Optimal DG Placement Considering Voltage Stability Enhancement Using PSO

Neenu Rose Antony1

PG Scholar Department of Electrical and Electronics

Amal Jyothi College of Engineering, Kerala iamneenurose@gmail.com

Sarin Baby2 Assistant Professor

Department of Electrical and Electronics Amal Jyothi College of Engineering, Kerala

sarinbaby@amaljyothi.ac.in

Abstract —The increasing energy demands are stressing the

generation and transmission capabilities of the power system. Distributed generation (DG), which generally located in distribution systems, has the ability to meet some of the growing energy demands. However, unplanned application of individual distributed generators might cause other technical problems. In this paper a DG placement method using Particle Swarm Optimization (PSO) based algorithm has been proposed to enhance the voltage stability margin and to reduce the real power losses of the system. Newton – Raphson power flow method Continuation Power Flow and Modal Analysis are used to identify the appropriate location for DG placement. To show the effectiveness of the proposed DG placement method, this approach is implemented in an IEEE-14 Bus System using PSAT which is a MATLAB toolbox environment.

Key Words — Distributed Generation, Continuation Power Flow, Modal Analysis, Voltage Stability Margin, Particle Swarm Optimization.

I. INTRODUCTION Distributed Generation plays a vital role in the electric

power system due to increased availability of small capacity generation technologies [1]. DG installations require special studies and attention to help maintaining system reliability and performance. Optimal allocation of DG effectively reduces the operational cost and increases the reliability and quality of power supply and also cuts down the power and energy losses. DG has significant impact on the voltage profile of the system. Voltage profile is defined as the change in the voltage of the system as the load changes. With the increased loading and exploitation of the existing power structure, the probability of occurrence of voltage collapse are significantly greater than before and the identification of the nodes which prone to the voltage fluctuations have attracted more attention for the transmission as well as the distribution systems. For operating a power system in a safe and secure manner, all unsecure operating states can be identified and DG placement can be done, in order to enhance the voltage stability margin [2]. Many researchers have introduced different DG placement algorithms using analytic or heuristic approaches. Only a few works have been concentrated on optimizing the effect DG in voltage stability improvement. A method of finding a continuum of power flow solutions starting at some base load and leading to the steady state voltage stability limit of the system was presented in[3]. A method for DG placement in radial distribution networks

which uses CPF to identify the most sensitive bus to voltage collapse has been applied in [4]. Voltage stability analysis of large power systems using a modal analysis technique was proposed in[5], which gives the idea about the proximity to voltage collapse. In [6] optimal DG allocation has been identified which is based on the modal analysis and compared the effectiveness of the method to the CPF method.� The determination of maximum loading is one of the most important problems in voltage-stability analysis that cannot be calculated directly by modal analysis. A method combining CPF and Modal analysis was proposed in [7] for the optimal DG placement considering voltage stability enhancement. Application of different optimization techniques in DG placement problem were also discussed in literature. Optimization techniques applied to DG placement and sizing, are genetic algorithm [8], tabu search [9], analytical and numerical based methods [10,11].

In this paper, a DG placement problem is solved by using Particle Swarm Optimization(PSO) algorithm, based on Newton – Raphson power flow method Continuation Power Flow and Modal Analysis, while the objective is to maximize the Voltage Stability Margin and reduce the power losses. Case studies are carried out in an IEEE-14 Bus System using Power System Analysis Toolbox (PSAT).

II. VOLTAGE STABILITY ANALYSIS Voltage stability is defined as the capability of electric

power system to restore the bus voltages at the specified values in steady state and transient conditions [12]. The analysis of voltage stability for planning and operation of a power system involves the examination of two main aspects:

1. Proximity to voltage collapse. 2. Mechanism of voltage collapse. Proximity can provide information regarding voltage

stability while the mechanism gives useful information for operating plans and system modifications that can be implemented to avoid voltage collapse. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. Some of the conventional methods are P-V curve method, V-Q curve method, methods based on singularity of power flow Jacobian matrix at the point of voltage collapse, continuation power flow method.

2013 International Conference on Control Communication and Computing (ICCC)

978-1-4799-0575-1/13/$31.00 ©2013 IEEE 394

A. P-V Curve Method This is one of the widely used methods of voltage stability

analysis. This gives the available amount of active power margin before the point of voltage instability. For radial systems, the voltage of the critical bus is monitored against the changes in real power consumption. This method works well in the case of an infinite bus and isolated load scenario. B. V-Q Curve Method

The V-Q curve method is one of the most popular ways to investigate voltage instability problems in power systems during the post transient. Unlike the P-V curve method, it doesn’t require the system to be represented as two bus equivalent. Voltage security of a bus is closely related to the available reactive power reserve, which can be easily found from the V-Q curve of the bus under consideration. The reactive power margin is the MVAR distance between the operating point and the nose point of the V-Q curve. Stiffness of the bus can be qualitatively evaluated from the slope of the right portion of the V-Q curve. The greater the slope, the less stiff is the bus, and therefore the more vulnerable to voltage collapse it is. Weak busses in the system can be determined from the slope of V-Q curve.

C. Modal Analysis There are many methods that uses the fact that the power

flow Jacobian matrix becomes singular at the point of voltage collapse. Modal analysis of the Jacobian matrix is one of the most popular methods [7].

Power flow equations can be written in matrix form as follows

P PV

Q QV

J JPJ JQ V

θ

θ

θ⎡ ⎤Δ Δ⎡ ⎤ ⎡ ⎤= ⎢ ⎥⎢ ⎥ ⎢ ⎥Δ Δ⎣ ⎦ ⎣ ⎦⎣ ⎦

(1)

Considering 0PΔ = , the reduced Jacobian matrix is obtained as,

1R QV Q P PVJ J J J Jθ θ

−= − (2)

RQ J VΔ = Δ (3) 1

RV J Q−Δ = Δ (4)

Let 1RJ − is represented as,

1 1RJ ξ η− −= Λ (5)

Where, ξ is the right eigenvector of RJ

η is the left eigen vector of RJ

Λ is the diagonal eigen value matrix of RJ Therefore,

1V Qξ η−Δ = Λ Δ (6) Or

i i

i i

V Qξ ηλ

Δ = Δ∑ (7)

The smallest eigen values of RJ are taken as least stable modes of the system. The rest of the eigen values are neglected and they are considered to be strong enough modes. If iλ is positive, the ith modal voltage and the ith modal

reactive power variations move in the same direction, indicating voltage stability of the system; whereas if 0iλ = , voltage collapses because any change in the modal reactive power causes an infinite change in the modal voltage. Participation factor kiP determines the degree of weakness of a bus in a particular mode.

ki ki kiP ξ η= (8)

kiP indicates the contribution of ith eigen value to the V-Q sensitivity at bus k.

D. Continuation Power Flow The determination of maximum loading is one of the most important problems in voltage-stability analysis that cannot be calculated directly by modal analysis. It is numerically difficult to obtain a power flow solution near the voltage collapse point, since the Jacobean matrix becomes singular. Continuation power flow overcomes this problem by avoiding the singularity in the Jacobian by slightly reformulating the power flow equations and applying a locally parameterized continuation technique. Continuation power flow finds successive load flow solutions according to a load scenario.

Fig.1: Illustration of prediction-correction steps

It consists of prediction and correction steps as shown in fig.1. From a known base solution, a tangent predictor is used so as to estimate next solution for a specified pattern of load increase. The corrector step then determines the exact solution using Newton-Raphson technique employed by a conventional power flow. After that a new prediction is made for a specified increase in load based upon the new tangent vector. Then corrector step is applied. This process goes until critical point is reached. The critical point is the point where the tangent vector is zero point. The Voltage Security Margin(VSM) is known as the distance from an operating point to a voltage collapse point.

III. PARTICLE SWARM OPTIMIZATION (PSO) Particle Swarm Optimization is a robust stochastic

optimization technique based on the movement and intelligence of swarms. It applies the social behaviour of bird flocking or fish schooling for problem solving. It was developed in 1995 by James Kennedy and Russel Eberhart. PSO is a population based search procedure which uses a number of individuals called particles, which constitute a swarm moving around in the search space, looking for the best solution.

In a PSO system, particles fly around in multi-dimensional search space. During flight, each particle adjusts its position

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according to its own experience (The value is called Pbest) and according to the experience of neighboring particle (This value is called Gbest), makes use of the best position encountered by itself and its neighbor. The modification can be represented by the concept of velocity. Velocity of each agent can be modified by the following equation. The velocity (position change) of the ith particle is denoted as,

( )( )

11 1

2 2

k k k ki k i besti i

k kbest i

V V a rand P X

a rand G X

ω+ = + × −

+ × − (9)

1 1k k k

i i iX X V+ += + (10) In the updating, a new velocity for each particle based

on its previous velocity kiV is determined. The particle’s

location at which the best fitness, ( kbestiP ) and the best particle

among the neighbors ( kbestG ) have been achieved. The learning

factors, a1 and a2, are the acceleration constants which change the velocity of a particle towards Pbest and Gbest. The random numbers, rand1 and rand2, are uniformly distributed numbers in range [0, 1]. Finally, each particle’s position is updated by (10).

IV. PROPOSED METHODOLOGY AND MODELLING

The proposed methodology consisted of finding the best suitable bus for connecting a Fuel Cell DG using Particle Swarm Optimization. In the proposed method, the weak buses in the system identified by modal analysis and Continuation power flow are considered as the candidate buses for DG placement. Slack bus, PV buses and buses connected to transformers are not considered as candidates.

A. Placement Algorithm

The modal analysis is used to determine the critical modes and their most associated buses. The bus which has the highest participation factor in each critical mode is selected as a candidate for DG placement. The buses which have a tendency of negative Q-V sensitivity are identified as critical buses. Similarly, Continuation Power Flow helps to identify the buses which are more sensitive to voltage collapse.

A Solid Oxide Fuel Cell DG is installed at the candidate buses and a new Modal Analysis and Continuation Power Flow are carried out on the system with the installed DG to determine the system minimum eigen value and maximum loading margin. Newton–Raphson method of power flow analysis is carried out in each case and real and reactive power losses are determined. The bus which gives the largest ‘minimum eigen value’, highest loading margin and lower real power losses can be selected as the best location for fuel cell DG using PSO algorithm. Fig. 2 shows the flowchart for the proposed PSO algorithm.

B. Formulation of Optimization Problem

The optimization of DG location is formulated as a multi objective Particle Swarm Optimization problem to maximize the Voltage Stability Margin(VSM) and real power loss reduction as,

Objective Function: Maximize 1 2 30.375 0.375 0.25F F F F= ∗ + ∗ + ∗ (11)

( )1 minF eig jacobi= (12)

Where jacobi is the load flow jacobian matrix, eig (jacobi)

returns all the eigen values of the Jacobian matrix, min(eig(Jacobi)) is the minimum value of eig (Jacobi), Max ( min ( eig (Jacobi))) is to maximize the minimal eigen value in the Jacobian matrix.

Fig.2 Flow Chart of proposed PSO algorithm

2 maxF λ= (13)

Where, maxλ is the maximum loading margin of the system, which indicates the level up to which the system can be loaded without causing voltage collapse.

0

0

3dgloss loss

loss

P PF

P

−= (14)

Where,

0lossP is the real power loss without DG and

dglossP is real power loss with DG in the system.

The optimization problem is subjected to the equality

constraints which are load balance equations and inequality constraints which include voltage limits, line flow limits and reactive power generation constraints.

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C. Modeling of IEEE test systems IEEE 14-bus system with Solid Oxide Fuel Cell DG has

been used in this paper for the analysis. The test systems were modeled and the power flow results are verified with the standard values using PSAT [14]. The model of IEEE 14 bus developed in PSAT is shown in Fig.3 .The Fuel Cell model has been explained in the next section.

D. Modeling of Solid Oxide Fuel Cell DG Among the available renewable energy sources, Fuel cells are static energy conversion devices that convert the chemical energy of fuel directly into electrical energy and show great promise in stationary power generation applications [15]. Fuel Cell DGs have many advantages, compared to other power plants such as high efficiency, zero or low emission (of pollutant gases), and flexible modular structure. Compared with other green DG technologies such as wind and photovoltaic generation, Fuel Cells have the advantage that they can be placed at any site in a distribution system, without geographic limitations, to provide optimal benefit. Generally, Fuel Cell DGs are installed locally by the consumers to improve the voltage profile and active power injection. When compared to other renewable sources like wind and solar, the certainty in availability of power from Fuel Cell DG is an added advantage which improves the power system stability and reliability [15]. Solid Oxide Fuel Cell (SOFC) DGs operate at high temperatures around 8000 - 10000 0C. In this section modeling of Fuel Cells is described which is helpful in evaluating their performance and for designing controllers. Fig.4 shows a SOFC connected to AC grid.

Fig.3: IEEE 14 Bus System Model

In this section modeling of Fuel Cells is described which is helpful in evaluating their performance and for designing controllers. Fig. 4 shows a SOFC connected to AC grid.

Fig. 4 SOFC connected to AC grid

The voltage E developed over a single cell is ideally described by the Nernst equation [13] as

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+=

OH

OH

ppp

FRTENE

2

22ln2

0 (14)

Here, E0 is the standard potential of the hydrogen/oxygen reaction (about 1.229 V), R is the universal gas constant, F is Faraday’s constant, T is the absolute temperature, and pH2 is the partial pressure of hydrogen. Similarly, pH2O and pO2 are partial pressures of water and oxygen.

V. CASE STUDY

A. Application of Placement Algorithm in IEEE 14 Bus System The IEEE 14 bus test system has 16 lines and 4

transformers. Among the 14 buses, 4 of the generator buses have static compensators. Total generation includes real power generation of 395.29 MW and 223.25 MVAr of reactive power. The load sums up to 362.6 MW real power load and 113.96 MVAr of reactive power load. Loads were modelled as constant power loads (PQ load) and were solved by using Newton-Raphson power flow routine. The load sharing between the system generators and the Fuel Cell DG is through the initial power angle setting.

Fuel Cell DG have been connected to the weak buses identified by modal analysis and Continuation power flow (other than slack bus and buses connected to transformers), voltage and angle settings of slack bus and Fuel Cell ratings are considered for minimising the active power loss.

Modal Analysis is performed in the test system developed and the fig.. 5 shows the smallest eigen value. It can be seen from the Table I that the smallest eigen value is 2.6035 and the most associated bus is bus 14.

Fig. 5: Smallest eigen value for 14 bus system without any DG

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TABLE I: SMALLEST EIGENVALUES AND ASSOCIATED BUSES

Most Participating

Bus

Eigen Value

5 15.9259 11 11.0193 12 5.4252 12 7.4745 13 18.626 14 2.6035

Continuation power flow is also performed on the test

system and fig.6 shows voltage profile at the point of voltage collapse.

From the results of Modal Analysis and Continuation power flow, the weak buses identified for the IEEE 14 bus system are 4,5,7,9,10,11,12,13 and 14. The generator buses and the voltage controlled buses have some capabilities to control the active and reactive powers at the buses and hence voltage. Buses having transformers are also eliminated from the list. And hence in the case of IEEE 14 bus system only Bus 10,11, 12, 13and 14 are considered for Fuel Cell DG placement.

Fig. 6: Voltage at the point of voltage collapse for IEEE 14 bus system without any DG

The results of the PSO based optimization program

showed that Bus 10 is the optimal location for Fuel Cell DG. The power flow analysis with Fuel Cell DG at Bus 10 shows that real power losses have been reduced to 0.2206 p.u. The minimum eigen value of the system and maximum loading level have been increased to 3.755 and 3.1742 p.u respectively. Table II gives the summary of the analysis with and without Fuel Cell DG. It is clear from the data that loss reduction and voltage stability enhancement depends on the placement of the Fuel Cell DG. The rate of reduction of the active power loss is best when SOFC DG is placed at Bus 10. Also, minimum eigen value and maximum loading margin are highest at Bus 10 compared to other DG locations considered.

TABLE II:�IMPACT OF FUEL CELL DG PLACEMENT

Bus with DG

Ploss (p.u)

λmax

Minm

Eigen value None 0.2945 2.8286 2.6035

10 0.2206 3.1742 3.755 11 0.2529 2.9841 2.99 12 0.2609 2.8941 2.6 13 0.2806 2.9327 2.66 14 0.2234 3.1507 3.506

The results of Continuation Power Flow on IEEE 14 bus

system without any DG has been shown that, the system load increased to about 2.8286 times the base load will lead to voltage collapse. Fig. 7 clearly shows that the voltage profile at this load point is best when DG is placed at Bus 10. The comparison between voltage profile of IEEE 14 Bus system without DG and DG at optimal location is shown in fig. 8.

Figure 7: Voltage profiles of IEEE 14 Bus system at the critical load point for different DG locations

Figure 8: Voltage profiles of IEEE 14 Bus system at the critical load point

The case studies conducted on IEEE 14 Bus system shows that the proposed PSO algorithm is much effective in determining the best location for DG. This PSO based method is suitable for DG allocation in large practical systems since it reduces the process time and computational efforts to a great extent.

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VI. CONCLUSION The growing demand of the load on the power system

combined with the economic constraints in expansion of transmission network has led to the emergence of new concept of distributed generation. An overloaded power system needs to be rescued from a total system blackout by incorporating distributed generators in a wisely manner. Fuel Cell DGs being a stable renewable source of energy, when integrated to a power system not only improves its loadability but also improves its reliability as well as power quality. A method to�find the best location for Fuel Cell DG placement for voltage stability enhancement and real power loss reduction is proposed. This is done by considering the weak buses (which are more sensitive to voltage collapse) identified from the Modal Analysis and Continuation Power Flow as candidate buses. The multi objective function was evaluated by placing Fuel cell DG at different candidate buses using a MATLAB program and the optimal location was identified with the help of PSO algorithm.

APPENDIX Table III presents data of Fuel Cell DG.

TABLE III: FUEL CELL DG DATA Electrical response time 0.8 s Fuel processor response time 5 s No. of cells 384 Ideal Standard Potential 1.18

Table IV presents PSO parameters.

TABLE IV : PSO PARAMETERS Number of particles

20

Number of iterations

50

Initial inertia weight

0.9

Final inertia weight

0.4

Particle velocity 1

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