Sine Cosine-based Optimization Method for Reactive Power Planning with Multitype FACTS Devices

doi:10.21203/rs.3.rs-4003455/v1

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Sine Cosine-based Optimization Method for Reactive Power Planning with Multitype FACTS Devices

https://doi.org/10.21203/rs.3.rs-4003455/v1

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The present work proposes the sine cosine-based algorithm (SCA) for the optimal coordination of multitype FACTS devices with all the existing VAr sources of a connected power network. IEEE 57 bus system was chosen as standard test system for this purpose. The objective of the present work was to investigate the efficacy of the proposed algorithm for the optimal usage of the VAr sources already present in the test network as well optimal installations of the different types of FACTS devices. Unified power flow controllers (UPFC), thyristor-controlled series compensators (TCSC), and static var compensators (SVC) were the FACTS devices installed, also sizing of the existing VAr sources i.e Q generations from generators, Shunt capacitor’s VAr output, OLTC tap setting arrangements were determined. Hence the present work may be considered as a reactive power planning problem, where the main purpose was to reduce the system loss as minimum as possible by suitable coordination of all the internal and external VAr sources. Particle swarm optimization (PSO), crow search algorithm (CSA) and pigeon-inspired optimization were the other three optimization techniques also applied along with the sine cosine-based algorithm (SCA). It has been observed that SCA yielded the most suitable result.

Active power loss

FACTS devices

reactive power planning

sine cosine algorithm

transmission cost

1.1 Overview

Reliability and security are the two main criteria generally targeted by the power system operators for satisfactory transmission and distribution of electrical power. Planning of Reactive power, an important factor in this delicate equilibrium, is essential for controlling voltage levels and guaranteeing system stability. To control voltage variations and to prevent grid instability, reactive power control is crucial. Traditionally, fixed compensating devices were employed to control different variables of interconnected power network. However, the conventional approaches for controlling electrical power can be modified with the invention of flexible alternating current transmission system (FACTS) devices. The regulation of reactive power flow has become much easier because of the flexible and reliable operation of these power electronics-based devices. Hence, the application of the FACTS devices in the field of electrical engineering may be a new but could be a promising area of research. Thyristor-controlled series compensators (TCSC), static var compensators (SVC), and unified power flow controllers (UPFC) are some kind of FACTS devices can be used in separate or combined modes in solving problems related to reactive power planning, distich etc.

1.2 Literature Survey

To reduce active power transfer losses and overall voltage deviation values in power systems, authors in [1] suggested a hybrid Krill herd algorithm for the optimal reactive power planning (ORPP) problem using FACTS devices. The authors in [2], suggested an improved genetic algorithm where the transmission congestion was reduced significantly. The authors in article [3] employed particle swarm optimization to investigate the effect of SVC and TCSC on active and reactive power flow on the IEEE 14 bus test system. To minimize the load shedding, alleviate voltage collapse problems, and to enhance the loadability of the power system, authors [4] proposed a method based on moth flame optimization (IMFO). The size of TCSC as well its location was determined by MFO. In [5], an RPP (reactive power planning) problem was explained and solved. Authors of article [6] proposed the whale optimization algorithm (WOA), where the RPP problem was solved by taking IEEE 30 and IEEE 57 bus system as standard networks. RPP problems were also solved by the authors using oppositional-based Harris Hawks optimization, [7], Ameliorated Harris Hawk optimizer (AHHO), [8] and Harris Hawk-Particle swarm optimizer [9]. In article [10], a performance analysis of the fractional order Darwinian particle swarm optimization with different fractional orders was presented to handle ORPD on the standard IEEE 30, IEEE 57 and IEEE 118 bus test systems by the optimal placement of TCSC and SVC. The authors in [11] proposed a hybrid differential evolutionary crow search algorithm on India’s 62 and 191 bus test systems. The reactive power planning problem was solved by the installation of SVC and TCSC at the locations already predefined beforehand. In the articles [12] the authors solved the reactive power problem ant lion optimization algorithm and its another modified form for the optimal placement of FACTS devices to solve the reactive power planning problem. The reactive power problem was solved using hybrid CSAJAYA method for IEEE 30 and UPSEV 75 bus system by the authors in [13], when the system’s behaviour was analyzed with different loading conditions. Backtraping-assisted elephant herding optimization (BAEHO) was introduced in the article [14] to address the ORPP problem with UPFC in a power system under unbalanced conditions. In the article, the solution of reactive power planning for normal load and certain increased load was provided along with the effects of the SVC on system performance under various conditions. The reactive power planning problem under normal load condition was solved in the article presented by [15]. System loading was gradually increased and how the installation of SVC can combat the effect of system loading was also presented in the same article. An improved Differential Evolutionary (IDE) algorithmic approach presented by [16] to solve RPP problem, where, standard IEEE networks were chosen as test systems. Authors in [17] introduced a novel improved differential evolutionary (IDE) algorithm to tackle the RPP problem for different loading conditions. The authors in [18] applied quasi-oppositional Salp swarm algorithm for reactive power planning. A Chaotic Chimp optimization algorithm was proposed to solve RPP problem using SVC and TCSC in article [19]. Gravitational search slgorithm (GSA) was proposed by the authors in article [20] to deal with RPP problem and validated on standard IEEE-30 and IEEE-57 bus sytems. An improved Krill herd algorithm was presented for the placement of TCSC and UPFC in solving RPP problem by the authors [21].

1.3 Motivation and Contribution

Studying thoroughly the above-mentioned articles describing RPP problems and their solutions, it is observed that most of the problems were solved by optimal installations of FACTS devices, may be through the series type or through the shunt type, or through the combination of series and shunt type FACTS devices. Merely a technique was found where UPFC was used for reactive power optimization. UPFC having its brilliant characteristics in controlling real and reactive power can surely be manifested as an important device for reactive power optimization. Again because of its sensitivity in real and reactive power flow, utmost care must be taken in determination of its placement, location and size. In the present work, TCSC, SVC and UPFC all three types of FACTS devices were used to solve the problem of reactive power optimization. The placement and positions of those FACTS devices were determined beforehand by power flow analysis.

1.4 Paper Orientation

The remaining section is organized as follows: Section 2 establishes the theory behind the research objective. Work methodology is discussed in section 3. Section 4 outlines the fitness function, along with equality and inequality constraints, and details the mathematical modeling of wind speed to power and DSM. Proposed and studied algorithms are presented in section 5. Section 6 covers the results and discussions of the research work and finally, Section 7 summarizes the key conclusions.

Reactive power optimization or optimal reactive power planning can be achieved by minimizing active power loss of the power network. This can be done by the optimal usage of the available VAr sources. Hence, a suitable optimization method is necessary in accomplishing this task. The purpose of this optimization technique would be to fix the optimal sizes of these VAr sources. In effect, though active power loss was reduced significantly but the installation cost of the VAr sources is to be taken into consideration.

So, the optimization problem becomes the minimization of the total operating cost of the system which is of two-fold. One component of the total cost is because of the cost due to active power loss or more specifically cost due to the energy loss calculated over the year. Other part is the cost of the VAr sources, mainly of the FACTS devices as the other VAr sources (Q generations of generators, OLTC setting position) do not contribute any cost into the total operating cost to be optimized.

Coordination of existing VAr sources with the installation of fact devices will produce an optimum solution if FACTS devices are installed at the exact locations of the connected power network. So, the determination of placement location is also an important parameter in this respect. Here, the technique of power flow analysis is employed to determine the weak nodes or branches of the power network as reactive power support to the weak nodes or branches will only result satisfactory effect. This will also eliminate congestion in heavier branches and cause the redistribution of active and reactive power flow in the branches nearby as well in the remote areas in the network. The branches and nodes those require VAr support are identified and shown in Table 3.

TCSCs, the thyristor-controlled series compensators (TCSC) are decided to be placed in the heavily loaded lines. SVCs, the static var compensators will provide VAr support to the weak nodes. UPFC positions were also chosen for wider control of active and reactive power flow.

Different optimization techniques are then used to determine the optimal setting of the control variables are generated randomly. These solution vectors are generated with their bounds as already specified. Now the optimization techniques will work upon these solution vectors and finally produce the optimum string. Fitness for each solution string is calculated while evaluating the objective function by that string. The fitness of solution vectors will be modified and updated at each step of the optimization process of a particular method. The optimization technique is continued till the objective of getting the best string is reached.

4.1 Active Power Loss Cost Component

The expense due to the active power loss, C_A can be described by the following equations.

C_A = real power loss× cost of energy

C _A = P _L ×0.06×10⁵ ×24×365 (US$/kWh) (1)

$${P_L}=\sum\limits_{{k=(i,j)}}^{m} {{g_k}\left[ {v_{i}^{2}+v_{j}^{2} - 2v_{i}^{{}}v_{j}^{{}}\cos ({\delta _i} - {\delta _j})} \right]}$$

4.2 Installation Cost of the FACTS Devices

The cost associated to the FACTS can be denoted by the equation given below, where, C_FACTs is the total cost due of FACTS, whereas, C_SVC, C_TCSC and C_UPFC are cost due to SVC, TCSC and UPFC respectively.

C _FACTS=C_SVC+C_TCSC+C_UPFC (3)

${C_{TCSC}}={\text{ }}0.0015\left( {Q_{{TCSC}}^{2}} \right) - 0.71301\left( {{Q_{TCSC}}} \right)+153.75$ (US$/kVAr) (4)

${C_{SVC}}={\text{ }}0.0003\left( {Q_{{SVC}}^{2}} \right) - 0.3051\left( {{Q_{SVC}}} \right)+127.38$ (US$/kVAr) (5)

${C_{UPFC}}={\text{ }}0.0003\left( {Q_{{UPFC}}^{2}} \right) - 0.2691\left( {{Q_{TCSC}}} \right)+188.22$ (US$/kVAr) (6)

4.3 Objective Function

The main objective is to minimize the total expense, C_T associated with the optimal power planning problem, which is based on active power loss along with the system operating cost.

Min C_T=C_FACTS+ C_A (7)

4.4 Equality Constraints

The equality constraints in load flow analysis are represented by the real and reactive power balancing equations. The limitations for both active and reactive powers can be written as follows:

$${P_{{G_i}}} - {P_{{D_i}}} - {V_i}\sum\limits_{{j=1}}^{{{n_b}}} {{V_j}\left[ {{G_{ij}}\cos ({\delta _i} - {\delta _j})+{B_{ij}}\sin ({\delta _i} - {\delta _j})} \right]} =0$$

$${Q_{{G_i}}} - {Q_{{D_i}}} - {V_i}\sum\limits_{{j=1}}^{{{n_b}}} {{V_j}\left[ {{G_{ij}}\sin ({\delta _i} - {\delta _j}) - {B_{ij}}\cos ({\delta _i} - {\delta _j})} \right]} =0$$

4.5 Inequality Constraints

Every system variable has to lies in the allowable range which can be defined as follows:

$$V_{{{G_i}}}^{{\hbox{min} }} \leqslant {V_{{G_i}}} \leqslant V_{{{G_i}}}^{{\hbox{max} }};\,\,\,\,\,\,\,for\,\,\,\,i=1,2,...,{n_b}$$

$$Q_{{{G_i}}}^{{\hbox{min} }} \leqslant {Q_{{G_i}}} \leqslant Q_{{{G_i}}}^{{\hbox{max} }}\,\,\,\,\,for\,\,\,\,i=1,2,...,{n_b}$$

$$tap_{i}^{{\hbox{min} }} \leqslant tap_{i}^{{}} \leqslant tap_{i}^{{\hbox{max} }}\,\,\,\,\,for\,\,\,\,i=1,2,...,{n_{tap}}$$

$$SVC_{i}^{{\hbox{min} }} \leqslant SVC_{i}^{{}} \leqslant SVC_{i}^{{\hbox{max} }}\,\,\,\,\,for\,\,\,\,i=1,2,...,{n_{SVC}}$$

$$TCSC_{i}^{{\hbox{min} }} \leqslant TCSC_{i}^{{}} \leqslant TCSC_{i}^{{\hbox{max} }}\,\,\,\,\,for\,\,\,\,i=1,2,...,{n_{TCSC}}$$

$$UPFC_{i}^{{\hbox{min} }} \leqslant UPFC_{i}^{{}} \leqslant UPFC_{i}^{{\hbox{max} }}\,\,\,\,\,for\,\,\,\,i=1,2,...,{n_{UPFC}}$$

4.6 String Representation of the Control Variables

As mentioned in earlier section, the Eq. (16) represents the string which encompasses Q-limits, OLTC tap settings, and three distinct types of FACTS devices.

$$\begin{gathered} {Q_{{G_1}}},{Q_{{G_2}}},...,{Q_{{G_{{n_b}}}}},tap_{1}^{{}},tap_{2}^{{}},...,tap_{{{n_{tap}}}}^{{}},SVC_{1}^{{}},SVC_{2}^{{}},...,SVC_{{{n_{SVC}}}}^{{}}, \hfill \\ TCSC_{1}^{{}},TCSC_{2}^{{}},...,TCSC_{{{n_{TCSC}}}}^{{}}\,,UPFC_{1}^{{}},UPFC_{2}^{{}},...,UPFC_{{{n_{UPFC}}}}^{{}} \hfill \\ \end{gathered}$$

5.1 Particle Swarm Optimization

The Particle swarm optimization (PSO) technique, introduced by James Kennedy and Russell Eberhart in 1995 [22], and has been widely employed to deal with the single and multi-objective optimization problems. Operating on the principles of social behavior within a swarm of particles, PSO adjusts the trajectory of each particle towards its individual best and the overall best solutions in each generation. PSO is known for its simplicity and quick convergence and is implemented through velocity (vel) and position update equations, involving parameters like inertia weight (ω), social and cognitive factors (c₁ and c₂). Where, x represents the position of particle i, individual best and global best positions are denoted by p_best and g_best.

$$vel_{{i,j}}^{{iter+1}}=\omega *vel_{{i,j}}^{{iter}}+{c_1}*rand()*(pbest_{{i,j}}^{{iter}} - x_{{i,j}}^{{iter}})+{c_2}*rand()*(gbest_{j}^{{iter}} - x_{{i,j}}^{{iter}})$$

$$x_{i}^{{iter+1}}=x_{i}^{{iter}}+vel_{i}^{{iter+1}}$$

5.2 Crow Search Algorithm

Crows exhibit a behaviour of observing and tracking other birds to discover the whereabouts of their food and seize the opportunity to take it when the owner is absent. Moreover, if a crow pilfers food from another bird or crow, it becomes notably cautious and consistently changes its own hiding place to prevent thefts in the future. Additionally, the crow utilizes its acquired knowledge to safeguard its food from potential robbers. These behaviors serve as the foundation for the crow search algorithm (CSA) [23], as formulated by Askarzadeh in 2016.

In the context of the algorithm, during iteration ‘iter’, if crow ‘j’ expresses a desire to reach its hiding location, and crow ‘i’ wishes to trail crow ‘j’ in the same iteration, two possible scenarios may unfold:

Case 1

Crow ‘j’ remains unaware that it is being followed by crow ‘i’ Consequently, crow ‘i’ successfully locates the food hidden by crow ‘j’.

Case 2

Crow ‘j’ becomes aware that it is being trailed by crow ‘i’ and opts to mislead it by guiding it to a different random location within the search space.

The positions of these two scenarios can be represented by the equation given below [23]:

$$x_{i}^{{iter+1}}=\left\{ \begin{gathered} x_{i}^{{iter}}+ran{d_i} \times f{l_i} \times (m_{j}^{{iter}} - x_{i}^{{iter}}),\,if\;\;ran{d_j} \geqslant A{P_j} \hfill \\ a\;random\;position,\,\,\,\,\,\,otherwise \hfill \\ \end{gathered} \right.$$

Where x_i^iter is the position of the i^th crow; ‘fl_i’ is the flight length of crow ‘i’, which can also be presented as the vicinity of the search space; AP a represents the awareness probability of crow ‘j’, with its value ranging between 0 and 1; while the random numbers (0 to 1) are represented by rand_i and rand_j. Eq. (20) updates the memory, where m_i^iter is the memory of i^th crow at iteration ‘iter’.

$$m_{i}^{{iter+1}}=\left\{ \begin{gathered} {x_i}^{{iter+1}},\;\,\,\,\,\,\,\,if\;f(x_{i}^{{iter+1}})\;is\,\,better\,\,than\;f(m_{i}^{{iter}}) \hfill \\ m_{i}^{{iter}},\,\,\,\,\,\,\,\,\,\,\,\,\,otherwise \hfill \\ \end{gathered} \right.$$

5.3 Pigeon-Inspired Optimization

Pigeon-inspired optimization (PIO) [24] is based on the characteristics observed in pigeons, two operators have been devised based on specific rules:

Map and compass operator: Pigeons create a conceptual map of the Earth's magnetic field by using magnetoreception to sense its magnetic field. They navigate by using the height of the sun as a compass. As they move closer to their destination, they become less dependent on the sun and magnetic particles.
Landmark operator: Pigeons rely on neighbouring landmarks to guide them as they get closer to their objective. They will travel straight to their location if they are familiar with these landmarks. On the other hand, pigeons those are not familiar with the area or their goal will follow other pigeons that are headed in the same direction.

Virtual pigeons are utilized naturally in the PIO model. The position x_i and velocity vel_i of pigeon ‘i’ are used to establish the rules in this map and compass operator. Each iteration updates the positions and velocities in a search space. Equations (20) and (21) may be used to determine the new location and velocity of Pigeon ‘i’ at iteration ‘iter’.

$$vel_{i}^{{iter+1}}=vel_{i}^{{iter}} \times {e^{ - R.iter}}+rand \times (gbes{t_{iter}} - x_{i}^{{iter}})$$

$$x_{i}^{{iter+1}}=x_{i}^{{iter}}+vel_{i}^{{iter+1}}$$

gbest _iter is the global best position at iteration iter, which can be found by comparing all of the pigeons' locations; R is the map and compass factor; and rand is a random number. vel_i^iter and x_i^iter are the velocity and position of i^th pigeon during iteration ‘iter’.

Whereas, in case of the landmark operator, N_P reduces the amount of pigeons by half with each generation. The pigeons are not familiar with the sights and are still a long way from their goal. Assume that every pigeon can fly directly to the destination and x_C(t) is the center of some pigeon's location during iteration, ‘iter’ and at the same iteration, the position update rule for pigeon ‘i’ can be expressed by the equations given below.

$$N_{P}^{{iter+1}}=\frac{{N_{P}^{{iter}}}}{2}$$

$$X_{C}^{{iter+1}}=\left\{ {\begin{array}{*{20}{c}} {\frac{{\sum {x_{i}^{{iter+1}}} .\frac{1}{{f\,(x_{i}^{{iter+1}})+\varepsilon }}}}{{{N_P}\sum {f(x_{i}^{{iter+1}})} }}\,\,\,\,\,\,\,\,\,for\,\,\,\hbox{min} imization\,\,problem} \\ {\frac{{\sum {x_{i}^{{iter+1}}} .f(x_{i}^{{iter+1}})}}{{{N_P}\sum {f(x_{i}^{{iter+1}})} }}\,\,\,\,\,\,\,\,\,\,\,\,for\,\,\,\hbox{max} imization\,\,problem\,\,\,\,\,\,} \end{array}} \right.$$

$$x_{i}^{{iter+1}}=x_{i}^{{iter}}+rand \times (x_{C}^{{iter+1}} - x_{C}^{{iter}})$$

For each individual pigeon, the optimal position of each pigeon during N_C^th iteration can be denoted by x_P, where, $x_{P}^{{}}=\hbox{min} \left[ {x_{i}^{1},x_{i}^{2},...,x_{i}^{{{N_C}}}} \right]$.

Half of the pigeons may far away from the desired location and will they have to follow the pigeons present near the desired location, which also means that two pigeons may be at the same position. The pigeons present near their target move towards the destination.

5.4 Sine Cosine Algorithm

A method for stochastic population-based optimization may be broken down into two stages. The first stage wides the search space and finds the promising area of a superior solution. This first stage is known as the exploration phase, uses very high rates of unpredictability in the random solutions of the fitness function. In the contrast, the degree of randomness reduces and modest, progressive adjustments are made to move the best possible solution toward a higher-quality solution in the second phase, this stage is also known as the exploitation phase. These two steps are used by the sine cosine algorithm (SCA) [25] in its governing equation, which is represented by the expression given below.

$$x_{i}^{{iter+1}}=\left\{ \begin{gathered} x_{i}^{{iter}}+ran{d_1} \times \sin (ran{d_2})*|ran{d_3}*(P_{i}^{{iter}} - x_{i}^{{iter}})|,\,\,\,if\;ran{d_4}<0.5 \hfill \\ x_{i}^{{iter}}+ran{d_1} \times \cos (ran{d_2})*|ran{d_3}*(P_{i}^{{iter}} - x_{i}^{{iter}})|,\,\,\,if\;ran{d_4} \geqslant 0.5\,\,otherwise \hfill \\ \end{gathered} \right.$$

Where x_i^iter is the position of the current solution, where P_i^iter is the position of the destination point in the ith dimention at iteration ‘iter’. rand₁, rand₂, rand₃ and rand₄ are the random numbers used in SCA.

Standard IEEE 57 bus system [26],[27] is taken as test system. Each optimization method was run with 80 number of populations and 2500 iterations. Placement locations of different VAr sources including FACTS devices are shown in Table 1. A fair comparison is done for with and without RPP. Results obtained with PSO, CSA, PIO and SCA techniques are shown in Table 2, whereas, the VAr outputs of generators, static var compensator (SVC), Thyristor Controlled Switched Capacitors (TCSC), OLTC settings, UPFC phase angle injection in radians are tabulated in Table 3 for each optimization method. From the results as seen from the Table 2 that SCA technique is the best among all the three techniques applied. It can be observed that for all the four methods, active power loss and total operating cost were reduced significantly. But the reduction in active power loss and system operating cost are more in SCA than other three methods. For a more vivid representation, Fig. 1 illustrates the comparison of active power loss and total cost in scenarios both with and without RPP. Figure 2 shows the bar representation of the bus voltages obtained by the SCA method, while the convergence characteristics of all four algorithms are represented in Fig. 3.

Table 1

Placement locations of control variables in IEEE 57 bus system.
Specifications	Quantity	Location
busses	57	-
lines	80	-
slack bus	1	bus no.: 1
PV busses	6	bus no.: 2, 3, 6, 8, 9, 12
OLTC	17	line no.: 19, 20, 31, 35, 36, 37, 41, 46, 54, 58, 59, 65, 66, 71, 73, 76, 80
UPFC	3	Buses 2, 8, 15
TCSC	4	Lines 37, 13, 61, 57
SVC	7	Buses 49, 25, 38, 39, 41, 22, 14

Table 2

Comparative analysis of active power loss (p.u.) and cost (US$).
Cases		Active power loss (p.u.)	Operating cost (*10⁷), (US$)
Without RPP		0.2779	1.4712
With RPP	PSO	0.2379	1.2665
	CSA	0.2156	1.1442
	PIO	0.2058	1.1022
	SCA	0.2019	1.0583

Table 3

Optimal system operating variables with multiple algorithms.
Control variables	Location (Line / Branch)		Algorithms
Control variables	Location (Line / Branch)		CSA	PSO	PIO	SCA
transformers’ tap setting (p.u.)	line	19	0.9344	0.8500	0.9242	0.9356
		20	1.0721	0.8500	0.9441	0.9356
		41	0.9369	0.8726	0.9117	0.9356
		80	0.8851	0.8540	0.9107	0.9356
		65	0.9749	0.8500	1.0437	0.9356
		54	1.0677	0.8500	0.9535	0.9356
		71	0.9436	1.1000	1.0460	0.9356
		66	1.0239	0.8548	1.0460	0.9356
		59	1.0075	0.8534	0.9929	0.9356
		58	0.9610	0.8500	0.9952	0.9356
		31	0.9649	0.9881	0.9466	0.9356
		35	1.0900	1.0736	1.0601	0.9356
		36	0.8639	0.8500	0.8991	0.9356
		37	0.9183	1.0152	0.9525	0.9356
		46	0.9644	0.9469	0.9745	0.9356
		76	1.0015	1.0245	0.9305	0.9356
		73	1.0708	1.0653	0.9971	0.9356
VAr limits of generators (p.u.)	bus	2	0.1275	0.5000	0.2507	0.1146
		3	0.1215	-0.1000	0.1107	-0.1000
		6	0.0917	0.2500	0.2064	0.0600
		8	-1.1066	0.5541	0.7634	0.5112
		9	0.0543	0.0836	0.0450	0.0052
		12	0.3483	0.4412	1.0303	-0.5000
SVC (mho, susceptance value in p.u.)	bus	49	0.0000	0.1036	0.2502	0.1243
		25	0.0000	0.0000	0.0722	0.1014
		38	0.0000	0.2016	0.1988	0.0771
		39	0.0000	0.0000	0.0227	0.0871
		41	0.0788	0.2700	0.2786	0.0943
		22	0.3107	0.0830	0.0180	0.0518
		14	0.0000	0.2548	0.3364	0.0842
TCSC (mho, reactance value in p.u.)	line	37	0.0422	0.0426	0.0426	0.0091
		13	0.0391	0.0391	0.0391	-0.0081
		61	0.0210	0.0210	0.0210	-0.0015
		57	0.0527	0.0527	0.0527	-0.0109
UPFC (mho, impedance value in p.u.)	bus	2	0.0782	-0.0440	0.0547	0.0239
		8	0.0424	0.0872	0.0872	-0.0166
		15	0.0763	0.0030	0.0607	-0.0114

CSA, PSO, PIO and SCA optimization approaches were applied for the optimal coordination of multitype FACTS devices with the other VAr sources of a connected power network. Three entirely different types of FACTS devices viz. TCSC, the series FACTS controller; SVC, the shunt type FACTS device and UPFC, another FACTS controller with superior active and reactive power control capability are used. Here not only optimal sizing of FACTS devices were determined, but also the optimal settings of the VAr sources present in the network were done. Placement locations of FACTS were defined by the power flow analysis technique. From the results yielded by the three optimization methods, it can be observed that the SCA method was the best among all the techniques applied. Hence, SCA technique can be regarded as a powerful method to solve reactive power planning problem.

Symbols
${\delta _i}/{\delta _j}$	Phase angle of i^th / j^th bus
${B_{ij}}$	Susceptance between bus i and j
${C_A}$	Active power loss cost component
C_SVC	Cost of SVC
${C_T}$	Total operating cost
${C_{FACTS}}$	Cost for FACTS devices
C_TCSC	Cost of TCSC
C_UPFC	Cost of UPFC
${G_{ij}}$	Conductance between bus i and j
${g_k}$	Conductance at k^th line
	Total number of lines
n_b	No. of busses
n_SVC	No. of SVC
n_tap	No. of OLTC settings
n_TCSC	No. of TCSC
n_UPFC	No. of UPFC
${P_{{D_i}}}$	Demand of real power at bus i
${P_{{G_i}}}$	Generated real power at bus i
${P_L}$	Real power loss
${Q_{{D_i}}}$	Demand of reactive power at bus i
${Q_{{G_i}}}$	Generated reactive power at bus i
${Q_{{G_i}}}$	Generated reactive power at i^th bus
$Q_{{{G_i}}}^{{\hbox{min} }}/Q_{{{G_i}}}^{{\hbox{max} }}\,$	Minimum/ Maximum limit of generated reactive power for i^th bus.
${Q_{SVC}}/{Q_{TCSC}}/{Q_{UPFC}}$	Operating values of the SVC / TCSC / UPFC
$SVC_{i}^{{}}$	Value of i^th Static Var Compensator
$SVC_{i}^{{\hbox{min} }}/SVC_{i}^{{\hbox{max} }}\,\,$	Minimum/ Maximum limit of i^th Static Var Compensator
$tap_{i}^{{}}$	Tap settings at i^th OLTC
$tap_{i}^{{\hbox{min} }}/tap_{i}^{{\hbox{max} }}\,\,\,$	Minimum/ Maximum limit of Tap settings for i^th OLTC
$TCSC_{i}^{{}}$	Value of i^th Thyristor-Controlled Series Capacitor
$TCSC_{i}^{{\hbox{min} }}/ \leqslant TCSC_{i}^{{\hbox{max} }}$	Minimum/ Maximum limit of i^th Thyristor-Controlled Series Capacitor
$UPFC_{i}^{{}}$	Value of i^th Unified Power Flow Controller
$UPFC_{i}^{{\hbox{min} }}/UPFC_{i}^{{\hbox{max} }}$	Minimum/ Maximum limit of i^th Unified Power Flow Controller
${V_{{G_i}}}$	Generator bus voltage at i^th bus
$V_{{{G_i}}}^{{\hbox{min} }}/V_{{{G_i}}}^{{\hbox{max} }}$	Minimum/ Maximum limit of generator voltage for i^th bus.
${V_i}$	Voltage at bus i
${v_i}/{v_j}$	Voltage magnitude at i^th / j^th bus

Ethical Approval

Not Applicable

Competing interests

The authors declare they have no financial interests.

Authors' contributions

All authors contributed to the study's conception and design. Simulation and analysis were performed by Biplab Bhattacharyya. The draft of the manuscript was written by Sourav Basak and Suraj Kumar Rajbhar. All authors read and approved the final manuscript.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Availability of data and materials

Data sharing does not apply to this article as no datasets were generated or analyzed during the current study.

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No competing interests reported.

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Sine Cosine-based Optimization Method for Reactive Power Planning with Multitype FACTS Devices

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Abstract

Figures

1. Introduction

1.1 Overview

1.2 Literature Survey

1.3 Motivation and Contribution

1.4 Paper Orientation

2. Establishment of research objective

3. Work Methodology

4. Mathematical Modelling

4.1 Active Power Loss Cost Component

4.2 Installation Cost of the FACTS Devices

4.3 Objective Function

4.4 Equality Constraints

4.5 Inequality Constraints

4.6 String Representation of the Control Variables

5. Optimization Technique

5.1 Particle Swarm Optimization

5.2 Crow Search Algorithm

5.3 Pigeon-Inspired Optimization

5.4 Sine Cosine Algorithm

6. Results and Discussions

7. Conclusions

Abbreviations

Declarations

References

Additional Declarations

Status:

Version 1

Symbols
\({\delta _i}/{\delta _j}\)	Phase angle of i^th / j^th bus
\({B_{ij}}\)	Susceptance between bus i and j
\({C_A}\)	Active power loss cost component
C_SVC	Cost of SVC
\({C_T}\)	Total operating cost
\({C_{FACTS}}\)	Cost for FACTS devices
C_TCSC	Cost of TCSC
C_UPFC	Cost of UPFC
\({G_{ij}}\)	Conductance between bus i and j
\({g_k}\)	Conductance at k^th line
	Total number of lines
n_b	No. of busses
n_SVC	No. of SVC
n_tap	No. of OLTC settings
n_TCSC	No. of TCSC
n_UPFC	No. of UPFC
\({P_{{D_i}}}\)	Demand of real power at bus i
\({P_{{G_i}}}\)	Generated real power at bus i
\({P_L}\)	Real power loss
\({Q_{{D_i}}}\)	Demand of reactive power at bus i
\({Q_{{G_i}}}\)	Generated reactive power at bus i
\({Q_{{G_i}}}\)	Generated reactive power at i^th bus
\(Q_{{{G_i}}}^{{\hbox{min} }}/Q_{{{G_i}}}^{{\hbox{max} }}\,\)	Minimum/ Maximum limit of generated reactive power for i^th bus.
\({Q_{SVC}}/{Q_{TCSC}}/{Q_{UPFC}}\)	Operating values of the SVC / TCSC / UPFC
\(SVC_{i}^{{}}\)	Value of i^th Static Var Compensator
\(SVC_{i}^{{\hbox{min} }}/SVC_{i}^{{\hbox{max} }}\,\,\)	Minimum/ Maximum limit of i^th Static Var Compensator
\(tap_{i}^{{}}\)	Tap settings at i^th OLTC
\(tap_{i}^{{\hbox{min} }}/tap_{i}^{{\hbox{max} }}\,\,\,\)	Minimum/ Maximum limit of Tap settings for i^th OLTC
\(TCSC_{i}^{{}}\)	Value of i^th Thyristor-Controlled Series Capacitor
\(TCSC_{i}^{{\hbox{min} }}/ \leqslant TCSC_{i}^{{\hbox{max} }}\)	Minimum/ Maximum limit of i^th Thyristor-Controlled Series Capacitor
\(UPFC_{i}^{{}}\)	Value of i^th Unified Power Flow Controller
\(UPFC_{i}^{{\hbox{min} }}/UPFC_{i}^{{\hbox{max} }}\)	Minimum/ Maximum limit of i^th Unified Power Flow Controller
\({V_{{G_i}}}\)	Generator bus voltage at i^th bus
\(V_{{{G_i}}}^{{\hbox{min} }}/V_{{{G_i}}}^{{\hbox{max} }}\)	Minimum/ Maximum limit of generator voltage for i^th bus.
\({V_i}\)	Voltage at bus i
\({v_i}/{v_j}\)	Voltage magnitude at i^th / j^th bus