# Pso For Generator Real Power Output Management Engineering Essay

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Power system congestion has become one of the most significant problems faced by system operators around the globe after the restructuring of the electricity industry. It creates hurdle in the smooth functioning of deregulated electricity market and causes an increased cost associated with it. So the investigation of congestion management techniques is of vital interest. This paper presents a congestion management algorithm by optimally rescheduling the generator active power outputs. But all the generators in the system may not be taking part in the rescheduling process. Participating generators are optimally selected based on the generator sensitivities to power flow on congested lines. The algorithm manages congestion effectively ensuring minimum rescheduling cost of participating generators satisfying power balance, generator operating limits and line flow constraints. Algorithm is based on Particle Swarm Optimization (PSO) which minimizes the deviation between the rescheduled and scheduled generator power output levels. The usefulness of this methodology has been studied using the IEEE standard test systems. The IEEE standard test systems used are IEEE 30 bus and IEEE 57 bus.

Keywords- Power system; Congestion management; Transmission system overload; Particle swarm optimization; Generator sensitivity.

Introduction

Because of the restructuring of electricity industry there is a wide change in planning, operation and management of power system. Deregulation of electricity markets has a lot of advantages; however it made the electricity industry to face many unprecedented problems. Electricity market has some major complexities like lack of major storage capability, the just-in-time-manufacturing nature of electricity and the central role played by the transmission and distribution networks. The deregulated electricity industry introduces increased number of market participants, i.e. generation, transmission and distribution companies and so the number of transactions in the system will be more in number. A transaction means the energy transfer between two points in the power system. All the transactions depend on the transmission system as a means of transportation. In the conventional electricity market the utilities had control over the generation and transmission facilities. The current transmission system was designed long before and was not planned for the deregulation in the market. This causes congestion in the transmission system.

The demand for electric power is increasing day by day and the utilities are increasing the generation in order to meet the demand. But the transmission lines have some limits in terms of thermal, stability and voltage limits. When such limits are exceeded, the system is said to be congested and the system operator has to ensure that these limits are not exceeded. When there is congestion in the transmission system, all the desired transactions may not be realized. These unrealized transactions may cause additional costs in the system. Energy may not be able to purchase from the supplier who offers it at the lowest cost and the same amount of power has to be purchased from a different supplier at a higher cost. The situation is severe where the demand is more, supply is less and to keep the balance power has to be imported from the neighbouring systems. So the transmission congestion occurs at the tie lines. After some years of restructuring, operating rules and procedures are still constantly changing. The main effort lies in providing an effective market design for the restructured environment. One of the key requirements for the implementation of competitive markets is an effective management of congestion.

Congestion is also caused by generator outages, increased load, transmission line outage, and equipment failures etc. The SO is responsible for taking necessary actions to ensure that no violations of the grid constraints occur. Transmission congestion can cause additional outages, increase the electricity prices in some regions and can threaten system security and reliability. The cost to relieve congestion can increase to a level that could present a barrier in electricity trading. Network overloading can be relieved by different controls like power generation rescheduling, operation of FACTS controllers, line switching, load shedding etc. The power transferring should satisfy customer requirement with lowest cost while solve the congestion problems. The installation of equipment should not be first choice for the SO to deal with congestion problems. Therefore the power redispatching approach is significant as the prior approach for congestion management.

Several techniques of congestion management can be found in literature [8]. The market structure deregulated electric power industry differs from region to region and country to country. Different models to represent the transmission limitations are presented in [24]. Congestion relieving methods applied to various kinds of market structures in electricity industry are presented in [25]. Electricity transactions prioritisation and related switching strategies in a system where pool and bilateral/multilateral dispatches exist together is proposed in [9]. Congestion management ensuring voltage stability is presented in [10]. An optimal topological configuration of a power system as a tool of congestion management is presented in [11]. A corrective switching operation of transmission lines is used to manage congestion in this paper.

Various publications can be found on optimal power flow (OPF)-based congestion management schemes for multiple transaction systems. An OPF-based approach that minimizes cost of congestion and service costs is presented in[12]. [13] presents a coordination mechanism between generating companies and system operator for congestion management using Benders cuts. For relieving congestions due to voltage instability and thermal overloads, a technique is presented in [14] which uses OPF and is solved by standard solvers. A congestion clusters based method is proposed in [26] that group the system users having similar effects on the transmission constraints of interest. Here, clusters of type 1, 2 and higher based on congestion distribution factors have been demarcated, with type 1 cluster consisting of those with strongest and non uniform effects on the transmission constraints of interest. A zonal model based on ac load flow is presented in [2] and [3] where sensitivity values are used to identify the zones. But in both [27] and [2], it is necessary to compute the sensitivity values for all the buses in the system .In the given practical power system, a large amount of computational effort is needed if this is the case. [16] uses sensitivities of line flow to changes in generation have been used to manage congestion but number of participating generators is not reduced. A technique has been proposed for selection of participating generators based on sensitivity to current flow on congested line as well as the generation bids in [5]. But the design variables are to be optimally selected for regulating the number of participating generators in this work. A method of transmission overload relief by real power generation rescheduling based on relative electrical distance (RED) concept is presented in [28]. This technique minimizes the system losses and maintains the voltage profile and the stability margin is improved. But the bids of individual generation units and costs of rescheduling are not taken into consideration. Generators having same RED but different price bids must reschedule their outputs in such a way that the total rescheduling cost is minimised. This is not addressed in [28].

Indicator techniques such as Generator Sensitivity (GS) are also discussed in the literature. GS technique is proposes in [1] for optimally selecting the participating generators.[2], [3] and [4] discuss about the transmission congestion distribution factors (TCDFs). [5] presents a technique based on sensitivity of current flow to congested line. [20] and [21] have proved that PSO is the best optimization technique among the various population based algorithms including GA, NN and EP.PSO is the best for complex problems as presented in [22] which is due to discontinuities, higher order nonlinearities, prohibit operating zone, ramp rate limits of generators etc. PSO is gradually gaining more and more acceptance for solving many power system problems as in [23] due to simplicity, superior convergence, and higher quality of the solution obtained.

The PSO algorithm has already been applied in several optimization problems in the power system. In [18], PSO has been applied to solve the economic dispatch of generators in a power system. A technique has been proposed in [19] to control reactive power and voltage to maintain power system security from voltage stability point of view. Congestion management based on sensitivity using PSO has been presented in [4] but, it does not discuss about procedure of handling of constraints.

This paper mainly intended to present a technique for reducing the number of participating generators in rescheduling. It also optimally reschedules their real power outputs while managing congestion at minimum rescheduling cost. In a congested power system, the incremental or decremental change in power outputs of all the generators may not equally affect the power transmitted on the congested line. So there is no need to reschedule the outputs of generators whose generations are less significant to the congested line flow. The sensitivities of the generators to the congested line are used to optimally select the participating generators. The second major purpose of the thesis is to discuss the ability of particle swarm optimization algorithm in solving the congestion management problem. The congested system is modelled as an optimization problem.

The usefulness of the proposed technique has been analysed on IEEE 30-bus and IEEE 57-bus systems.

GENERATOR SENSITIVITY FACTOR

The generators in the system have different sensitivities to the power flow on the congested line. A change in real power flow in a transmission line n connected between bus j and bus k due to change in power output of generator G is called generator sensitivity to congested line (GS). Mathematically, GS for line k can be expressed as

(1)

Where Pjk is the real power flow on congested line-n; is the real power output of the Gth generator.

The basic power flow equation on congested line can be written as

(2)

Where Vj and θj are the voltage magnitude and phase angle respectively at the jth bus; Gjk and Bjk represent the conductance and susceptance of the line respectively. Neglecting P-V coupling, above equation can be expressed as

(3)

(4)

(5)

= (6)

(7)

(8)

Where T is the number of buses in the system.

(9)

(10)

Neglecting P-V coupling, the relation between change in active power at system buses and the phase angles of voltages can be expressed in matrix form as

(11)

(12)

(13)

= (14)

(15)

The generator sensitivity values obtained as above are with respect to the slack bus as the reference. So the sensitivity of the slack bus generator will be always zero for any congested line in the system. The generators having non uniform and large magnitudes of sensitivity values have to be selected for rescheduling and to participate in congestion management.

PROBLEM FORMULATION FOR CONGESTION MANAGEMENT

Based on the bids received from the participating generators, the required amount of real power for rescheduling is calculated by solving the optimization problem expressed below.

Minimize (16)

Subjected to

(17)

Where l=1,2….L

Where GE = 1,2,…NG (18)

(19)

Where is the real power change at bus-GE and are the incremental and decremented price bids submitted by generators. These are the prices at which the generators are adjusting their real power outputs. is the power flow in a particular line caused by all contracts in need of a transaction. is the line flow limit of the particular line connecting bus-j and bus-k. NG is the number of participating generators and L is the total number of transmission lines in the system. and in the above expressions represents the minimum and maximum limits of generator outputs. The power balance is taken care by the constraints. Final generation allocation at slack bus is obtained at the end of optimization process after taking care of the system losses.

PARTICLE SWARM OPTIMIZATION ALGORITHM

In the thesis work PSO is used as the optimization technique and a particular particle size is selected. Each particle has N variables where N is the total number of generators taking part in congestion management. Each variable represents real power outputs of participating generators submitting the bidding prices. Each particle is evaluated based on fitness of particles and selection operation of GB (global best) and Pi(local best), is used to meet the constraints.

Fitness is an index used to evaluate the dominance of the particle. The objective function is regarded as the fitness function. Each particle will be used after all the constraints are satisfied, if not particle will be regenerated. Optimal objective fitness is equal to the value of the objective function which represents the cost of active power rescheduling.

The PSO algorithm works as follows.

Step 1) Particles are generated. They are initialized randomly. Each particle has N dimensions where N denotes the number of participating generators. The values of these N variables are the amount of real power output rescheduling required by generators to manage congestion.

Step 2) Equation gives the power balance after rescheduling and is tested based on the system states represented by an individual particle. If that particle does not satisfy the equality constraints, it is regenerated.

Step 3) The constraints are evaluated and if not satisfied, the particle is regenerated.

Step 4) The optimal objective fitness values are calculated for all the particles. Then the values for particle best and global best are calculated.

Step 5) Position and velocities of particles are updated.

Step 6) If the maximum number of iterations is exceeded or some pre-specified exit criteria is satisfied, the program is stopped. Else program control is returned to Step 2 and continue till the exit criteria is satisfied.

NUMERICAL EXAMPLES

The proposed PSO algorithm for congestion management has been implemented using MATLAB/PSAT tool box. The performance of the algorithm has been studied on IEEE 30 bus system and IEEE 57 bus system.

The influence of various parameters of PSO is also studied in this work.

## The IEEE 30 Bus System

The IEEE 30 bus system is considered for showing the effectiveness of the proposed algorithm. IEEE 30 bus system has 6 generators, 30 buses, 37 lines, 4 transformers and 21 loads. Total real and reactive power of load 357.2 MW and 127.0706 MVAR respectively. The upper and lower limits of reactive power generation is taken to be 100MVAR and -30 MVAR respectively. Bus data, line data and incremental and decremental price bids are taken from the references. Load bus voltages are maintained to be between 0.8 and 1.2 per unit.

Table 1: Simulated test case

Type

Congested Line

Line flow

Total Power Violation

Outage of line 1-3

1-2

258 MW

158MW

In power system, congestion may occur due to several reasons including line outage. From the analysis done it is found that line outage in the line 1-3 results in severe overload in the line 1-2. Simulated test case is shown in the table 1.

For the test case N.R. Power flow analysis is carried out and amount of power overload is identified as shown in table 1. In the test case the power flow limit for the line is 100MW and a power flow violation of 158MW is found in the line 1-2. For secure system the power flow in the transmission line should not exceed the power flow limit. Hence the suitable corrective actions are to be done to alleviate the above said overload. So using Particle swarm optimization algorithm the optimal power reallocation is done to manage this overload.

## Parameter Selection of PSO

In this work the generator outputs are taken as the control variables which constitute one particle. The set values for generator outputs are generated randomly which satisfies the problem criteria mentioned in the congestion management problem formulation section. Then the NR power flow analysis is done. If it is not feasible (exceeds the limit) then the corresponding particle is regenerated. This is repeated for all the particles in the population. The set of feasible solutions are taken as the initial population for PSO. The performance of the PSO greatly depends on the cognitive as well as social parameter C1, C2 and weight factor W. The balance among these factors determines the balance between local and global searching capability. Hence the different values for parameters are selected based on minimum objective value. Effect of variation in PSO parameters is shown in table 2.

Table 2 : Effect of variation of PSO parameters on total cost($/hr)

S.No

Wmax

Wmin

C1

C2

Cost of rescheduling ($/day)

1

0.8

0.5

2

2

1559.23

2

0.9

0.2

1.4

1.4

1566.48

3

0.5

0.4

1

1

1558.54

4

0.9

0.4

2

1.5

1561.25

5

0.8

0.4

1.5

1.5

1555.55

6

0.9

0.4

2

2

1566.22

## 7

## 0.9

## 0.4

## 2

## 1.5

## 1554.25

The effect of variation of total cost by variation in particle size is given in table 3.

Table 3 : Effect of variation of total cost by particle size.

S.No

Particle Size

Cost of rescheduling in ($/day)

1

10

1627.5

2

20

1575.01

3

30

1555.55

4

40

1559.72

5

50

1554.31

6

60

1557.65

## 7

## 70

## 1554.25

8

80

1555.25

9

90

1556.37

10

100

1556.48

So after the above studies the parameters set for the PSO algorithm is wmax=0.9, wmin=0.4, C1=2 and C2=1.5 and the particle size is selected as 70.

Generator outputs before and after rescheduling is given in table 4.

Table 4 : Comparison of generator outputs

Generator No

Initial power output(MW)

Power output after rescheduling

(MW)

Amount of power rescheduled

(MW)

1

225.80

265.45

39.65

2

57.56

57.69

0.13

5

24.56

15.01

-9.55

8

16.91

24.53

7.62

11

35.00

12.00

-23.00

13

17.93

10.00

-7.93

Power flow in the previously congested line is obtained to be 98MW where as the limit is 100MW and the total cost for congestion management is found to be 1554.98$/day.

PSO convergence characteristics is shown in the figure

Figure 1: Convergence characteristics for IEEE 30 bus system

## Generator Sensitivity factor

The generators in the system under consideration have different sensitivities to the power flow on the congested line. So the optimal selection of generators for rescheduling is done based on the generator sensitivity factor. The system operator selects the generators having non uniform and large magnitudes of sensitivity values as the ones most sensitive to the power flow on the congested line and to participate in congestion management by rescheduling their power outputs.

Since all the sensitivity factors are very close except slack bus are rescheduled. Since the IEEE 30 bus system is a smaller system for almost all the contingency cases all the generators will be participating in congestion management.

Table 5: Generator Sensitivity factor for 30 bus system

Generator

1

2

5

8

11

13

Generator sensitivity

0

-.8833

-.8615

-.7705

-.7498

-.7107

## IEEE 57 bus system

Effectiveness of the proposed approach is tested using the IEEE 57 bus system also which has 7 generators, 57 buses, 63 lines, 17 transformers and 42 loads. Total real and reactive power of load 1250.8 MW and 312.1744 MVAR respectively. The upper and lower limits of reactive power generation is taken to be 100MVAR and -30 MVAR respectively. Bus data, line data and incremental and decremental price bids are given in references. Load bus voltages are maintained to be between 0.8 and 1.2 per unit.

Table 6 : simulated test case for IEEE57 bus system

Type

Congested Line

Line flow

Total Power Violation

Outage of line 2-3

1-15

678 MW

378MW

Congestion is created by simulating the outage of line 2-3 and due to this congestion is created in line 1-15 as in table 6. For this particular line overload the generator sensitivity factors are given in table 7.

Table 7: Generator sensitivity factor for 57 bus system

Generator Index

Generator sensitivity

1

0

2

-0.0834

3

-0.3721

6

-0.3815

8

-0.3655

9

-0.3732

12

-0.368

When all the generators are selected for congestion management total cost of congestion management is found to be 11738.5$/day where as when 5 generators are selected for generation rescheduling the total cost is found to be 8893.43$/day. The generators selected are 3,6,8,9 and 12

The PSO convergence characteristics are shown in figure 2 and 3. Also the comparison of the generator rescheduling with and without considering the generator sensitivity factors are given in the table 8.

GENERAL OBSERVATIONS

From the results of the two analysed systems, it can be seen that congestion management can be successfully done by generator rescheduling using PSO. The convergence of PSO algorithm with parameter selection is also studied. Convergence characteristics shows that rescheduling cost progressively decreases with number of iterations and converges to a minimum value and also indicate that the selection of PSO parameters is appropriate.

Table 8: comparison of the generator rescheduling with and without considering the generator sensitivity factors

Gen. No

Initial Generation

(MW)

Final generation- 7generators participating (MW)

Final generation-

4 Generators participating

(MW)

Pg

ΔPg

Pg

ΔPg

1

4.8164

6.0807

1.2643

5.79

.9736

2

0

0.0051

.0051

0

0

3

0

0

0

1.48

1.48

6

0.4000

0.4104

.0104

.418

.018

8

4.5000

1.3406

-3.1594

1.4

-3.1

9

0.0000

1.0000

1

.684

.684

12

3.1000

4.1000

1

3.6

0.5

Total Cost

11738.5 $/day

8893.43

$/day

Figure 2: Convergence characteristics of IEEE57 bus system with all generators participating in congestion management.

Figure 3: Convergence characteristics of IEEE57 bus system where only 4 generators are participating.

CONCLUCION

The paper concentrates on presenting a technique for optimum selection of generators for congestion management. Also it shows the application of PSO in the solution of the congestion management problem. Generators are selected for congestion management based on their sensitivities to the active power flow of the congested. Congestion is relieved by corrective rescheduling of the generator outputs. Congestion management problem is modelled as an optimization problem and optimization technique used in this work is particle swarm optimization .