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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 1, FEBRUARY 2003

Adequacy Assessment of Distributed Generation Systems Using Monte Carlo Simulation Y. G. Hegazy, Member, IEEE, M. M. A. Salama, Fellow, IEEE, and A. Y. Chikhani, Senior Member, IEEE

Abstract—This paper presents a Monte Carlo-based method for the adequacy assessment of distributed generation systems. The state duration sampling approach is employed in this paper to model the operating histories of the installed distributed generators. A general procedure to assess the ability of the system power capacity to meet the total demand is presented and implemented in a typical case study where several distributed generation units are running in parallel within a sample distribution system and the system margins and the average amount of unsupplied loads are estimated using Monte Carlo simulation. The results obtained are presented and a new perspective to the power management of distribution systems is discussed. Index Terms—Adequacy assessment, distributed generation, Monte Carlo simulation.

I. INTRODUCTION

F

OR MANY YEARS, distribution systems whether they are radial-type systems or ring-type systems were designed to deliver the electric energy to the consumer without any generation on these systems. However, due to the major changes in the legislative framework for the electric sector and the fast move toward liberalization of the electricity markets, generating units were introduced to distribution systems. These units are of limited size (100 MVA or less) and can be connected directly to the distribution network or on the customer site of the meter [1]. These generating units are referred to as distributed generation (DG). Recent studies have predicted that by year 2010, distributed generation will account for up to 25% of all new generation [2], [3]. The main reasons behind the expected widespread of DG are [4] 1) Deregulation in the power market, which encourages public investment to sustain the development in the power demand. This development has led to the breaking up of investments (small generating units); 2) Emergence of new generation techniques with small ratings, ecological benefits, increased profitability, and which can be combined with heat generation; 3) Saturation of existing networks and the continuous growth of the demand.

Manuscript received September 16, 2002. Y. G. Hegazy is with the Electrical Power and Machines Department, Ain Shams University, Cairo 11371, Egypt (e-mail: [email protected]). M. M. A. Salama is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, N2L 3G1 Canada. A. Y. Chikhani is with the Electrical and Computer Engineering Department, Royal Military College of Canada, Station Force, Kingston, ON, K7K 7B4 Canada. Digital Object Identifier 10.1109/TPWRS.2002.807044

The technical merits associated with the implementation of distributed generation include voltage support, energy-loss reduction, release of system capacity, and improve utility system reliability [5]. On the other hand, the parallel operation of DG with the existing system and the difficulties in the operation and control of the different types of DG are still the main challenges associated with the use of DG in distribution systems [6]. This paper addresses the stochastic nature of the distribution system operation when customer-controlled DG units are running in parallel within the system. The locations of such DG are determined by the customers and are known to the utility; however, the instant of switching on and off of each DG is based on the customer’s desires and needs. Different customers would have different strategies for operating their DG and accordingly, the process of turning on and off each DG unit will be a random process. The random on and off cycle of each DG will result in a random contribution of this DG to the system power capacity. Consequently, the overall system power capacity will vary randomly and the determination of this capacity requires proper modeling of the random operation state of the system. In this paper, the adequacy assessment of distribution systems, including consumer-controlled DG, is performed using Monte Carlo simulation. Adequacy assessment implies the determination of the actual distribution system power capacity and the ability of this capacity to meet the total system demand. The term “distribution system power capacity” is introduced in this paper to account for the generating power from the available DG plus the received power from the transmission system. Mathematically, distribution system power capacity ( ) is defined by (1) is the power received from transmission system where is the power generated by the DG in megawatts and can be treated as a large generated power in megawatts. is the expected contribution located at the substation site. of all the online DG where (2) where is the power output of DG unit in megawatts and is the number of working DG units. The adequacy assessment of generating systems has been studied considerably in literature [7]; however, to the best of the authors’ knowledge, the implementation of such an analysis in distribution systems has not been performed before. Therefore, the authors consider that the work introduced in this paper will pave the road for more studies in this field.

0885-8950/03$17.00 © 2003 IEEE

HEGAZY et al.: ASSESSMENT OF GENERATION SYSTEMS USING MONTE CARLO SIMULATION

The work done in this paper is presented according to the following sections: Section II presents the formulation of the problem in hand, Section III highlights the approach used for the adequacy assessment, Section IV shows a case study along with a discussion of the results obtained and, finally, the main conclusions of this paper are offered in Section V.

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Fig. 1. Proposed two-state model for each DG.

II. PROBLEM FORMULATION In an engineering form, the adequacy assessment of a distribution system with a number of customer-controlled DG running in parallel within the system is given by A. Given A distribution system supplying a load with known hourly load characteristics. The available energy in the system at any given hour is the combination of transmitted energy and DG-generated energy. The DG energy is a random amount since only the on DG at this hour will contribute to the total energy of the system and the rest will be idle.

Fig. 2. Simulated annual operating cycle for a DG unit.

drawing a random variable following the exponential distribution with (3) (4)

B. Required To evaluate the ability of the system power capacity to satisfy the total system load and to predict the average amount of the unsupplied demand per hour for a given year. C. Approach The problem of the summation of the output power of all the working DG is treated as a random process. Therefore, Monte Carlo simulation is used to handle this problem. The detailed description of the simulation process is given in the next section. III. ADEQUACY ASSESSMENT The behavior pattern of the working DG will be different in varying degrees even if they are all identical. This is due to the random nature of the DG duty cycles, their failure rates, and their times for service restoration. The adequacy assessment of distribution system, therefore, will require the prediction of the operating state of each DG and the system state will be determined accordingly. The procedure carried out to perform this assessment and to estimate the power capacity of the system is summarized as follows A. Step I A two-state-model (up state and down state) is used to model the operation of each DG. The up state indicates that the DG is in its operating state and the down state implies that the element is inoperable due to a failure or a scheduled off. Fig. 1 shows is the mean time to the two-state-model. In this figure, is the mean time to repair. This model is used failure and to provide an artificial operating history of each DG unit in the form of an up-and-down cycle. Fig. 2 depicts a typical operating cycle for a simulated unit. The parameters 1 and 0 referred to the up and down state of this ) and unit. The duration of the up state is the time to failure ( . The the duration of the down state is the time to repair and the can be calculated by sampling values for the

are two uniformly distributed random number where and sequences between [0,1]. [7] B. Step II The operating cycles of all the DG are combined to obtain ). This is then added the power capacity of the DG ( in order to obtain the overall available capacity of the to the is assumed to be the power capacity of a large system. The substation. This capacity is considered to be a random value ranging from 80 to 100% of the nominal substation capacity. C. Step III The system available capacity curve is superimposed on the chronological hourly load curve to obtain the system available margin model. A positive margin indicates that the system generation is sufficient to meet the system load, while a negative margin denotes that the system demand is not satisfied. The average amount of the unsupplied load per hour during each year (AUL) is estimated in this step by running Monte Carlo simulation for a large number of sample years and evaluating the following equation: MW of Negative Margin where

(5)

is the number of Monte Carlo experiments. IV. CASE STUDY

The distribution system under consideration is supplied from a 3100-MW, 132/33-kV substation and is comprised of customer-controlled distributed generators. The structure of the system is shown in Fig. 3. This system supplies different combinations of loads. All loads are aggregated at the 11-kV busses. The annual hourly peak load curve is given in Fig. 4.

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 1, FEBRUARY 2003

Fig. 5. Hourly available margin without DG.

Fig. 3. Distribution system under study. Fig. 6.

Fig. 4. Annual hourly peak load in megawatts.

The starting hour of this figure is the first hour of the year (1 A.M. of January 1st.). The peak system load is 2850 MW. The data required to construct this load model are presented as a part of the IEEE reliability test system in reference [7]. The analysis of this case study is done in two phases. In the first phase, the adequacy assessment is performed on the system represented by only its . In the second with the system phase, the distributed generation is included in the analysis and is represented by (1). the system A. Phase I: Determination of the System Margin This phase is concerned with the evaluation of the available capacity of the distribution system in the absence of the DG. The goal of this step is to determine whether the substation received power will be enough to cover the demand of the system all year round or there is a need for a substation expansion. To achieve is assumed to vary randomly in the range from this goal, the 80 to 100% of the substation nominal capacity (3100 MW). The system margin is estimated by subtracting the peak load from the received power every hour. The obtained system margin for a sample year is depicted in Fig. 5. It is clear from this figure is not that the system encountered several hours where the enough to satisfy the required demand, and therefore, there is

Negative margin during one sample year.

a need for an increase of the overall system available capacity. To estimate the amount of extra power needed for this system, the negative margin at each hour of the sample year is recorded. Fig. 6 illustrates the distribution of the recorded negative margins over the sample year. The maximum difference between the and the load peak is 380 MW during the end-of-year holiday season. This result, although it shows a high deficiency of the system, cannot be used to assess the system adequacy because the analysis was performed for one sample year. During this sample is considered to be a random variable; therefore, year, the different margin patterns will be expected for different sample years. In order to determine the actual estimate of the amount of the unsupplied load for any sample year, Monte Carlo simulation was performed for a large number of sample years. The average amount of unsupplied load for each hour was calculated using (5). Fig. 7 portrays the Monte Carlo convergence process. The average unsupplied load is estimated to be 5.689 MW for each hour of the year. This figure reflects the great need for system capacity increase and the inadequacy of the system in its current structure to meet the installed demand. In the next section, the effects of running some customer-controlled DG in parallel with the existing substation upon the system overall capacity are presented. B. Phase II: Determination of the System Margin With DG In this phase, identical DG units are assumed to run in parallel with the existing substation. The customers usually determine the locations of these DG; however, to make the analysis in this study more general. Each 11-kV bus was assigned a DG unit. The ratings of each DG unit can be in the range from 20 kW to 100 MW, depending on the function of this unit. For example, a residential DG system would comprise small units

HEGAZY et al.: ASSESSMENT OF GENERATION SYSTEMS USING MONTE CARLO SIMULATION

Fig. 7. Convergence of Monte Carlo simulation for the average unsupplied load in megawatts per hour.

Fig. 8.

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Hourly available margin with DG.

TABLE I FAILURE RATE  AND THE REPAIR RATE  OF EACH DG.

in the range of 100 kW whereas, an industrial DG system would involve larger units in the range of 100 MW or even higher. In this study, large DG units of 100-MW ratings are selected to examine the extreme operating conditions of the system under study. The following assumptions were made to ensure the credibility of the results. 1) all of the DG units are of the same type and size; 2) the system cables and switchgear are well designed to carry the expected demand. Although all of the DG units are identical, the operating cycle of each unit will be different in varying degrees because of the random nature of their on and off periods. The procedure explained in Section III is used to generate artificial history of the operating cycle of each DG for a given sample year. The parameters required to generate the operating cycle of each DG are the failure rate (failures per hour) and the repair rate (repairs per hour). The numerical values of these parameters used in this study are given in Table I. [7] The generated artificial operating cycles of all the DG are . Then, the is combined together to obtain the system to determine the overall superimposed on the available . The system margin is estimated by subtracting the hourly demand from the hourly available power. The obtained system margin for a sample year is depicted in Fig. 8. The negative margin in any hour indicates that there is an unsupplied load at this hour. Fig. 9 shows the hourly-unsupplied load during the sample year. The comparison between the results shown in Fig. 9 and those obtained for the system without DG (Fig. 6) reveals that having the DG running in parallel with the substation has eliminated most of the negative margins during the year. However, the criteria to judge the adequacy of the system in this case are still the average amount of unsupplied load in each hour of the year. This figure is estimated for this case study by running Monte Carlo simulation and applying (5). The convergence of the results of this simulation for large number of sample years is presented in Fig. 10. The amount of unsupplied load in each hour for any sample year is found to be

Fig. 9. Negative margin (in megawatts) during one sample year.

Fig. 10. Convergence of Monte Carlo simulation for the average unsupplied load in megawatts per hour.

0.8 MW. This value constitutes 0.028% of the maximum load and 0.0407% of the average load. Therefore, the available capacity of the system in this case is considered sufficient to meet the system demand. The conclusion drawn directly from this result is that distributed generation units, if well managed, can give a good support to the existing system. A discussion of this aspect is found in the next section. V. DISCUSSION For years, distribution systems relied on the capacity of the available substations to be the only source of electric power in the system. When an increase of the system demand is forecasted, the available options to meet this increase in demand were either to expand the existing substations or to build a new one. In some emergency cases, tie lines with other networks were used to cover the system negative margins. The study presented in this paper gives a new perspective to the power management of distribution systems. A quick and reliable solution for an expected increase in the demand would be installing and running a DG unit in parallel with the system. In addition, the

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technology for this DG can vary from gas turbines to fuel cells or even ocean energy according to the available resources and environmental considerations.

[6] F. V. Edwards, G. J. Dudgeon, J. R. McDonald, and W. E. Leithead, “Dynamics of distribution networks with distributed generation,” Proc. IEEE Power Eng. Soc. Summer Meeting, pp. 1032–1037, 2000. [7] R. Billinton and W. Li, Reliability Assessment of Electric Power Systems Using Monte Carlo Methods, New York: Plenum, 1994.

VI. CONCLUSIONS This paper presents a Monte Carlo-based method for the adequacy assessment of distribution networks when customer-controlled distributed generation units are running within the system. The duty cycle of each DG represents the main source of the random operation of this DG. A general procedure based on state duration sampling is implemented in this paper to assess the ability of the system power capacity to meet the total demand. A typical case study is analyzed where several distributed generation units are running in parallel within a system and the system margins and the average amount of unsupplied loads are estimated using Monte Carlo simulation. The results obtained showed that DG can enhance the overall capacity of the distribution system and be used as an alternative to the substation expansion in case of expected demand growth. REFERENCES [1] T. Ackermann, G. Andersson, and L. Soder, “Distributed generation: A definition,” Elect. Power Syst. Res., vol. 57, pp. 195–204, 2001. [2] R. H. Lasseter, “Control of distributed resources,” in Proc. Bulk Power Syst. Dynamics Control IV, Santorini, Greece, Aug. 1998, pp. 323–329. [3] T. Ackermann, G. Andersson, and L. Soder, “Electricity market regulations and their impact on distributed generation,” in Proc. Int. Conf. Elect. Utility Deregulation Restructuring Power Technol., London, U.K., Apr. 2000, pp. 608–613. [4] N. Hadjsaid, J. Canard, and F. Dumas, “Dispersed generation increases the complexity of controlling and maintaining the distribution systems,” IEEE Comput. Appl. Power, vol. 12, pp. 23–28, Apr. 1999. [5] P. P. Barker, “Determining the impact of distributed generation on power systems: Part 1-Radial distribution systems,” Proc. IEEE Power Eng. Soc. Summer Meeting, pp. 1645–1656, 2000.

Y. G. Hegazy (M’96) received the B.Sc. and M.Sc. degrees in electrical engineering from Ain Shams University, Cairo, Egypt, in 1986 and 1990, respectively, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1996. Currently, he is an Assistant Professor in the Department of Electrical Power and Machines at Ain Shams University, and a Visiting Assistant Professor at the University of Waterloo. His interests include power distribution systems, power quality, and probabilistic analysis of power systems.

M. M. A. Salama (F’02) received the B.Sc. and M.Sc. degrees in electrical engineering from Cairo University, Giza, Egypt, in 1971 and 1973, respectively, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1977. Currently, he is a Professor in the Electrical and Computer Engineering Department at the University of Waterloo. His interests include the operation and control of electric distribution systems, power-quality analysis, and insulation systems. He has consulted widely with government agencies and the electrical authority.

A. Y. Chikhani (SM’87) received the B.Sc. degree in electrical engineering from Cairo University, Giza, Egypt, in 1971. He received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1976 and 1981, respectively. He joined the Department of Electrical Engineering at the Royal Military College (RMC) in Kingston, ON, in 1980, and became Head of the department in 1990. In 1994, he became Dean of Engineering at RMC. His interests include the operation and control of power distribution systems, power-quality analysis, and cables and microprocessor applications to power systems. Dr. Chikhani is a past chairman of the IEEE Kingston section.