Optimal location and sizing of DG units to improve the voltage stability in the distribution system

GRD Journals | Global Research and Development Journal for Engineering | International Conference on Innovations in Engineering and Technology (ICIET) - 2016 | July 2016

e-ISSN: 2455-5703

Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients 1A.

Marimuthu 2K. Gnanambal 3R. Pooja Eswari 4T. Pavithra 1,2,3,4 Student 1,2,3,4 Department of Electrical and Electronics 1,2,3,4 K.L.N College of Engineering Abstract

The introduction of distributed generation unit in distributed system improves the voltage profile and reduces the system losses.

Optimal placement and sizing of Distributed Generation units plays a major role in reducing system losses and improving voltage profile .The different technical issues are combined using weighting coefficients and solved under various operating constraints using Particle Swarm Optimization with Time – Varying Acceleration Coefficient (PSO-TAC). In general Distributed generation is defined as generation of electricity within distributed networks. The distributed capacities minimize the requirement for over dimensioning of transmission and distribution system. If the value of the voltage stability index is increased system is increased significantly, then it is possible to operate the system away from voltage instability condition .The Particle Swarm optimization can be used to find the best location of Distributed Generation units considering voltage stability and short circuit level in the distribution system.

Keyword- Distributed Generation, Distribution System, Voltage Stability, Particle Swarm Optimization. __________________________________________________________________________________________________

I. INTRODUCTION In general, DG can be defined as the generation of electricity within distribution networks or on the consumer side of the network. The distributed capacities minimize the requirements for over dimensioning of transmission and distribution system [1].

The various renewable and non-renewable technological options available for DG and their current status were discussed in literature [2]. The various technical based indices are used in Ref. [3] to determine the benefits of DG in terms of voltage profile improvement, line-loss and environmental impact reduction of the distribution system. The various technical issues and negative impacts of DG on the network are discussed [4, 5].To identify the most sensitive node in the radial distribution system a new voltage stability index (VSI) has been used [6, 7]. In Ref. [8], the author presented the network reconfiguration using a fuzzy genetic algorithm for improvement of voltage stability in the radial distribution system. If the value of VSI is improved significantly, it is possible to operate the system away from voltage instability condition. The optimal location and sizing of DG in the distribution system using analytical methods is reported in Refs. [9, 10]. If the number of DGs gets increased, finding the optimal location and sizing of DGs using analytical expressions is more complicated. Soft computing techniques can reduce such complexities raised due to increase in the number of DG units in the distribution system. The genetic algorithm (GA) is used to obtain the optimal location and sizing of single and multiple DG units within the distribution system, considering various technical issues of impact indices in the literature [11, 12]. Particle Swarm Optimization (PSO) techniques have been implemented to find the best location of DGs considering voltage stability and short circuit level in the distribution system [13,14]. Moradi and Abedini [15] proposed a hybrid GA–PSO algorithm to find the optimal location and sizing of DG units based on power loss reduction within the distribution system. Determining the optimal location and sizing of DGs in the distribution system using Kalman filter, Artificial Bee Colony (ABC) and bacterial foraging optimization algorithm have been reported in Refs. [16–18]. The authors have been presented in Refs. [19, 20], the voltage stability and power losses are considered as the placement of DGs in the distribution system. developed a GA based fuzzy approach to determine the optimal sizes of fixed and switched capacitors to improve the volt-age profile in a radial distribution system. The general discussion about the various types of load models and dynamic performances of power flow study has been reported in Ref. [22]. The

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Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

distribution system is normally in unbalanced loading condition and is having a high R/X ratio. The forward and backward propagation base. Efficient load flow solution technique has been implemented in the practical radial distribution system [23].

The PSO algorithm uses less number of control parameter, and better approach for solving the multi-modal and multidimensional optimization problems. The PSO algorithm mimics the character of flock of birds in searching food sources and transfers the information with other birds. A population with different flying patterns support the algorithm to increase the diversity of solutions. This provides the effectiveness of the algorithm to maintain a suitable balance between the process of exploration and exploitation [24–28]. The basic PSO algorithm has been implemented for the constrained optimization problems, in which the convergence rate is poor.

In the literature[29,30], the modified versions of PSO algorithm have been introduced and applied for solving the real world optimization problems. The PSO technique has been implemented in different real world optimization problem. The major drawback of PSO algorithm is being trapped at local optimal solution. The performance of PSO algorithm is improved by incorporating Time Varying Acceleration coefficients.

In this paper, to improve the exploitation ability of PSO algorithm is integrated with chaos to construct a Particle Swarm Optimization algorithm for solving the optimization problem. From the survey of earlier works on location and sizing of DGs, it is observed that the real power loss index, reactive power loss index, voltage profile index and MVA capacity index have been considered as the objectives for minimization. In order to improve the loading capacity of the distribution system, voltage stability index (VSI) is included as an additional objective while finding the optimal location and sizing of DGs.. Simulation results show the potential of the algorithm for identifying the optimal location and sizing of DGs in the distribution system.

II. LOAD MODELS AND RELATED IMPACT INDICES The load model in the distribution system represents the mathematical relationship between a bus voltage and power or current flowing into the load bus. In this approach, the voltage dependent load models are used, which is mathematically expressed as, (1) Pi  PoiVi Qi  QoiVi 

(2)

Where Pi and Qi are real and reactive power at bus i, Poi and Qoi are real and reactive operating points at bus i, Vi is the voltage at bus i, a and b are real and reactive power exponents. In this approach, several technical issues are considered that are associated to the power loss index, line flow limit index, voltage profile and voltage stability index to form the objective function

III. REAL AND REACTIVE POWER LOSS INDEX (ILP AND ILQ) The system operates at maximum performance represent as reduces the losses. In this case, the real and reactive power loss indices are defined as [12], [P ] (3) ILP  LDG [ PL ] [QLDG ] (4) ILQ  [QL ] Where PLDG and QLDG are the total real and reactive power loss of the distribution system with DG. PL and QL are the total real and reactive power loss of the distribution system without DG. The optimal location and sizing of DGs will decrease the total network losses, which means near zero values of ILP and ILQ.

IV. VOLTAGE STABILITY INDEX (VSI) The VSI gives a significant detail about the voltage stability of the radial distribution systems. In this approach, VSI is taken as the decisive factor which variation of this value indicating the system voltage stability for the presence and absence of DGs connect to the test systems. The VSI can be defined as [6] (5) VSI (m2) | V (m1) | 4 4.0{P(m2) x( jj)  Q(m2)r ( jj)}2  4.0{P(m2)r ( jj)  Q(m2) x( jj)} | V (m1) |2 where NB = total number of nodes; jj = branch number; VSI(m2) = voltage stability index of node m2 (m2 = 2, 3,. . ., NB); r(jj) = resistance of branch jj; x(jj) = reactance of branch jj; V(m1) = voltage of node m1; V(m2) = voltage of node m2; P(m2) = real power load fed through node m2; Q(m2) = reactive power load fed through node m2.

The intensity of stability can measure the distribution system using the VSI and thereby necessary action, possibly taken if the index indicates the instability condition of the system. The system operates at secure and stable condition the evaluated VSI values are greater than zero, otherwise instability occurs.

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Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

V. LINE FLOW LIMIT INDEX (IC) The DGs connected with the system significantly changes the power flow in various sections of the network. The acceptable limit of line flow is very important to avoid the overloading of the line. The IC index gives in detail of line flow and currents through the network concerning the maximum capacity of conductors. The value of this index less than unity indicate the acceptable limits of line flows, whereas the values higher than unity point out the violation of the limit: NL

| S ij |

i 1

| CS ij |

IC  max

(6)

Where S ij - MVA flow in the line connecting bus i and j;

CSij – MVA capacity of line i and j; NL – Number of lines.

VI. VOLTAGE PROFILE INDEX (IVD) The DG connected to the distribution system greatly improves the voltage at each node (except first node) and better performance of the network. The voltage profile related to the IVD index can be defined as follows, (7) Where Vnominal = 1.00 p.u. (69-node radial distribution system) NN = number of nodes.

Normally the voltage limit is considered as a technical constraint at a particular bus and thus the IVD value is normally small and within the permissible limits

VII.

PROBLEM FORMULATION

The multi objective performance index of the distribution networks is computed taking into account Real power loss index is the first part of the objective function inward a significant weight factor of 0.35. The second part of the objective function is the reactive power loss index receives 0.15 as weight factor. The IVD index receives a weight factor of 0.15 due to voltage profile on the system. The PSO-TAC algorithm has to be simulated so that the swarm can move over the feasible region and limit in the search space.

VIII. POWER CONSERVATION LIMITS The algebraic sum of all receiving and sending powers including line losses over the complete distribution network and power produced from the DG unit should be equal to zero.

NB

NL

NDG

i 2

j 1

k 1

Pss (i, V )   PD (i,V )   Ploss ( j ,V ) 

P

DG

(k , V )

(8) Where PD – total system real power demand (MW); Ploss – Total system real power loss (MW); PDG – total real power generated by Distributed Generation (MW); NDG – number of DG.

IX. DG REAL POWER GENERATION LIMITS The real power generated by each DG (PDG) is limited by its lower and upper limits as, min max PDG  PDG  PDG

(9)

X. VOLTAGE PROFILE LIMITS The voltage magnitude of each node in the radial distribution system is defined as, Vi min  Vi  Vi max

(10) O.90  Vi  1.00

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368

Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

The voltage at each node of the distribution system should be maintained within limits.

XI. LINE THERMAL LIMITS The distribution of power is done through the feeder in the radial distribution system, and the feeder should not exceed the thermal capacity of the line.

S ij  S ijmax

(11)

The inequality constraints of voltage and line flow limits are satisfied under certain size-location pairs, allow the pairs for next generation population. It is not satisfied reject the size-location pairs in the next generation. Evaluate the size-location pairs for minimum MOPI.

XII.

PROPOSED PSO-TAC ALGORITHM

The particle swarm optimization is a population based optimization technique that was introduced by Kennedy and Eberhart in 1995. This modern heuristic technique is inspired by social behavior of the swarm of fishes and flocks of birds searching for the food. The main advantages of the PSO algorithm compared to other optimization methods are simple, easy to implement, less storage requirement and able to find a global optimum solution. In PSO, each particle represents the possible solutions to the problem. Initially, a random population of particles (or solution) is generated in d-dimensional (or variable) search space. A j j particle i at iteration j is represented as position vector xi j = [ xi1 , xi j2 ,.. xid ] and velocity vector vij  [vi1j , vij2 ,...... vidj ] . Based on the evaluation function value, each particle in current iteration has its

own best

position represented as pbesti  [ pbest , pbest , ,...... pbest ] .The best particle in a population is defined as global best gbestdj  [ gbest1j , gbest2j ,....., gbestdj ] . The velocity and position of each particle are updated using equations below: j

j i1

j i2

j id

vidj 1  w j vidj  c1 r1 ( pbestidj  xidj )  c 2 r2 ( gbestdj  xidj ) (12) j 1 j j 1 xid  xid  vid

(13)

Where r1 and r2 are random numbers between 0 and 1, c1 is the cognitive acceleration coefficient which pushes the particles towards pbest, c2 is the social acceleration coefficient which pushes the particles towards gbest and w is the inertia weight factor. The inertia weight controls the impact of the previous velocity on updating velocity of a particle. A proper selection of w can provide a good exploration and exploitation to find the optimum solution. A large initial value of w can provide a better global exploration while smaller values of w facilitate better exploitation in local search. The linearly decreasing of w is computed as

 w  wmin   * j w j  wmax   max j max   Where

(14)

wmin and wmax are the initial and final inertia weights respectively and jmax

is the maximum iteration number.

This equation is used to calculate the particle's new velocity according to its previous velocity and the distances of its current position from its own best experience (position) and the group's best experience. Then the particle flies towards a new position according to equation. The performance of each particle is measured according to a predefined fitness function, which is related to the problem to be solved.

In the procedure of the particle swarm paradigm, the value of maximum allowed particle velocity Vmax determines the resolution, or fitness, with which regions are to be searched between the present position and the target position. If Vmax is too high, particles may fly past good solutions. If Vmax is too small, particles may not explore sufficiently beyond local solutions.

Thus, the system parameter Vmax has the beneficial effect of preventing explosion and scales the exploration of the particle search. Generally, the acceleration coefficients store the fitness value of Gbest. The acceleration coefficients are varied according the following j (15) c1  c1i  (c1 f  c1i ) * j max j (16) c 2  c 2 i  (c 2 f  c 2 i ) * j max Where c1i and c1f are the initial and final values of cognitive coefficient respectively and c2i and c2f are the initial and final values of social coefficient respectively. As iteration proceeds, the c2 value is linearly increased to encourage particles towards global gbest value. Therefore, the exploration and exploitation capability of PSO-TVAC is improved, thus providing good solution quality and consistent results near to the global optimum.

To enhance exploration and exploitation of particle towards optimum solution, both coefficients should be varies according to

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Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

the iteration number. A large value of cognitive component and small social component in initial iteration pushes the particles to move to the entire the solution space. As iteration increases, the value of cognitive will decrease and the value of the social components will increase, which pull the articles to the global solution.

XIII.

BASIC PSO ALGORITHM

The step by step procedure of PSO algorithm is given as follows: 1) Initialize a population of particles as 2) Pi= (Pi1, Pi2, Pi3……………...Pi, N) (17) ‘N’ is number of generating units Population is initialized with random values and velocities within the d-dimensional search space. Initialize the maximum allowable velocity magnitude of any particle Vmax. Evaluate the fitness of each particle and assign the particle's position to P-best position and fitness to P-best fitness. Identify the best among the P-best as G-best and 3) Change the velocity and position of the particle according to equations and, respectively.

For each particle, evaluate the fitness, if all decisions variable are within the search ranges 4) Compare the particle's fitness evaluation with its previous P-best. If the current value is better than the previous P-best, then set the P-best value equal to the current value and the P-best location equal to the current location in the d-dimensional search space.

5) Compare the best current fitness evaluation with the population G-best. If the current value is better than the population Gbest, then reset the Gbest to the current best position and the fitness value to current fitness value.

6) Repeat steps 2-5 until a stopping criterion, such as sufficiently good G-best fitness or a maximum number of iterations/function evaluations is met.

Fig. 1: A flowchart of Basic PSO-TAC algorithm

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Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

Table 1. Parameter setting for the selected algorithm

A. PSO with time-varying acceleration Coefficients Though the PSO technique with time varying inertia weight can locate good solution at a significantly fast rate, its ability to fine tune the optimum solution is weak, mainly due to the lack of diversity at the end of the search. It has been observed by most researchers that in PSO, problem-based tuning of parameters is a key factor to find the optimum solution accurately and efficiently. With this in view, a novel PSO strategy in which time varying acceleration coefficients are employed is being applied in this paper to solve the complex problem of ED with valve point loading effects and POZ. Kennedy and Eberhart stated that a relatively higher value of the cognitive component, compared with the social component, results in roaming of individuals through a wide search space. On the other hand, a relatively high value of the social component leads particles to a local optimum prematurely. Most studies set each of the acceleration coefficients. The idea behind TVAC is to enhance the global search in the early part of the optimization and to encourage the particles to converge towards the global optima at the end of the search. This is achieved by changing the acceleration coefficients’ c1 and c2 with time. With a large cognitive component and small social component at the beginning, particles are allowed to move around search space instead of moving toward the population best during early stages.

On the other hand, a small cognitive component and a large social component allow the particles to converge to the global optima in the latter part of the optimization process.

The performance of PSO is dependent to the proper tuned parameters that results in the optimum solutions. Generally, the acceleration coefficients for cognitive (c1) and social components (c2) are set to constant values. To enhance exploration and exploitation of particle towards optimum solution, both coefficients should be varies according to the iteration number.

XIV.

THE PSO ALGORITHM PROCEDURE

The particle swarm optimizer (PSO) algorithm is a random evolution method based on intelligent search of optimization problems. The results obtained by this approach satisfy all the constraints at the minimum cost.

The PSO-based approach for solving OPDG problem to minimize the loss takes the following steps: Step 1: Input line and bus data, and bus voltage limits. Initialize a population of particles, Population is initialized with random value and velocities within the d-dimensional search space. Initialize the maximum allowable velocity magnitude of any particle Vmax. Evaluate the fitness of each particle and assign the particle's position to P-best position and fitness to P-best fitness.

Identify the best among the P-best as G-best and store the fitness value of G-best.

Step 2: Calculate the loss using distribution load flow based on Forward sweep.

Step 3: Randomly generates an initial population (array) of particles with random positions and velocities on dimensions in the solution space. Set the iteration counter k=0.

Step 4: For each particle if the bus voltage is within the limits, calculate the total loss. Otherwise, that particle is Particle.

Bus No

18

Size of DG

PDG

QDG

MW

MVAR

0.382

0.269

Power Factor

Ploss

Ploss

Qloss

Qloss

Witho ut DG

With DG

Witho ut DG

With DG

225 KW

4.27 KW

102 KVAR

6.92 KVAR

Total

PDG

of 3DG

Total

QDG 3DG

of

Critical Voltage p.u

Critical Voltage p.u

Without DG

With DG

0.909 @ 65

0.993 @ 50

0.815

61

1.675

1.197

0.813

11

0.497

0.345

0.821

2.552 MW

1.812 MVAR

Table 2. Power losses and critical voltage for 69 node system with DG

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Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

Is infeasible Step 5: For each particle, compare its objective value with the individual best. If the objective value is lower than Pbest, set this value as the current Pbest, and record the Corresponding particle position.

Step 6: Choose the particle associated with the minimum individual best Pbest of all particles, and set the value of This Pbest as the current overall best Gbest.

Step7: Update the velocity and position of particle Step 8: If the iteration number reaches the maximum limit, go to Step 9. Otherwise, set iteration index k=k+1, and go back to Step 4.

Step 9: Print out the optimal solution to the target problem. The best position includes the optimal locations and size of, DG, and the corresponding fitness value representing the minimum total real power loss.

A. Numerical results The various related impact indices, MOPI, optimal location and sizing of DGs for all types of load model for the 69-node system.

The base case result of the constant type load model considered that the real power loss in the system without DG KW. 0.012

0.01

Power Loss (p.u.)

0.008

0.006

0.004

0.002

0

5

10

15 No of Iterations

20

25

30

Fig. 2: Graph between No.of iterations and Power

Loss in p.u.

1.2

1

Bus Voltage

0.8

0.6

0.4

0.2

0

0

10

20

30 40 Bus Number

50

60

70

Fig. 3: Graph between Bus Number and Bus Voltage

Application of DGs are connected to the nodes 18 ,61 and 11 with optimal size, which effects that the real power loss is consequent that the real power loss is reduced to 98% compared to without DG. The real and reactive power losses are reduced with presence of DGs.

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Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

With the DGs connected, the weakest node of the system is identified as 50 (VSImin) which effects that the load factor is greatly increased with the presence of DGs. In this way, the system is improved in the voltage stability and operates distant from the voltage instability condition.

Fig. 4: A flowchart of PSO-TAC algorithm is used for

The line flow of the system should be controlled which indicates that the value of IC is nearby zero. The value of voltage profile index is reduced, which effects that the voltage deviation of the system is considerably reduced and it is improving the voltage profile. It is demonstrated that the voltage profile improvement of the test system and quality of supply to customer terminals.

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Optimal Location and Sizing of DG Units to Improve The Voltage Stability in The Distribution System Using Particle Swarm Optimization Algorithm with Time Varying Acceleration Coefficients (GRDJE / CONFERENCE / ICIET - 2016 / 060)

XV.

CONCLUSION

In this paper, multi objective performance index is used for finding the optimal location of real power DG units and their capacities. The various impact indices such as a power loss index, line flow limit index, voltage profile index are considered and are combined using weighting coefficients. The multi objective problem is solved using PSO-TAC algorithm for various types of load models. From the results, it can be concluded that the presence of DGs in optimal location reduces the real and reactive power losses and improves the voltage profile of the system. Moreover, the power flows on all the lines are within their specified limit. From the results obtained, it is observed that with lesser number of cycles itself, PSO-TAC has the ability to find the optimal solution. This shows that there is a considerable increase in speed of convergence in solving DG size – location planning problem using Particle Swarm Optimization algorithm with Time varying acceleration coefficients

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