Journal of Electrical and Computer Engineering

Volume 2018, Article ID 4790942, 13 pages

https://doi.org/10.1155/2018/4790942

## Multiobjective Optimization Approach for Coordinating Different DG from Distribution Network Operator

^{1}College of Information Science & Technology, Hebei Agricultural University, Baoding, China^{2}China Electric Power Research Institute, Beijing, China^{3}College of Information and Electrical Engineering, China Agricultural University, Beijing, China

Correspondence should be addressed to Limei Zhang; moc.621@hchzml

Received 21 May 2018; Revised 5 September 2018; Accepted 14 October 2018; Published 15 November 2018

Guest Editor: Mustafa I. Fadhel

Copyright © 2018 Limei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Integrating with analysis of uncertainties, this paper presented a multiobjective optimization approach for coordinating different DG from the perspective of Distribution Network Operator (DISOPER). Aiming to three uncertain factors including fuzzy variable, random variable, and interval variable, the information entropy and interval analysis methods are adopted to construct multistate models of multisource uncertainty. The information entropy method is to convert fuzzy variable into equivalent random variable. Interval analysis method is to transform random variables into interval variables by setting a confidence level. Then plenty of simulation analysis based on the small probability event and expectation are investigated to reduce the computational burden and eliminate invalid computation. Subsequently, multiobjective formulations based on multistate are built by analyzing systematical power loss, voltage quality, reliability, and environment change provide some reference for DISOPER in dealing with access of privately owned DG units. Furthermore, based on network topology analysis and modified nondominated sorting genetic algorithm (NSGA), a combinatorial optimization method is proposed to reduce search space and solve the constructed formulations efficiently. Simulations are carried out on IEEE 37-bus systems and results are presented and discussed.

#### 1. Introduction

Environmental deterioration, energy shortages, and climatic anomaly compel many countries to take renewable energy as future alternatives [1]. Consequently, distributed generation (DG) such as wind turbines (WTs) and photovoltaic (PV) systems are considered the most promising technologies to meet electrical loads because of their outstanding advantages such as environmentally benign, clean, and inexhaustible [1, 2]. Constrained by traditional power grid, one main application of DG in China is DG access to distribution system for the purpose of giving full play to the function of interests’ integration [3, 4]. However, different from conventional power sources, DG penetration has a significant influence on power system due to its stochastic nature [2, 3]. Previous research has shown that the effect of DG access is closely related to siting and size of DG [4]. Therefore, the appropriate planning of DG in distribution system plays a crucial role in fully exerting DG advantages as well as restraining its disadvantages [5–7].

Apparently, DG planning in distribution network is an extraordinarily complicated problem, which is attributed to not only the diversity and intermittent nature of DG but also the complex structure and abundant metadata information of distribution network. So far, loads of researches have been reported [7–23]. Earlier studies focused on certain situation because of restrictions imposed by the treatment of uncertainty. In Reference [8], Shuffled frog leaping algorithm is presented for the placement of DG in distribution systems to reduce the real power losses and cost of the DG. When constructing multiobjective formulas, influence of load models is considered in siting and sizing of DG [9]. In Reference [10], the authors optimized three objectives including maximum DG utilization, minimizing system loss, and minimum environmental pollution by improving Pareto evolutionary algorithm. From DG Owner’s and Distribution Company’s Viewpoints, multiobjective optimization is proposed from the operational aspects and economic analysis [11]. These models and calculation methods can be used for optimum design of controlled DG and good effect can be obtained.

However, due to the profound effect of uncertainty on optimization results, certain programming models and algorithms lack adaptability for dealing with planning problem with plenty of uncertainties, which is especially prominent in planning renewable energy like WTs and PV generation. Therefore, uncertainty modeling and optimization algorithm are focused on recently published documents [9–29]. In describing uncertainty, the probability density functions is usually employed to model load, wind power, PV power, electricity market price, and so on [12–22]. Also, few studies have explored fuzzy mathematics models to describe uncertainties like load [3, 20] and constraints for voltage profile, feeder current, and substation capacity [25]. Treatment techniques of uncertainty involved Monte Carlo simulation [22, 24], scenario analysis [19, 23, 25, 26], and multistate model constructed by applying probability density functions [17, 18, 22]. In objective formulations, most of them were analyzed from economic benefits [9, 27–30], environmental concerns [30, 31], and technical constraints [9, 27, 28]. In optimization solution, some intelligent algorithm [28] and uncertain programming theory [14] were introduced to adapt to planning problems with plenty of uncertainties. Based on chance-constrained programming, a planning model is presented integrated with random characteristic of load and renewable DG power [14]. In Reference [29], Monte Carlo simulation is employed to deal with uncertainties, and NSGA-II is applied to find Pareto optimal front of two minimum objectives including system total cost and technical risk. Considering technical constraint dissatisfaction, costs, and environmental emissions, stochastic dynamic multiobjective model is constructed in Reference [25], and it applied a binary particle swarm algorithm and a fuzzy satisfying method to obtain the optimal solution. A sample average approximation algorithm-based technique is proposed in Reference [32] to solve the optimal placement of DG units, which is formulated as a stochastic optimization problem.

All these researches offer valuable contributions, but they lack the following important features. For one thing, multisource uncertainty is rarely considered together in distribution network optimization studies. For another thing, access control mechanisms for privately owned DG units are overlooked in terms of DISOPER.

In fact, there has been all kind of available DG in the market. It will be an inevitable trend that multitype and multiresource DG access power grid simultaneously, which is dominated by different factors such as policy interventions, benefit actuation, and traditional resource restriction. The advent of more charging stations for electric cars, whose charging were noted for variation in time and space, gave rise to frequent load fluctuation [17, 19, 20]. The implications of DG and load change make it necessary for DISOPER to integrate considerations regarding multisource uncertainty into DG planning of the distribution network. For the treatment of uncertainty, Monte Carlo Simulation requires enormous computational burden and is unsatisfactory to deal with complex models [33]. When multistate models and scenario analysis techniques [17–19, 22, 23, 25, 26] are applied to cope with uncertainties, selection of state or scenario apparently influences on the accuracy of optimization results. In this paper, three uncertainties including fuzzy variable, random variable, and interval variable are analyzed by information entropy and interval analysis methods to construct multistate model of uncertainties. Simultaneously, small probability event and expectation for multistate models as well as proportion compensation method are investigated to obtain representative state which can reduce invalid computation, improve computational efficiency, and guarantee the accuracy of results.

According to distribution network planning studies, the objective functions involving active power losses, emission, and reliability have been presented in many researches. However, existing papers have the drawback of overlooking the private ownership feature of DG units. Under current rules, it does not state clearly that DISOPER can randomly reject privately owned DG units whose accesses have an adverse impact on distribution network operation. But as the operator of distribution network, DISOPER has the right to change connected location of privately owned DG units to assure safe operation of distribution network. In addition, DG access concerned to multifaceted problems such as technicality, economics, environment, and social characteristics, which potentially correlate to DISOPER’s benefits. However, it is difficult for DISOPER to qualify some of them in monetary terms alone. Therefore, based on the proposed multistate model, this article developed multiobjective optimization formulations through analyzing power loss improvement, voltage quality, systematical reliability, and environment change so as to provide some reference for DISOPER in dealing with access of privately owned DG units.

Furthermore, it has been studied and concerned widely in solving multiobjective optimization problems of strong constrained condition in the fields of engineering. At present, nondominated sorting genetic algorithm (NSGA-II) has been recognized as one of the most promising algorithms, primarily because it has the feature of high convergence speed, low computational complexity and good global convergence property [34, 35]. Compared with contemporary constraint-handling strategy, application of NSGA-II is encouraged to solve more complex and real-world multiobjective optimization problems [34]. NSGA-II has also played an indispensable role in solving constrained multiobjective optimization of the electric industry [35–37]. Fast and elitist NSGA-II algorithm is employed to avoid artificially balanced solutions [35]. In Reference [36], NSGA-II is applied to deal with simultaneously determining optimal capacities of active and reactive power reserve. NSGA-II and fuzzy set theory is chosen to find the best compromise solution [37]. In Reference [38], the authors adopted a novel building energy/exergy simulation tool with multiobjective optimization capabilities based on NSGA-II for carrying out simultaneously analysis of building energy use and design’s Net Present Value. NSGA-II algorithm is used to the design of a standalone HRES comprising WTs, PV panel and battery bank [39]. In this paper, we proposed a combinatorial algorithm integrating network topology analysis and modified NSGA in order to reduce search space and efficiently solve the constructed formulations. The purpose of network topology is to eliminate obvious impossible access location of DG and avoid entire network search. In NSGA-II, the modified contents refer to nondominated sorting operator, individual crowding distance operator, and genetic operators. The purpose is to obtain effective Pareto solutions, assure uniform distribution of solutions, accelerate convergence rate of algorithm, and avoid local optimal or missing Pareto optimal solutions.

The main contribution of this paper is as follows. Firstly, three uncertainties including fuzzy variable, random variable, and interval variable are analyzed by information entropy and interval analysis methods to construct multistate model. Simultaneously, small probability event and expectation for multistate models as well as proportion compensation method are investigated to obtain representative state. Subsequently, from the perspective of DISOPER of dealing with privately owned DG units, multiobjective formulations based on multistate are constructed by analyzing power loss improvement, voltage quality, systematical reliability, and environment change. Also a combinatorial algorithm integrating network topology analysis and modified nondominated sorting genetic algorithm (NSGA) is presented to reduce search space and efficiently solve the constructed formulations.

#### 2. Descriptions and Treatment for Multisource Uncertainties

The involved uncertainties in DG planning are related to not only connotation (e.g., load variations and renewable DGs fluctuation) but also extension (e.g., electricity market change, policy and regulation adjustment, and availability of system facilities). For simplification and integrating with research contents, three uncertainties including random variable, fuzzy variable and interval variable, which are related to load variations and DG fluctuation, are portrayed and treated.

##### 2.1. Descriptions for Load and DG Uncertainties

Uncertainties of load and DG have been widely studied. Here, frequently used load and electric vehicle charging stations [40] are considered, and RES-based DGs include wind turbines (WTs) and photovoltaic generators (PVs).

Integrating with existing researches, the frequently used load is modeled by using uniform distribution of interval and truncated Gaussian distribution [14–16], which is a normal distribution that restricts the range of variable value [41]. Simultaneously, taking into account the unavailability of historical data, here, electric vehicle charging stations are modeled in (1) according to quick charging mode [17, 19, 20]:where is the charging efficiency for charger, is the Charging voltage for the electric vehicle, and is the current sum of all recharging battery. Here, assume that is a fuzzy variable with the triangular membership function.

Output power of WTs is directly related to wind speed, which is usually taken as Weibull distribution. Research for the intermittent and stochastic of WTs has been relatively mature [13, 22]. The expression of wind power can be found in Reference [22].

Similar to WTs, PVs is also related to natural factors, geographic envissronment, season variation, etc. Here, PVs output power is given according to the composition of Grid-connected PV generation system [3]:where is the efficiency under the ambient temperature, is the total area of illumination, is solar radiation intensity of inclined plane, is the distribution efficiency, and is the efficiency of power regulating system, which has very strong diurnal patterns [3, 23, 42]. can be shown in the following equation:where is reference temperature, whose value is 298 K. is the conversion efficiency of PVs at the reference temperature. is the temperature coefficient of solar cell, which generally is 0.005. is the temperature at time . From (2) and (3), uncertainty of PVs output power is concerned to solar radiation intensity and the temperature. It is well known that temperature is affected by sunlight and changed with different weather conditions. That is, the temperature changes quickly in sunny days while it changes slowly in cloudy or rainy weather [43]. Furthermore, real output of PVs is still relate to illumination inhomogeneity, dust, production deviance, installation error, etc. Apparently, it is not easy to express such change through random uncertainty model. For simplification and ensuring rationalization, here PVs output power is simplified into (4) according to (2):where is real output and is the conversion efficiency related to weather conditions. Here, assume that is a fuzzy variable considering that there is an inevitable fuzziness in conversion efficiency of representing the weather conditions. And integrated with under sunny, cloudy, and rainy days given in [3], here is modeled as trapezoid membership function shown in the following equation:

##### 2.2. Treatment for Multisource Uncertainties

The purpose of treatment for multisource uncertainties is to convert various uncertainties into multistate variables to improve computational efficiency and reduce invalid computation. Based on the concept of possibility-probability consistency, information entropy is adopted to transform fuzzy number to stochastic variable. Interval analysis is applied to convert random variables into limited discrete intervals by setting a certain confidence level, and meanwhile, composite state is obtained by analyzing small probability event and expectation.

Entropy is the best measure to uncertainty. Fuzzy entropy measures fuzziness of uncertainty, while probability entropy measures randomness of uncertainty [44]. Here, set is equal to , then fuzzy variable is converted into an equivalent random variable in normal distribution with mean and variance shown in the following equations:where is the fuzzy membership function of fuzzy variable and is variance. And mean is obtained when membership degree takes 1 [45, 46]. For improving calculating efficiency and ensuring data integrity, transformation of random variables to interval variable includes the following:(i)Determination of the upper and lower limits. The method is to calculate cumulative probability of random variable. The value should be close to 1 and never lower than a specified confidence level, which is often more than 90%.(ii)Division of interval variable. Setting interval number *m*, interval is divided by regularly or irregularly step-length on the basis of actual situation. Subsequently, a binary state sequence with state and its probability is obtained. The *i*th state probability in interval can be obtained by

Simultaneously, the normalization processing is carried out by the proportion compensation method to assure that the sum of state probability is 1 [47], whose principle is to assign loss probability based on the proportion of interval probability. The revised form of state probability is shown in the following equation:

The composite state for multisource uncertainty is analyzed under the independence assumption among random variables. Assuming that the *k*th composite state is composed of three binary sequence , and from three uncertainties, the number of composite state and the *k*th joint probability are obtained bywhere and are the number of variables and interval, respectively. Subscript , , and are orderly on behalf of fuzzy, random, and interval variables.

From (9), the number of composite state increases exponentially with increase of interval number. From (10), the consequence of interval division is noticeable. Too small interval will increase tendency to small probabilities, while too large range will reduce accuracy of solution. To avoid these, plenty of simulations based on the small probability event and expectation are carried out besides setting a confidence level. The simulations are to analyze the number of small probability events and guarantee reasonable expectation of the given formulation, while the application of confidence level is to reduce the number of composite state. Similarly, the normalization is also carried out by (8).

#### 3. Multiobjective Formulations

DG penetration has significant impacts on systematical loss, voltage, reliability, etc. And compared with conventional power, DG cost is higher. However, DISOPER cannot randomly reject privately owned DG units although its accesses have an adverse impact on distribution network operation under the condition that the technical parameter is in conformity with access standard. Therefore, sometimes DISOPER has to change connected location of privately owned DG units or sacrifice personal economic interests to assure safe operation of distribution network. From the viewpoint of economics and technology, here, four maximum objectives are constructed by analyzing reduction of power loss, enhancement of voltage quality, improvement of reliability, and change of environment to optimize the location and capacity of DG, thereby providing reference for DISOPER in coordinating access of privately owned DG units.

##### 3.1. The Reduction of Power Loss

The power loss rate in (11), which is defined as the ratio of power loss reduction with DG and power loss without DG, is proposed to reflect impact of DG on power loss:where and denote the number of composite state without DG and with DG, respectively. and are state probability at the *q*th and *s*th composite state. and are power loss at the *q*th and *s*th composite state.

##### 3.2. Enhancement of Voltage Quality

Currently, besides the consumers’ higher requirements for power supply because of the rapid development of modern power electronic devices, electric market reform has brought fierce competition among enterprises. To improve vitality and competitiveness, DISOPER has to reinforce system to better control over voltage variations [48, 49], which is closed linked to technical and potential economic interest. Therefore, the quantification of DG impact on voltage quality is very necessary. Here, the improvement of systematical voltage offset, which is defined as the ratio of nodal voltage offset before and after DG installation, is given in (12) to quantify DG enhance on voltage quality:where subscripts and are without and with DG, respectively; is the load node set; and are the real voltage magnitude and the nominal voltage at the *i*th load node.

##### 3.3. Improvement of Reliability

DG access can improve reliability of load in island if DG island operation is feasible after system fault. Here Ratio of Expected Energy Not Supplied Reduction shown in (13) is employed to measure DG impact on systematical reliability:where is expected energy not supplied; is the *i*th load fault rate (number of faults per year); and is the average durations of fault (hour per time). The equations for and are proposed in [48–50].

##### 3.4. Improvement of Environment

Without a doubt, electricity industry is playing an inescapable role for environmental pollution. DG is also propelled to meet requirements of low carbon emissions. Here, only carbon emission is taken into account because the others are looked as being proportion to it. The environmental improvement is investigated by the rate of carbon emission reduction in the following equation:where is the electricity from main grid without DG (kWh); is the electricity from main grid with DG (kWh); is the electricity from DG; and is the amount of carbon emission per unit electricity (kg/kWh). Subscript is the conventional energy.

##### 3.5. The Constraints

For safe and stable operation, the optimization problem is subject to power flow equations constraint and some inequation limits like node voltage, branch capacity, etc. These constraints are shown in the following equations:where is the power from the main grid; is DG power; is systematical losses; are the number of operating state; represents the probability of an event; and are the *i*th nodal upper and lower of voltage; and are real line capacity at the *q*th state and permitted maximum line capacity; and are the real number and the allowable ceiling of DG location; and are confidence level of bus voltage and line capacity; and are base load and DG power at node *i*; and *k*% is the penetration rate of DG.

#### 4. Optimization Method Based on Network Topological Analysis and Modified NSGA-II

Besides the inherent complexities of power flow calculation in DG planning, the previously constructed multiobjective optimization formulations are obviously constrained, nonlinear, with mixed integer variables. Consequently, optimization computation is a tremendously complex task. In order to improve the computational efficiency without influencing the accuracy of solutions, the topological analysis and modified NSGA are adopted to carry on combinatorial optimization. The purpose of topological analysis is to reduce search space by determining DG candidate locations in accordance with the actual situation, while that of modified NSGA is to improve convergence speed as well as avoid falling into local best during optimizing the constructed formulations.

##### 4.1. Determination of DG Candidate Locations Based on Network Topology Analysis

Previous researches showed that DG impacts on distribution network are related to the connected bus as well as all others buses, but the bigger influence occurs on the bus near DG [51]. And DG layouts should try to keep decentralized to limit potential of interfering with each other in undesired ways. In addition, DG location is restricted by geographical position and local natural resources. Therefore, here DG candidate locations area is proposed to determine one DG location when carrying out multiobjective optimization. The number of DG candidate locations areas is corresponding to the maximum number of DG installation locations. Each area, which determines DG candidate locations set, is obtained through the limited depth-breadth priority algorithm. A DG candidate locations set is obtained according to nodal electric distances, nodal load moment, and reliability requirement. The detailed process is described as following:

*Step 1*. Obtain the DG candidate location area. Based on the maximum number of DG installation location *h*, the distribution network is divided into *k* area. Partitioning method is to add the base load starting from the end of line according to the limited depth-breadth priority algorithm. The sum of all base loads in one area is approximately equal to the value of the total base load divided by *h*.

*Step 2*. Select DG candidate locations based on the principle of reducing the power loss. Generally, the bus far from substations produced more power line losses. Therefore, here the nodal electric distance *d* is applied to determine the DG candidate locations. The selected node *i* is obtained bywhere is electric distance and is the alternative bus.

*Step 3*. Select DG candidate locations based on the principle of improving the nodal voltage. It has been proved that the constant PQ DG can definitely boost up the nodal voltage, while PV DG also can achieve the same effect under the condition that the connected nodal voltage is lower than the voltage of PV DG [51]. Furthermore, the voltage loss is in correspondence with the nodal load moment. Therefore, through the descending order of the nodal load moment, the first half is selected as DG candidate location.

*Step 4*. Select DG candidate locations based on the reliability requirements. As mentioned previously, DG access can improve the reliability in island load. Thus, buses having high reliability requirements are chosen as candidate location.

*Step 5*. Form DG candidate locations sets by combining and abandoning candidate locations in view of the partitioning area. One candidate location set is corresponding to one area. The principle of abandon and combination includes the following: (a) to reserve all candidate locations based on reliability, (b) to abandon the candidate locations without locating in installation locations area, (c) to abandon inaccessible geographical location, and (d) to keep candidate locations coming from both step 2 and step 3.

##### 4.2. DG Island Separation Based on Network Topology Analysis

As mentioned in [48], DG impact on reliability is mainly concerned to the island’s load. Then improvement of reliability is closely associated with the formation of the island. Consequently, DG island separation has a significant influence on reliability. Starting from DG connected bus, this paper goes into distribution network’s structure using breadth search, giving the island scope by the following equation:where is the number of load points in island; are the load value at the *s*th state; is power output at the *i*th DG; and is the threshold.

The formation of the island is described as following:(i)Select the connected bus of DG as the reference node of determining electrical distance, and then obtain the electrical distance of all loads.(ii)Give a lateral stratification of loads in accordance with electrical distance. Loads on the same layer are ranked in order of importance, which is represented in weighted coefficients of load.(iii)Perform breadth search starting from the innermost layer. When the total load in the island is closed to threshold, the loads on the outermost layer are chosen according to the weighted coefficients of load.

To understand it more clearly, take Figure 1 as an example. Assume that threshold is constant, and bus 4 is selected as DG location. By carrying on the width search, the next-linked buses 3, 5, 7, 8 are selected. If the sum of these load value is not satisfied with (18), buses 2, 9, 6 are considered. If they are all chosen, the sum will gone beyond the threshold . Therefore, according to weighted coefficients of loads at buses 2, 9, 6, bus 9 with larger weighty is chosen. Then the buses in island include 3, 5, 7, 8, 9.