Abstract: This study presents the application of particle swarm optimization algorithm to find the optimal location of multi type FACTS devices in a power system in order to eliminate or alleviate the line over loads. The optimizations are performed on the parameters, namely, the location of the devices, their types, their settings and installation cost of FACTS devices for double contingencies. The selection of UPFC and TCSC suitable location uses the criteria on the basis of improved system security. The effectiveness of the proposed method is tested for IEEE 6 bus and IEEE 30 bus test systems.
INTRODUCTION
Power system security, congestion management, power quality and power regulations are major concepts that draw the attention of power researchers in deregulated surroundings. Security assessment is an issue of utmost grandness under open market access system to render authentic and procure electricity to its customers under all conditions. In a day to day operation it may be beyond the operator scope to take preventive control during emergencies. However, the operator can use various control devices and FACTS devices to restore the system to normal conditions (Paserba et al., 1995; Gerbex et al., 2001).
Contingency screening and ranking is one of the components of on-line system security assessment. The target of contingency ranking and screening is to rapidly and precisely grade the decisive contingencies from a large list of plausible contingencies and rank them according to their severity for further rigorous analysis. Various PI-based methods for contingency screening and ranking have been reported in literature (Ejebe and Wollenberg, 1979; Mikolinnas and Wollenberg, 1981; Lauby et al., 1983; Chen and Bose, 1989).
FACTS devices are solid state converters that have the capability of control of various electrical parameters in transmission networks. FACTS devices include Thyristor Controlled Series Compensator (TCSC), Static Var Compensator (SVC), Unified Power Flow Controller (UPFC) and Static Compensator (STATCOM) etc. (Hingorani and Gyugyi, 1999).
FACTS devices control the power flow in the network, reduces the flow in the heavily loaded lines thereby resulting in increase load ability, improved security and stability of the network (Krishna and Padiyar, 2005; Kazemi and Sohrforouzani, 2006).
Thyristor Controlled Series Compensator (TCSC) is one such device which offers smooth and flexible control for security enhancement with much faster response compared to the traditional control devices (Huang and Zhu, 2001).
Unified Power Flow Controller (UPFC) is capable of providing active, reactive and voltage magnitude control under normal and network contingencies conditions without violating the operating limits (Visakha and Jenkins, 2004).
Population based co-operative and competitive stochastic search algorithms are very popular in the recent years in the research area of computational intelligence. Some well established search algorithms such as GA (Gerbex et al., 2001) and Evolutionary Programming (Venkatesh et al., 2003) are successfully implemented to solve the complex problems. The PSO algorithm was introduced by Kennedy and Eberhart (1995) and Shi and Eberhart (1999) and further modifications in PSO algorithm were carried out in (Ratnaweera et al., 2004). PSO is applied for solving various optimization problems in electrical engineering (Yoshida et al., 1999; Saravanan et al., 2007).
TCSC is used for static security enhancement in order to eliminate or reduce line overloads (Yunqiang and Abur, 2002). In this study, only single contingencies were considered due to complexity of the problem.
This study depicts the use of multi-type devices, combination of TCSC and UPFC during double contingencies are investigated. UPFC is modeled as a combination of a TCSC in series with a line and SVC connected across the corresponding buses between which the line is connected. Contingency severity index values are calculated for every branch using (Yunqiang and Abur, 2002). This index is used to decide on the best location for the multi type devices. Once located, the type and optimal settings of FACTS devices with respect to double contingencies can be obtained by optimization. The objectives used in this problem are eliminating or alleviating the line overloads and minimizing the installation cost of the multi type FACTS devices. Computer simulations are done for IEEE 6 bus, IEEE 30 bus test systems. From the test results it is observed that the number of over loads and installation cost are reduced after placing certain number of FACTS devices. Further increase of FACTS devices, shows no improvement in reduction of overloading or cost of installation.
PROBLEM FORMULATION
Optimal Placement of Facts Devices
The essential idea of the proposed multi type FACTS devices, UPFC and TCSC
placement approaches is to determine a branch which is most sensitive for the
large list of double contingencies. This section will describe the definition
and calculation of the contingency severity index CSI and the optimal placement
procedure for the UPFC and TCSC.
The Participation Matrix U
This is an (mxn) binary matrix, whose entries
are 1 or 0 depending upon whether or not the corresponding branch is overloaded,
where n is the total number of branches of interest and m is the total number
of double contingencies.
The Ratio Matrix W
This is an (mxn) matrix of normalized excess
(overload) branch flows. It’s
(i, j)th element, wij is the normalized excess power flow
(with respect to the base case flow) through branch j during contingency i and
is given by:
| (1) |
Where:
| Pij,cont | = | Power flow through branch j during contingency i |
| Poj,Base | = | Base case power flow through branch j |
The Contingency Probability Array P
This is an (mx1) array of branch outage probabilities. The probability of
branch outage is calculated based on the historical data about the faults occurring
along that particular branch in a specified duration of time. It will have the
following form:
| (2) |
Where:
| pi | = | Probability of occurrence for contingency i and is taken as 0.02 |
|
m |
= | No. of contingencies |
Thus the CSI for branch j is defined as the sum of the sensitivities of branch j to all the considered double contingency and is expressed as:
| (3) |
where, uij and wij are elements of matrices U and W, respectively.
CSI values are calculated for every branch using Eq. 3. Branches are then ranked according to their corresponding CSI values. A branch has high value of CSI will be more sensitive for security system margin. The branch with the largest CSI is considered as the best location for FACTS device.
Optimal Settings of FACTS Devices
In this study UPFC is modeled as combination of a TCSC in series with the
line and SVC connected across the corresponding buses between which the line
is connected. After fixing the location, to determine the best possible settings
of FACTS devices for all possible double contingencies, the optimization problem
will have to be solved using PSO technique.
The objective function for this work is:
obj = minimize {SOL and IC} |
| (4) |
Where:
| m | = | No. of double contingency considered |
| n | = | No. of lines |
| ak | = | Weight factor = 1 |
| Pk | Real power transfer on branch k | |
| Pkmax | = | Maximum real power transfer on branch k. |
| IC | = | Installation cost of FACTS device |
SOL=Represents the severity of overloading
Installation cost includes the sum of installation cost of all the devices and it can be calculated using the cost function given by:
| (5) |
| (6) |
Where:
| S | = | Operating range of UPFC in MVAR |
| S | = | |Q2-Q1| |
| Q1 | = | MVAR flow through the branch before placing FACTS device |
| Q2 | = | MVAR flow through the branch after placing FACTS device |
The objective function is solved with the following constraints:-
Voltage Stability Constraints
VS includes voltage stability constraints in the objective function and
is given by:
| (7) |
Vb- voltage at bus b
FACTS Devices Constraints
The FACTS device limit is given by:
| (8) |
Where:
| XL | = | Original line reactance in p.u |
| XTCSC | = | Reactance added to the line where UPFC is placed in p.u |
| Qsvc | = | Reactive power injected at SVC placed bus in MVAR |
Power Balance Constraints
While solving the optimization problem, power balance equations are taken
as equality constraints. The power balance equations are given by:
| (9) |
Where:
| ΣPG | = | Total power generation |
| ΣPD | = | Total power demand |
| PL | = | Losses in the transmission network |
| (10) |
| (11) |
Where:
| Pi | = | Real power injected at bus i |
| Qi | = | Reactive power injected at bus i |
| θi, θk | = | The phase angles at buses i and k, respectively |
| Ei, Ek | = | Voltage magnitudes at bus i and k, respectively |
| Gi, Bik | = | Elements of Y- bus matrix |
OVER VIEW OF PSO AND ITS IMPLEMENTATION FOR OPTIMAL LOCATION OF FACTS DEVICES
PSO is initialized with a group of random particles and the searches for optima by updating generations. In every iteration each particle is updated by following two best values. The first one is the best solution (fitness value) it has achieved so far. This value is called Pbest. Another best value that is tracked by the particle swarm optimizer is the best value obtained so far by any particle in the population. This best value is the global best called Gbest. After finding the best values the particles update its velocity and position with the following equation:
| (12) |
| (13) |
| (14) |
Where:
The velocity of the particle is modified by using Eq. 12 and the position is modified by using Eq. 13. The inertia weight factor is modified according to (14) to enable quick convergence.
Calculation of fitness function:
| (15) |
Where:
| λ1 | = | Penalty factor |
| λ2 | = | Scaling factor |
Algorithm
| Step 1: | The bus data, line data and number of FACTS devices are given as inputs |
| Step 2: | The initial population of individuals is created in normalized form so as to satisfy the FACTS device’s constraints given by Eq. 8 |
| Step 3: | For each individual in the population, the fitness function given by (15) is evaluated in denormalized form after simulating all possible double contingencies by using AC Load flow |
| Step 4: | The velocity is updated by using (12) and new position is created by using (13) |
| Step 5: | If maximum iteration number is reached, then go to next step else go to step 3 |
| Step 6: | Print the best individual’s settings |
RESULTS AND DISCUSSION
The solutions for optimal location of FACTS devices to minimize the installation cost of FACTS devices and overloads for IEEE 6 bus, IEEE 30 bus test systems were obtained and discussed in this section. The simulation studies were carried out on Intel Pentium IV Processor computer with 3 GHz, 256 MB RAM, 40 GB Hard drive using MATLAB 7.0 version.
IEEE 6-Bus, Eleven Branch System
The bus data and line data of the six bus test system are taken from (Allen and Wollenberg, 2003). This system is analyzed for double contingencies.
Double Contingency
Considering two branches outaged at a time for 11 branches, 55 double contingency combinations are available. Considering all the double contingency combinations, the 11 branches are ranked based on their CSI values which are given in Table 1.
Table 1 shows that, branch number 3-6 is chosen as the best location to place the first available multi type FACTS devices for double contingencies. Depending on the available budget, the placement of other FACTS devices can proceed where branch 2-3 will be the second choice, branch 1-2 are the third choice and so on. Once the location is determined, their type, their optimal settings and cost of installation can be obtained by solving the optimization problem using PSO technique.
Table 2 Shows that the severity index (SOL) and the number of overloads are reduced from 188 to 175 when three FACTS devices are placed for double contingencies. Further increase of devices, shows no improvement in reduction of severity, overloading and cost of installation, rather they start increasing. Hence in this case, three number of FACTS devices is considerable for optimal system security enhancement for double contingencies. The optimal settings, line number and the type of device are obtained by solving optimization algorithms using PSO which is shown in Table 3.
| Table 1: | Ranking of Branches |
*: Remaining branches having less CSI value | |
| Table 2: | Overloading of branches before and after placing multi type FACTS devices |
| Table 3: | Optimal settings of multi type facts devices |
| Fig. 1: | Fitness convergence curve for IEEE 6bus system-double contingency |
Figure 1 represents the fitness convergences curve for IEEE 6 bus system for double contingencies. Number of population taken in x-axis and Fitness function taken in y-axis. PSO parameters used in this study are:
| • | No. of population = 30 |
| • | Max Generation = 150 |
| • | C1 = C2 = 2 |
IEEE 30-Bus, Forty One Branch Systems
The IEEE 30 bus system consists of 41 branches. Line data, bus data are taken from (Pai, 1979). This system is also analyzed for double contingencies.
Double Contingency
Considering two branches outaged at a time, for 41 branches, 820 double
contingency combinations are available. Leaving the branches connected to isolated
buses, the remaining double contingency combinations are considered in this
study. These contingencies are ranked based on CSI values which are given in
Table 4.
After raking of the branches the PSO algorithm is used to find out the location of the devices, their types and settings to alleviate the line overloads and to improve the system security margin which is given in Table 5 and 6.
| Table 4: | Ranking of branches |
| Table 5: | Overloading of branches-before and after placing multi type FACTS devices |
| Table 6: | Optimal settings of multi type facts devices |
| Fig. 2: | Fitness convergence curve for IEEE 30 bus system-double contingency |
Figure 2 represents the fitness convergence curve for IEEE 30 bus system for single and double contingencies. Number of population taken in X axis and Fitness function taken in Y axis. PSO parameters used in this work are:
| • | No. of population = 25 |
| • | Max Generation = 100 |
| • | C1 = C2 = 2 |
CONCLUSION
This study presents a procedure to place multi type FACTS devices along the system branches based on the Contingency Severity Index (CSI) values to alleviate system overloads and to improve the system security margin during double contingencies. TCSC and UPFC, the combination of TCSC and SVC were considered in this work. Simulations were performed on IEEE 6 and 30 bus systems. The location of multi type FACTS devices, the type of device to be placed and their settings were taken as the optimization parameters for double contingencies. In double contingencies, it is observed that the system security margin cannot be improved further after placing certain optimal number of multi type FACTS devices. These settings can be effectively used on-line to enhance the system security margin without investing in additional transmission resources.
IEEE 6 bus, IEEE 30 bus test systems are used to evaluate the performance of this approaches. Numerical results confirm the effectiveness of the proposed procedures.