low efficiency, high costs, and intermittency [5], [6]. As the penetration of DG units increases in the distribution system, it is in the best interest of all players involved to allocate

Manuscript received June 18, 2010; revised November 18, 2010; accepted December 12, 2010. Date of publication February 4, 2011; date of current version November 22, 2012. The authors are with the School of Information Technology and Electrical Engineering, the University of Queensland, Brisbane, Qld. 4072, Australia (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TIE.2011.2112316

them in an optimal way such that it will increase reliability, reduce system losses, and hence improve the voltage profile while serving the primary goal of energy injection. DG units are modeled as synchronous generators for small hydro, geothermal, and combined cycles; combustion turbines; and wind turbines with power electronics. Induction generators are used in wind and small hydropower generation. DG units are considered as power electronics inverter generators or static generators for technologies such as photovoltaic (PV) plants and fuel cells [7], [8]. For instance, DG using a PV grid-connected converter is controlled on the basis of the droop-control technique presented in [9]–[17]. The converter is capable of providing active power to local loads and injecting reactive power to stabilize load voltages. Furthermore, the type of DG technology adopted will have a significant bearing on the solution approach. For example, in [18], the installation of synchronous machine-based DG units that are close to the loads can lead to a gain in the system voltage stability margin; on the other hand, in the case with an induction generator, the system stability margin is reduced. Given the choice, DG units should be placed in appropriate locations with suitable sizes and types to enjoy system-wide benefit. It is evident that any loss reduction is beneficial to distribution utilities, which is generally the entity responsible to keep losses at low levels. Loss reduction is, therefore, the most important factor to be considered in the planning and operation of DG [19], [20]. For instance, multiobjective index for performance calculation of distribution systems for single DG size and location planning has been proposed [19]. For this analysis, the active and reactive power losses receive significant weights of 0.40 and 0.20, respectively. The current capacity receives a weight of 0.25, leaving the behavior of voltage profile at 0.15. In a radial feeder, depending on the technology, DG units can deliver a portion of the total real and/or reactive power to loads so that the feeder current reduces from the source to the location of DG units. However, studies [21]–[23] have indicated that if DG units are improperly allocated and sized, the reverse power flow from larger DG units can lead to higher system losses. Hence, to minimize losses, it is important to find the best location and size given the option of resource availability. A technique for DG placement using “2/3 rule” which is traditionally applied to capacitor allocation in distribution systems with uniformly distributed loads has been presented [22]. Although simple and easy to apply, this technique cannot be applied directly to a feeder with other types of load distribution or to a meshed distribution system. In [24], an analytical approach has been presented to identify the location to optimally place

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HUNG AND MITHULANANTHAN: MULTIPLE DG PLACEMENT IN PRIMARY DISTRIBUTION NETWORKS FOR LOSS REDUCTION

single DG with unity power factor in radial as well as meshed networks to minimize losses. However, in this approach, the optimal sizing is not considered. The genetic algorithm (GA)based method has been presented to determine the size and location of DG [25], [26]. GA is suitable for multiobjective problems and can lead to a near optimal solution but demand higher computational time. An analytical approach based on an exact loss formula has been presented to find the optimal size and location of single DG [21]. In this method, a new methodology has been proposed to quickly calculate approximate losses for identifying the best location; the load flow is required to be performed only twice. In the first time, it is applied to calculate the loss of the base case, and in the second time, it is used to find the minimum total loss after DG placement. Although this method requires less computation, single DG capable of delivering real power only is considered. A probabilistic-based planning technique has been proposed for determining the optimal fuel mix of different types of renewable DG units (i.e., wind, solar, and biomass) in order to minimize the annual energy losses in the distribution system [23]; however, DG units capable of delivering real power only is considered in this paper. Recently, the authors in [27] have presented an effective method based on improved analytical (IA) expressions to place four different types of single DG for loss reduction. However, multiple DG unit placement has not been addressed in this paper. To overcome limitations in previous works, this paper proposes an IA method for allocating four types of multiple DG units for loss reduction in primary distribution networks. This method is based on IA expressions in [27] to calculate the optimal size of four different DG types and a methodology to identify the best location for multiple DG allocation. The importance of DG operation (i.e., real and reactive power dispatch) for loss minimization along with a “fast approach” as a simple way to quickly select the power factor of DG units that is close to the optimal power factor is also presented. The proposed methodology is computationally less demanding. Moreover, voltage profile enhancement is also examined. The remainder of this paper is organized as follows: Section II explains the proposed IA method. Procedure for multiple DG placement using IA method and loss sensitivity factor (LSF) method is also elaborated in this section. Section III portrays the test distribution systems and numerical results along with some observations and discussions for multiple DG placement. Finally, the major contributions and conclusions are summarized in Section IV.

in calculation; however, it can lead to a completely optimal solution. Its numerical results are presented in Section III. A. Power Losses The total real power loss in a power system is represented by an exact loss formula [28] PL =

N  N 

where αij =

rij cos(δi − δj ); Vi Vj

Vi ∠δi rij + jxij = Zij Pi and Pj Qi and Qj N

βij =

rij sin(δi − δj ) Vi Vj

complex voltage at the bus ith; ijth element of [Zbus] impedance matrix; active power injections at the ith and jth buses, respectively; reactive power injections at the ith and jth buses, respectively; number of buses.

B. IA Method In this paper, an effective methodology is proposed to find the optimal location, size, and power factor of multiple DG units in distribution networks. A brief description of the IA expressions and optimal power factors for single DG allocation is presented as follows [27]: 1) IA Expressions: Type 1 DG (i.e., 0 < P FDG < 1) is capable of injecting both real and reactive power (e.g., synchronous generators). The optimal size of DG at each bus i for minimizing losses can be given by (2) and (3) PDGi =

αii (PDi + aQDi ) − Xi − aYi a2 αii + αii

QDGi = aPDGi

(2) (3)

in which   a = (sign) tan cos−1 (P FDG ) sign = +1 DG injecting reactive power n  j=1 j=i

This section focuses on a detailed description of IA method. To check the effectiveness and applicability of the proposed method, LSF and exhaustive load flow (ELF) methods for allocating multiple DG units are used. LSF method has been employed to select the candidate locations for single DG placement to reduce the search space. A brief description of LSF algorithm for multiple DG units is given at the end of this section. ELF method, known as a repeated load flow solution, demands excessive computational time since all buses are considered

[αij (Pi Pj + Qi Qj ) + βij (Qi Pj − Pi Qj )] (1)

i=1 j=1

Xi = II. M ETHODOLOGY

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(αij Pj − βij Qj ) Yi =

n 

(αij Qj + βij Pj ).

j=1 j=1

The aforementioned equations give the optimum size of DG for each bus i, for the loss to be minimum. Any size of DG other than PDGi placed at bus i will lead to a higher loss. This loss, however, is a function of loss coefficients α and β. When DG is installed in the system, the values of loss coefficients will change, as it depends on voltage and angle. Updating the values of α and β again requires another load flow calculation. However, numerical results showed that the accuracy gained in the size of DG by updating α and β is small and negligible [21]. With this assumption, the optimum size of

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repeated approach is also introduced to check the effectiveness of the fast approach. It is interesting to note that, in all the three test systems used in this paper, the optimal power factor of DG units placed for loss reduction is found to be closer to the power factor of the combined load of respective systems. a) Fast Approach: The power factor of the combined load of the system (P FD ) can be expressed by (6). The total active and reactive power of the load demand is expressed as

Fig. 1. Simple distribution system with single DG.

DG for each bus, given by the aforementioned relations, can be calculated from the base case load flow (i.e., without DG case). This methodology requires the load flow to be carried out only two times for single DG allocation, one for the base case and another at the end with DG included to obtain the final solution [21], [27]. Type 2 DG (i.e., 0 < P FDG < 1) is capable of injecting real power but consuming reactive power (sign = −1) (e.g., induction generators). Similar to type 1 DG, the optimal size of type 2 DG at each bus i for the minimum loss is given by (2) and (3). Type 3 DG (i.e., P FDG = 1, a = 0) is capable of injecting real power only (e.g., PV, microturbines, and fuel cells which are integrated to the main grid with the help of converters/ inverters). The optimal size of DG at each bus i for the minimum loss is given by reduced (4) PDGi = PDi −

N 1  (αij Pj − βij Qj ). αii j=1

(4)

j=i

Type 4 DG (i.e., P FDG = 0, a = ∞) is capable of delivering reactive power only (e.g., synchronous compensators). The optimal size of DG at each bus i for the minimum loss is given by reduced (5) QDGi

N 1  = QDi − (αij Qj + βij Pj ). αii j=1

(5)

j=i

2) Power Factor Selection: Consider a simple distribution system with two buses, a source, a load, and a DG connected through a transmission line as shown in Fig. 1. The power factor of the single load (P FD ) is given as P FD = 

PD 2 PD

+ Q2D

.

(6)

The power factor of the single DG injected (P FDG ) is given as P FDG = 

PDG . 2 PDG + Q2DG

(7)

It is obvious that the minimum loss occurs when the power factor of the single DG as (6) is equal to that of the single load as (7). To find the optimal power factor of DG units for a radial complex distribution system, a fast approach is proposed. A

PD =

N  i=1

PDi

QD =

N 

QDi .

i=1

The “possible minimum” total loss can be achieved if the power factor of DG (P FDG ) is selected to be equal to that of the combined load (P FD ). That can be expressed as P FDG = P FD .

(8)

b) Repeated Method: In this method, the optimal power factor is selected by calculating a few power factors of DG units (change in a small step of 0.01) that are near to the power factor of the combined load. The sizes and locations of DG units at various power factors with respect to losses are identified from (2) and (3). The losses are compared, and the optimal power factor of DG units at which the total loss is at minimum is determined. 3) Optimization Algorithm for Multiple DG Allocation: This algorithm is made on the basis of the IA expressions [27] to find the optimal buses at which the losses are the lowest and where multiple DG units are best placed. The IA expressions help reduce the solution space. Fig. 2 illustrates the flowchart of IA method for multiple DG allocation. The descriptions of each step in detail are given as follows. In this paper, based on an idea of updating the load data after each time of DG placement, the algorithm is proposed to solve optimal multiple DG placement. First, a single DG is added in the system. After that, the load data are updated with the first DG placed and then another DG is added. Similarly, the algorithm continues to allocate other DG units until it does not satisfy at least one of the constraints in step 7 as described as follows. The computational procedure to allocate multiple DG units on the basis of the IA expressions is described in detail as follows. Step 1) Enter the number of DG units to be installed. Step 2) Run the load flow for the base case and find losses using (1). Step 3) Calculate the power factor of DG using (8) or enter the power factor of DG. Step 4) Find the optimal location of DG using the following steps. a) Calculate the optimal size of DG at each bus using (2) and (3). b) Place the DG with the optimal size, as mentioned earlier, at each bus one at a time. Calculate the approximate loss for each case using (1) with the values α and β of the base case.

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Fig. 3. Flow chart of LSF method to allocate multiple DG units.

C. LSF Method Fig. 2.

Flow chart of IA method to allocate multiple DG units.

c) Locate the optimal bus at which the loss is at minimum. Step 5) Find the optimal size of DG and calculate losses using the following steps. a) Place a DG at the optimal bus obtained in step 4, change this DG size in “small” step, update the values α and β, and calculate the loss for each case using (1) by running the load flow. b) Select and store the optimal size of the DG that gives the minimum loss. Step 6) Update load data after placing the DG with the optimal size obtained in step 5 to allocate the next DG. Step 7) Stop if either the following occurs: a) the voltage at a particular bus is over the upper limit; b) the total size of DG units is over the total load plus loss; c) the maximum number of DG units is unavailable; d) the new iteration loss is greater than the previous iteration loss. The previous iteration loss is retained; otherwise, repeat steps 2 to 6.

In this paper, the sensitivity factor of active power loss is employed to find the most sensitive buses to place DG units which are capable of injecting active power only (i.e., type 3 DG). The sensitivity factor method is based on the principle of linearization of the original nonlinear equation around the initial operating point, which helps reduce the number of solution space. The LSF at the ith bus is derived from (1) with respect to active power injection at that bus, which is given as [21] αi =

N  ∂PL =2 (αij Pj − βij Qj ). ∂Pi j=1

(9)

Fig. 3 shows the flow chart of LSF method for multiple DG placement. Similar to IA method, the procedure to find the optimal locations and sizes of multiple DG units using the LSF is described in detail as follows. Step 1) Enter the number of DG units to be installed. Step 2) Run the load flow for the base case and find losses using (1). Step 3) Find the optimal location of DG using the following steps. a) Find LSF using (9). Rank buses in descending order of the values of their LSFs to form a priority list. b) Locate the highest priority bus.

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Step 4) Find the optimal size of DG and calculate losses using the following steps. a) Place a DG at the bus with the highest priority obtained in step 3, change this DG size in “small” step, update the values α and β, and calculate the loss for each case using (1) by running the load flow. b) Select and store the optimal size of the DG that gives the minimum loss. Step 5) Update load data after placing the DG with the optimal size obtained in step 4 to allocate the next DG. Step 6) Stop if either the following occurs: a) the voltage at a particular bus is over the upper limit; b) the total size of DG units is over the total load plus loss; c) the maximum number of DG units is unavailable; d) the new iteration loss is greater than the previous iteration loss. The previous iteration loss is retained; otherwise, repeat steps 2 to 5.

TABLE I DG P LACEMENT BY VARIOUS T ECHNIQUES FOR 16-B US S YSTEM

III. N UMERICAL R ESULTS A. Test Systems The proposed methodology is tested on three test systems with varying sizes and complexities. The first system used in this paper is a 16-bus test radial distribution system with a total load of 28.7 MW and 5.9 MVAr [29]. The second one is a 33-bus test radial distribution system with a total load of 3.7 MW and 2.3 MVAr [30]. The last one is a 69-bus test radial distribution system with a total load of 3.8 MW and 2.69 MVAr [31]. Based on the proposed methodology, an analytical software tool has been developed in MATLAB environment to run the load flow, calculate power losses, and identify the optimal size and location of multiple DG units. Although the tool can handle four different DG types and various load levels, the results of type 3 DG and type 1 DG at the peak load level, respectively, are presented.

B. Assumptions and Constraints The following are the assumptions and constraints for this paper: 1) The lower and upper voltage thresholds are set at 0.90 and 1.05 pu, respectively. 2) The maximum number of DG units is three, with the size each from 250 kW to the total load plus loss, and the maximum DG penetration is 100%.

C. Type 3 DG Placement 1) 16-Bus Test System: Table I presents the simulation results of placing DG units by various techniques. The results

of the base case and three cases with DG numbers ranging from one to three are compared. The results include the optimal sizes and locations of DG units with respect to the total losses by each technique. The loss reduction, computational time, and schedule of installed DG units of each technique are also presented in the table. For all the cases, IA leads to a completely optimal solution as compared with ELF, i.e., the optimal locations and sizes of DG units by IA is the same as those by ELF. Among all the cases, LSF yields the lowest loss reduction due to poor choice of locations. For instance, placing single DG by IA, ELF, and LSF yields loss reductions of 67.06%, 67.06%, and 62.15%, respectively. IA demands shorter computational time compared to ELF as expected. However, LSF is the quickest among all methods. 2) 33-Bus Test System: Similar to 16-bus system, Table II presents the results of the optimal sizes and locations of DG units by various techniques. For single DG, the loss reduction by IA, at 47.39%, is the same as that by ELF. Among all the cases, LSF produces a loss reduction of only 30.48%. For two DG units, the loss reduction by IA, at 56.61%, is slightly lower than that by ELF, at 58.51%. In contrast, it is higher than the loss reduction by LSF at only 52.32%. For three DG units, IA achieves a loss reduction of 61.62%, compared with ELF at 64.83%. However, it is better than LSF that yields a loss reduction of 59.72%. In general, for this system, IA method can lead to an optimal solution for single DG and a near optimal solution for two and three DG units. IA needs a short computational time. Particularly, for three DG units, the time by IA is 0.40 s, nearly twice longer than that

HUNG AND MITHULANANTHAN: MULTIPLE DG PLACEMENT IN PRIMARY DISTRIBUTION NETWORKS FOR LOSS REDUCTION

TABLE II DG P LACEMENT BY VARIOUS T ECHNIQUES FOR 33-B US S YSTEM

TABLE III DG P LACEMENT BY VARIOUS T ECHNIQUES FOR 69-B US S YSTEM

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TABLE IV DG P LACEMENT AT O PTIMAL AND C OMBINED L OAD P OWER FACTORS FOR 16-B US S YSTEM

and sizes of DG units. However, it is better than ELF in terms of computational time. Particularly, for three DG units, the time by IA is 0.71 s, nearly 33 times shorter than that by ELF at 23.16 s. It is quite longer than the time by LSF at 0.52 s. In addition, IA achieves better loss reduction than LSF. For instance, for two DG units, IA reaches a loss reduction of 67.94%, while LSF obtains that of 54.97%.

D. Type 1 DG Placement

by LSF at 0.23 s. In contrast, it is approximately eight times shorter than the time by ELF at 3.06 s. 3) 69-Bus Test System: Table III presents the results of optimal sizes and locations of DG units by various techniques. For all the cases, IA leads to a globally optimal solution as compared with ELF; particularly, the results by IA are the same as those by ELF in terms of loss reduction, optimal locations,

1) 16-Bus Test System: Table IV shows the simulation results of the optimal sizes, locations, and power factors of DG units by IA for this system. The results of the base case and three cases with DG units at the optimal and combined load power factors are compared. The power factor of the combined load is 0.98 lagging. The optimal power factor of DG units is identified at 0.99 lagging. In all the cases, the results of loss reduction at the optimal power factor are slightly higher compared to those at the combined load factor power. As a result, selection of the power factor of DG units can be based on combined load power factor. Among the cases, three DG units at the optimal power factor yield a maximum loss reduction of 86.70%, while one DG at this power factor obtains a minimum loss reduction of only 68.21%. As the number of DG units is increased, the loss reduction becomes more effective. These results are obtained with the help of the proposed method and verified by ELF solutions. 2) 33-Bus Test System: Table V shows the simulation results of the optimal sizes, locations, and power factors of DG units by IA. The power factor of the combined load is 0.85 lagging. The optimal power factor of DG units is identified at 0.82 lagging. In all the cases, the results of loss reduction at the optimal power factor are slightly higher as compared with those at the combined load factor power. Therefore, selection of the power factor of DG units that is equal to that of the combined load is feasible for this case.

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TABLE V DG P LACEMENT AT O PTIMAL AND C OMBINED L OAD P OWER FACTORS FOR 33-B US S YSTEM

TABLE VII VOLTAGES OF C ASES FOR 16-B US T EST S YSTEM

TABLE VIII VOLTAGES OF C ASES FOR 33-B US T EST S YSTEM

TABLE VI DG P LACEMENT AT O PTIMAL P OWER FACTOR FOR 69-B US S YSTEM

TABLE IX VOLTAGES OF C ASES FOR 69-B US T EST S YSTEM

Similar to 16-bus test system, three DG units at the optimal power factor produce a maximum loss reduction of 89.45%, while one DG at this factor obtains a minimum loss reduction of only 67.85%. The more the number of DG units is installed, the better the loss reduction increases. 3) 69-Bus Test System: Table VI shows the simulation results of the optimal sizes, locations, and power factors of DG units by IA. The results of the base case and three cases with DG units at the optimal power factor are compared. The optimal power factor of DG units is determined to be equal to the combined load power factor at 0.82 lagging. As a result, selection of the power factor of DG units that is equal to that of the combined load can lead to an optimal solution for this system. Similar to 16-bus and 33-bus test systems, three DG units at the optimal power factor result in a maximum loss reduction of 97.74%. In contrast, one DG at that factor yields a minimum loss reduction of only 89.68%. As the number of DG units becomes larger, the loss reduction increases. E. Results of Voltages Tables VII–IX indicate the minimum and maximum voltages for all the cases of 16, 33, and 69-bus test systems, respectively. In all the cases, after DG units are added, the total losses can

reduce significantly while satisfying all the power and voltage constraints. This was checked with exhaustive power flow. It is interesting to note that the voltage profile improves when the number of DG units installed in the system is increased. Power factors of DG units too have an influence on voltage profiles as expected. IV. C ONCLUSION This paper has presented IA method for multiple DG allocation for loss reduction in large-scale distribution systems while fulfilling the main objective of energy injection. This method is based on IA expressions for finding the size of four different DG types and an effective methodology to find the

HUNG AND MITHULANANTHAN: MULTIPLE DG PLACEMENT IN PRIMARY DISTRIBUTION NETWORKS FOR LOSS REDUCTION

best location for DG allocation. In this method, a fast approach to obtain an optimal or near optimal power factor has been also presented for placing DG units capable of delivering real and reactive power. Moreover, this paper has also introduced the LSF and ELF methods. The proposed IA method is effective as corroborated by ELF and LSF solutions in terms of loss reduction and computational time. LSF method may not lead to the best choice for DG placement. The number of DG units with appropriate sizes and locations can reduce the losses to a considerable amount. Given the choice, DG(s) should be allocated to enjoy other benefits as well such as loss reduction. Among different DG types, the DG capable of delivering both real and reactive power reduces losses more than that of DG capable of delivering real power only in one or two or three DG cases. For DG capable of delivering real and reactive power, their power factors too play a crucial role in loss reduction. In all the test systems used in this paper, the operating power factor of DG units for minimizing losses has been found to be closer to the power factor of combined load of the respective system. This could be a good guidance for operating DG units that have the capability to deliver both real and reactive power for minimizing losses. R EFERENCES [1] D. Singh and R. K. Misra, “Effect of load models in distributed generation planning,” IEEE Trans. Power Syst., vol. 22, no. 4, pp. 2204–2212, Nov. 2007. [2] I. El-Samahy and E. El-Saadany, “The effect of DG on power quality in a deregulated environment,” in Proc. IEEE Power Eng. Soc. Gen. Meet., 2005, vol. 3, pp. 2969–2976. [3] T. Ackermann, G. Andersson, and L. Soder, “Distributed generation: A definition,” Elect. Power Syst. Res., vol. 57, no. 3, pp. 195–204, Apr. 2001. [4] M. N. Marwali, J. W. Jung, and A. Keyhani, “Stability analysis of load sharing control for distributed generation systems,” IEEE Trans. Energy Convers., vol. 22, no. 3, pp. 737–745, Sep. 2007. [5] W. Li, G. Joos, and J. Belanger, “Real-time simulation of a wind turbine generator coupled with a battery supercapacitor energy storage system,” IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1137–1145, Apr. 2010. [6] A. Pigazo, M. Liserre, R. A. Mastromauro, V. M. Moreno, and A. Dell’Aquila, “Wavelet-based islanding detection in grid-connected PV systems,” IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4445–4455, Nov. 2009. [7] H. B. Puttgen, P. R. MacGregor, and F. C. Lambert, “Distributed generation: Semantic hype or the dawn of a new era?” IEEE Power Energy Mag., vol. 1, no. 1, pp. 22–29, Jan./Feb. 2003. [8] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, “Overview of control and grid synchronization for distributed power generation systems,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1398–1409, Oct. 2006. [9] J. C. Vasquez, R. A. Mastromauro, J. M. Guerrero, and M. Liserre, “Voltage support provided by a droop-controlled multifunctional inverter,” IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4510–4519, Nov. 2009. [10] W. Yao, M. Chen, J. Matas, J. M. Guerrero, and Z. Qian, “Design and analysis of the droop control method for parallel inverters considering the impact of the complex impedance on the power sharing,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 576–588, Feb. 2011. [11] J. M. Guerrero, J. C. Vasquez, J. Matas, L. Garcia de Vicuna, and M. Castilla, “Hierarchical control of droop-controlled AC and DC microgrids—A general approach toward standardization,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 158–172, Jan. 2011. [12] J. C. Vasquez, J. M. Guerrero, A. Luna, P. Rodriguez, and R. Teodorescu, “Adaptive droop control applied to voltage-source inverters operating in grid-connected and islanded modes,” IEEE Trans. Ind. Electron., vol. 56, no. 10, pp. 4088–4096, Oct. 2009. [13] J. M. Guerrero, J. C. Vasquez, J. Matas, M. Castilla, and L. G. de Vicuna, “Control strategy for flexible microgrid based on parallel line-interactive ups systems,” IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 726–736, Mar. 2009.

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[14] J. M. Guerrero, L. Hang, and J. Uceda, “Control of distributed uninterruptible power supply system,” IEEE Trans. Ind. Electron., vol. 56, no. 8, pp. 2845–2859, Aug. 2008. [15] J. M. Guerrero, J. Matas, L. Garcia de Vicuna, M. Castilla, and J. Miret, “Decentralized control for parallel operation of distributed generation inverters using resistive output impedance,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 994–1004, Apr. 2007. [16] J. M. Guerrero, J. Matas, L. G. de Vicuna, M. Castilla, and J. Miret, “Wireless-control strategy for parallel operation of distributed-generation inverters,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1461–1470, Oct. 2006. [17] J. M. Guerrero, L. Garcia de Vicuna, J. Matas, M. Castilla, and J. Miret, “Output impedance design of parallel-connected ups inverters with wireless load-sharing control,” IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1126–1135, Aug. 2005. [18] W. Freitas, J. C. M. Vieira, A. Morelato, L. C. P. da Silva, V. F. da Costa, and F. A. B. Lemos, “Comparative analysis between synchronous and induction machines for distributed generation applications,” IEEE Trans. Ind. Electron., vol. 21, no. 1, pp. 301–311, Feb. 2006. [19] D. Singh and K. S. Verma, “Multiobjective optimization for DG planning with load models,” IEEE Trans. Power Syst., vol. 24, no. 1, pp. 427–436, Feb. 2009. [20] L. F. Ochoa, A. Padilha-Feltrin, and G. P. Harrison, “Evaluating distributed time-varying generation through a multiobjective index,” IEEE Trans. Power Del., vol. 23, no. 2, pp. 1132–1138, Apr. 2008. [21] N. Acharya, P. Mahat, and N. Mithulananthan, “An analytical approach for DG allocation in primary distribution network,” Int. J. Elect. Power Energy Syst., vol. 28, no. 10, pp. 669–678, Dec. 2006. [22] H. L. Willis, “Analytical methods and rules of thumb for modeling DGdistribution interaction,” in Proc. IEEE Power Eng. Soc. Summer Meet., 2000, vol. 3, pp. 1643–1644. [23] Y. M. Atwa, E. F. El-Saadany, M. M. A. Salama, and R. Seethapathy, “Optimal renewable resources mix for distribution system energy loss minimization,” IEEE Trans. Power Syst., vol. 25, no. 1, pp. 360–370, Feb. 2010. [24] C. Wang and M. H. Nehrir, “Analytical approaches for optimal placement of distributed generation sources in power systems,” IEEE Trans. Power Syst., vol. 19, no. 4, pp. 2068–2076, Nov. 2004. [25] K. H. Kim, Y. J. Lee, S. B. Rhee, S. K. Lee, and S. K. You, “Dispersed generator placement using fuzzy-GA in distribution systems,” in Proc. IEEE Power Eng. Soc. Summer Meet., 2002, vol. 3, pp. 1148–1153. [26] A. Silvestri, A. Berizzi, and S. Buonanno, “Distributed generation planning using genetic algorithms,” in Proc. IEEE Int. Conf. Elect. Power Eng., PowerTech Budapest, 1999, p. 257. [27] D. Q. Hung, N. Mithulananthan, and R. C. Bansal, “Analytical expressions for DG allocation in primary distribution networks,” IEEE Trans. Energy Convers., vol. 25, no. 3, pp. 814–820, Sep. 2010. [28] D. P. Kothari and J. S. Dhillon, Power System Optimization. New Delhi: Prentice-Hall, India, 2006. [29] S. Civanlar, J. J. Grainger, H. Yin, and S. S. H. Lee, “Distribution feeder reconfiguration for loss reduction,” IEEE Trans. Power Del., vol. 3, no. 3, pp. 1217–1223, Jul. 1988. [30] M. A. Kashem, V. Ganapathy, G. B. Jasmon, and M. I. Buhari, “A novel method for loss minimization in distribution networks,” in Proc. IEEE Int. Conf. Elect. Utility Deregulation Restruct. Power Technol., 2000, pp. 251–256. [31] M. E. Baran and F. F. Wu, “Optimum sizing of capacitor placed on radial distribution systems,” IEEE Trans. Power Del., vol. 4, no. 1, pp. 735–743, Jan. 1989.

Duong Quoc Hung (S’11) received the M.Eng. degree in electric power system management from the Asian Institute of Technology, Bangkok, Thailand, in 2008. He is currently working toward the Ph.D. degree at the School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, Australia. From 1999 to 2006 and from 2008 to 2010, he was with the Technical Department, Southern Power Corporation, Electricity of Vietnam, Ho Chi Minh City, Vietnam. His research interests are distribution system design and operations, distributed generation, and application of optimization techniques in distribution systems.

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Nadarajah Mithulananthan (SM’10) received the Ph.D. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2002, the B.Sc. (Eng.) degree from the University of Peradeniya, Peradeniya, Sri Lanka, in May 1993, and the M.Eng. degree from the Asian Institute of Technology, Bangkok, Thailand, in August 1997. He was an Electrical Engineer with the Generation Planning Branch of the Ceylon Electricity Board and as a Project Leader with Chulalongkorn University, Bangkok, Thailand. He is currently a Senior Lecturer with the University of Queensland (UQ), Brisbane, Australia. Prior to joining UQ, he was an Associate Professor with the Asian Institute of Technology. His research interests are the integration of renewable energy in power systems and power system stability and dynamics.