Optimal Location and Sizing of Distributed Generators Using a Hybrid Methodology and Considering Different Technologies L. F. Grisales, A. Grajales, O. D. Montoya, R. A. Hincapié and M. Granada Program of Electrical Engineering Universidad Tecnológica de Pereira Pereira, Colombia
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[email protected] Abstract—In this article, a hybrid methodology for selecting and location of Distributed Generators (DG) in distribution systems is presented. The mathematical model proposed has a linear combination as objective function, which relates the active power losses reduction, improve the voltage regulation and investment costs reduction. Three DG technologies are considered with the possibility to be penetrated in the distribution system; these technologies are: Wind Generation (WG), Photo Voltaic Powerstations (PV) and Smaller-Scale Hydroelectric Powerstations (SSH), which have been selected according to the topographical and meteorological characteristics of the area where the distribution system is located. A hybrid algorithm between Chu-Beasly Genetic Algorithm (CBGA) and Particle Swarm Optimization (PSO) is used. CBGA is used to determine the candidate nodes to install DG and the optimal level of power injection is determined by using PSO. To reduce the solution space, three heuristic strategies are used, based on knowledge of the operating system. To demonstrate the efficiency of the proposed methodology, adaptations of IEEE 33-nodes system and Baran and Wu 69-nodes system are used. Index Terms— CBGA, distribution system, generators, heuristics based on knowledge, PSO.
distributed
n: w1 :
Number of nodes in the distribution system. Factor for standardizing active power losses.
w2 :
Factor for standardizing voltage error. Factor for standardizing the investment costs of the DG. Function that represents the active power losses. Function that represents the sum of the mean square error of the nodal voltage. Function that represents the total investment cost of the DG. Voltage of the node i.
f1 : f2 : f3 : Vi :
i : j:
Angle of the node i. Binary variable that represents the decision of installing DG unit at node i. Angle of the impedance of the line i-j.
Ri :
Impedance of the line i-j [Ω].
i :
Reactance of the line i-j [Ω].
Pgi : PGinsti : Pdi : Qgi : Qdi :
Active power generated at node i.
Current injected into the node i [A]. Ceiling value of active power generated at node i. Active power demanded at node i. Reactive power generated at node i. Reactive power demanded at node i.
Pgi
Min
:
Minimum active power generated at node i.
Pgi
Max
:
Minimum reactive power generated at node i.
Vi
Min
:
Minimum permitted voltage at node i.
Vi : VBase :
Maximum permitted voltage at node i.
Yj :
Admittance at node j.
Max
Sgi
Max
Base voltage of the system. :
CIGDi :
Maximum active power generated at node i. Cost of installing a DG at node i.
I. INTRODUCTION
NOMENCLATURE
w3 :
Xi : Ii :
In distribution system planning, it is always desired that resulting system presents lower levels of energy losses with the best stability indices and voltage regulation [1], at the same time, with the lowest cost of investment and operation. When the distribution systems exist, it is necessary to propose expansion and operation strategies that reduce the number of changes in the system, given the cost involved; this is where the optimal location and sizing of DG is presented as an excellent alternative for improving the quality of service provision, without drastically altering the current system topology. To choose the location and capacity of the DGs, it is necessary to take into account the investment capacity and how the injection of power affects the stability indices, reliability indices, voltage regulation and all operative characteristics of the system [1-3]. With the above, the penalizations of the regulatory bodies can be reduced, thus, the economic benefits of the utilities are increased and the service is improved.
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In specialized literature, several alternatives have been proposed to solve the optimal location and sizing of the DG problem, among which the following papers are highlighted. In [4], a CBGA is presented to solve the problem of the optimal location of DGs, an optimal flow is used to select the DGs capacities. A PSO is used in [5] to find the optimal location and sizing for different types of DGs. In [6], the problem of the optimal location and sizing of DG is solved by using exact optimization methods like Branch and Bound and Sequential Quadratic Programming; the goal is to reduce the power losses of the distribution system.
Equation (1) is the objective function, it depends on three factors (w1 , w 2 , w 3 ) , which normalize the equations (2) to (4) and create a fair analysis for each of them in (1). Equation (2) represents the power losses of the distribution system in [MW]. The mean square error of the nodal voltage is given by (3), and (4) represents the investment costs for installing DGs in [US$MW]. B. Constraints To define all constraints, the parameters of the system are presented in Fig. 1.
II. PROBLEM FORMULATION A. Optimal location and sizing of DG In this work, the problem of the optimal location and sizing of DGs is presented considering the existence of topographical and climatological analysis, which allows to know the best technology to install at candidates nodes. For any technology selected, the problem of the location and sizing of DGs is formulated by a one-objective function and weighting factors which allow combining linearly the objectives of power losses reduction, improve the voltage regulation and reduce the investment costs, subjected to a set of classical operative constraints of the distribution systems and maximum level of penetration of DGs. The location and sizing of DGs depends largely on the size of the distribution system, as the solution space grows in combinatorial manner. Additionally, it is not enough to know the geographical location of the DGs; it also must be known the optimal level of power injected into the system with which the system efficiency is improved. Therefore, it is necessary to know the location and number of generators to be connected at the system. This can be achieved by implementing heuristics that explore the distribution system and analyze in which nodes there is more impact when DGs are installed on them with sensitivity indices. Then, search techniques are used to find the set of DGs that presents the best voltage regulation with lower power losses and investment costs. For each configuration of candidate nodes to install DG, it must find the optimal injection of power. It must find the optimal injection, for this, it created a codification that works on both search techniques that form the hybrid methodology. The mathematical model proposed is presented below:
min Z w1 * f1 w2 * f 2 w3 * f3
(1)
Where, n
f1 ( Pgi Pdi )
(2)
i 1 n
f 2 (Vi Vbase )2
(3)
i 1
n
f3 PGinsti * CIGDi * i i 1
(4)
Fig. 1. Single-line diagram simplified of distribution system
All nodes must satisfy the following equations: n
Pgi Pdi Vi * Vj *Yj *cos( i j j ) 0 (i) n
(5)
j 1 n
Qgi Qdi Vi * Vj *Yj *sin( i j j ) 0 (i) n
(6)
j 1
V min i Vi V max i
Pg
min i
Pgi Pg
(i) n
max i
(i) n
(7) (8)
Equations (5) and (6) represent the balance of active and reactive power on each node. Equation (7) presents the maximum and minimum limits for nodal voltage and (8) shows the capacity for DGs. III. PROPOSED METHODOLOGY To solve the problem of the optimal location and sizing of DGs, a hybrid methodology between CBGA and PSO is used. First, CBGA is used to find the optimal location of DGs [7]; this finds a set of candidate nodes to install DGs at them. Then, the optimal injection of power (sizing of DGs) is found by using a PSO. Fig. 2 represents the implementation of the hybrid methodology. The proposed methodology is highly dependent on the candidate nodes to install different technologies of generation (WG, PV and SSH), it is necessary the implementation of heuristics methods based on the knowledge of the operating system and allowing the reduction of the solution space. In this article three heuristics are used. A. Heuristic based on overload of the lines This heuristic analyses the overload of the lines by selecting nodes downstream which can help to reduce congestion of the lines and the same time, improve voltage regulation [8].
C. Heuristic based on stability indices Stability indices are analyzed in all the nodes and those that are below a given level are selected [9]. The expression used for this calculation can be found in [10].
Read data of the system
Generate initial population
IV. TEST AND RESULTS For the location of distributed generation, the following considerations were taken into account:
Calculate the objective function by using PSO
Find the incumbent and capacity of DGs
Generate an offspring through the tournament, recombination and mutation
Calculate the objective function by using PSO
No
The offspring is different from all individuals of the population and at least a better one?
The type of technology for DGs at each node is located by a previous study of the location zone, which allows selecting the best technology to install. 40 % of the power generated by the slack node is considered as the maximum injection of power by DGs. Values of factors used were determined by using a search method which implemented a PSO. Three types of technologies were implemented and the best technology for each node was determined according to the location of the zone. The types and costs of DGs are presented in Table I. The costs of installation of DGs were taken from [10] and updated by using producer price indices ratio. TABLE I. DG’S COST INSTALLATION Type of DG’s Cost installation technology [US$/MW] WG PV SSH
Yes Replace the worse, find the incumbent and capacity of DGs
No
The stopping criterion is fulfilled?
1,330,000 8,560,000 1,090,000
To demonstrate the efficiency of the proposed methodology, the IEEE 33-nodes system and Baran and Wu 69-nodes system are used. The information of the systems was taken from [11]. The proposed methodology was developed in Matlab and the power flow was determined using Matpower. The initial states of the systems are presented in Table II. TABLE II. DG’S COST INSTALLATION System
f1 [MW]
f2 [V]
33 nodes 0.2110 3,880 69 nodes 0.2422 3,999 Yes Stop Fig. 2. Proposed methodology
B. Heuristic based on nodal voltages In this heuristic, after evaluating a load flow, the nodes with nodal voltages below 0.95 p.u. and above 1.05 p.u are taken as candidates.
f3 [US$/MW] 0 0
By using the methodology proposed in the test systems, the objective functions presented in Tables III and IV are obtained, which correspond to the location of the generators presented in Tables IV and VI with their respective type and generating capacities and types. TABLE III. INITIAL STATE OF THE IEEE 33-NODES SYSTEM System
f1 [MW]
f2 [V]
33 nodes 0.0912 756.9
f3 [US$/MW] 1,993,667
TABLE IV. DGS INSTALLED AT IEEE 33-NODES SYSTEM Installed Injected capacity power Type of DG [MW] [MW]
Node 12 16 18 32 33 TOTAL
0.4 0.5 0.1 0.6 0.1 1.7
0.3729 0.4484 0.0612 0.5970 0.0907 1.5703
SSH WG WG SSH SSH -----
TABLE V. INITIAL STATE OF THE BARAN AND WU 69-NODES SYSTEM System
f1 [MW]
f2 [V]
69 nodes 0.0883 716.3
f3 [US$/MW] 2,386,369
TABLE VI. DGS INSTALLED AT BRAN AND WU 69-NODES SYSTEM Installed Injected capacity power Type of DG [MW] [MW]
Node 21 63 66 TOTAL
0.2 1.2 0.3 1.7
0.3729 0.4484 0.0612 0.8825
SSh WG WG -----
Table VII presents the reduction of the power losses and the mean square error of the nodal voltage, justifying the investment in DGs. TABLE VII. REDUCTION OF THE POWER LOSSES AND THE MEAN SQUARE ERROR WHEN INSTALLING DGS System 33 nodes 69 nodes
Power losses reduction Mean square error reduction (f1) [MW] (f2) [V] 56.77 % 63.54 %
80.49 % 82.08 %
V. CONCLUSIONS The main advantage of locating DGs in distribution systems is that they can be planned both at the stage of system design and operation status, allowing the utilities to improve their quality and meet current regulations. A hybrid strategy between CBGA and PSO is presented as an excellent tool to find the optimal location and sizing of DGs, showing a significant reduction of active power losses with the lowest investment cost. The main advantage of using PSO to find the optimal dimension of DGs is that the objective function can vary depending on the needs of utilities, because in some cases it is necessary to reduce the power losses of the system and, in others cases, the need is to improve the voltage regulation. According to the objective, the levels of investment can be higher or lower. For future research, wind profile variation, the solar radiation level and hydrological aspects could be considered in order to formulate the problem of location and sizing of DGs as a more realistic representation.
ACKNOWLEDGMENT This work was supported by the Universidad Tecnológica de Pereira (Colombia) under Internal Project, and the Young Research Program of the National Department of Science, Technology and Research (COLCIENCIAS) of Colombia (JI6-14-2). REFERENCES [1] E. Buzarquis, O. A. Ojeda and F. Garcés, “Optimización del tamaño y ubicación de generación distribuida en las redes de distribución con base en energías renovables como fuentes primarias de suministro de energía – estado del arte,” XIII ERIAC, Décimo tercer encuentro regional iberoamericano de CIGRE, 2009. [2] Yadav and L. Srivastava, “Optimal placement of distributed generation: An overview and key issues,” Power Signals Control and Computations (EPSCICON), International Conference, pp. 1-6, 2014. [3] A. Picciariello, K. Alvehagand and L. Soder, “State-of-art review on regulation for distributed generation integration in distribution systems,” European Energy Market (EEM), 9th International Conference on the, pp. 1-8, 2012. [4] S. Kaur, G. Khumbar and J. Sharma, “A MINLP technique for optimal placement of multiple DG units in distribution systems,” Electrical Power and Energy Systems 63, pp. 609-617, 2014. [5] W. Ouyanga, C. Haozhong, X. Zhang and L. Yao, “Distribution network planning method considering distributed generation for peak cutting,” Energy Conversion and Management 51, pp. 2394-2301, 2010. [6] K. Kumar and M. P. Selvan, “Planning and operation of Distributed Generations in distribution systems for improved voltage profile,” Power Systems Conference and Exposition. PSCE '09. IEEE/PES, pp. 1-7, 2009. [7] M. H. Moradi and M. Abedeni, “A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems,” Electrical Power and Energy Systems 34, pp. 66-74, 2012. [8] I. F. Prado and L. P. Garces, “Chu-Beasley genetic algorithm applied to the allocation of distributed generation,” Innovative Smart Grid Technologies Latin America (ISGT LA), IEEE PES Conference On, pp. 1-7, 2013. [9] M. Sedighi, A. Igderi, and A. Parastar, “Sitting and sizing of Distributed Generation in distribution network to improve of several parameters by PSO algorithm,” IPEC, Conference Proceedings, pp. 1083-1087, 2010. [10] D. N. Hussein, M. H. El-sayed and H. A. Attia, “Optimal sizing and siting of Distributed Generation,” International Middle East Power System Conference, 2006. [11] B. Venkatesh, S. Chandramohan, N. Kayalvizhi, R. P. Kumudini Devi, “Optimal reconfiguration of radial distribution system using artificial intelligence methods,” Science and Technology for Humanity (TIC-STH), IEEE Toronto International Conference, pp. 660-665, 2009.
