Accepted Manuscript Fossil Fuel Cost Saving Maximization: Optimal Allocation and Sizing of Renewable-Energy Distributed Generation Units Considering Uncertainty Via Clonal Differential Evolution Madihah Md Rasid, Junichi Murata, Hirotaka Takano PII: DOI: Reference:
S1359-4311(16)32232-3 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.030 ATE 9232
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
8 April 2016 18 August 2016 8 October 2016
Please cite this article as: M. Md Rasid, J. Murata, H. Takano, Fossil Fuel Cost Saving Maximization: Optimal Allocation and Sizing of Renewable-Energy Distributed Generation Units Considering Uncertainty Via Clonal Differential Evolution, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng. 2016.10.030
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TITLE
Fossil Fuel Cost Saving Maximization: Optimal Allocation and Sizing of Renewable-Energy Distributed Generation Units Considering Uncertainty Via Clonal Differential Evolution
AUTHOR NAMES AND AFFILIATION
Given name : Madihah Family name : Md Rasid Kyushu University Department of Electrical and Electronic Engineering, 744, Motooka, Nishi-ku Fukuoka 819-0395 Japan.
[email protected] Permanent address: University Teknologi Malaysia Faculty of Electrical Engineering Skudai Johor Bahru 81310 Malaysia (corresponding author)
Given name : Junichi Family name : Murata Kyushu University Department of Electrical Engineering, 744, Motooka, Nishi-ku Fukuoka 819-0395 Japan.
[email protected]
Given name : Hirotaka Family name : Takano University of Fukui Department of Electrical and Electronic Engineering, 3-9-1 Bunkyo, Fukui 910-8507 Japan.
[email protected]
FOSSIL FUEL COST SAVING MAXIMIZATION: OPTIMAL ALLOCATION AND SIZING OF RENEWABLE-ENERGY DISTRIBUTED GENERATION UNITS CONSIDERING UNCERTAINTY VIA CLONAL DIFFERENTIAL EVOLUTION
ABSTRACT Renewable-Energy Distributed Generation Units (REDGs) are attractive alternative power sources to solve economic, environmental and fuel depletion problems. Maximizing their benefits, however, requires a proper size and location planning considering various aspects of the planning problem. This paper proposes a problem formulation of REDG location and size planning that considers various constraints, relevant uncertainties and load variations aiming at maximizing benefits of the distribution company in a distribution network where the company installs and owns REDGs. The main benefit is cost reduction that is achieved by replacing the power from fossil fuel-consuming main grid generators with power from REDGs. The fossil fuel cost saving is evaluated as the expected value due to the REDG output uncertainty. The constraints include the voltage limits, the REDG injection limit, the payback period limit, the REDG installation limit and the geographical constraint. An improved Differential Evolution (DE) with enhanced exploration capability, Clonal Differential Evolution (CDE), is introduced and applied to REDG planning for a 33-bus test system. The obtained plan satisfies all the constraints and highlights the importance of uncertainty consideration. The comparative studies have proven that the CDE is capable of speeding up the convergence, three times faster than ordinary DE. Keywords: Renewable-Energy Distributed Generation, Clonal Differential Evolution, and Fossil Fuel Cost Saving. NOMENCLATURE k : a suffix indicating the kth possible photovoltaic (PV) power output h : a suffix indicating hour h d : a suffix indicating day d : annual fossil fuel cost Cffcs saving (FFCS) : FFCS ,, : probability of PV power П ,, output ,, : fossil fuel cost for the main generators when no REDGs placement ,, : fossil fuel cost for the main generators with REDGs placement a : the number of REDGs b : the number of buses c : the number of lines : size of PV at bus i : size of mini-hydro (MH) at bus i : active power supplied by a ., substation feeder : reactive power supplied by ., a substation feeder : active power load of bus i ,,, : reactive power load of bus ,,, i : active power loss of line l ,,, : reactive power loss of line ,,, l : PV power output as a ,,, percentage of the PV size at bus i
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MH power output as a percentage of the MH size at bus i fossil fuel price ($/kW) payback period payback coefficient voltage of bus i minimum permissible voltage of bus i maximum permissible voltage of bus i PV installation cost ($/kVA) MH installation cost ($/kVA) available budget REDG active power of bus i vector in jth target generation
jth mutant vector in generation
jth trial vector in generation
PV power output in subinterval rated PV power output solar irradiance in subinterval rated value of solar irradiance
1. INTRODUCTION In traditional power systems, centralized power generators supply electrical power generated from nonrenewable-energy sources through extensive transmission lines to meet the end consumer demand. This situation causes high dependence on fossil fuel, thus may lead to a high fossil fuel cost. As an effective solution, the Renewable-Energy Distributed Generation units (REDGs) are installed in distribution networks, which assist in providing the electricity in the sites close to the users. Other potential benefits of REDGs installation are power system stability and power supply reliability improvement, loss reduction and transmission cost reduction [1][2]. Nevertheless, those benefits cannot be fully derived unless REDGs suitable sizes are located at appropriate places [3]–[6]. For this reason, several valuable studies have been conducted to treat the optimal REDG location and size planning. There are various different purposes of installing REDGs and the objectives of the studies vary accordingly [7]–[13]. The authors in [7]–[9] evaluated the costs essential in the REDG planning such as capital cost, operation and maintenance costs and REDG profits. The voltage fluctuation problem that is caused by the REDG presence is addressed in [10]. Reduction of carbon emission is focused in [11]. Minimization of power lossess is treated in [12][13]. The problems treated in the studies are usually large-scale optimization problems typically including both continuous and discrete variables. The determination of REDG sizes and locations depends on each other, which makes the problems complicated. Therefore, simultaneous optimization is required and thus meta-heuristic algorithms are often applied, but the specific algorithms implemented vary from study to study, and sometimes efficient enough. Meanwhile the consideration of various aspects such as economic, environmental, technical and geographical aspects is essential in the optimal REDG planning, each of the above-mentioned studies mainly focused on a single aspect. In addition to these aspects, the intermittent nature of some types of REDG such as wind turbines and photovoltaic (PV) is one of the challenges, which must be appropriately considered in the planning. Most of these studies applied called Monte Carlo Simulation (MCS) to deal with the uncertainty of REDG resources. This requires a proper, usually huge, number of simulations to obtain exact enough results. The literature mentioned above reveals that there is no established solution for the optimization problem that considers all the important practical aspects. There is a need for improving the REDG planning to face challenges from various practical constraints in terms of technical, economic and environmental aspects, and uncertainties in the REDG output and the load. Moreover, a more efficient solution method is necessary to tackle the large scale planning problems. In this paper, a model of REDGs-installed distribution network is considered where REDGs are owned by the monopolistic power company, and the aim is to maximize the company's benefits. The company is responsible for all the planning and the operations at the generation, transmission and distribution sides. This type of power utilities company are found in some countries. Here, the main benefit is cost reduction that is achieved by replacing the power from fossil fuel-consuming main grid generators with power from REDGs. Based on the above, a problem formulation of REDG location and size planning that considers various constraints and relevant uncertainties is proposed. The formulation considers potential REDG locations based on renewableenergy resource availability, worth of REDG investment, uncertainties in REDG output and their dependency on time of day and seasons, and hourly and monthly changes in load demand. The proposed formulation is not restricted to this particular model, but can be easily applied to other models, e.g., REDGs-installed microgids, with only a slight modification. To solve the problem that is formulated using proposed formulation, this paper introduces an improved Differential Evolution (DE) called Clonal Differential Evolution (CDE). The CDE which is the combination of DE and Clonal Selection Algorithm (CSA) is capable of enhancing the exploration ability by cloning the population. Parts of the problem formulation and the CDE were already proposed in the authors’ previous papers [14] and [15], respectively. However, the CDE in [15] used one specific way of treating its control parameter and was applied to a different type of problem. In this paper, various ways to treat the control parameter are conducted and evaluated. 2. PRELIMINARIES: DE AND CSA 2.1. Differential Evolution Differential Evolution (DE) developed by Storn and Price [16] is a population-based algorithm for the optimization with continuous variables in multi-dimensional spaces. The DE has been successfully employed to tackle a wide range of optimization problems [17]–[20] because the algorithm has only a few design parameters, easier to handle and more efficient compared to others [21]–[23].
DE optimizes a function f(X) of a D-dimensional vector X. Value of function f or its appropriately transformed value is called a fitness. First it creates an initial population P(0), which is a set of randomly generated NP solution candidates, or individuals, Xj(0). At each generation, G, a new candidate, or trial vector, Uj(G) is produced in population P(G) for each individual Xj(G), which is called a target vector, and the better of two in terms of their fitness values is selected and survives to the next generation to form population P(G+1). Through the repeated generation of new candidates and selection of better ones the population converges to an approximately optimal solution. Success of these generation-and-selection-based algorithms relies on proper control of exploration and exploitation. They have to search wider area to not miss good solutions (exploration), while utilizing what they know from current population that survived previous selections to search for better solutions efficiently (exploitation). The wisdom of DE is in its way to form a trial vector Uj(G). A mutant vector Vj(G) is produced according to (1),
V j (G ) = X j1(G ) + F .( X j 2 (G ) − X j 3(G ) )
(1)
where vectors Xj1(G), Xj2(G) and Xj3(G) are randomly chosen individuals in P(G), and F is a parameter called a scaling factor. A trial vector Uj(G ) is then generated by a crossover operation on Xj(G) and Vj(G), typically choosing an element from either Vj(G) or Xj(G) for each of D elements of Uj(G) with a probability CR. In this way, a new candidate Uj(G) is generated principally based on the current individuals, and therefore its location complies with their distribution. For example, the individuals that spread over the searching region causes the scattered trial vectors, and this implements exploration. In contrast, the individuals that are close to each other places the trial vector is near them, and this leads to exploitation. DE has two parameters, F and CR. Scaling factor F controls the size of search step, and indirectly controls the algorithm’s convergence. Unsuitable choice of F contributes to slow convergence or premature convergence [24], which have been demonstrated in [25] and [26]. However, finding an appropriate F value for a given function is challenging [27]. Although a good F is identified, it is only suitable for particular evolution stages. To overcome these limitations, adaptive DE algorithms have been introduced. FADE introduced in [27] utilizes a fuzzy logic controller for adjusting the parameters. JADE in [28] proposed a new updating strategy for parameters by employing the best solution with an optional external archive. A Controlled-Randomized F and CR values is presented in [29]. All of these approaches improve the ordinary DE in terms of convergence and robustness perspective. 2.2. Clonal Selection Algorithm Clonal Selection Algorithm (CSA) proposed in [30] applies ideas gathered from immunology in order to construct new adaptive algorithms, which is capable of solving a wide range of optimization problems. Enhancing exploration capability of population-based optimization algorithms can be done by enlarging populations so that they contain more diversified individuals. However, this might be inefficient, because it may contain unsuitable individuals. In biological immune systems, a limited number of antibodies can work efficiently against vastly different types of antigens. This is enabled by proliferating and mutating those antibodies that have recognized given antigens. CSA mimics this mechanism and have three major operators: clonal proliferation, hyper-mutation and clonal selection [30]–[33]. CSA algorithm generates a population of antibodies (candidate solutions). At each iteration, the antibodies that recognize an antigen (pending problem) proliferate by the clonal proliferation operatorand are mutated by the hyper-mutation operator to construct a new candidate population. Then antibodies with low affinities (objective function values) are discarded by the clonal selection operator. This process is repeated. 3. CLONAL DIFFERENTIAL EVOLUTION (CDE) Cloning operation in CSA generates more diversified solution candidates efficiently. Motivated by this fact, the DE is combined with CSA to form a new algorithm, called Clonal Differential Evolution (CDE). The main idea of CDE is to generate more than one trial vector for each target vector while maintaining the population size. This algorithm allows us to increase the exploration ability and favors the exploitation in the next generation since the selection is tougher. In CDE, the cloning process is introduced as an additional operation to the ordinary DE. At each generation, the population is duplicated to form m clone populations. A trial vector is created in each of the original population and m clone populations independently. The resulting m+1 trial vectors and the target vector compete with each
other for only one position in the next generation. This way, CDE creates and evaluates m+1 times as many new solution candidates as ordinary DE algorithm do while keeping the same population size. Consequently, the exploration ability can be enhanced while filling the population with survivors of more competitive selections. Figure 1 illustrates the basic flow chart of CDE. As stated in section 2.2, simply enlarging the population size also enhances exploration capability, but this is not necessarily efficient. Superiority of CDE will be demonstrated in simulation later on.
4. REDG SIZE AND LOCATION PLANNING WITH CDE IMPLEMENTATION The main objective of this paper is to maximize the FFCS in the generation side while satisfying various start Apply m+1-to-one competition
Read all parameters Select the best vector to proceed to the next G G=0 no Generate initial population and calculate the fitness value of each target vector, Xj(G)
Duplicate the population to form m populations
j=NP?
j=j+ 1
yes
Stopping condition is met?
j=1
no
yes end
G=G+ 1
Apply mutation and crossover operations to each population to generate m+1 trial vectors for Xj(G)
Figure 1 Basic flow chart of CDE practical constraints, and considering relevant uncertainties. Firstly, a model of REDGs-installed distribution network is considered. The Mini-Hydro (MH) and PV are promising REDGs, thus are considered in this paper. MH produces power continuously due to a reliable form of energy at most of the time. In contrast, PV is a typical intermittent power source. Wind turbines have similar nature. They can be treated the same as PVs and therefore are not considered here. 4.1 Consideration of REDGs output uncertainty MH is considered as a stable REDG that has no uncertainty. In contrast, the power that is produced from PV fluctuates, which must be appropriately considered because it causes a difficulty during planning. Hence, the PV power output is treated as a random variable, and the expected value is used to evaluate the Fossil Fuel Cost Saving (FFCS) that depends on the PV output uncertain at the time of planning. The stochastic features of solar
irradiance are modelled using a beta Probability Density Function (PDF) derived from its historical data for each hour and each season. The expected value is calculated numerically. First the possible PV output range is divided into a large enough number of intervals. The probability that PV output falls in each interval is then calculated by the beta PDF, conversion is made from solar irradiance to PV output, and a representative PV output value is assigned for each interval. This representative PV output is called a possible PV output in the following. The expected value is obtained by summing the products of the FFCS and its probability over the possible PV output values. MH output is deterministic, and when necessary its PDF is defined so that it takes a value of one at its deterministic output and zero elsewhere. The ordinary deterministic load flow is implemented for each possible PV output to obtain the voltage and current value and the FFCS. 4.2 Consideration of load variations Power consumed by end users varies from hour to hour and this influences the determination of REDGs sizes and locations. Thus, this planning considers the hourly and monthly load variations. 4.3 Consideration of geographical features The potential locations for both of MH and PV are considered based on geographical features such as availability of water resource for MH and a large enough open area required for PV panel installation, respectively. 4.4 Introduction of payback period Payback Period is defined by the number of years required for the REDG installation cost to be repaid by the annual FFCS. The payback period is introduced as an economical constraint for assessing the cost benefit ratio. As a result, the REDG planner is able to ensure the REDG investment is worth it. 4.5 CDE implementation The REDG sizes at all the potential locations are the variables to be optimized. Each individual Xi(G) is represented by a D-dimensional vector of integers. Here D is the total number of possible REDG locations. Usually a finite number of REDG sizes are listed in manufactures' catalogs. Thus, each of them is represented by an integer. For instance, suppose a catalogue lists four REDG sizes: 0.2, 0.4, 0.6 and 0.8 MW. Then Xi(G)=1 corresponds to 0.2 MW, whereas Xi(G)=4 corresponds to 0.8 MW. Zero indicates the absence of REDG. In the CDE process, non-integer values can appear, which are rounded to the nearest smaller integers. The resulting integer-valued REDG sizes identify both the optimal sizes and locations of REDGs simultaneously. 5. PROBLEM FORMULATION The objective function and the constraints of the problem are described below. The variables to be optimized are sizes of PV, SPV SIZE i and sizes of MH, SMH SIZE i at all the possible locations (buses). Actual output value from REDGs are determined as described in section 6.1 and 6.2 below. 5.1 Objective function The annual FFCS for the possible REDG outputs is to be maximized which is defined by (2) using equations (3), (4) and (5).
annual C ffcs = ∑∑∑ C ffcs k ,h ,d * Π C k ,h ,d ,
(2)
C ffls k ,h,d = CNO REDG fl k ,h ,d − CWITH REDG fl k ,h,d ,
(3)
k
d
h
b
c
i =1
l =1
CNO REDG fl k ,h,d = ξ ffl [∑ PD i ,k ,h,d + ∑ Ploss l ,k ,h,d ], b
c
a
i =1
l =1
i =1
CWITH REDG fl k ,h ,d = ξ ffl [∑ PD i ,k ,h ,d + ∑ Ploss l ,k ,h,d − ∑ PREDG i ,k ,h,d ],
(4)
(5)
5.2 Constraints Power balance equations, permissible voltage limits, REDG injection limit are categorized as operational constraints while economic constraints contain payback period limit and REDG installation limit. These constraints are treated as penalty functions to solve the constrained optimization problem using the
unconstrained optimization technique. The geographical constraints that determine possible installation locations for each REDG type are prespecified as stated in Section 4.3. 5.2.2 Power Balance Equations Total power generated in the network is equal to the summation of total load and the total power losses. b
b
c
i =1
i =1
l =1
∑ ( PPV i ,k ,h,d * S PV SIZE i + PMH i ,k ,h,d * SMH SIZE i ) + PG k ,h,d = ∑ PD i,k ,h,d + ∑ Ploss l ,k ,h,d , b
c
i =1
l =1
QG k ,h ,d = ∑ QD i ,k ,h ,d + ∑ Qloss l ,k ,h ,d .
(6)
(7)
5.2.3 Permissible Voltage Limit The voltage of each bus must be within the permissible limits as shown in (8).
Vi min ≤ Vi ,k ,h ,d ≤ Vi max .
(8)
5.2.3 REDG Injection Limit The summation of power injected from REDG must be equal to or less than the total load. b
b
i =1
i =1
∑ PREDG i,k ,h,d ≤∑ PD i,k ,h,d .
(9)
5.2.4 Payback Period Limit The REDG is allowed to be installed only if the period is less than a specific number of years, which is determined based on the REDG lifetime. A simple calculation of payback period is as in (10) and is to satisfy (11). PP = total REDG installation cost annual C
ffcs
,
PP ≤ α * REDG lifetime.
(10) (11)
5.2.5 REDG Installation Limit Total installation cost of PV and MH must be equal to or less than the available budget as stated in (12). b
b
i =1
i =1
PV MH X inst * ∑ S PV SIZE i + X inst * ∑ SMH SIZE i ≤ Cbudget .
(12)
6. MODELLING AND SIMULATION SETTINGS In order to implement the proposed REDG planning, this section describes the modelling of REDGs, load and the distribution network. This section also presents the parameter settings required before conducting the simulation.
6.1 PV Probabilistic nature of PV output originates from solar irradiance and depends on time of day and seasons. Since the planning deals with a distribution network, the solar irradiance is assumed almost equal over the target area. Historical data of solar irradiance are utilized to estimate PDFs at different time of day in different seasons. A beta PDF has two parameters and are from the historical data. In the simulations below, four-year hourly data are used to estimate PDFs for each hour and each month. PV output is assumed to be proportional to solar irradiance with its maximum value being determined by its size (capacity) or rated output. In order to calculate expected values numerically, the range of PV output and the corresponding solar irradiance is divided into subintervals. For subinterval n, the relation between them is represented by equation (13),
PPV n
sin ⎧ , 0 ≤ sin ≤ sirated ⎪ Prated * sirated =⎨ , ⎪ Prated , sirated ≤ sin ⎩
(13)
In this paper, the rated value of solar irradiance is 1000 kW/m2 and the length of its subinterval is 0.1 kW/m2. In addition, PVs are modeled as PQ-buses (real and reactive power specified buses) in load flow analysis with unity power factor. According to IEEE standard 1547-2003 [34], the Distributed Generation (DG) units should always operate in PQ mode with known active and reactive power generation. This is to ensure the voltage magnitude of point of common coupling of DG with distribution system is kept constant. 6.2 MH The output of a MH is assumed same as its size (capacity) and does not change depending on hours. MH is also modeled as a PQ-bus with unity power factor. 6.3 Load Power consumed by end users has different profiles on weekdays and weekend. For each month, hourly load curve on weekdays and weekend are used. The modelling of hourly and monthly load variations follows the IEEE-Reliability Test System [35]. 6.4 Distribution Network The 33-bus test system is used in this paper. The test systems shown in Fig. 2 consists of 33 buses and 32 branches and is connected to the main substation of 132/12.66 kV. The power and voltage base values are 100 MVA and 12.66kV, respectively. The load data listed in Appendix A are annual peak values [36]. In [35], ratios of hourly peak load data to weekly peak load data and ratios of weekly peak load data to annual peak load data are given, and these are used to calculate necessary load data. Moreover, several parameter values required by REDG planner are presented in Table 1. This paper assumes seven possible locations for REDG installation due to geographical conditions. Buses 4, 12 and 23 are the possible locations for MHs while possible locations for PVs are buses 8,17, 19 and 26.
19
20
21 26
22
18
19 20 21
1
2
3
25
4
5
27
28
29 30 31 32
33
26 27 28 29 30 31 32
6
7
8
9
10 11 12
13 14
15 16 17
132/12.66kV 2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18
22 23 24 23
24
Figure 2 33-bus test system
7. ALGORITHMS CDE algorithm with one clonal population is used, namely m=1. Independent F values are used in the original and the clonal populations. Specific Fs are chosen randomly as samples from uniform distributions over [0.1, 0.8] at each generation. To investigate effects of this choice of random Fs and the use of CSA principle, several algorithms with different F values are employed and their results are compared, which are listed in Table 2. Large F values tends to enhance diversified search while small values are favorable in terms of convergence speed. Therefore two fixed F values, 0.1 and 0.8 are tested. Double DE refers to a DE algorithm where the population size is doubled, which is similar to the proposed CDE in the number of candidates solutions generated in each generation but differs in that the selection in double DE is looser. Other parameters are kept the same. Twenty trials are performed with different pseudo random number sequences. Table 1 Data required by REDG planner
Data Cost budget Installation cost for PV Installation cost for mini-hydro Fuel price REDG lifetime REDG size increment Payback coeeficient, α
Value 12.012 million dollars $4004/kVA $3000/kVA $0.63/kWh 10 years 0.1MW 0.5
Table 2 Algorithms with different F values
algorithms DE Double DE CDE CDE CDE CDE
0.8 0.8 0.1 0.8 0.8 rand[0.1,0.8]
0.1 0.8 0.1 rand[0.1,0.8]
8.NUMERICAL RESULTS AND DISCUSSIONS The best, the worst and the average FFCS, and their standard deviation over the 20 trials are presented in Table 3. Table 4 shows the mean of convergence time. Here an algorithm is judged to converge when no improvement is seen on the fitness value and the convergence time is assessed by the number of fitness evaluations. Results in Tables 3 and 4 show that CDE(rand[0.1,0.8],rand[0.1,0.8]) gives higher FFCS stably (with a smaller standard deviation over 20 trials) and fast (with a shorter convergence time). The difference in FFCS from all the algorithms is not significant. However, the main focus of this paper is on the computational time, since the performance of ordinary DE might decrease due to many aspects to be considered while planning. The results indicate that the mean convergence time of CDE algorithm is, regardless to the scaling factors used, much smaller than that of ordinary DE. Next, effects of cloning population and randomized Fs in the algorithms will be discussed first, and then features of the derived solution will be investigated. 8.1 Effect of cloning population CDE clones its population when producing new solution candidates, which results in increasing the number of new candidates (doubling in this simulation setting) and enhancing its exploration capability. In the selection phase, however, it throws away low fitted candidates and shrinks the number of candidate to the original population size. The double DE, on the other hand, simply doubles its population size and keeps this doubled number of candidates in its selection phase. When the ordinary DE, CDE and double DE with the same F values, 0.8 are compared, double DE(0.8,-) does not improve stability or convergence speed over the ordinary DE(0.8,-). Conversely, CDE(0.8,0.8) gives the best FFCS in shorter convergence time as presented in Tables 4 and 5. This happens because simply increasing the number of solution candidates as is done in double DE forces the evolution process to consume much time exploring the unnecessary area of the searching region. In contrast, CDE discards the regions with low performance through the evaluation process. CDE is capable of keeping the
variety of individuals without requiring many individuals to survive. This implies that the CDE algorithm is suitable for the multi-dimensional problems with uncomplicated fitness landscape. 8.2 Effect of scaling factor A large F tends to produce mutant vectors at the peripheral area of population as implied by equation (1) and enhances exploration. CDE(0.8,0.8) offers a high FFCS but its stability is not as others. On the contrary, a small value has tendency to create mutant vectors within the population and hence strengthen exploitation. CDE(0.1,0.1) achieves better convergence time than the others. However, its fitness value is not good. This can be explained that too much exploitation increases the convergence speed but typically ends up with a local minimum or premature convergence. CDE uses multiples populations and each has its own scaling factor. Its selection process selects better individuals across the populations and also serves as choosing a better scaling factors. In CDE(0.1,0.8) better scaling factor is selected from 0.1 and 0.8 of every generation and gives stably high FFCS. However, it is unsure if 0.1 and 0.8 are the only good possible values. Better results, especially better stability, are obtained when the CDE(rand[0.1,0.8],rand[0.1,0.8]) algorithm randomly generates the scaling factors every generation. The REDG planner may choose CDE(0.1,0.1) if time is the priority, for example when dealing with a very large distribution network. If the cost becomes the main concerns in their planning, then CDE(rand[0.1,0.8], rand[0.1,0.8]) is the best solution while CDE(0.8,0.1) is another choice when the planner requires to plan within the specific duration time but allows sacrifice on the cost benefit slightly.
Table 3 The best, the worst and average fossil fuel cost saving and their standard deviations over 20 trials
Algortihm ( , )
Best ($)
Worst ($)
Average ($)
DE (0.8,-) Double DE (0.8,-) CDE (0.1,0.1) CDE (0.8,0.8) CDE (0.8,0.1) CDE (rand[0.1,0.8], rand[0.1,0.8])
489,532,374 489,532,374 489,531,975 489,532,605 489,532,589 489,532,589
489,531,085 489,529,708 489,529,572 489,525,494 489,531,860 489,532,506
489,531,754 489,531,797 489,530,475 489,530,334 489,532,198 489,532,533
Standard deviation ($) 478 919 924 2897 274 79
Table 4 convergence time
Algorithm ( , ) DE (0.8,-) Double DE (0.8,-) CDE (0.1,0.1) CDE (0.8,0.8) CDE (0.8,0.1) CDE (rand[0.1,0.8], rand[0.1,0.8])
Mean convergence time (total number of fitness evaluations) 10,710 11,160 2,700 8,280 6,300 8,820
8.3 REDGs locations and sizes determined by CDE(rand[0.1,0.8], rand[0.1,0.8]) Table 5 shows the determined DG locations and sizes. A total of 1.5MW of REDGs are located at five out of the seven possible locations, of which 1.1MW is MHs and 0.4MW is PVs. The total REDG size is determined as the maximum REDG injection limit is reached. The constraints are checked in every possible PV output value that used to calculate expected values. It is guaranteed that the constraints are satisfied in every situation from the minimum to the maximum possible PV output. Fig. 3 shows the load and the maximum and the minimum possible DREG total outputs. Each month is represented by one day from any weekdays and another day from its weekend days. As the result, each month has 48 hours of duration where the first 24 hours correspond to its weekday and the second 24 hours to its weekend. It can be observed that the maximum possible REDG output hits the load on the weekday of March. In this way, the worst case values determine the total REDG size. The total REDG size is then distributed over a number of REDGs. This distribution is determined so as to maximize FFCS, and REDG types and distribution line losses play key roles here. MH has more stable output than PV and is preferred. Referring to the equation (5), the distribution line losses strongly affect the FFCS value and the
distribution of PVs and MHs among the possible locations is determined to minimize the losses. Fig. 4 shows the annual maximum and the annual minimum voltages at each bus before and after REDGs installation. This result proves that the voltage limit constraints are always satisfied and the proper sizes and locations of REDGs provide an advantage on voltage profile improvement. The results and facts defined above indicate that the intermittent nature of PV, the load variations and the distribution line losses are important to find the optimal sizes and locations for each type of REDGs. The results also suggest that the REDG injection limit is the most critical constraint compared to the other constraints in seeking the optimal solution. Another method that can be applied to the allocation and sizing of REDGs is using separate optimization, where their sizes and locations are determined by different techniques. In the method conducted by R. S. A. Abri et al. in [37], the REDG locations were identified based on the voltage criteria. The location that has a high probability for voltage collapse becomes the first priority for REDG allocation. The REDG size for that location were then optimized using the optimization technique. However, as proven in the study conducted by authors in [38], this method does not provide good solution in term of objective value when compared to the simultaneous optimization.
Table 5 Determined locations and sizes of REDGs
Potential locations (buses) PV [MW] Mini-hydro [MW]
4
8 none
0.3
12
17 0.1
0.6
Jan
active power(MW)
Feb
March
Apr
May
June
July
Aug
Sept
Oct
Nov
23
26 0.3
0.2
4
3.5
19 none
maximum possible REDG output minimum possible REDG output load
Dec
3
2.5
2
1.5
1
0
24
48
72
96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 time(hour)
1.1
annual maximum voltage with REDG annual minimum voltage with REDG annual maximum voltage without REDG annual minimum voltage without REDG maximum voltage limit minimum voltage limit
1.05
voltage (p.u)
1 0.95 0.9 0.85 0.8 0.75
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 bus number
Figure 3 REDG injection and load Figure 4 annual maximum and minimum voltage
9. CONCLUSIONS This paper proposed the optimal REDG location and size planning. Various features including the intermittent nature of PV, the load variations, economic, technical and geographical aspects are considered in the planning. This optimization problem is then solved by the improved DE, CDE. The results achieved from the analysis have proven the effectiveness of the planning. CDE is capable of accelerating the convergence, three times
faster than ordinary DE hence reducing the computational time. The optimal REDG sizes and locations are determined by the worst condition, which shows that the uncertain PV output and load variations are essential in the planning. In addition, highest FFCS is achieved by applying CDE. The scaling factor is the critical parameter that must be carefully chosen because it strongly influences the performance of the CDE. Several sets of scaling factor are generated, and each of them has shown their own advantages. Selection for which set of F is suitable depends on the requirement that has to be fulfilled and this part is left for REDG planner. This situation suggests further research regarding the selection of F. Implementation of adaptively controlled parameters in the CDE as an example would be of great help in overcoming this problem. References [1] R. Viral and D. K. Khatod. Optimal planning of distributed generation systems in distribution system: A review. Renewable and Sustainable Energy Reviews, vol. 16, no. 7. pp. 5146–5165, 2012. [2] P. Karimyan, G. B. Gharehpetian, M. Abedi, and A. Gavili. Long term scheduling for optimal allocation and sizing of DG unit considering load variations and DG type. International Journal Electrical Power Energy System, vol. 54, pp. 277–287, 2014. [3] P. S. Georgilakis, and N. D. Hatziargyriou. Optimal distributed generation placement in power distribution networks : models, methods, and future research. IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 3420–3428, 2013. [4] N. S. Madhuri, K. M. Reddy, and G. V. S. Babu, “The optimal sizing and placement of renewable distributed generation in distribution system. International Journal of Engineering Research and Technology, vol. 3, no. 10, pp. 916–922, 2014. [5] C. L. T. Borges and D. M. Falcão. Impact of distributed generation allocation and sizing on reliability, losses and voltage profile. Proceedings of IEEE Bologna PowerTech - Conference, vol. 2, pp. 396–400, 2003. [6] K. Balamurugan, D. Srinivasan, and T. Reindl. Impact of Distributed Generation on Power Distribution Systems. Energy Procedia, vol. 25, pp. 93–100, 2012. [7] S. Montoya-Bueno, J. I. Munoz, and J. Contreras. Optimal expansion model of renewable distributed generation in distribution systems. Proceedings of Power System Computation Conference, p. 7 pp. –, 2014. [8] Z. Wang, B. Chen, J. Wang, J. Kim, and M. M. Begovic. Robust optimization based optimal DG placement in microgrids. IEEE Transaction on Smart Grid, vol. 5, no. 5, pp. 2173–2182, 2014. [9] V. Vahidinasab. Optimal distributed energy resources planning in a competitive electricity market: Multiobjective optimization and probabilistic design. Renewable Energy, vol. 66, pp. 354–363, 2014. [10] O. Ausavanop, A. Chanhome, and S. Chaitusaney. An optimal allocation of distributed generation and voltage control devices for voltage regulation considering renewable energy uncertainty. IEEJ Transaction on Electrical and Electronic Engineering, vol. 9, no. S1, pp. S17–S27, 2014. [11] J. H. Braslavsky, J. R. Wall, and L. J. Reedman. Optimal distributed energy resources and the cost of reduced greenhouse gas emissions in a large retail shopping centre. Applied Energy, vol. 155, pp. 120– 130, 2015. [12] C. Wang and M. H. H. Nehrir. Analytical approaches for optimal placement of distributed generation sources in power systems. IEEE Transaction on Power System, vol. 19, no. 4, pp. 2068–2076, 2004. [13] L. F. Ochoa and G. P. Harrison. Minimizing energy losses: Optimal accommodation and smart operation of renewable distributed generation. IEEE Transaction on Power System, vol. 26, no. 1, pp. 198–205, 2011. [14] M.M. Rasid, J. Murata and H. Takano. Determination of optimal sizes and locations of renewable distributed generations considering uncertainty by differential evolution. Proceedings of International Conference MICROGENIV, 2015. [15] M.M. Rasid, J. Murata and H. Takano. Optimal allocation and sizing of renewable-energy distributed generation units for system reliability improvement and benefit of fuel cost saving using clonal differential evolution. Proceedings of International Conference Electrical Engineering (ICEE), 2016. [16] R. Storn and K. Price. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal Global Optimization., pp. 341–359, 1997. [17] Z. Cai, W. Gong, C. X. Ling, and H. Zhang. A clustering-based differential evolution for global optimization. Applied Soft Computing, vol. 11, no. 1, pp. 1363–1379, 2011. [18] D. Zou, H. Liu, L. Gao, and S. Li. A novel modified differential evolution algorithm for constrained optimization problems. Computers and Mathematics with Applications, vol. 61, no. 6, pp. 1608–1623, 2011. [19] L. D. Arya, S. C. Choube, and R. Arya. Differential evolution applied for reliability optimization of radial distribution systems. International Journal of Electrical Power Energy System, vol. 33, no. 2, pp.
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Appendix A From Bus 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 19 20 21 3 23 24 6 26 27 28 29 30 31 32
To Bus 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
DATA FOR 33-BUS TEST SYSTEM R (ohm) X (ohm) P-load (MW) 0.0922 0.0477 0.100 0.4930 0.2511 0.090 0.3660 0.1864 0.120 0.3811 0.1941 0.060 0.8190 0.7070 0.060 0.1872 0.6188 0.200 0.7114 1.2351 0.200 1.0300 0.7400 0.060 1.0400 0.7400 0.060 0.1966 0.0650 0.045 0.3744 0.1238 0.060 1.4680 1.1550 0.060 0.5416 0.7129 0.120 0.5910 0.5260 0.060 0.7463 0.5450 0.060 1.2890 1.7210 0.060 0.7320 0.5740 0.090 0.1640 0.1565 0.090 1.5042 1.3554 0.090 0.4095 0.4784 0.090 0.7089 0.9373 0.090 0.4512 0.3083 0.090 0.8980 0.7091 0.420 0.8960 0.7011 0.420 0.2030 0.1034 0.060 0.2842 0.1447 0.060 1.059 0.9337 0.060 0.8042 0.7006 0.120 0.5075 0.2585 0.200 0.9744 0.963 0.150 0.3105 0.3619 0.210 0.341 0.5302 0.060
Q-load (MVAr) 0.060 0.040 0.080 0.030 0.020 0.100 0.100 0.020 0.020 0.030 0.035 0.035 0.080 0.010 0.020 0.020 0.040 0.040 0.040 0.040 0.040 0.050 0.200 0.200 0.025 0.025 0.020 0.070 0.060 0.070 0.100 0.040
Highlights 1. 2. 3. 4. 5.
A formulation for optimization of REDG sizes and location is proposed. The uncertainty and practical aspects are considered in the formulation. The Clonal Differential Evolution is introduced to optimize the REDGs. The consideration of the uncertainty and practical aspects determines optimal REDGs. The Clonal Differential Evolution converges faster than Differential Evolution.
