Optimal Placement of IPFC Device for Enhancing Transmission System Performance Using WIPSO

Abstract

The Interline Power Flow Controller (IPFC) is an important component in order to enhance both the static and dynamic performance of a power system network. In order to regulate power flow, automated generation control, oscillation damping, congestion management, power system status estimation and power system protection, the Interline Power Flow Controller (IPFC) is a set of Flexible AC Transmission Systems (FACTS). The placement of the IPFC in the power system affects its performance, so there is a need to choose the best place for the device. In addition, the best location for one application may not be the best location for other applications. The weighted PSO is used to optimally place the device in the power system to reduce power loss. MATLAB was used to simulate IEEE 5, 9 and 30 bus systems. Finally, the WIPSO findings were compared to the PSO and genetic algorithm results produced.

1 Introduction

Energy is a vital sector in any economy. There are various forms and sources of energy. Coal, water, wind and sunlight are various sources through which electric energy can be generated. Electric power is today used more importantly as source of green energy. The future of world economies is heavily dependent of electric power after the exhaust of fossil fuels. Electric vehicles, appliances and industrialization and household needs are all dependent on uninterrupted supply of electricity. A blackout or collapse of grid would the functioning of industries, communication sector, and transport, banking, and medical care, supply of water, policing and even online businesses and education sector as well. Failures in power supply are also due to high levels of pressure on the transmission lines. This has necessitated the need for an effective power supply management system to avert blackouts and collapse of grids [1]. The most versatile and contemporary devices in the process of enhancing transfer capacity of transmission lines are IPFC, voltage sources converter and UPFC [2]. One shunt converter is used in IPFC to control the costs in power flow control. Ensuring active and reactive power balance across multiple lines is the main objective of using IPFC. Besides, it makes up for the reactive power relating to the line and builds the effect of the compensation system for disturbance transient and dynamic [3]. In addition to improving the power handling capacity or new generation plant installation, the use of IPFC in the power system helps in lowering the generation costs by using the available excess power [4–6].

How IPFC performs in a power system is investigated in this research paper. IPFC power injection model which is an elaborated mathematical model is presented in this research article [7]. The effect of Interline Power Flow Controller on the power system can be understood with the help of this model. The IPFC injection model can without problems be integrated into the constant-state power flow model. Demonstration of the features of IPFC is the objective of proposed model. In the present paper indicates IPFC possess capacity of controlling bus voltages, active power flow, reactive power flow and reducing electricity losses concurrently. Reduction in loss of power using the PSO algorithm is the main purpose of optimization explained in this paper. IPFC cost, VSI and power loss are the three terms of objective function formulation MATLAB software simulation.

2 Mathematical Modelling of IPFC

To facilitate series compensation for different lines, DC-to-AC converters are employed in IPFC. The converters in IPFC are connected to transmission lines in series format. IPFC comprises various SSSC. IPFC uses series coupling transformers. The two back-to-back DC-to-AC converters are connected in series with two lines of transmission. As depicted in Fig. 1, a common DC link connects DC connections of converters. Besides facilitating series reactive compensation, IPFC will also be used to control any converter in the process of supplying active power to DC link extracted from power transmission line [8].

Fig. 1

IPFC—schematic representation

Figure 2 shows the steady state model derived using the corresponding circuit of an Interline Power Flow Controller. This model of IPFC comprises two controllable voltage sources. These voltage sources are connected in series VcR and ZcR-series-coupling transformer impedances. Moreover, a dynamic power control equation, connecting two voltage sources in series, is required.

Fig. 2

Representation of IPFC—identical circuit

The configurable series injected voltage sources are represented as:

$$V_{{{\text{cR}}1}} = V_{{{\text{cR}}1}} e^{{j\theta_{cR1} }} \,{\text{and}}\,V_{{{\text{cR}}2}} = V_{{{\text{cR}}2}} e^{j\theta 2} (\therefore V_{{{\text{seik}}}} = V_{{{\text{CR}}1}} \,{\text{and}}\,V_{{{\text{seij}}}} = V_{{{\text{CR}}2}} )$$

(1)

It should be carried out by the limitations of inequality imposed by the admissible limits of the corresponding angle and series-injected voltage magnitude:

$$V_{{{\text{cR}}1\min }} \le V_{{{\text{cR}}1}} \le V_{{{\text{cR}}1\max }} \,{\text{and}}\,0 \le \theta_{{{\text{cR}}1}} \le 2\Pi$$

(2)

$$V_{cR2\min } \le V_{cR2} \le V_{cR2\max } \,{\text{and}}\,0 \le \theta_{cR2} \le 2\Pi$$

(3)

The current source is given as [3]

$$I_{{{\text{se,in}}}} = - \,{\text{jb}}_{{{\text{se,in}}}} V_{{{\text{se,in}}}}$$

(4)

The active power (inject a current in phase with the grid voltage) and reactive power (to phase shift the injected current with respect to the grid voltage) injections at $i{\text{th}}$ bus are

$$P_{{{\text{inj}},i}} = {\text{Real}}(S_{{{\text{inj}},i}} ) = \sum\limits_{n = j,k} {(V_{i} V_{{\text{se,in}}} b_{{\text{se,in}}} } {\text{Sin}} (\theta_{i} - \theta_{{\text{se,in}}} ))$$

(5)

$$Q_{{{\text{inj}},i}} = {\text{Imag}}(S_{{{\text{inj}},i}} ) = \sum\limits_{n = j,k} {(V_{i} V_{{\text{se,in}}} b_{{\text{se,in}}} } {\text{Cos}} (\theta_{i} - \theta_{{\text{se,in}}} ))$$

(6)

At $n{\text{th}}$ bus, the active power and reactive power injection after simplification are

$$P_{{{\text{inj}},i}} = {\text{Real}}(S_{{{\text{inj}},i}} ) = - V_{n} V_{{\text{se,in}}} b_{{\text{se,in}}} {\text{Sin}} (\theta_{i} - \theta_{{\text{se,in}}} )$$

(7)

$$Q_{{{\text{inj}},i}} = {\text{Imag}}(S_{{{\text{inj}},i}} ) = - V_{n} V_{{\text{se,in}}} b_{{\text{se,in}}} {\text{Cos}} (\theta_{i} - \theta_{{\text{se,in}}} )$$

(8)

From Eqs. (5–8), three-phase power injection across buses i, j and k of power injection method of IPFC will be depicted in Fig. 3.

Fig. 3

Power injection method of two converters

NR power flow algorithm is implemented with IPFC power injection model wherein the power mismatch equations are added with power injections. The power balance equations will be given below

$$\Delta P_{j} = \Delta P_{j}^{0} + P_{{{\text{inj}},j}}$$

(9)

$$\Delta Q_{j} = \Delta Q_{j}^{0} + Q_{{{\text{inj}},j}}$$

(10)

$$\Delta P_{n} = \Delta P_{n}^{0} + P_{{{\text{inj}},n}}$$

(11)

$$\Delta Q_{n} = \Delta Q_{n}^{0} + Q_{{{\text{inj}},n}}$$

(12)

3 Weight-Improved Particle Swarm Optimization

The similarity of swarm of bird flocking and fish schooling is the basis for the PSO suggested by Eberhart and Kennedy in the process of development of AI techniques. In comparison to other mathematical models, it is easy to implement and compute the efficiency with the simple concept proposed under PSO model which became popular in recent times. Reactive power and voltage control, economic dispatch, transient stability optimal power transmission and several applications are the various optimization problems where the PSO techniques have been successfully tested [9–12].

The weight parameter is very significant in PSO method. Weight is one such parameter which influences speed of convergence and accuracy of solution. Weight-improved particle swarm optimization is an alternative put forward by researchers in the recent past. In WIPSO, the problem of maximization is addressed by swarm particles. The own experience of swarm particles along with the experience of its participating particles helps the swarm to adjust their position. The location and speed of ith molecule in N-dimensional search area are shown in the below representation. The velocity theory represents modification done. Velocity of individual unit can be modified by the given expression:

$$V_{i}^{k + 1} = WV_{i}^{k} + C_{1} \times r_{1} \times (P_{{{\text{besti}}}} - S_{i}^{k} ) + C_{2} \times r_{2} \times (G_{{{\text{besti}}}} - S_{i}^{k} )$$

(13)

$$W = W_{\max } - \frac{{W_{\max } - W_{\min } }}{{{\text{iter}}_{\max } }} \times {\text{iter}}$$

(14)

The above expression represents inertia weights approach (IWA) equation. The diversification trait is gradually reduced by using the above equation. Then velocity which slowly passes through the present search area near $P_{{{\text{best}}}}$ and ${ }G_{{{\text{best}}}}$ is calculated. The present location (search point the solution space) can be altered by the below expression:

$$S_{i}^{k + 1} = S_{i}^{k} + V_{i}^{k + 1}$$

(15)

WIPSO method is the source for improved weight parameter function. Changes are made to inertia weight, social and cognitive factors to obtain a better acceptable solution by using the PSO traditional algorithm. The velocity of a single agent of WIPSO is calculated by

$$V_{i}^{k + 1} = W_{{{\text{new}}}} V_{i}^{k} + C_{1} \times r_{1} \times (P_{{{\text{besti}}}} - S_{i}^{k} ) + C_{2} \times r_{2} \times (G_{{{\text{besti}}}} - S_{i}^{k} )$$

(16)

$$W_{{{\text{new}}}} = W_{\min } + W \times r_{3}$$

(17)

$$W = W_{\max } - \frac{{W_{\max } - W_{\min } }}{{{\text{iter}}_{\max } }} \times {\text{iter}}$$

(18)

$$C_{1} = C_{1,\max } - \frac{{C_{1\max } - C_{1\min } }}{{{\text{iter}}_{\max } }} \times {\text{iter}}$$

(19)

$$C_{2} = C_{2,\max } - \frac{{C_{2\max } - C_{2\min } }}{{{\text{iter}}_{\max } }} \times {\text{iter}}$$

(20)

4 Cost of IPFC and Fitness Function (K)

Considering that, there is not much variation in the development of IPFC and UPFC (i.e. we consider that UPFC and IPFC along with control circuit have two inverters and two transformers); the same cost function can be used for obtaining the cost function for Interline Power Flow Controller [13]. The cost function of unified power flow controller can be altered as

$$C_{{{\text{IPFC}},A}} = 0.00015S_{i}^{2} - 0.01345S_{i} + 94.11,\,{\text{US}}\$ /{\text{kVAR}}$$

(21)

$$C_{IPFC,B} = 0.00015S_{j}^{2} - 0.01345S_{j} + 94.11,\,{\text{US}}\$ /{\text{kVAR}}$$

(22)

$$C_{{{\text{IPFC}}}} = C_{{{\text{IPFC,}}A}} + C_{{{\text{IPFC}},B}}$$

(23)

where the corresponding cost function for converters connected to bus i and j is $S_{i} = \left| {Q_{i2} } \right| - \left| {Q_{i1} } \right|$, $S_{j} = \left| {Q_{j2} } \right| - \left| {Q_{j1} } \right|$, $S_{i} , S_{j}$. The reactive power flows in $i{\text{th}}$ line prior to and later positioning of Interline Power Flow Controller are $Q_{i1}$ and $Q_{i2}$. The reactive power flows in $j{\text{th}}$ line prior to and later positioning of Interline Power Flow Controller are $Q_{j1}$ and $Q_{j2}$.

$${\text{Function}} = K_{1} (L_{j,\max } ) + K_{2} (C_{{{\text{IPFC}}}} ) + K_{3} ({\text{PowerLoss}})$$

(24)

The Voltage Stability Index (L-reference) equation utilized to indicate jth node could be implemented as below [10–12, 14],

$$L_{{j,\max }} = \left| {1 - \sum\limits_{{i = 1}}^{{i = g}} {\left| {F_{{ji}} } \right|} \frac{{|V_{{i|}} |}}{{|V_{j} |}}(F_{{ji}}^{r} + jF_{{ji}}^{m} )1 - \sum\limits_{{i = 1}}^{{i = g}} {\left| {F_{{ji}} } \right|} \frac{{|V_{i} |}}{{|V_{j} |}}\angle (\theta _{{ij}} + \delta _{i} - \delta _{j} )} \right|$$

$$L_{{j,\max }} = \left| {1 - \sum\limits_{{i = 1}}^{{i = g}} {\left| {F_{{ji}} } \right|} \frac{{|V_{{i|}} |}}{{|V_{j} |}}(F_{{ji}}^{r} + jF_{{ji}}^{m} )} \right|$$

5 Simulated Results

In this proposed simulation, MATLAB simulation for WIPSO, GA and PSO, a modified power flow algorithm was developed and integrated to include IPFC. The authentication of applied techniques WIPSO, GA and PSO algorithms were put to test on the IEEE 5, 9 and 30-Bus test systems for installation. The magnitude of maximum number of generation for all GA, PSO and WIPSO value is 100. A design parameter is 2, and population size is 20 which are listed in Table 1.

Table 1 Parameter values for GA, PSO and WIPSO

5.1 Location of IPFC

To identify whether a bus is weak or critical, electric voltage stability reference (L-index) approach was utilized. The bus possess the highest L-reference magnitude will be considered as weak bus. Weak or critical bus impacts first disruption in the system. Across the load bus, only this L-reference finds out utilizing Eq. (17). For IEEE 5, 9 and 30 Bus Test System, the L-index values are calculated. In IEEE 5 Bus Test System, that was analysed that fifth bus possesses the highest L-reference magnitude, i.e. 0.0391, that was contemplated as weak or critical bus. The greatest value, 0.0483, is found on the fourth bus in the IEEE 9 Bus test system, while the highest L-index value, 0.0636, is found on the 24th bus in the IEEE 30 Bus test system, indicating that these are the places for IPFC. L-index values for IEEE 5, 9 and 30 Bus Test System are as given in Table 2, respectively.

Table 2 L-index for IEEE 5, 9, and 30 bus test system

5.2 IPFC Bus Voltage Results

For the IEEE 5 Bus System, two generators (bus 1 and bus 2), three electric buses (from bus 3 to bus 5) and seven power transmission lines are introduced. Similarly, the IEEE 9-Bus System includes three generators (buses 1, 2 and 7) besides six electric buses (electric buses 3, 4, 5, 6, 8 and 9) and eleven transmission lines. For the IEEE 30-Bus System, there are six generators (bus 1, 2, 5, 8, 11, 13), 21 load buses (bus 2, 3, 4, 5, 7, 8, 20, 12, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 26, 29, 30) and 41 transmission lines. Tables 3, 4, and 5 show the bus voltage for the IEEE 5, IEEE 9 and IEEE 30 Bus systems with GA, PSO and WIPSO.

Table 3 Electric bus voltage utilized for IEEE 5 bus systems in p.u with GA, PSO and WIPSO

Table 4 Electric bus voltage utilized for IEEE 9 bus systems in p.u with GA, PSO and WIPSO

Table 5 Bus voltage with GA, PSO and WIPSO used in IEEE-30 bus systems in p.u

For the IEEE 5-Bus System, the bus voltage is 0.959 per unit (p.u.) in the absence of GA, PSO and WIPSO, but 0.970 p.u. in the presence of GA, 0.984 p.u. in the presence of PSO and 1.000 p.u. in the presence of WIPSO. Table 3 exemplifies how IPFC improves bus voltage.

The bus voltage for the IEEE 9-Bus System across electric bus number 8 is 0.9898 per unit (p.u.) without GA, PSO or WIPSO, i.e. 0.9899 p.u. besides GA, 0.9990 p.u. with PSO and 1.000 p.u. with WIPSO. Table 4 shows the IPFC-enhanced bus voltage.

For the IEEE-30 Bus System, for the bus voltage at bus number 24 with absence of GA, PSO and WIPSO was 0.9490 p.u, though we are utilizing GA, the value of 0.9510 p.u, besides PSO that was 0.9582 p.u and in the case of WIPSO, it is determined to be 1.000 p.u. Table 5 represents the bus voltage enhances with IPFC. Tables 3, 4, and 5 show a positive change in load bus voltage.

From Tables 3, 4, and 5, it is evident that the results from PSO and GA are outperformed by those attained with WIPSO. Figures 4, 5, and 6 show the graphical representation of voltage for the IEEE 5, 9-bus, and IEEE-30 Bus test systems, respectively.

Fig. 4

Using GA, PSO and WIPSO to simulate the IEEE 5 bus system voltage magnitude in a P.U

Fig. 5

Using GA, PSO and WIPSO to simulate the IEEE 9 bus system voltage magnitude in a P.U

Fig. 6

Using GA, PSO and WIPSO to simulate the IEEE 30 bus system voltage magnitude in a P.U

5.3 The Best Fitness Function of IPFC Outcomes

It was discovered that in the IEEE 5 Bus system, bus 4 is extremely sensitive to security. Therefore, to improve electric power system security/stability, Bus 5 possesses maximum economical situation for IPFC. The fitness function (K) of the IPFC via WIPSO for IEEE 5 Bus System was 42.206 and PSO, GA is 43.100 and 43.309, and the graphical simulate of fitness function (K) with GA, PSO and WIPSO for IEEE 5 bus System is shown in Fig. 7. Comparison of fitness function (K) using optimization techniques is shown in Table 6.

Fig. 7

IEEE 5 bus system fitness function (K) using GA, PSO and WIPSO

Table 6 Using optimization techniques for comparison of fitness function (K)

For IEEE 9 Bus system, it is evident the bus 4 is more sensitive across security. So, in order to improve electric power system security/stability, Bus 4 is high optimal location for IPFC. For IEEE 9 Bus System, the fitness function (K) of the IPFC via WIPSO was 50.800, and PSO and GA are 51.210 and 55.200. Figure 8 presents the graphical representation of fitness function (K) for IEEE 9 bus system with GA, PSO and WIPSO. In Table 6, fitness function (K) is compared using optimization techniques.

Fig. 8

Fitness function (K) using GA, PSO and WIPSO for IEEE 9 bus system

Bus 24 is observed to be highly sensitive towards security for IEEE 30 Bus system. Therefore, electric Bus 24 possesses more minimal situation for IPFC to improve electric power system security/stability. For IEEE 30 Bus System, the fitness function (K) of the IPFC via WIPSO was 127.683, and PSO and GA are 127.77 and 128.00. For IEEE 30 bus system, the graphical representation of fitness function (K) with GA, PSO and WIPSO is shown in Fig. 9. Comparison of fitness function (K) using optimization techniques is shown in Table 6.

Fig. 9

Fitness function (K) for IEEE 30 bus system using GA, PSO and WIPSO

6 Conclusions

Voltage Stability Index is used for identification of economical situation of IPFC electric power system network. Minimization in FACTS device cost of installation, power loss reduction, enhancement in voltage profile in the power system network is the objective of both GA, PSO and WIPSO methods. The present cost function of UPFC is used to obtain the cost function for IPFC. IEEE 5 bus, IEEE 9 bus and IEEE 30 bus test systems are the standard platforms on which the proposed methods are tested. Considerable reduction in loss of power, improvement in voltage profile and increase in power flow are the result of proposed methodology for research. For all the test cases, illustration of the optimal location for the induction of IPFC is clearly shown. The convergence rate and complexities involved in calculation for both WIPSO and GA and PSO methods are explained. The outcomes of this method are a testimony that the proposed WIPSO methodology is effective in getting both an acceptable solution and good convergence rate when compared to the results of GA and PSO methods.