J. Cent. South Univ. (2013) 20: 715−723 DOI: 10.1007/s11771­013­1539­2

Comparative study of effectiveness of different var compensation devices in large­scale power networks

Reza Sirjani, Azah Mohamed, Hussain Shareef

Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan, Bangi 43600, Malaysia

© Central South University Press and Springer­Verlag Berlin Heidelberg 2013

Abstract: A comparison of the effectiveness of installing reactive power compensators, such as shunt capacitors, static var compensators (SVCs), and static synchronous compensators (STATCOMs), was presented in large­scale power networks. A suitable bus was first identified using modal analysis method. The single shunt capacitor, single SVC, and single STATCOM were installed separately on the most critical bus. The effects of the installation of different devices on power loss reduction, voltage profile improvement, and voltage stability margin enhancement were examined and compared for 57­ and 118­bus transmission systems. The comparative study results show that SVC, and STATCOM are expensive compared to shunt capacitor, yet the effect of installing STATCOM is better than SVC and the effect of installing SVC is better than that of shunt capacitor in achieving power loss reduction, voltage profile improvement and voltage stability margin enhancement.

Key words: shunt capacitor; static var compensator; static synchronous compensator; power loss; voltage profile; voltage stability

Received date: 2012–05–02; Accepted date: 2012–07–30 Corresponding author: Reza Sirjani, PhD; Tel: +60−166191510; E­mail: reza.sirjani@gmail. com

1 Introduction

Shunt compensation has been used to influence the natural electrical characteristics of transmission lines to increase steady­state transmittable power and control the voltage profile along the line [1]. Providing adequate reactive power support at appropriate locations not only leads to the reduction in power loss and improvement in voltage profile but also solves voltage instability problems. A number of reactive compensation devices have been used by modern electric power utilities for this purpose, and each device has its own characteristics and limitations. At present, utilities aim to achieve this purpose using the most efficient compensation device [2]. Traditionally, shunt capacitors are installed in power networks to compensate reactive power and are used for many purposes, such as reducing power loss, improving voltage profile, and increasing the maximum transmitted power in cables and transformers [3]. Among the available reactive compensation devices, shunt flexible AC transmission system (FACTS) devices play an important role in controlling the flow of reactive power to the power network, thereby affecting system voltage fluctuations and stability [4]. Static var compensator (SVC) is the most widely used shunt FACTS device in power networks because of its low cost and good system enhancement performance. It is a shunt­connected static

var generator (SVC) or absorber with an adjustable output, which allows the exchange of capacitive or inductive current to provide voltage support. Installed at a proper location, SVC can also reduce power losses [5]. Static synchronous compensator (STATCOM) is also a shunt compensator and an important member of the FACTS family, increasingly used in long transmission lines in modern power systems. STATCOMs have various applications in the operation and control of a power system, including power flow scheduling, reducing the number of unsymmetrical components that damp power oscillation, and enhance transient stability [3].

It is known that SVC and STATCOM perform better than a simple shunt capacitor; however, these controllers are more expensive [2]. The benefits of reactive power compensation greatly depend on the placement and size of the installed compensators. Installation of shunt controllers in all buses is unnecessary and economically impossible. Identifying the best location for var compensators involves the calculation of steady­state conditions of the network. The use of shunt capacitor, SVC, and STATCOM for static voltage stability improvement has been compared in Ref. [2]. Various performance measures were compared under different operating system conditions for the IEEE 14­bus test system. The results showed that shunt capacitor, SVC, and STATCOM increase static voltage stability margin

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and power transfer capability. However, SVC and STATCOM showed better performance in terms of power loss reduction and voltage profile improvement [2]. A comparison was made between the performances of a wind farm equipped with SVC and STATCOM to improve the wind­farm stability during and after a fault [6]. Simulation results showed that both devices can enhance system stability during and after a disturbance, especially when the network is weak. Moreover, STATCOM performed much better compared with SVC in improving the wind­farm stability and provided better reactive power support to the network [6]. The effect of SVCs and STATCOMs on a power system presented in Ref. [7], showed that both devices significantly improve the transient voltage behavior of power systems. Although SVC and STATCOM operate on different principles, their effects in increasing power system transmission capacity are comparable [7].

This work analyzed the effects of installing the most commonly used shunt compensation devices on large­scale power networks. A suitable bus was first identified using modal analysis, and the effectivenesses of shunt capacitor, SVC, and STATCOM in power loss reduction, voltage profile improvement, and voltage stability margin enhancement were then analyzed and compared. The comparative study was performed on the 57­and 118­bus transmission systems, respectively.

2 Shunt compensation devices

Shunt compensation can be used to provide reactive power compensation. Traditional shunt capacitors or the newly introduced FACTS controllers can be used for this purpose. However, FACTS controllers are very expensive compared to shunt capacitors. Table 1 presents an idea of various shunt controller costs [8–9]. Descriptions of each of these controllers are given in the next sections.

Table 1 Cost comparison of shunt controllers Shunt controller Cost/ (10 −3 US $⋅Var −1 )

Shunt capacitor 8

SVC 40 (Controlled portion) STATCOM 50 (Controlled portion)

2.1 Shunt capacitor Shunt capacitors are relatively inexpensive to install

and maintain, and installing them in load areas or at points where they are needed increases voltage stability. However, their voltage regulations are very poor, and beyond a certain level of compensation, a stable operating point is unattainable. Furthermore, the reactive power delivered by a shunt capacitor is proportional to

the square of the terminal voltage. Var support drops during low­voltage conditions, thereby compounding the problem [10].

2.2 SVC ideal model SVC is a shunt­connected static var generator/load

whose output can be adjusted to exchange capacitive or inductive current to maintain or control a specific power system variable [11–12]. In its simplest form, SVC consists of a thyristor­controlled reactor in parallel with a bank of capacitors. From operational perspective, SVC behaves like a shunt­connected variable reactance, which either generates or absorbs reactive power to regulate the voltage magnitude at the point of connection to the AC network. It is used extensively to provide fast reactive power and voltage regulation support. The thyristor’s firing angle control enables SVC to provide an almost instantaneous response speed. As an important component for voltage control, it is usually installed at the receiving node of transmission lines. Figure 1 shows an SVC that has been considered as a shunt branch with a compensated reactive power QSVC, set by available inductive and capacitive susceptances [5, 13].

Fig. 1 Circuit diagram of SVC

From Fig. 1, the current drawn and the reactive power injected by the SVC can be expressed as

SVC SVC j I B V = × ( 1 )

2 SVC SVC j Q B V = − × (2)

where Bsvc, Isvc, and Qsvc are the susceptance, injected current, and injected reactive power of SVC, respectively.

SVC size is expressed as the amount of reactive power supplied to a bus whose voltage is 1 p.u. SVC either operates in a capacitive state (generating reactive power and injecting it into the network) or in an inductive state (where the SVC absorbs reactive power from the network) [14].

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2.3 STATCOMmodelling STATCOM is usually used to control the

transmission system voltage through shunt compensation of the reactive power. Typically, an STATCOM consists of a coupling transformer, an inverter, and a DC capacitor. For an ideal steady­state analysis, the active­power exchange between the AC system and the STATCOM can be assumed as negligible, and only reactive power is exchanged between them [15–16]. The schematic representation of STATCOM and its equivalent circuit are shown in Figs. 2(a) and (b), respectively.

In Fig. 2(a), the shunt­connected transformer is assumed to be ideal. STATCOM is implemented so that the active­power flow between the AC source and the voltage source converter (VSC) is controlled by the phase angle, and the reactive power flow is determined mainly by the magnitude of the voltage source (Vk) and the VSC output fundamental voltage (VvR). VSC generates reactive power when VvR>Vk and consumes reactive power when VvR<Vk. During normal operation, a small amount of active power flows into the VSC to compensate for the power losses inside the VSC, and δ is kept slightly larger than zero (i.e., lagging) [16]. The STATCOM equivalent circuit shown in Fig. 2(b) is used to derive the mathematical model of the controller for inclusion in the power flow algorithm.

Fig. 2 STATCOM system: (a) VSC connected to AC network via shunt­connected transformer; (b) Shunt solid­state voltage source [16]

The power flow equations for bus i of the power system with no FACTS controllers are given by

2

1 [ cos( ) sin( )]

n

i i ii i m im i m im i m m

P V G VV G B θ θ θ θ =

= − − + − ∑ (3)

2

1 [ cos( ) sin( )]

n

i i ii i m im i m im i m m

Q V B VV G B θ θ θ θ =

= − + − − − ∑ (4)

With the addition of STATCOM connected at bus k, the system power flow equations remain the same as the equations of a system without a STATCOM for all buses given by Eqs. (3) and (4) except for bus k. The equations for bus k are given below. The power flow equations for the STATCOM in the two­bus system in Fig. 2(b) are obtained from first principles using the following voltage source representation.

vR vR vR vR (cos j sin ) E V δ δ = + ⋅ (5)

Based on the shunt connection shown in Fig. 1(b), the following equation can be written:

* * * vR vR vR vR vR vR ( ) k S V I V Y V V = = − (6)

After some complex operations are performed, the following active and reactive power equations are obtained for the converter and bus k [15].

2 vR vR vR vR vR vR vR vR [ cos( ) sin( )] k k k P V G V V G B δ θ δ δ = − − + −

(7)

2 vR vR vR vR vR vR vR vR [ cos( ) sin( )] k k k Q V B V V B G δ θ δ δ =− + − − −

(8)

2 vR vR vR vR vR vR [ cos( ) sin( )] k k k k k P V G V V G B θ δ δ δ = − − + −

(9)

2 vR vR vR vR vR vR [ cos( ) sin( )] k k k k k Q V B V V B G θ δ θ δ = − + − − −

(10)

Thus, for an n­bus power system, the active and reactive power equations for bus k (i.e., the bus where the STATCOM is connected) are obtained from Eqs. (3), (4), (9), and (10), and defined as

2 vR vR vR vR vR vR vR [ cos( ) sin( )] k k k k P V G V V G B δ θ δ δ = − − + − +

2

1 [ cos( ) sin( )]

n

k kk k m km k m im k m m V G V V G B θ θ θ θ

= − − + − ∑

(11)

2 vR vR vR vR vR vR [ cos( ) sin( )] k k k k k Q V B V V B G θ δ θ δ =− + − − − +

2

1 [ cos( ) sin( )]

n

k kk k m km k m km k m m

V B V V G B θ θ θ θ =

− + − − − ∑ (12)

3 Modal analyses for optimal placement of var compensators

In addition to providing an accurate estimate of the system proximity to instability using system eigenvalues,

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the modal analysis method identifies the elements of the power system that contribute the most to incipient voltage instability (i.e., critical load buses, branches, and generators) [17]. In the modal analysis method, the Jacobian matrix of the operating point of the power system is calculated [10]. For this purpose, the power flow equation linear around the operating point is used as

P PV

Q QV

J J J J

θ

θ

∆ ∆ = ∆ ∆

θ P Q V

(13)

where, ∆P is the incremental change in the bus active power, ∆Q is the incremental change in the bus reactive power, ∆θ is the incremental change in the bus voltage angle, and ∆V is the incremental change in the bus voltage magnitude. JPθ, JPV, JQθ, and JQV are the Jacobian matrix elements representing the sensitivity of the power flow to bus voltage changes.

System voltage stability is affected by both P and Q; However, at each operating point, P can be kept constant, and voltage stability can be evaluated by considering the incremental relationship between Q and V. If the active power P is kept constant in Eq. (11), then ∆P=0 and

R ∆ = ∆ Q J V ( 1 4 )

where JR is the reduced Jacobian matrix system given by

1 R [ ] J J J J − = − QV Q P PV J θ θ (15)

The power network modes can be defined by the eigenvalues and eigenvectors of JR. We assume that

R =ξΛη J (16)

where ξ is the right eigenvector matrix of JR, η is the left eigenvector matrix of JR, and Λ is the diagonal eigenvalue matrix of JR

1 1 R − − = J ξΛ η (17)

The incremental changes in the reactive power and voltage are related to Eq. (14). Substituting Eq. (17) into Eq. (14) yields

1 ( ) − ∆ = ∆ V Q ξΛ η (18)

or

i

i i λ

∆ = ∆

∑ ξ η V Q (19)

where λi is the i­th eigenvalue, i ξ is the i­th column right eigenvector of JR, and i η is the i­th row left

eigenvector of JR, i λ , i ξ , and i η define the i­th mode of the system.

Therefore, the i­th modal reactive power variation is

mi i i ∆ =κ ξ Q (20)

where i κ is a normalization factor such that

2 2 1 i ij J

κ ξ = ∑ (21)

where ij ξ is the j­th element of i ξ . The i­th modal voltage variation can therefore be

written as

1 mi mi

i ∆ = ∆

λ V Q (22)

From Eq. (22), the stability of mode i with respect to reactive power changes is defined by the modal eigenvalue, λi. Large values of λi suggest small changes in the modal voltage for reactive power changes. As the system is stressed, the value of λi becomes smaller, and the modal voltage becomes weaker. If the magnitude of λi is equal to zero, the corresponding modal voltage collapses because it undergoes an infinite change for a finite reactive power change. A system is therefore defined as voltage stable if all the eigenvalues of JR are positive. The bifurcation or voltage stability limit is reached when at least one eigenvalue reaches zero, i.e., when one or more modal voltages collapses. If any of the eigenvalues are negative, the system is unstable. The magnitude of the eigenvalues provides a relative measure of the proximity of the system to instability. Critical modes (associated with the minimum eigenvalues) are critically important in voltage stability analysis [17].

The left and right eigenvectors corresponding to the critical modes in the system can provide information concerning the mechanism of voltage instability by identifying the elements involved in these modes. The bus participation factor that measures the participation of the k­th bus in the i­th mode can be defined as

ki ki ik P ξ η = (23)

Bus participation factors corresponding to critical modes can predict areas or nodes in the power system susceptible to voltage instability. Buses with large participation factors in the critical mode are the most critical system buses.

4 Objective function for solving optimal sizing of var compensators

A multi­objective function consisting of shunt var compensator size was considered in searching for an optimal solution. This multi­objective function, which

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not only maximizes the voltage stability margin but also minimizes voltage deviation, active­power loss, and cost, is explained below [5, 14].

1) Active­power loss minimization The total active­power loss in an electric power

system is given by

2 2 2 loss

1 1 1, [ 2 cos( )] cos

n n n

l l i j i j i j ii ij l l j i j

P R I V V VV Y θ θ φ = = = ≠

= = + − − ∑ ∑ ∑ (24)

where n is the number of lines; Rl is the resistance of line l; Il is the current through line l; Vi and θi are the voltage magnitude and angle at node I, respectively; Yij and ϕij are the magnitude and angle of the line admittance, respectively.

2) Voltage deviation minimization The voltage improvement index of a power system

is defined as the deviation from unity of the voltage magnitudes in all the buses. Thus, for a given system, the voltage improvement index is defined as

2 , ref

1 , ref

n i i v

i i

V V L

V =

− =

∑ (25)

where n is the number of buses, Vi, ref is the reference voltage at bus i, and Vi is the actual voltage at bus i.

3) Voltage stability margin maximization From the voltage stability viewpoint, critical modes

with the lowest eigenvalues are extremely important. The minimum eigenvalue should increase to maximize the stability margin Ref. [18].

4) Cost minimization The shunt controller costs in US $/kVar are listed in

Table 1. The objective function for solving the optimal sizing problem of shunt var compensators is calculated using Eqs. (24) and (25) and Table 1. The problem constraints do not explicitly contain the variables. Therefore, the effect of the constraints must be included in the fitness function value. Incorporating all the objective functions in the same mathematical function is impossible because the three objective functions are different. Thus, an overall fitness function in which each objective function is normalized with respect to the base system without a var compensator is considered. This fitness function is given by

base

Crtical(base) Loss 1 2 3

Loss base Critical ( ) v P L f x

f V

λ ω ω ω

λ = + + +

∆ ∆ ∑ ∑

Shunt 4

MAX

C C

ω (26)

where PLoss, Lv, λCritical, and CShunt are the total active­power loss, voltage deviation index, smallest

eigenvalue, and the total var compensator cost, respectively. ω1, ω2, ω3 and ω4 are the coefficients of the corresponding objective functions,

base Loss f ∆ ∑ is the total active­power loss in the network of the base system,

base V ∑ is the total voltage deviation of the base system, λCritical(base) is the smallest eigenvalue of the base case, and CMAX is the maximum cost.

5 Implementation procedure for installing different var compensators in a power network

The most critical system buses (i.e., buses with large participation factors) considered suitable for shunt var compensator installation are first identified using the modal analysis method. One shunt capacitor, one SVC, and one STATCOM are installed separately on the most critical bus. The total power loss, voltage deviation, and smallest eigenvalue are calculated for each case to compare the effectiveness of the capacitor, SVC, and STATCOM on power loss reduction, voltage profile improvement, and voltage stability margin enhancement. The comparison and analysis procedures of the effect of the installation of different var compensators on a power system are described as follows:

1) Specify system parameters, such as bus, branch, and generator data;

2) Calculate the Jacobian matrix and eigenvalues for the base system;

3) Calculate eigenvectors and bus participation factors for the smallest eigenvalue;

4) The bus with the largest participation factor is determined and considered suitable for shunt var compensator installation;

5) A single shunt capacitor, a single SVC, and a single STATCOM are installed separately on the most critical bus;

6) The power flow program is run to calculate the power loss, voltage deviation, and the eigenvalues for each case;

7) The effectiveness of the shunt capacitor, SVC, and STATCOM on power loss reduction, voltage profile improvement, and voltage stability margin enhancement are compared and analyzed.

6 Case study and results

The comparative study is performed in 57­ and 118­bus transmission systems. The 57­bus system consists of seven generators (in which one is the slack node), 50 load buses, and 80 lines. The system data can be found in Ref. [19]. The base configuration system load is 12.508 p.u., and the system power loss is 28.41 MW. The 118­bus system consists of 54 generators (in

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which one is the slack node), 64 load buses, and 186 lines. The system power loss is 132.86 MW, and the system data can be found in Ref. [19].

6.1 Results for 57­bus test system The eigenvalues of the reduced Jacobian matrix are

first generated to obtain the relative proximity of the system to instability. The bus participation factors are then generated for the critical mode to identify the critical buses in the system (i.e., buses with the smallest margins to instability). The smallest eigenvalue of this system for the base configuration is calculated as 0.234 4. The largest bus participation factors for the smallest eigenvalue are listed in Table 2.

Table 2 Largest bus participation factors for smallest eigenvalue in 57­bus test system

Bus No. Participation

31 0.1833

33 0.1744

32 0.1704

30 0.133

Table 2 verifies that buses with the highest participation factors have the lowest reactive stability margins in the system and therefore correctly correspond to the critical system buses. The bus with the highest participation factor is considered suitable for var compensator installation. The most critical bus in the 57­bus test system is bus 31.

The variations in power loss, voltage deviation, and smallest eigenvalue relative to the var compensator size using different devices are shown in Figs. 3–5, respectively. This work is conducted with the restriction that the injected Q does not exceed 50 MVar in the 57­bus test system.

Fig. 3 Power loss versus var compensator size after installation of different devices in 57­bus test system

Fig. 4 Voltage deviation versus var compensator size after installation of different devices in 57­bus test system

Fig. 5 Smallest eigenvalue versus var compensator size after installation of different devices in 57­bus test system

Figure 3 shows that the power loss variation curves initially decrease and then increase after the installation of shunt capacitor, SVC, and STATCOM. The effects of installing shunt capacitor, SVC, and STATCOM with sizes less than 10 MVar are very similar; however, based on the enhancement of the var compensator size, the effect of STATCOM on power loss reduction is better than that of SVC, and the effect of SVC is better than that of the shunt capacitor.

Figure 4 shows that the voltage deviation variation curves initially decrease and then increase after the installation of the shunt capacitor, SVC, and STATCOM. Based on the enhancement of the var compensator size, the effect of STATCOM on the voltage profile improvement is better than that of SVC, and the effect of SVC is much better than that of the shunt capacitor.

Figure 5 shows that, based on the var compensator size increment, the effect of STATCOM on the increase in the smallest eigenvalue and voltage stability

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enhancement is better than that of SVC, and the effect of SVC is much better than that of the shunt capacitor.

The variation curves of the objective function value relative to var compensator size using different devices are shown in Fig. 6. The total cost with respect to the type and the cost of each added var compensator is calculated using Table 1. The objective function is calculated using Eq. (26). The coefficients of the objective functions are defined as ω1 = 0.3, ω2 = 0.3, ω3 = 0.3, and ω4 = 0.1, based on the lower significance of the total cost objective function compared with the power loss reduction, voltage profile improvement, and voltage stability enhancement functions.

Fig. 6 Objective function value versus var compensator size after installation of different devices in 57­bus test system

From Fig. 6, the best size for single shunt var compensator at the most critical bus is approximately 12 MVar. The effects of installing the 12 MVar capacitor, 12 MVar SVC, and 12 MVar STATCOM at the weakest bus of the 57­bus test system are compared, as listed in Table 3.

From Table 3, the following points can be highlighted:

1) The effect of installing a single capacitor, SVC, and STATCOM on power loss reduction in the 57­bus test system is not significant, and the power loss reduction after the installation of different devices is less than 2%. The effect of installing a single STATCOM on power loss reduction is better than that of a single SVC,

and the effect of installing a single SVC is better than that of a single shunt capacitor.

2) The effect of the installing a single capacitor, SVC, and STATCOM on voltage profile improvement in the 57­bus test system is significant, and the voltage deviation reduction after the installation of different devices is greater than 16%. The effect of installing of a single STATCOM on voltage profile improvement is better than that of a single SVC, and the effect of installing a single SVC is much better than that of a single shunt capacitor.

3) The effect of the installing a single capacitor, SVC, and STATCOM on voltage stability enhancement in the 57­bus test system is substantial, and the smallest eigenvalue improvement after the installation of different devices is about 9.3%. The effect of the installation of a single STATCOM on voltage stability enhancement is better than that of a single SVC, and the effect of the installation of a single SVC is much better than that of a single shunt capacitor.

4) In this relatively large­scale test system, installing only one var compensation device to achieve all the aforementioned objectives is definitely not sufficient. To obtain more significant results, optimal placement and sizing of multi­var compensator are necessary.

6.2 Results for 118­Bus test system The smallest eigenvalue of this system for the base

configuration is calculated as 3.942 5. The largest bus participation factors for smallest eigenvalue are listed in Table 4.

Table 4 verifies that buses with the highest participation factors have the lowest reactive stability margins in the system and therefore correctly correspond to the critical system buses. As listed in Table 4, the most critical bus in the 118­bus test system is bus 21.

The variations in power loss, voltage deviation, and smallest eigenvalue relative to the var compensator size using different devices are shown in Figs. 7–9, respectively. This study is conducted with the constraint that the injected Q does not exceed 120 MVar in the 118­bus test system.

From Figs. 7 and 8, the variation in the curves of both power loss and voltage deviation first descend and then ascend after the installation of the shunt capacitor,

Table 3 Comparison of effects of different var compensators installed at weakest bus of 57­bus test system With capacitor (12 MVar)

With SVC (12 MVar)

With STATCOM (12 MVar) Parameter Base case

Value Improvement/% Value Improvement/% Value Improvement/%

Power loss/MW 28.41 28.03 1.3 27.98 1.5 27.91 1.7

Voltage deviation 0.265 0.221 16.7 0.193 27.3 0.181 31.8

Smallest eigenvalue 0.234 4 0.258 6 9.3 0.269 7 13.1 0.275 7 15.0

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Table 4 Largest bus participation factors for smallest eigenvalue of 118­bus test system

Bus No. Participation 21 0.426 8 22 0.339 0 20 0.227 4 23 0.006 8

SVC, and STATCOM. Although the effects of installing shunt capacitor, SVC, and STATCOM on power loss reduction are very similar, that is, less than 20 MVar, but after var compensator size increment, the effect of STATCOM on both power loss reduction and voltage improvement is better than that of SVC, and the effect of SVC on voltage profile improvement is much better than that of the shunt capacitor.

Fig. 7 Power loss versus var compensator size after installation of different devices in 118­bus test system

Fig. 8 Voltage deviation versus var compensator size after installation of different devices in 118­bus test system

Figure 9 shows that based on the var compensator size increment, the effect of STATCOM on increasing the smallest eigenvalue and voltage stability enhancement is better than that of SVC, and the effect of SVC is much better than that of the shunt capacitor.

Fig. 9 Smallest eigenvalue versus var compensator size after installation of different devices in 118­bus test system

The variations in the objective function values relative to the var compensator size using different devices are shown in Fig. 10. The objective function is calculated using Eq. (26), and the coefficients for the objective functions are assumed to be the same as those in the 57­bus test system.

Fig. 10 Objective function versus var compensator size after installation of different devices in 118­bus test system

From Fig. 10, the best size of a single shunt var compensator for the most critical bus is approximately 64 MVar. The effects of installing the 64 MVar­capacitor, 64 MVar­SVC, and 64 MVar­ STATCOM on the weakest bus of the 118­bus test system are compared in Table 5.

From Table 5, the following points can be highlighted:

1) The effect of installing a single capacitor, SVC, and STATCOM on power loss reduction in the 118­bus test system is not very significant, and the power loss reduction after the installation of different devices is less than 0.4%. However, the effect of the installation of a single STATCOM on power loss reduction is better than that of a single SVC, and the effect of the installation of a single SVC is better than that of a single shunt capacitor.

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Table 5 Comparison of effects of different var compensators installed on weakest bus in 118­bus test system With capacitor (64 MVar) With SVC (64 MVar) With STATCOM (64 MVar) Parameter Base

case Value Improvement/% Value Improvement/% Value Improvement/% Power loss/MW 132.86 132.72 0.1 132.61 0.2 132.52 0.3 Voltage deviation 0.294 0.293 0.4 0.289 1.9 0.287 2.5 Smallest eigenvalue 3.942 5 4.467 8 11.8 5.014 2 21.4 5.267 8 25.2

2) The effect of installing a single capacitor, SVC, and STATCOM on voltage profile improvement in the 118­bus test system is not very significant, and the voltage deviation reduction after the installation of different devices is less than 3%. The effect of the installation of a single STATCOM on the voltage profile improvement is better than that of a single SVC, and the effect of the installation of a single SVC is much better than that of a single shunt capacitor.

2) The effect of installing a single capacitor, SVC, and STATCOM on voltage stability enhancement in the 118­bus test system is significant, and the smallest eigenvalue improvement after the installation of different devices is more than 11%. The effect of the installation of a single STATCOM on voltage stability enhancement is better than that of a single SVC, and the effect of the installation of a single SVC is much better than that of a single shunt capacitor.

4) In this large­scale test system, installing only one var compensation device to achieve all the afore­ mentioned objectives is definitely not sufficient. Optimal placement and sizing of multi­var compensators is necessary to obtain better results.

7 Conclusions

1) The effectiveness of the most commonly used shunt compensation devices such as shunt capacitor, SVC, and STATCOM on power loss reduction, voltage profile improvement, and voltage stability margin enhancement has been compared and analyzed.

2) Overall, the effect of the installation of a single STATCOM in achieving the aforementioned objectives is better than that of a single SVC, and the effect of the installation of a single SVC is better than that of a single shunt capacitor. However, SVC and STATCOM are expensive compared with shunt capacitor.

3) In large­scale test systems, installing only one Var compensation device to achieve all the aforementioned objectives is definitely insufficient. Optimal placement and sizing of multi­var compensators is necessary.

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(Edited by DENG Lü­xiang)