There is a high increase in the complexity of power systems of today’s times due to deregulation of the electric power market. Due to the pronounced increase in the competition, optimal utilization of the existing power supplies has become mandatory. On the other hand, due to increase in power flow the transmission lines are constantly facing a problem of congestion because of carrying power at their maximum transmission limits and sometimes higher. Continued congestion in the lines can pose a great risk to power system security, reliability and stability. FACTS devices have been suggested by researchers for various power system related issues . Proper placement and tuning of the devices are necessary for utilizing the benefits of the devices to the utmost level. Various metaheuristic methods  have been used of late for placement and tuning of the FACTS devices for various purposes.
Several authors have used Genetic algorithm and its variants for obtaining the optimal location of FACTS devices and have applied OPF technique for various objective functions [3-5]. Ya-Chin et al.  implemented Particle Swarm optimization method for a multi-objective function using SVC to improve transmission system loading margin (LM) to a certain degree and reduce network expansion cost. Rao et al.  have used OPF technique in the presence of SVC for the improvement of network security under contingency condition. The performance of BAT and Firefly algorithm have been compared to find the optimal location and size of Static VAR Compensator (SVC) in a power system for a multi objective function to improve voltage stability. Khandani et al.  improved the voltage profile by optimal placement of Static VAR Compensator (SVC) using a novel hybrid Genetic Algorithm and Sequential Quadratic Programming (GA-SQP) method. Phadke et al.  have used a fuzzy based index for the effective location of SVC for a multi-objective function. Jirapong et al.  determined the optimal placement of multi-type FACTS devices with new hybrid evolutionary algorithm (HEA) for simultaneously maximizing the total transfer capability (TTC) and minimizing system real power losses of power transfers between different control areas. Roselyn et al.  has used multi-objective GA to solve the OPF problem to improve voltage stability of the system.
Mishra et al.  proposed the placement of IPFC based on Composite Severity Index (CSI). CSI is a combination of line stability index and real power performance index for management of contingency. The IPFC was then tuned using Differential Evolution (DE). CSI is found to be a more accurate measure of severity in comparison to the individual indices. Voltage instability has been quoted as the major indication of power system instability and insecurity. Parallel FACTS devices are apt at resolving the voltage related issues in the power systems. SVC is a parallel FACTS device; hence it is a suitable choice to overcome the voltage instability problem. Optimal placement and tuning of SVC is important for proper use of the device. Index-based method of placement of the FACTS device has been found to be a simple and effective method. L-index and Vi/Vo index can be a very effective combination to rank the vulnerable buses. Optimal tuning of the generators and FACTS devices is very well achieved with metaheuristic algorithm. Krill Herd algorithm  was introduced in the year 2012 and has been found to be very successful.
In this paper, a metaheuristic method, namely, Krill herd algorithm has been used for the optimal power flow in the presence of SVC. A Combinatory Index (CI), composing of L-index and Vi/Vo has been formulated to obtain the optimal location of the SVC device. The optimal tuning of generators has been done for a multi-objective function. The multiple objectives are reduction in voltage deviation, reduction of fuel cost and reduction in transmission line loss. The constraints taken are real and reactive power generation values and voltage limits for buses during the optimization. The results obtained by OPF in the presence of Krill-herd algorithm has been compared with Genetic algorithm. The results of optimal tuning without and with SVC have been compared to prove the effectiveness of the proposed method.
2 Proposed Combinatory Index
A combinatory index is formulated using L-index and Vi/Vo index given in equation (1).
Where, Z1 and Z2 are the weighting factors. The values of Z1 and Z2 are 0.5 respectively.
I1 is the L-Index given by equation (2)
L-index I1 has value between 0 to 1. Lower is the value of the index enhanced is the stability of the system.
Fji which is one of elements in F-matrix is Load participation factor. F-matrix is the sub-array of partial inverse for node admittance matrix. Fji represents complex elements. Vi represents voltage magnitude at bus I and Vj represents voltage magnitude at bus j.
Index I2 is the Vi/Vo index given by equation (3) in which Vi is the reference voltageand Vo is the output voltage.
3 Problem Formulation
A multi-objective function comprising of fuel cost, real power loss and voltage deviation is used for the optimal tuning of generators.
Where, F1 is the Fuel cost given by
Ng is the number of generators in the power system and a, b, c are the fuel cost coefficients. The value for the coefficients for various generators has been mentioned in Table 1.
Values of a, b, c for fuel cost
|Generator bus No.||a (p.u.)||b (p.u.)||C (p.u.)|
F2 is the Real power loss
Where number of transmission lines is ntl and the total complex power flows from bus j to bus k in line I is Sjk.
F3 is the Voltage deviation
Vk is the actual value of voltage magnitude at bus k and Vkref is the reference value of voltage magnitude at the bus.
Power Balance Constraint
Where i=1, 2, 3, …N and N = no. of. Bus, PL is the active power loss of the system.
Voltage balance constraint
Where, Gi=1, 2, 3, …ng and ng = number of Generator buses.
Generation limit real power
Where, Gi=1, 2, 3, …ng
PGi is the active power generated at bus i, PDi is the power demand at bus i. The voltage limits of the generator buses are taken between 0.9 p.u and 1.1 pu.
4 Proposed Methodology
The steps involved for minimization of objective function using SVC are listed below in Fig. 1.
5 Results and Discussion
The proposed methodology has been tested on an IEEE 30 bus system shown in Fig. 2. Initially the proposed methodology has been tested for normal condition. A line outage condition has then been taken into consideration to test the proposed method under adverse conditions.
The parameters of SVC used are Qsvc = 0.06789 p.u. and B = 0.06789 p.u.The CI value at each bus is calculated and the results have been presented in Fig. 3. It is observed that Bus no. 30 has maximum CI of 0.10495 p.u. Hence, Bus 30 is the weakest bus of the system. Different combinations of NR and NK have been used and the value of the objective function has been presented in Fig. 4. It is observed that NR = 20 = NK, which has been used for the study, gives the minimum average and best value of the objective function.
5.1 OPF for Normal Condition
Different combinations of weights of the objective function have been used and the objective function values have been observed and tabulated in Table 2. It is observed that w1 = 0.7, w2 = 0.15, w3 = 0.15 gives the minimum value of the objective function and hence has been chosen for the study.
Non dominant solutions for Cost, Losses and Voltage deviation objectives krill
The voltage profile for OPF without and with SVC has been compared in Fig. 5. OPF in the presence of SVC improves the voltage at the buses. The real power generation of the system and at individual generators, real and reactive power loss, voltage deviation and real power generation cost for KH-OPF without SVC, GA-OPF without SVC, KH-OPF with SVC and GA-OPF with SVC have been compared in Table 3. It is observed that krill herd is much more suitable for the multi-objective optimization problem chosen in comparison to GA. Also, it is observed that OPF in the presence of SVC is much more effective in comparison to without SVC. Thus, the device proves to be highly effective for the optimization of the generators. The performance of a single objective function has been compared with multi-objective function in Table 4. A multi-objective function is found to be more suitable for improvement multiple parameters of the power system.
Comparison of OPF solution for 30 bus system without and with SVC using Krill-OPF
|S.No||Parameter||Krill-OPF without SVC||GA-OPF without SVC||Krill-OPF with SVC||GA-OPF with SVC|
|1||Real power generation (MW)||PG5||26.47||27.3348||32.7||28.1988|
|2||Total real power generation (MW)||290.69||291.4713||288.8||291.2267|
|3||Total real power loss (MW)||6.618||8.0713||5.42||7.8267|
|4||Total reactive power loss (MVAR)||19.16||35.35||8.632||15.55|
|5||Voltage Deviation (p.u.)||1.8355||2.5||0.2852||0.2853|
|6||Total real power generation cost ($/h)||1355.33||1366.9||1258.37||1283.2|
Comparison of different objective using different objective functions using Krill Algorithm without SVC
|Total real power generation (MW)||289.4||292.34||291.5443||290.69|
|Total real power generation||1407||1360||1380.9||1365.33|
|Active power Loss (MW)||6||8.9451||8.145||6.618|
|Voltage deviation (p.u.)||2.5156||2.1545||1.8125||1.8355|
|Objective function||6 (MW)||1360($/h)||1.8125(p.u.)||209|
*OF- Objective Function OF1 – only losses OF2- only cost OF3- only voltage deviation OF4 – multi objective function
5.2 OPF for Contingency Condition
Contingency analysis for the IEEE 30 bus system is performed and it is observed that removal of line 27-28 causes maximum stress to the system indicated by the maximum CI value of 0.3998 p.u as shown in Table ??. It is also observed that for the above considered contingency, bus number 30 is the weakest bus. In order to verify whether the bus indicated by CI is actually the best location for the placement of SVC, the device has been placed at various other locations and the results have been presented in Table 6. It is observed that the real and reactive power loss is reduced to the maximum extent by the placement of SVC at the location indicated by CI. Hence, n – 1 contingency for line 27-28 and SVC at bus 30 has been considered for the study.
Lj, Vi/v0 and CSI values of for some line outage of IEEE 30 Bus Test System
|Line outage FB-TB||Bus no with max. (Lj)||Lj Value (p.u.)||Bus no. with max. (1-Vi/V0)||(1-Vi/V0) (p.u.)||Bus no with max (CI)||CI (p.u.)|
|2 to 5||30||0.1209||30||0.2483||30||0.1766|
|27 to 28||30||0.4522||30||0.3474||30||0.3998|
|27 to 29||29||0.1613||29||0.1761||29||0.1687|
|27 to 30||30||0.1793||30||0.189||30||0.1841|
|29 to 30||30||0.1163||30||0.142||30||0.1291|
|8 to 28||30||0.0891||30||0.1223||30||0.1057|
|6 to 28||30||0.1298||30||0.1583||30||0.1440|
Comparison of real and reactive power losses with placement of SVC in different locations under 36th line (27-28) Contingency
|SVC placement Bus no.||Real power losses (MW)||Reactive power losses(MVAR)|
Table 7 compares the value of various parameters without contingency and with contingency, with SVC placement and sizing. It is observed that, the CI value after OPF is reduced to the maximum extent when optimal placement and sizing of the SVC has been performed. The system parameters for individual objectives and multi-objective function have been observed in Table 8. A multi objective function is observed to be more suitable for catering to the various aspects of the power system parameters.
Comparison of results without contingency, with contingency at line (27-28)
|Parameter||Values in different system state|
|Without contingency||With Contingency At 27-28||With optimal placement of SVC||With optimal sizing of SVC using Krill Algorithm|
|Active Power Loss(MW)||10.78||15.36||10.64||6.596068|
|Reactive Power Loss(MVAR)||29.98||46.5||22.69||6.6361|
|Lj of Severe bus (p.u.)||0.0895||0.4522||0.0721||0.058468|
|(1-Vi/V0) of Severe bus (p.u.)||0.1204||0.3474||0.0496||0.030961|
|CI of Severe bus (p.u.)||0.10495||0.3998||0.06085||0.043747|
|Voltage Deviation (p.u.)||2.3176||4.0516||0.4252||0.29268|
|Overall Lj (p.u.)||1.2089||3.1974||0.6179||0.500657|
|Overall (1-Vi/V0) (p.u.)||1.8984||3.5476||0.3801||0.280652|
|Overall CI (p.u.)||1.55365||3.3725||0.499||0.390655|
Comparison of different objective using different objective functions using Krill Algorithm with SVC (SVC located at Bus no 30)
|Total real power generation (MW)||288.119||288.7328||288.633||289.975|
|Total real power generation cost($/hr)||1263.59||1255.94||1261.07||1261.7|
|Active power Loss (MW)||4.7213||5.3343||5.2353||6.596|
|Voltage deviation (p.u.)||0.29206||0.2920||0.29215||0.2926|
|Objective function value||4.7213(MW)||1255.9($/hr)||0.29215(p.u.)||193.923|
*OF- Objective Function OF1 – only losses OF2- only cost OF3- only voltage deviation OF4 – multi objective function
Various parameters of the power system have been compared for without contingency and with contingency condition for OPF without and with SVC in Table 9. The OPF with SVC is observed to be the optimal solution in both normal and contingency condition. KH shows a better performance in comparison to GA for the multi-objective function. In Fig. 6, the multi-objective function values have been compared; KH seems to give a lower value of 193.923 p.u. in comparison to that of GA which is 199.7049 p.u. The voltage profile in the presence of KH-OPF SVC improves to a great extent.
Comparison of Real power losses, Cost and Voltage deviation for normal & line outage with SVC placed at bus number 30
|Condition||Parameters||KH OPF without SVC||GA OPF without SVC||KH OPF with SVC||GA OPF with SVC|
|SVC Rating (p.u.)||–||–||0.06789||0.0682|
|Total Real power generation (MW)||290||291.4713||288.8||291.2267|
|Without Contingency||Real power losses (MW)||6.61||8.0713||5.42||7.8267|
|Total generation cost ($/hr)||1355.3||1366.9||1258.3||1283.2|
|Voltage Deviation (p.u.)||1.835553||2.5013||0.285292||0.2853|
|SVC Rating (p.u.)||–||–||0.087||0.1527|
|Total Real power generation (MW)||293.17||297.5454||289.97||293.493|
|27 to 28 Line outage||Real power losses (MW)||9.79||14.1453||6.596||10|
|Total generation cost ($/hr)||1374.06||1390.5||1261.74||1283.9|
|Voltage Deviation (p.u.)||3.291027||4.9205||0.29268||0.3835|
Optimal power flow is an essential requirement for effective utilization of the various components of the power system. Optimal power flow method in the presence of SVC has been proposed in this paper for overcoming the voltage instability issues of the power systems and reduction of losses. A Combinatory Index has been formulated for obtaining the location for the SVC. The results obtained by CI have been verified, in order to confirm that the index gives the optimal position for the FACTS device. A multi-objective function has been considered, viz., reduction in voltage deviation, fuel cost and transmission line loss. Krill Herd algorithm has been used to optimize the generators for the multi-objective function that was considered. It is found from the results that SVC is very efficient in improving the voltage profile of the system. Optimal reallocation of the generators and tuning of the device with Krill Herd algorithm further improves the voltage profile. The combinatory index indicates an improvement in voltage stability after optimal power flow has been performed in the presence of SVC. It has been proven from the results that KH gives superior results in comparison to GA for the chosen problem.OPF in the presence of SVC has been found to be an optimal solution for improvement of the power system performance as depicted by the improvement in the values of the power system parameters.
Flexible AC Transmission System
Optimal Power Flow
Static VAR Compensators
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