Abstract-.The paper proposes NSGA-II algorithm for Micro Grid Placement in distribution system by taking into account the voltage stability index and loss sensitivity factor. The micro grid considered is limited to the DGs such as wind, Solid cell battery, and biomass and micro hydro generations. Both the optimal size and location are obtained various types of DGs. The objective is to minimize the losses in the distribution system without compromising on load voltage deviation. Because of the mutual conflicting nature of the problem NSGAII algorithm is used. The software is coded in Matlab and tested with IEEE 33 bus system. The results are quite promising which gives the optimal location of DGs and their setting. The optimal setting and sizing of the DG results in capacity saving, maximum system loadability and increased voltage stability margin at reasonable voltage deviation and system losses..
Index Terms-Distributed Generation (DG), Micro-grid (MG), Load Factor (LF) and Load Margin (LM) Voltage Regulation (VR).
Nomenclature
Net real power injection at bus .
Net reactive power injection at bus .
Line resistance between bus and .
Voltage magnitude at bus .
Voltage phase angle at bus .
System power loss, in kW.
Number of buses.
Voltage stability index
Complex power.
Mutual admittance, in pu.
Angle of
Angle of complex power ()
Angle of voltage ()
Voltage at sending end bus, in pu.
Actual voltage magnitude at bus , in p.u.
Reference value of the voltage magnitude at bus ,
in p.u. (usually set to 1.0 p.u.).
Decision variables for a two-entry vector of DG size
and location.
Real power generated by generating unit (including slack bus), in kW.
Reactive power generated by generating unit (including slack bus), in kVAR.
Load demand at bus , in kW.
Load demand at bus , in kVAR.
Upper real power generating limit of unit , in kW.
Lower real power generating limit of unit , in kW.
Branch power in branch , in kW.
Power flowing through feeder .
Rated loading capacity of the feeder .
Active base load at bus , in kW.
Reactive base load at bus , in kVAR.
Minimum value of the objective function among
all non-dominated solutions.
Maximum value of the objective function among
all non-dominated solutions.
Membership function (varied between 0 and 1).
INTRODUCTION
Micro-grig (MG) is formed by grouping DG units placed in a closer vicinity. MG can be defined as a group of DG units and load operating as a single entity that is integrated into a distribution system and operates in a coordinated and independent manner. It appears to grid as a single load. MG architecture ensures that it follows grid and/or distribution codes and does no harm to existing consumers. MG concept will allow a high penetration of DG without requiring redesign and reengineering of the distribution system [1].
Operation of MG includes grid connected mode and island mode. In grid connected mode, DG units can supply a pre-specified amount of power so as to reduce imports from the grid. Each DG is rated in such a way that they always supply specific amount of real and reactive power to customer (PQ-bus) or supply pre-specified real power and regulate its terminal voltage (PV-bus). The excess load beyond DG units' capacity will be taken care by utility supply. MG will be driven into island mode of operation in case of short circuit leading to partial blackouts. During island mode of operation, depending upon load and generation capacity of the system, either total load or only a part of load will be supplied by MG. There may be a partial load shedding to match load demand and generation in distribution system where MG is located [2]. In [3], they economic feasibility study of the best possible combination and optimal size of DGs to supply energy demands of MG which is electrified in a rural area in India. A technique to determine optimal location and sizing of DG units in a MG based on simulated annealing technique on network configuration along with heat and power requirements at various loads points is developed by [4]. An optimization algorithm for finding optimal combination of DG units to form MG in distribution network is presented in [5]. Several islanding scenarios of a distribution system from the main grid and its autonomous operation as a MG are investigated in [6]. The study concentrates on stability issues and voltage quality at designated buses during islanding transients. Strategy behind having same protection for both grid-connected as well as islanded mode of operation during different types of fault conditions is discussed in [7]. However, only single objective is considered.
This paper proposes a two stage multi-objective optimization for MG planning and operation of MG in a primary distribution system. In the first stage, loss sensitivity factor and voltage stability index are proposed to identify the MG area in a primary distribution system and a Pareto-based NSGA-II is proposed to find numbers, locations and sizes of DG in MG. Different multiobjective functions include system real power losses and load voltage deviation. The final decision making will be determined by the fuzzy method. system.
The rest of this paper is organized as follows: Section III illustrates the MG planning problem formulation. Section IV presents a NSGA-II approach for the MG planning. Result and discussion on the test system are presented in section V. Section VI concludes the paper.
Microgrid Planning problem formulation
Location of MG
In general, MG should not exist in all lateral branches of a primary distribution system. The opportunity to form MG depends on availability of resources, load demands, economic parameters and closeness of a grid to resource. The optimal subdivision of a given distribution network with DG installed into MGs may be viewed as cluster of DG units and loads (i.e. characterized by a reasonable probability that the DG feeds MG in either fully or partially autonomous operation). To find a proper location of MG within a distribution system, loss sensitivity factors and voltage stability index have been used for ranking and selecting a proper location of MG in a primary distribution network. Load in lateral branches (except substation which is a slack bus) are lumped together and sensitivity analysis is performed in such system to find a proper location of MG.
Loss sensitivity index
Loss sensitivity factors determine how sensitive system loss is to real or reactive power injection at a bus. It is a systematic approach to select those locations in a network which have maximum impact on real power loss with respect to nodal real or reactive power injection. The real power total loss in the system is given by (1), which is referred to as "exact loss" formula [8].
(1)
where,
(2)
Loss sensitivity factors can be formulated from the exact loss formula as follows:
The analytical expression of real power loss sensitivity factor with respect to real power injection,, can be expressed using (3).
(3)
Similarly the expression for real power loss sensitivity to reactive power injection, sensitivity factors are given in (4).
(4) Equation (4) is used to find the sensitive locations for reactive power injection. If MG with DG units is capable of injecting both real and reactive power, (3) and (4) can be used to identify suitable locations.
Voltage stability index
The voltage stability index indicates the status of the system and approximately shows how close the operating point to the point of collapse. The voltage stability index ( Lv) can be used to detect voltage stability in radial distribution systems. When the value of the index equals to 0 that means there is no load, and between 0 and 1 the system operates in the stable region and the values greater than 1 means that the system is unstable. The value of the index depends on the load apparent power and power factor; also it depends on the value of the admittance of the line and the voltage at the sending end and its angle.
This method gives the critical values of active and reactive power needed to plot the voltage stability boundary in the P-Q plane. The voltage stability index is given in (5) [x].
(5)
If MG includes renewable DG units, the loss sensitivity factor and voltage stability index methods can be combined with other factors (such as potential of existing resource and technology used for generation, closeness of a grid to resource, or environmental impact) to configure an MG. An application of Geographical Information System (GIS) based approach for evaluating of multifarious local renewable energy sources is presented in [9].
Multi-objective MG planning
Once MG location is identified, appropriate number and size of DGs and their suitable location should be within the MG. Selection of suitable size of DG units and their proper location within MG is an utmost importance task. An optimal size of DG units is necessary for economical operation. Sizing and location of DG units within MG could depend upon objective(s) to be optimized. The objectives to determine the optimal locations and size of DG units within MG are as follow:
Multi-objectives
(6)
where and represent real power losses and load voltage deviation respectively.
a) Real Power Losses Objective
(7)
b) Load Voltage Deviation Objective
(8)
Constraints
Equality constraints include the power balance equations. The inequality constraints include real and reactive power limits of generators, upper and lower limit of voltage and thermal limits of the lines.
(9)
Distribution generator model
At present, there are several technologies of DG from traditional to non- traditional power generation. The former is non-renewable technologies such as internal combustion engines, combined cycles, combustion turbines and micro-turbines. The latter is fuel cells, storage devices and renewable technologies (solar, photovoltaic, wind, geothermal, ocean, etc.) DGs are modeled as synchronous generators for small hydro power, geothermal power, combined cycles and combustion turbines. They are treated as induction generators, for wind and micro hydro power. DGs are considered as power electronic inverter generators such as micro gas turbines, solar power, photovoltaic power and fuel cells [x].
In this paper, three types of DGs have been considered viz wind, biomass and battery. Wind is modeled as Double fed induction generation which is having active reactive power compensation.[]. Biomass is modeled as an synchronous generator and battery used is Solid oxide fuel cell. Wind is modeled as weibull distribution with an average wind speed of 15m/s.
TABLE I
Power system component model in PSAT [x]
Power System Component
Order/Type/Algorithm
Wind model
Weibull distribution
Wind Turbine
Doubly fed induction generator
Biomass
Synchronous
Battery
Solid Oxide Fuel Cell
Load
Constant PQ Model
NSGA-II for Microgrid Planning
The region for MG using loss sensitivity factor is identified, and a NSGA-II combined with distribution load flow is used to solve multi-objective optimization to identify appropriate numbers, sizes and locations of DG units within MG. The final decision making is made by the fuzzy method.
NSGA-II algorithm
In case of multiple conflicting objectives, there may not exist one solution which is the best compromise for all objectives. Therefore, "trade-off" solution is needed instead of single solution in multi-objective optimization. Non-dominated sorting genetic algorithm (NSGA) uses no dominated sorting and sharing has not been widely used mainly because of (i) high computational complexity, (ii) no elitism approach and (iii) the need for specifying a sharing parameter. NSGA-II is developed to overcome these difficulties [10], [11].
NSGA-II is one of the most efficient algorithms for multiobjective optimization on a number of benchmark problems [11]. In addition, with NSGA-II based approach, the multiobjective of MG planning is retained without the need for any tunable weights or parameters. As a result, the proposed methodology is applicable to solving microgrid planning in a distribution network. NSGA-II has been developed to determining location and size of DG units within MG area. The procedure of the proposed algorithm is given as follows.
Step 1:
Randomly generate the initial population satisfying
problem constraints (location and size of DG units);
Step 2:
Compute fitness of each individual in the initial
population;
Step 3:
Determine the initial secondary population obtained from the initial population;
Step 4:
Current Population ↠initial population;
While (number of iterations is not attained) do
Step 5:
Build the next generation population;
5.1 Apply elitism;
5.2 Select individuals from the current population
by binary tournament;
5.3 Apply genetic operators;
Step 6:
Evaluate solutions; Apply dominance test;
Step 7:
Update secondary population;
Step 8:
Current population ↠main population;
This procedure aims at finding a good compromise among the different non-dominated solutions for sizing and placement of DG units in a distribution network. It is to provide the decision maker with information about the universe of potential (non-dominated) solutions and the underlying trade-offs, which could be used to support the choice of a satisfactory compromise plan.
Solution coding and decoding
Best location of DGs within MG and their optimal size is solved by optimizing multi-objective function using NSGA-II technique combined with distribution load flow. Assuming that the network structure is fixed and all branches between nodes are known, the evaluation of objective functions, described in section III-B, depends on size and location of DG units within MG. Each solution can be coded by using a vector, the size of which is equal to the number of nodes within MG area and size of DG units. Decimal real number coding would be sufficient to solve DG location and rating problem. Here, the initial population vector is randomly generated using equations (12) and (13) as follows:
(12)
(13)
where, rand is a function that randomly generates any number between 0 and 1.
DG location within MG area can be generated by decoding an index as shown in Table I. For example, if the randomly generated location index is 2, the DG location within MG area is bus number 17. In this way, any DG size up to its maximum size and its location at any bus within MG can be randomly generated. In this paper, DG can supply both real and reactive power. Each population of the initial population vector consists of DG size and corresponding generated bus location for each population.
TABLE I
Coding and decoding of dg location within mg area.
Locaton_index
1
2
…
Total number of DG location
DG_location
15
17
…
33
Fuzzy method for best compromised solution
Once the Pareto optimal set is obtained, it is practical to select one solution from all solutions that satisfies different goals to some extent. Such a solution is the best compromise solution. In this paper, a simple linear membership function is considered for each of the objective functions. The membership function is defined as follow [13].
(15)
The membership function is varied between 0 and 1, where = 0 indicates incompatibility of the solution with the set, while = 1 mean full compatibility.
The compromised solution can be found by using the normalized membership function [14]. For each non-dominated solution, the normalized membership function is calculated as:
(16)
where, is the number of non-dominated solutions, and is the number of objective functions. The function can be considered as a membership function of non-dominated solutions in a fuzzy set, where the solution having the maximum membership in the fuzzy set is considered as the best compromise solution.
The following steps are used to locate a MG and evaluate the performance of distribution MG system.
Distribution system is modified by lumping all loads in lateral branches (except root node).
Loss sensitivity factor is used in the modified distribution system to identify a proper location to form a MG.
Number of DG and their appropriate sizes within MG are determined by the PSAT and NSGA-II. A fuzzy decision making analysis is used to determine the final solution.
Results and discussions
Analytical Tool and Test System
The load flow analysis based on iterative backward/forward sweep methods has been carried out using MATLAB [15]. Multiobjective optimization problem is solved by NSGA-II. Moreover, P-V curves and hence, loadability of the system is obtained from Power System Analysis Toolbox (PSAT) [16]. The distribution system used in this paper is depicted in Figure 1. The system is modified version of the system present in [17] (without MG). The branch numbering approach [18] is used to solve load flow analysis based on backward/forward sweep methods. Bus data and branch data for 33-bus radial distribution system based on peak load are from [17].
Fig. 1. 33-bus radial system with MG.
Evaluation of MG configuration
1) MG location
Ranking of buses based on loss sensitivity analysis with respect to real and reactive power injections in 33-bus system and voltage stability index are shown in Tables III. Note both sensitivity factors lead to the same ranking. It is clear that MG should be formed at location j in Fig. 1; they are buses 15, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 32, 33 in the original system.
In case of both sensitivity factors have the different ranking, a decision maker should select the proper location to form MG in a primary distribution system based on which aspect of system performance (i.e. real or reactive power related) is to be improved. The injection of reactive power at a bus helps to control the bus voltage. The variation of power loss is relatively less sensitive to voltage changes when compare to the size of real power injections at a bus. The amount of real power injection at a bus has strongly influence the minimization of power loss [19]. This means that the reactive power compensation can control bus voltage independently of its real power control to minimize power loss.
TABLE II
Ranking of buses for MG siting based on
, and (peak load)
Rank
dPL/dPi
Bus No.
dPL/dQi
Bus No.
LVI
Bus
No.
1
0.0757
j
0.0166
j
0.0186
j
2
0.0751
i
0.0154
i
0.0128
f
3
0.0724
h
0.0153
h
0.0007
c
4
0.0481
g
0.0094
g
0.0004
g
5
0.0370
f
0.0066
f
0.0003
i
6
0.0314
e
0.0040
e
0.0003
d
7
0.0258
d
0.0040
d
0.0003
e
8
0.0052
c
0.0006
c
0.0002
b
9
0.0045
b
0.0006
b
0.0001
h
10
0.0000
a
0.0000
a
0
a
2) MG configuration
The set of nodes where DG will be installed within MG is {15, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33}. The decision variables considered are the location and size of DG units. The number of DG to be installed will be chosen at the beginning. Here, the number of DG is fixed as two DGs. Different configuration plans have been solved using NSGA-II combined with distribution load flow. The system operates within voltage limits of 5% of normal and thermal limits of 5.0 MVA for all lines. A series of simulations have been carried out for optimal connection points and capacities of DG. The results are sensitive to algorithm parameters, typical of heuristic techniques. Hence, it is required to perform repetitive simulation to find suitable values for the parameters. The best parameters for the NSGA-II, selected through ten test simulation runs, are given in Table III.
TABLE III
Best parameters for evaluation of MG configuration
NSGA-II (parameters)
Parameter values (type)
Population size, Np
200
Number of iterations
500
Pc, Crossover probability
0.8
Pm, Mutation probability
0.33 (1/3)
For the above conditions with population size of 200 and after 500 iterations, 200 dominated solutions are found by the proposed algorithm. Figure 2 shows the Pareto front, in the objective function space (objective function system losses and voltage deviation). This set of solutions on the non-dominated frontier is used by the decision maker as the input to select a final compromise solution by using the normalized membership function in (18). The best configuration plan of DG within MG is found at buses 15 and 27 with sizes of 2.981 MW and 0.463 MW, respectively. Their optimal setting of reactive power found to be 0.783 MVAR and 0.218 MVAR, respectively.
Fig. 2. Pareto front to find optimum location and size of DG units within MG
area by NSGA-II.
The above results were compared with the exhaustive load flows or repeat load flow (RLF) approach. The computation procedure of RLF is based on the following steps:
Step1: Run the base case load flow (without MG).
Step2: Place DG at the bus within MG area.
Step3: Change the size of DG in "small" step and calculate
loss for each by running load flow.
Step4: Store the size of DG that gives minimum loss.
Step5: Compare system loss with previous solution. Replace
the previous solution if new solution is lower.
Step6: Repeat from Step 3 to 5 for all buses in MG area.
The procedure above is used to find the best location and size of two or more DG units within MG area, minimizing system loss. Assuming DG units will regulate bus voltage. The best location and size of the first DG is obtained by RLF method. In the same way, second DG size and location is found by fixing the first DG at the original location and size.
For the comparison, NSGA-II and RLF method system loss, load voltage deviation (LVD) and penetration level are considered. The penetration level can be defined as the total DG power generation over the total load demand.
(17)
Table IV shows the comparison between results of two different approaches. It has been found that optimum system power loss for different combinations of DG size and locations obtained from RLF method is lower than NSGA-II method but LVD is higher in case of RLF method. In addition, the penetration level of NSGA-II approach has higher reach of 92.7%. It can be concluded from these two results that there is tradeoff between system loss and LVD. Considering penetration level as one more factor for the decision, NSGA-II technique is better as the front looks smaller in terms of LVD and penetration.
TABLE iv
Comparison of the results of different approaches
Method
Bus
No.
DG size (MVA)
Bus
No.
DG size (MVA)
PL
(kW)
LVD
Penetration Level (%)
Case of a 33 bus (without MG)
211.2
1.806
0
RLF
15
2.697
32
0.520
59.4
0.342
70.8
NSGA-II
15
3.082
27
0.512
73.0
0.225
92.7
conclusion
The paper proposes an efficient two stage multi-objective MG planning in a primary distribution system. In the first stage, loss sensitivity factor is used to identify the MG area in a primary distribution system and a Pareto-based NSGA-II is used to find numbers, locations and sizes of DG for MG planning. NSGA-II is used to find a set of well distributed optimal solutions along the Pareto front. At the end, the final decision making will be determined by the fuzzy method. In the second stage, static performance of MG in a primary distribution system studied is proposed by considering total power loss, voltage profile, feeder current and loadability of the system. Based on numerical results, MG can improve performances of distribution system in both scenarios, leading to lower loss and higher security margin.
TABLE A.I
33-bus test system (base case) [17]
Bus data
Branch data
No
Fn
Tn
Pd
Qd
R
X
B
(MW)
(Mvar)
(p.u.)
(p.u.)
(p.u.)
1
1
2
0.100
0.060
0.0058
0.0030
0
2
2
3
0.090
0.040
0.0102
0.0098
0
3
2
4
0.090
0.040
0.0308
0.0157
0
4
3
5
0.090
0.040
0.0939
0.0846
0
5
4
6
0.120
0.080
0.0228
0.0116
0
6
4
7
0.090
0.050
0.0282
0.0192
0
7
5
8
0.090
0.040
0.0255
0.0298
0
8
6
9
0.060
0.030
0.0238
0.0121
0
9
7
10
0.420
0.200
0.0560
0.0442
0
10
8
11
0.090
0.040
0.0442
0.0585
0
11
9
12
0.060
0.020
0.0511
0.0441
0
12
10
13
0.420
0.200
0.0559
0.0437
0
13
12
14
0.060
0.025
0.0127
0.0065
0
14
12
15
0.200
0.100
0.0117
0.0386
0
15
14
16
0.060
0.025
0.0177
0.0090
0
16
15
17
0.200
0.100
0.1068
0.0771
0
17
16
18
0.060
0.020
0.0661
0.0583
0
18
17
19
0.060
0.020
0.0643
0.0462
0
19
18
20
0.120
0.070
0.0502
0.0437
0
20
19
21
0.060
0.020
0.0649
0.0462
0
21
20
22
0.200
0.600
0.0317
0.0161
0
22
21
23
0.045
0.030
0.0123
0.0041
0
23
22
24
0.150
0.070
0.0608
0.0601
0
24
23
25
0.060
0.035
0.0234
0.0077
0
25
24
26
0.210
0.100
0.0194
0.0226
0
26
25
27
0.060
0.035
0.0916
0.0721
0
27
26
28
0.060
0.040
0.0213
0.0331
0
28
27
29
0.120
0.080
0.0338
0.0445
0
29
29
30
0.060
0.010
0.0369
0.0328
0
30
30
31
0.060
0.020
0.0466
0.0340
0
31
31
32
0.060
0.020
0.0804
0.1074
0
32
32
33
0.090
0.040
0.0457
0.0358
0
Substation Voltage (kV) = 12.66 kV, Base MVA = 10.0 MVA
Rating of all branch in the system = 5.0 MVA
Pd and Qd are the load at bus Tn
