Chance-Constrained Optimization-Based Unbalanced ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 28, NO. 3, JULY 2013

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Chance-Constrained Optimization-Based Unbalanced Optimal Power Flow for Radial Distribution Networks Yijia Cao, Member, IEEE, Yi Tan, Student Member, IEEE, Canbing Li, Senior Member, IEEE, and Christian Rehtanz, Senior Member, IEEE

Abstract—Optimal power flow (OPF) is an important tool for active management of distribution networks with renewable energy generation (REG). It is better to treat REG as stochastic variables in the distribution network OPF. In addition, distribution networks are unbalanced in nature. Thus, in this paper, a chance constrained optimization-based multiobjective OPF model is formulated to consider the forecast errors of REG in the short-term operation of radial unbalanced distribution networks. In the model, expected total active power losses of distribution lines, expected overload risk and voltage violation risk with respect contingencies are minimized, and inequality constraints to in the normal state are satisfied with a predefined probability level. Thus, the profitability and security can be balanced in the presence of stochastic REG. The proposed multiobjective OPF problem is solved by the multiobjective group search optimization and the two-point estimate method. Simulation results show that distribution network economy and postcontingency performance deteriorate with increased penetration level of REG, and the penetration level has a greater impact than the forecast errors of REG.

Active and reactive powers at swing bus, respectively. Reactive power compensation at bus . The th contingency. Predefined probability level.x Expectation of a random variable. Standard deviation of a random variable. Ratio between expectation and standard deviation. Occurring probability. Severity of a contingency. Voltage magnitude of bus Apparent power of the th distribution line.

Index Terms—Chance-constrained optimization, distributed generation (DG), unbalanced distribution networks, multiobjective optimal power flow.

Setting of th tap-changing transformer. Injected current matrixes of zeroand negative-sequence circuits, respectively.

NOMENCLATURE Total active power losses of distribution lines.

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Voltage violation risk. Overload risk. Active power of th nonrenewable distributed generator. Reactive output of th distributed generator. Manuscript received December 02, 2012; revised February 23, 2013, March 30, 2013, and April 13, 2013; accepted April 17, 2013. Date of current version June 20, 2013. This work was supported by the National High Technology Research and Development Program of China (863 Program) under Grant 2011AA050203. Paper no. TPWRD-01305-2012. Y. Cao, Y. Tan, and C. Li are with the College of Electrical and Information Engineering, Hunan University, Changsha 410082, China (e-mail: yjcao@hnu. edu.cn; [email protected]; [email protected]). C. Rehtanz is with the Institute of Energy Systems, Energy Efficiency and Energy Economics, TU Dortmund University, Dortmund 44227, Germany (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2013.2259509 0885-8977/$31.00 © 2013 IEEE

Node voltage matrixes of zero- and negative-sequence circuits, respectively. Admittance matrices of zeroand negative-sequence circuits, respectively. Number of buses. Positive-sequence transfer susceptance between bus and bus . Positive-sequence conductance between bus and bus . Positive-sequence voltage angle difference between bus and bus . Positive-sequence injected active and reactive powers at bus , respectively. Positive-sequence voltage magnitudes at bus and bus , respectively. Lower and upper limits of respectively.

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Lower and upper limits of respectively.

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Position of a member at the th iteration. A Pareto-optimal solution at the th iteration. Head angle of a member at the th iteration. Search direction at iteration , calculated by polar to Cartesian coordinate transformation. Normally distributed random number with mean 0 and standard deviation 1. dimensional vector distributed uniformly in the range (0, 1). dimensional vectors distributed in the range (0, 1). Producers, scroungers, rangers. Maximum pursuit angle. Maximum turning angle. Maximum pursuit distance. I. INTRODUCTION

A

S GLOBAL energy crisis and environment problems worsen, renewable energy generation (REG) has been receiving more attention around the world [1]. In the future, a great number of distributed generators (DGs),1 such as wind generation, will be integrated into distribution networks [1], [3]. Therefore, the dispatchable resources in distribution networks will become richer, and the management will become more intelligent and active [4]. Optimal power flow (OPF) is an important tool for the active management of distribution networks [5]. A lot of research has been conducted in the field of distribution system OPF. Zhu et al. [6] proposed an OPF model and algorithm to dispatch 1Generally speaking, DG can be categorized into renewable DG and nonrenewable DG [2]. REG is the same as the renewable DG in distribution networks.

the capacitors and reactive outputs of DGs. In [7], an OPFbased congestion-management method was introduced, and the detailed formulation and case study were presented in [8]. In [9], an active-reactive optimal power-flow model was proposed to control voltage and maximize REG. In [10], a similar OPF model was proposed to take wind power and energy storage into consideration that was not addressed in [9]. Distribution network planning is a very important field for OPF applications. Dent et al. [1] proposed an OPF model considering voltage step constraints for DG capacity assessment. In [11], a hybrid genetic algorithm (GA) and OPF algorithm were presented to assess the DG capacity. Particularly, multiperiod OPF has been focused on in a lot of literature. Ochoa et al. [12] proposed a multiperiod OPF to take time-varying load and wind generation into account. The power factor control of the wind generator was also considered. Further, Ochoa et al. proposed a multiperiod OPF model to minimize the energy losses [13] and reactive power support for DG [3]. The balanced distribution networks are adopted in all of the aforementioned research. However, distribution networks are unbalanced in nature due to single-phase loads, untransposed distribution lines, and so no. Therefore, some researchers have proposed OPF models for unbalanced distribution networks (OPF-UDN) [14]–[16]. However, DGs were not taken into account in [14], and the active outputs of nonrenewable DGs were not considered as the control variables in [15] and [16]. In addition, uncertainties were not considered either in [14]–[16]. The stochastic REG plays an important role in secure and economic operation of power systems, and has been considered in bulk power system economic dispatch [17] and unit commitment [18]. Also, stochastic REG is considered in distribution network operation. In [19], fuzzy optimization is used to consider uncertain wind power for distribution system Volt/Var control. Though Niknam et al. [20] proposed a scenario-based approach to consider stochastic REG for Volt/Var control of both unbalanced and balanced distribution networks, the contingencies are not considered. In addition, the inequality constraints are required to be satisfied in all scenarios, thus security and profitability cannot be well balanced. Thus, more research needs to focus on the field of OPF–UDN. Chance-constrained optimization (CCO) is an effective stochastic optimization algorithm that has been applied widely in bulk power system unit commitment [18], OPF [21], and reactive power optimization [22], [23]. In CCO, the inequality constraints are satisfied by a predefined probability level; thus, it can be used to balance the profitability and reliability [21]. That means reliability can be well controlled when dealing with optimization problems under uncertainties. Hence, it is a promising approach. Thus, in this paper, a chance-constrained optimizationbased–multiobjective unbalanced OPF (CCO–UOPF) is formulated for radial unbalanced distribution networks to deal with forecasted active outputs of REG as random variables in short-term operation (e.g., 1 h ahead). The dispatchable DGs, such as the microturbine generator, are also considered [9]. In the model, the expected total active power losses of distribution lines, the expected overload risk and voltage violation risk that characterize the postcontingency performance are minimized

CAO et al.: CHANCE-CONSTRAINED OPTIMIZATION-BASED UNBALANCED OPF

simultaneously while inequality constraints, such as voltage limits, are satisfied with a predefined probability level. Therefore, good economy and postcontingency performance can be achieved simultaneously while bus voltage and line loading in the normal state are guaranteed within operational limits by a predefined probability level. II. CCO–MUOPF MODEL

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In (4), a bus voltage become risky once it deviates from the nominal voltage. The closer a bus voltage is to the nominal voltage, the less risk there is. Therefore, the voltage rise and LV problems can be reflected. With (4), the VVR could be calculated by (2) further. 2) OR: Overload could cause line outages, leading to a system stability problem. It is of great importance to assess the line loading and its severity. According to [24] and [26], for line , given , the overload severity function is defined as follows:

Security and economy are the two important factors of power system operation. In [24], a multiobjective OPF is formulated to simultaneously optimize the generation cost and risk that characterizes the postcontingency performance. The integration of DGs into distribution networks may not only affect economic operation, but also the security (e.g., voltage rise problem [25]). Thus, the OPF framework in [24] is adopted to formulate the CCO–MUOPF.

In (5), a line becomes risky once its loading exceeds 90% of the MVA rating [24], [26]. Then, the OR can be calculated by (2).

A. Objective Functions

B. Variables

In this paper, the expected total active power losses of distribution lines, the expected overload risk, and voltage violation risk are used as the objective functions of CCO–MUOPF as follows:

1) Random Input Variables: The active outputs of REG are influenced greatly by climate, and cannot be forecasted accurately. Thus, in this paper, the forecasted active outputs of REG are regarded as random variables. According to [27] and [28], forecasted wind power may follow normal distribution. In addition, the normal distribution assumption is also widely used in [29] and [30]. Therefore, forecasted active outputs of REG are assumed to be normally distributed in this paper. Particularly, the uncertainties of load are neglected because primary energy of REG, such as wind energy, has more variability than load [17]. 2) Decision Variables: In CCO–MUOPF, the decision variables include active outputs of nonrenewable DGs (e.g., microturbine generator), reactive outputs of all DGs, transformer tap settings, and VAR compensations (e.g., capacitor banks). Particularly, transformer tap settings and VAR compensations are discrete decision variables.

(1) (2) The definition of risk comes from [24]. It is a good index to assess postcontingency performance, and has two major advantages [24], [26]: • It is a comprehensive assessment that considers the probability and severity of contingencies, while deterministic security assessment neglects probability. • It is a continuous security assessment, and the security level can be indicated. The deterministic security assessment only tests whether power systems are secure or not. In this paper, the voltage violation risk (VVR) and the line overload risk (OR) are analyzed in detail as follows. 1) VVR: VVR is to reflect the expected violations and near violations of bus voltages after contingencies, and their severity. Generally, bus voltages are expected to work within their limits. The low voltage (LV) may cause such problems as induction motor starting problem and outages of wind generators. Thus, LV should be avoided. According to [24] and [26], for bus , given the voltage , LV severity function can be illustrated as follows:

(5)

C. Equality Constraints In CCO–MUOPF, the unbalanced power-flow equations are the equality constraints. In this paper, the unbalanced distribution network power-flow formulation with DGs is adopted as follows [31]: (6) (7) (8)

(3) is a predefined voltage value that is less than the where nominal voltage. As shown in (3), the bus voltage becomes risky when it is below the nominal voltage. The voltage rise problem could be caused by DGs [25], but it was not considered in (3). Thus, with reference to the voltage deviation objective function in [20], the modification is made as follows:

(4)

(9) In (6)–(9), the unbalanced power flow is decomposed into three subproblems (positive-sequence, negative-sequence, and zero-sequence problems) that have weak couplings and, thus, the problem size can be reduced [31]. For simplicity, only threephase DGs are considered and they are assumed to be operating in PQ mode. In this paper, the unbalanced power-flow algorithm shown before is implemented in the MATLAB environment, and the MATPOWER software package [32] is embedded to

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solve the positive-sequence power-flow equations in the unbalanced power-flow algorithm. D. Inequality Constraints for Decision Variables (10)

optimal solution set and the producer of each objective are determined first, and then all the members perform searching. The detailed searching behavior is summarized as follows: 1) Producers: Producers are the members that own the best resources for the corresponding objectives. The producers perform local searching by scanning three points as follows:

(11) (12) (13) (19) E. Chance Constraints for State Variables In CCO, chance constraints are formulated to ensure that the inequality constraints for state variables are satisfied by a predefined probability value. The predefined probability value reflects the system reliability level. Generally, joint chance constraints are used to confine the inequality constraints together. However, it is hard to deal with joint chance constraints in the OPF problem [21]. Thus, the single-chance constraint formulation recommended in [21] is adopted for state variables as follows: (14) (15) (16)

If producers find better resources for the corresponding objectives, they will move to the positions; otherwise, they will keep still and rotate head angles as follows: (20) If producers do not find better resources after generations, the head angles return to the value generations before (21) 2) Scroungers: Scroungers search resources by following one of the producers and one member in the current Pareto-optimal solution set as follows:

(17) III. SOLUTION A. Pareto Optimization Pareto optimization is a widely used multiobjective optimization strategy. In the Pareto optimization, given objective function , if the solutions and meet the following conditions: (18) dominates [33]. Pareto optimization is then the solution to find a set (Pareto Front) in which any solution is not dominated by the other solutions. That means, in the Pareto-optimal solution set, a solution give better value on at least one objective, but not all the objectives. Pareto optimization can provide decision makers a set of solutions to choose. B. Multiobjective GSO Algorithm Group search optimization (GSO) is a heuristic optimization algorithm that simulates animal searching [34]. GSO and its variations have been proved to perform well in many optimization problems, such as economic dispatch [35], [36]. In [33], a Pareto optimization-based multiobjective GSO (MGSO) is proposed for the optimal location of flexible ac transmission systems (FACTS). In this paper, MGSO is adopted for the global optimization of the CCO–MUOPF problem. In the MGSO, all members are divided into three groups: producers, scroungers, and rangers. At each iteration, the Pareto-

(22) where the operator “ ” represents the Hadamard or Schur product. It means, given matrices of the same dimensions, if , then . In order to simulate other foraging behavior, scroungers also rotate their head angles at each iteration (23) 3) Rangers: Rangers search randomly in the environment as follows: (24) (25) (26) At each iteration, scroungers and rangers will automatically switch to the corresponding producer, if they have found current best resource for the th objective. With the Pareto optimal solution set, the fuzzy method is used to give the best compromise solution in MGSO [33]. C. Chance Constraint In CCO–MUOPF, it is very important to address chance constraints. In [18], chance constraints were transformed into equivalent deterministic constraints for stochastic unit commitment. The method may be not suitable to OPF because OPF is a highly nonlinear problem. In [21], a monotonic analysis-based method was proposed to deal with chance constraints in the


bulk power system OPF. Whether the method is applicable to unbalanced optimal power flow needs to be verified further. In [22], Monte Carlo simulation (MCS) was used to solve the chance-constrained programming-based reactive power planning problem, but it is time-consuming. In [23], cumulant-based probabilistic load flow was used to address chance constraints in reactive power dispatch. It is much faster, but it is less precise than the MCS, because linearizations around expectations of random variables were used in [23]. Two-point estimate method is also a widely used method for probabilistic power flow in which linearized power flow is not required [37], [38]. In this paper, the two-point estimate method [38] is adopted to calculate probabilistic load flow for dealing with chance constraints in CCO–MUOPF. The algorithm is summarized as follows. Assume the vector represents the random active outputs of REG, where is the active output of th REG. The and represent the mean, standard deviation, and skewness coefficient of , respectively. Let be the load-flow results, and is the th component of . Then, the two-point estimate method can be performed as follows: First, two probability concentrations around are calculated as follows:

(27) Then, the th moment of

can be approximated as follows:

(28) where

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Fig. 1. Flowchart for the CCO–MUOPF algorithm.

loads. Thus, in this paper, only expectation and standard deviation are needed to determine probability density function (PDF) by the two-point estimate method, because forecast errors of REG are assumed to be normally distributed. It should be noted that though only the stochastic nature of REG is considered, the two-point estimate method is also applicable when load is considered to be stochastic [38]. In addition, according to (28), the expected power losses, and the expected overload risk and voltage violation risk can be calculated at the same time because the first moment is equal to the expectation. Based on the aforementioned description, the flowchart for solving CCO–MUOPF based on MGSO and the two-point estimate method are shown in Fig. 1. IV. CASE STUDY

Particularly, the first moment is equal to the expectation, and the standard deviation can be computed by (29) With the moments, the probability distribution of can be approximated by some methods such as the Von Mises method [23]. In [39], the bus voltage and line power flow were approximated to be the linear expression of bus power injections in radial unbalanced distribution networks. Therefore, bus voltage and line power flow would be distributed normally, if forecast errors of bus power injections follow normal distribution [39]. Though only load uncertainties were considered in [39], the conclusion is also applicable when three-phase REG is considered because they could be treated as negative balanced three-phase

The IEEE 34-bus system [40] is an unbalanced distribution system with both three-phase and single-phase lines. Some of the loads are distributed loads. In this paper, distributed loads are addressed as equivalent spot loads connected to the center of lines [41]. Two capacitors banks are placed at buses 844 and 848, respectively. As shown in Fig. 2, to validate the proposed approach, the following modifications and assumptions are made further: • Three DGs, namely, DG1, DG2, and DG3, are connected to buses 814, 834, and 836 via step-up transformers, respectively. The DG1 and DG2 are REG, and DG3 is a nonrenewable DG. • The base MVA is assumed to be 1 MVA, and the dotted line in Fig. 2 represents the tie line that is operated after contingencies occur. No voltage regulator is considered. • The distributed load on line 832-858 is transferred to a new bus named 892. The length of line 832-858 is reduced by a

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Fig. 2. Modified IEEE 34-bus system integrated with DGs.

Fig. 3. Parameters . (a): PDF of apparent power of Line 814–850 (phase-B). (b): PDF of voltage magnitude of bus 808 (phase-B).

half. The parameters of the new line 832-892 are assumed to be the same as line 832-858. This is to make the voltage rise problem more severe. A. MCS Verification In this section, the MCS is adopted to verify the effectiveness of the method that is used to deal with chance constraints. The number of runs is set to 10000 for MCS. Assume the active and reactive outputs of DG3 are 0.1328 and 0.0250, respectively. The capacitors banks at bus 848 and bus 844 are set to 0.05 and 0.11, respectively. The taps of transformer T1-T4 are set to 1.02, 1.00, 1.00, and 1.02, respectively. Two different scenarios are simulated and PDFs of the voltage amplitude of bus 808 (phase-B) and the apparent power of line 814–850 (phase-B) are shown in Figs. 3 and 4, respectively. From the two figures, one can observe that in the two scenarios, the PDFs obtained by the two-point estimate method fit the results of the Monte Carlo method well. The differences are relatively small. Therefore, the two-point estimate method is suitable to deal with chance constraints in the CCO–MUOPF problem.

Fig. 4. Parameters: 0.15; 0.05. (a): PDF of apparent power of Line 814–850 (phase-B). (b): PDF of voltage magnitude of bus 808 (phase-B).

B. Influence of Probability Level on CCO–MUOPF In this section, the contingency set is assumed to be lines 806-808, 812-814, 852-854 , and the corresponding probability vector is [0.0001, 0.0002, 0.0003]. The operating ranges of tap-changing transformers are assumed to be [0.95, 1.05] with a discrete step size of 0.01, and the ranges of capacitors banks are set to [0, 0.10] with a discrete step size of 0.01. The upper and lower limits of all bus voltages are 1.05 and 0.95, respectively. The parameters of DG1 and DG2 are assumed to be , and . Other parameters are directed to Tables I–III and [40]. The settings of MGSO are directed to [33] and [34]. In Table IV, the predefined probability level varies from 0.65 to 0.95 with a step size of 0.10 to analyze influences of the reliability level. Since MGSO is a stochastic optimization algorithm, each case runs 20 times. For each case, the number of iterations is set to 100, and the population size is set to 30. As shown in Table IV, as the predefined probability level decreases, one can see that the expected OR and power losses decrease significantly. That is because feasible solution space increases as the predefined probability level decreases. Thus, it is


MVA RATINGS

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TABLE I OF DISTRIBUTION LINES

TABLE III PARAMETERS OF TRANSFORMERS IN THE MODIFIED IEEE 34-BUS SYSTEM

Fig. 5. Pareto optimal solution set.

TABLE IV EFFECTS OF THE PREDEFINED PROBABILITY LEVEL ON CCO–MUOPF

TABLE II PARAMETERS OF GENERATORS IN THE MODIFIED IEEE 34-BUS SYSTEM

TABLE V BEST COMPROMISE SOLUTION

more likely to find better solutions for modern heuristic multiobjective optimization algorithms. The results are similar to the conclusions in [21]. VVR also has a similar pattern, but it remains unchanged between 0.85 and 0.75 in this simulation. The reason for the same VVR is that better solutions cannot be guaranteed by increased feasible solution space. In addition, there is a tradeoff between the three conflicting objectives. However, overall, if it is required that the limits of bus voltage and line loading in the normal state are met by a high probability (high security requirement), expected power losses, OR and VVR will be likely to increase. Thus, it can be also concluded that the security level of the normal state and the security level with respect to contingencies are conflicting. A tradeoff should be made between them. Fig. 5 shows a Pareto optimal solution set obtained in a single run when the predefined probability level is 0.95. The corresponding best compromise solution is given in Table V. From Fig. 5, one can see that expected power losses, OR and VVR are conflicting, it is therefore reasonable to use multiobjective optimization when optimizing the distribution network power flow with REG.

C. Influence of Forecast Errors on CCO–MUOPF In this section, the upper limit of active power of the swing bus is set to 0.60, and the predefined probability level is set to 0.95. Other parameters are the same as those in Section V-B. To analyze the influence of forecast errors on the distribution network operation, is decreased from 0.15 to 0.06 with a step size of 0.03. Simulation results are shown in Table VI. From the table, as the forecast error of active power output of DG1 decreases, the expected power losses, OR and VVR decrease. Therefore, both security and economy of distribution network operation can be enhanced by improving the prediction accuracy of REG. Particularly, the expected OR increases much faster as the forecast

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error rises. That means the forecast error of REG has a larger influence on distribution line loading in the case of contingencies. In addition, the forecast error could represent system uncertainty level, thus it can be also concluded that the secure and economic operation of distribution networks can be improved effectively by reducing the uncertainties in distribution networks. Therefore, nonrenewable DGs could be preferable because their outputs can be controlled well. D. Influence of Penetration Level on CCO–MUOPF In this section, is varied from 0.40 to 0.55 to analyze the influences of penetration level of REG on CCO–MUOPF. is set to 0.15 and other parameters are the same as those in Section V-C. The simulation results are summarized in Table VII. From Table VII, it can be concluded that the expected power losses, VVR, and OR decrease with the declined expected active output of DG1. Therefore, the increased penetration level of REG gives adverse impacts on the safe and economic operation of distribution networks. The REG level should be limited according to the economy and postcontingency performance requirements. It should be also noted that the OR rises sharply between and . That means the postcontingency network congestion becomes much more severe when the penetration level increases to some extent. Further, when is varied from 0.55 to 0.40 (by 27.27%), it shows that the expected power losses, OR, and VVR are reduced by 20.79%, 99.83%, and 2.61%, respectively. In contrast, as shown in Table VI, when is varied from 0.15 to 0.06 (by 60%), the expected power losses, OR, and VVR are reduced by 0.86%, 99.68%, and 0.75%, respectively. The decreases in expected power losses and VVR are much less. Thus, this suggests that the penetration level has a greater impact than the forecast error level of REG. E. Computational Performance In this section, the number of maximum iterations is varied from 80 to 120 to evaluate the computational performance of the proposed method. The parameters of DG1 and DG2 are assumed to be and , and the other parameters are the same as those in Section V-D. The simulations were executed on a computer with an Intel(R) Core(TM) i7-2600 CPU (3.40 Hz, 3.40 Hz) with 16-GB RAM. As shown in Table VIII, the average execution time varies from 20.3 to 30.6 min with different maximum iterations. It is relatively time-consuming. However, the computational performance can be improved a lot because the sequence–based three-phase power flow can be solved by parallel computing, and the power system dispatch centers are always deployed with servers that own much higher floating point and integer processing rates [42]. In addition, it should be noted that the proposed method is implemented in MATLAB without consideration of computational efficiency. Thus, it is promising that the execution time can be reduced to an acceptable level. From Table VIII, it can be also seen that the results vary differently as the maximum iterations change. Generally speaking, it is because one objective can be improved with the increased


TABLE VI EFFECTS OF FORECAST ERROR ON CCO–MUOPF

TABLE VII EFFECTS OF THE PENETRATION LEVEL OF REG ON CCO–MUOPF

TABLE VIII COMPUTATIONAL PERFORMANCE EVALUATION ON CCO–MUOPF

number of searches (iterations) in a single objective optimization problem. Because it is a multiobjective problem, in some cases, some objectives may deteriorate as other objectives are improved due to a tradeoff between the conflicting objectives. V. CONCLUSIONS AND FUTURE WORKS In this paper, a chance-constrained optimization-based OPF model is proposed to deal with stochastic REG for short-term operation of radial unbalanced distribution networks (e.g., 1 h ahead). In the model, the expected power losses, the expected overload risk and voltage violation risk with respect to contingencies are regarded as the objectives, and the limits of line loading and bus voltages in the normal state are formulated as the chance constraints that are satisfied by a predefined probability value. The chance constraints are solved by the two-point estimate method-based probabilistic power flow. Since it is a multiobjective optimization problem, MGSO is used to give the best compromise solution. Simulations on the modified IEEE 34-bus system show that the high predefined probability level results in both high risk level with respect to contingencies and the poor economy and, thus, the security level of the normal state and the security level with respect to contingencies are conflicting. In addition, the simulation results show that the penetration level of REG has a greater impact than the forecast error level of REG, and the expected power losses, overload risk, and voltage violation risk decrease with a declined penetration level. Thus, the penetration level of REG should be well controlled. Single-phase DGs and electric-vehicle load also present considerable impacts on distribution network operation. However,


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Yijia Cao (M’98) received the Ph.D. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 1994. Currently, he is a Full Professor and Vice President of Hunan University, Changsha, China. His research interests are smart-grid optimization, smart-grid stability control, and the application of intelligent systems in smart grids.

Canbing Li (M’06–SM’13) received the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 2006. Currently, he is an Associate Professor with Hunan University, Changsha, China. His research interests include smart-grid dispatch as well as planning and applying energy-saving technology to smart grids.

Yi Tan (S’12) received the B.Eng. degree in electrical engineering from South China University of Technology, Guangzhou, China, in 2009 and is currently pursuing the Ph.D. degree in electrical engineering at Hunan University, Changsha, China. He is visiting the Institute of Energy Systems, Energy Efficiency and Energy Economics, TU Dortmund University, Dortmund, Germany.

Christian Rehtanz (M’96–SM’06) was born in 1968. He received the Ph.D. degree in electrical engineering from TU Dortmund University, Dortmund, Germany, in 1997. Currently, he is a Full Professor and the Director of the Institute of Energy Systems, Energy Efficiency and Energy Economics, TU Dortmund University. Dr. Rehtanz holds the MIT World Top 100 Young Innovators Award 2003.