Effects of series compensation on spot price power markets

Effects of series compensation on spot price power markets

G.B. Shrestha*, Wang Feng

Power Market Research Group, School of EEE, S2, Nanyang Technological University, Singapore 639798, Singapore

Received 24 June 2003; revised 9 February 2005; accepted 3 March 2005

Abstract

The operation of a deregulated power market becomes more complex as the generation scheduling is dependent on suppliers’ and

consumers’ bids. With large number of transactions in the power market changing in time, it is more likely for some transmission lines to face

congestion. Series compensation, such as TCSC, with its ability to directly control the power flow can be very helpful to improve the

operation of transmission networks. The effects of TCSC on the operation of a spot price power market are studied in this paper using the

modified IEEE 14-bus system. Optimal Power Flow incorporating TCSC is used to implement the spot price market. Linear bids are used to

model suppliers’ and consumers’ bids. Issues of location and cost of TCSC are discussed. The effects of levels of TCSC compensation on

wide range of system quantities are studied. The effects on the total social benefit, the spot prices, transmission congestion, total generation

and consumption, benefit to individual supplier and consumer etc. are discussed. It is demonstrated that though use of TCSC makes the

system more efficient and augments competition in the market, it is not easy to establish general relationships between the levels of

compensation and various market quantities. Simulation studies like these can be used to assess the effects of TCSC in specific systems.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: TCSC (Thyristor Controlled Series Compensator); Power markets; Spot price; Optimal power flow; TCSC cost

1. Introduction

The main objective of introducing competition in

electricity markets is to make them more efficient. The

basic idea is that if fair and equitable market structures are

established to give all market participants incentives to

maximize their own individual welfare, then the market as a

whole will behave in a manner which maximizes welfare for

everyone in a deregulated power market. A method used to

dispatch generation and load in an economic manner is to

use spot pricing theory. In a competitive market suppliers

and sometimes consumers submit bid curves to the pool

operator who determines the dispatch results to optimise the

system operation. Suppliers are then paid a price according

to their bids and consumers must pay a price according to

their bids.

Transmission network has to be shared by all market

participants, and uncontrollable nature of transmission lines

0142-0615/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijepes.2005.03.001

* Corresponding author.

E-mail address: [email protected] (G.B. Shrestha).

may limit the competitive bids by sellers and buyers.

Flexible AC Transmission Systems (FATCS) devices,

which can provide direct and flexible control of power

transfer, can be very helpful in the operation of competitive

power markets. Functions of FACTS devices or controllers

include increasing power transfer capacity of transmission

networks and to provide direct control of power flow over

designated transmission routes. With open access to

transmission systems and more delivery transactions due

to competition, transmission lines more likely to operate

near their transmission limits. Many studies have focused on

the implementation of FACTS in electricity market [1–3].

This paper presents simulation studies on the spot price

market incorporating Thyristor Controlled Series Compen-

sation (TCSC) to study the effects of TCSC on various

aspects of electricity market such as the overall social

benefit, spot prices, wheeling fees, transmission loss, etc.

The paper is organized as follows. Section 2 discusses the

spot price market model where linear bid curves have been

used to model the supplier and consumer bids. Modelling of

TCSC devices and modified Optimal Power Flow incorpor-

ating TCSC device is outlined in Section 3. Case studies to

investigate the effects of TCSC on various aspects of system

Electrical Power and Energy Systems 27 (2005) 428–436

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G.B. Shrestha, W. Feng / Electrical Power and Energy Systems 27 (2005) 428–436 429

operation are presented in Section 4 followed by con-

clusions in Section 5.

2. Spot price market model

The main objective of introducing competition in power

markets is to make them more efficient. A method adopted

to dispatch generation and load in an economic manner is to

use spot pricing theory. Spot pricing theory was presented

by Schweppe in [4]. Hogan applied the model in

competitive power market [5]. Several recent studies have

been reported which utilize spot price concepts in the

management of power system congestion [16,17].

In spot price market model, there are three types of

participants: the consumers, the suppliers, and the trans-

mission/distribution operator, who determines the market

price and operates the system. The suppliers and consumers

submit bid curves that define amounts of energy (MW), and

the corresponding price ($/MW-h). These bids of suppliers

are often directly related to the marginal cost curves. The

pool operator treats the submitted bids as the true marginal

cost curves of the suppliers and the true marginal benefit

curves of the consumers and uses the Optimal Power Flow

(OPF) to minimize the total costs in order to determine the

generation dispatch and related spot prices.

Zij= rij +j xij

- j xc Bus-i Bus-j

jB i0 jBj0

(a)

Zij= rij +j xij

Sic Sjc

Bus-i Bus-j

(b)

Fig. 1. TCSC modeling. Transmission line with TCSC. (b) Injection model

of transmission line with TCSC.

2.1. Bid functions

Linear bid functions are used for both the supplier and

the consumer. The minimum price ps,min and the slope ms

specify the generation bid Sp of the suppler. The bid price is

modelled as:

ps Z ps; min CSp

ms

(1a)

then, the generation cost function C(x) is given by:

CðxÞ Z

ðx

0ps;min C

Sp

ms

� �dsp Z ps; minx C

x2

2ms

(1b)

In a traditional market, load is not considered as a variable

because of the inability of utilities to directly or indirectly

control loads. In a spot market, the consumer demand d is a

function of the price pc. The linear demand function may be

mathematically expressed with the slope md as:

d Z dmax Kmdpc (2a)

where, dmax is the maximum demand of the consumer.

Then, the inverse of this demand function can be

expressed as

pc Z pc; max Kd

md

(2b)

where

pc; max Zdmax

md

This inverse demand function represents the marginal

benefit of consuming unit quantity of electricity.

The integral of this function becomes the benefit function

B(x) which is a quadratic formulation:

BðxÞ Z

ðx

0

dmax

md

KD

md

� �dD Z

dmax

md

x K1

2md

x2 (2c)

The loads are considered to maintain constant power

factor. Further details on the bid curves in spot price markets

are given in [6].

3. Optimal power flow (OPF) incorporating TCSCs

Modelling of FACTS devices for various purposes and

approaches and formulations of low flow analysis incorpor-

ating FACTS devices have been reported in recent literature

[18–20], while the issues in OPF in the context of pool

paradigm has been discussed by Gross and Bompard [21].

This section outlines the OPF methodology used in the

studies in Section 4.

3.1. TCSC model

During steady state TCSC can be considered as a

additional reactance—jxc. The value of xc can be adjusted

according to control schemes specified. The simple steady

static model of a transmission line with a TCSC connected

between bus-i and bus-j is shown in Fig. 1(a).

The change in the line flow due to series capacitance

can be represented as a line without series capacitance with

power injected at the receiving and sending ends of the line

as shown in Fig. 1(b). The real power injections at bus-i (Pic)

and bus-j (Pjc) can be expressed as [6].

Pic Z V2i DGij KViVjðDGijcos dij CDBijsin dijÞ (3a)

Pjc Z V2j DGij KViVjðDGij cos dij KDBij sin dijÞ (3b)

G.B. Shrestha, W. Feng / Electrical Power and Energy Systems 27 (2005) 428–436430

Similarly, the reactive power injections at bus-i (Qic) and

bus-j (Qjc) can be expressed as:

Qic ZKV2i DBij KViVjðDGij sin dij KDBij cos dijÞ (4a)

Qjc ZKV2j DBij CViVjðDGij sin dij CDBij cos dijÞ (4b)

where

DGij Zxcrijðxc K2xijÞ

ðr2ij Cx2

ijÞðr2ij C ðxij KxcÞ

2Þ;

DBij ZKxcðr

2ij Kx2

ij CxcxijÞ

ðr2ij Cx2

ijÞðr2ij C ðxij KxcÞ

2Þ

(5)

These steady Power Injection Model of TCSC is used to

properly modify the parameters of transmission lines with

TCSCs [7] for optimal power flow algorithms in the

following studies.

3.2. TCSC cost

The cost of a multi-module TCSC is represented in the

form of a linear equation as [8].

Cf ;k Z cxc;k

S2max

SB

(6)

where

c is the cost coefficient of TCSC ($/MVA-year); in this

study cZ22,000 $/MVA-year is adopted [9];

Smax is the thermal limits of line where kth FACTS

device is placed (MVA);

SB is the base power (MVA);

xc,k is the kth series capacitive reactance (pu).

The formulation allows the capital cost of TCSC to vary

with the TCSC capacity (MVA). The thermal limit included

in the formulation helps to satisfy the thermal limit of the

transmission line when a TCSC is added to that line.

3.3. Objective function

The objective function in the spot market is the

maximization of social benefits including the cost of

FACTS devices which can be expressed as:

MaxXi2D

BiðxiÞKXj2G

CjðxjÞKXk2Nc

Cf ;kðxc;kÞ (7)

where xc,k is the kth series compensation device and Nc is the

total number of series compensation devices in the system.

3.4. Operating constraints

All operating constraints of the transmission networks

are to be satisfied.

(i)
Power injection: the net injections of real and reactive
power at each bus should be zero.

Pi Z Vi

XN

jZ1

½Vj½gij cosðdi KdjÞCbij sinðdi KdjÞ��

KPGi CPCi Z 0

Qi Z Vi

XN

jZ1

½Vj½gij sinðdi KdjÞKbij cosðdi KdjÞ��

KQGi CQCi Z 0

(8)

(ii)
Generation limits: the limits on the maximum and
minimum outputs of the generators are incorporated as:

Pg; min %Pg%Pg; max Qg; min %Qg%Qg; max g2G (9)

(iii)
Demand limits: the limits on consumers’ maximum
and minimum demands are imposed as

Pc; min %Pc%Pc; max Qc; min %Qc %Qc; max c2C

QcZc

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 Kpf 2

c

ppfc

!Pc ð10Þ

(iv)
Transmission limits: the limit on the MVA flow on a
transmission line in incorporated as:

jSijj2 %S2

ij max (11)

(v)
Voltage limits: voltage limit at each bus is expressed as:
Vi; min %Vi%Vi; max; i2N (12)

(vi)
After including TCSC devices, the inequality con-
straints will include the limits of these devices, which

means the maximum and minimum values of equival-

ent reactance (xc) [10].

xci; min %xci%xci; max

i2Nc

)TCSC (13)

for all Nc number of TCSCs.

3.5. Solution technique

The Lagrange function of the optimisation problem

incorporating all the constraints in the objective function is

Table 1

OPF results without TCSC

Social benefit ($/h) Generation cost ($/h) Customer benefit ($/h)

1577.3 1417.0 2994.3


formed as:

Lð,ÞZXi2D

BiðxiÞKXj2G

CjðxjÞKXk2Nc

Cf ;kðxc;kÞ

KXi2G

miPG; minðPGi; min KPGiÞ

KXi2G

miPG; maxðPGi KPGi; maxÞ

KXi2G

miQG; minðQGi; min KQGiÞ

KXi2G

miQG; maxðQGi KQGi; maxÞ

KXi2D

miPC; minðPCi; min KPCiÞ

KXi2D

miPC; maxðPCi KPCi; maxÞ

KXi2D

miQC; minðQCi; min KQCiÞ

KXi2D

miQC; maxðQCi KQCi; maxÞKXi2N

lipðPiÞ

KXi2N

liQðQiÞKXi2C

lipf Qi K

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1Kpf 2

i

pf 2i

s!Pi

!

KXi2N

Xj2N

mij; maxðjSijjKSij; maxÞ

KXi2N

Xj2N

mji; maxðjSjijKSji; maxÞ

KXi2N

miv; minðVi; min KViÞKXi2N

miv; maxðVi; max KViÞ

KXi2Nc

mci; minðxci; min KxciÞKXi2Nc

mci; maxðxci; max KxciÞ

Table 2

System operation data without TCSC

Bus no. Voltage Generation

Mag. (pu) Ph. Ang. (deg) P (MW) Q (MVAr)

1 1.100 0.0 95.6 38.8

2 1.089 K2.282 100.0 50.0

3 1.100 K1.111 100.0 40.0

4 1.011 K6.639 – –

5 1.007 K6.681 – –

6 1.035 K9.301 53.0 12.4

7 1.051 K9.661 –

8 1.090 K9.661 0.0 24.0

9 1.037 K11.245 – –

10 1.018 K11.826 – –

11 1.002 K11.663 – –

12 0.993 K10.602 – –

13 1.008 K10.604 – –

14 0.976 K13.118 – –

Total 348.6 165.2

Sequential Quadratic Programming (SQP) method is

used for the solution of the OPF problem, which can provide

all the marginal prices directly. The detailed development of

the solution procedure along with its detailed implemen-

tation process in MATLAB environment is described in

[15].

4. Case studies

The modified IEEE 14-bus system [11] has been used to

investigate the effects of TCSC device on market operation

including the social benefit and the benefits of each market

participant. The system diagram is shown in Fig. 2. Bus 1, 2,

3, 6 are the buses where power suppliers G1, G2, G3, G4 are

located. Bus 4, 5, 9–14 are those buses where power

consumers D1–D8 are located. Further details on para-

meters are given in [12]. The generator cost functions and

the consumer benefit functions are given by Eqs. (2) and (5),

respectively. The coefficients of the cost function are

adopted from [13]. Based on the values in [14],

the coefficients of the benefit functions are shown in

Appendix A. The voltage magnitude limits and transmission

line ratings are also shown in Appendix A. In this study, the

load power factor is kept constant at 0.9 (lag).

4.1. System operation without TCSC

The base case of power system operation obtained from

OPF without any TCSC is listed in Tables 1–3. It can been

seen that congestions occurred in line 13, 14, 15, and 16

which implies that although some power consumers did bid

higher price in power markets they cannot access to the

cheaper power due to the transmission limits. This is caused

by the physical characteristics of transmission network.

Long-term congestion may lead to large amount of waste in

Load Spot Price

P (MW) Q (MVAr) P ($/MVAr h) Q ($/MW h)

– – 5.68 0.0

– – 5.80 0.28

– – 5.73 0.28

107.6 52.1 6.50 0.57

116.2 56.3 6.25 0.56

– – 4.95 0.0

– – 7.30 1.02

– – 7.30 0.95

5.0 2.4 7.74 1.28

20.8 10.1 8.54 1.72

20.7 10.5 8.67 1.41

26.0 12.6 9.97 2.27

5.0 2.4 11.29 2.26

29.4 14.2 9.90 2.16

331.7 160.6 – –

Table 4

OPF result with TCSC

Social benefit ($/h) Generation cost ($/h) Customer benefit ($/h)

1595.9 1432.1 3030.9

Table 3

Line flows limited by line ratings

Line (From) bus (To) bus Line rating

(MVA)

Line flow

(MVA)

13 9 10 25 25.0

14 6 11 25 25.0

15 6 12 25 25.0

16 6 13 25 25.0


social benefits. For pool operator such as ISO, it is necessary

to encourage competition and reduce the waste. FACTS

devices can detour the power through the congested

transmission line and hence enable cheaper power to be

transferred from generators to consumers.

4.2. Locations of TCSCs

Several studies have been reported which investigate the

optimal placement of FACTS devices for various network

purposes [22,23]. In this study, the location of TCSC is

taken as the best when it achieves the maximum total social

benefit. The maximum series capacitive compensation of

TCSC is limited to 70% reactance of the line reactance

where is placed. A trial-and-error method is used to

determine the best location. Since the congestion in the

network occurred on the upper part of the transmission

network, which is composed of two loops, it is reasonable

that TCSC mounted on one of transmission line between

these two loops should be effective. It is found that the best

Table 5

System operation data with TCSC

Bus no. Voltage Generation

Mag. (pu) Ph. Ang. (deg) P (MW) Q (MVAr)

1 1.100 0.0 95.9 39.8

2 1.085 K0.748 100.0 50.0

3 1.095 0.193 100.0 40.0

4 0.994 K6.425 – –

5 0.991 K6.329 – –

6 1.031 K8.245 55.7 12.5

7 1.034 K9.606 –

8 1.073 K9.606 0.0 24.0

9 1.020 K11.273 – –

10 1.000 K11.812 – –

11 1.000 K10.695 – –

12 0.989 K9.541 – –

13 1.004 K9.521 – –

14 0.983 K11.266 – –

Total 351.6 166.3

location for TCSC is on line 17 because it increases the

social benefit most. When multi-TCSC devices are to be

considered, similar heuristic method is adopted to determine

the locations. Line 17 and 13 are deemed the best locations

for two TCSCs and lines 17, 13, and 15 are the best positions

for three TCSCs.

4.3. System operation studies with TCSC

4.3.1. System-wide effects

Operation of the power market is studied with one TCSC

placed on line 17 at different levels of TCSC compensation.

The details of results at 70% compensation are shown in

Tables 4–6. Table 7 lists the value of important system

quantities at different levels of TCSC compensation placed

on the line 17.

It is seen that the social benefit increases gradually from

1577 to 1596 $/h with the increase in the level of

compensation from 0 to 70%. There are the net increases

in social benefit after accounting for the cost of the TCSC

devices, which also increases with the level of compen-

sation to $3/h at 70% compensation. It should be noted that

the increase in social benefit is the combined result of the

changes in the consumer benefit and the generation cost.

Consumer benefit is found to increase monotonously from

2994 $/h at 0% compensation to 3031 $/h at 70% compen-

sation, while the generation cost is reduced initially from

1417 $/h at 0% compensation to 1413 $/h at 20% compen-

sation and then gradually increases to 1432 $/h at 70%

compensation. Thus the introduction of TCSC makes the

production of some extra power feasible in the power

market, which is also indicated by: (i) the increase in the

generation output from 349 MW at 0% compensation to

352 MW at 70% compensation, and (ii) the increase in total

consumption from 332 MW at 0% to 335 MW at 70%

compensation.

Load Spot price

pu (MW) pu (MVAr) P ($/MVAr h) Q ($/MW h)

– – 5.70 0.0

– – 5.82 0.26

– – 5.75 0.27

107.7 52.2 6.50 0.57

116.2 56.0 6.27 0.54

– – 5.14 0.0

– – 7.61 1.02

– – 7.61 0.95

5.0 2.4 8.22 1.27

26.8 12.6 8.59 1.30

15.4 7.4 8.99 1.13

25.9 12.6 9.99 2.22

9.2 4.5 10.55 2.30

29.5 14.3 9.96 2.02

334.5 162.0 – –

Table 6

Line flows limited by line ratings


(MVA)

Line flow

(MVA)

13 4 9 25 25.0

14 6 11 25 25.0

15 6 12 25 25.0

16 6 13 25 25.0


It is apparent that the installation of TCSC produces

benefit that far exceeds its cost for the system conditions

studied. The net benefit may not be so significant during low

levels of load or generation. And studies over extended

periods would be necessary would be necessary if we need

to evaluate the feasibility of FACTS device installation.

Although, the effects of TCSC on different facets of the

market operation may be too complex for analytical

treatment, simulation studies like these can certainly be

helpful in evaluating the likely effects. This study can be

readily extended to evaluate the total benefits for extended

periods of time (a day, a week or longer) by incorporating

system operating data (hourly generation and demand bids)

for the entire period of investigation.

Table 7

Impact of TCSC with different limits on maximum compensation

Compensation of TCSC 0% 10%

Cost of TCSC ($/h) 0 0.4

Social benefit ($/h) 1577 1580

Consumer benefit ($/h) 2994 2996

Generation cost ($/h) 1417 1415

Total generation (MW) 349 348

Total consumption (MW) 332 331

Real power losses (MW) 16.9 17.0

Table 8

Generation output with different TCSC maximum compensation limits

Real power (MW) Compensation of TCSC

Gen Bus 0% 10% 2

G1 Bus 1 95.6 95.5 9

G2 Bus 2 100 100 1

G3 Bus 3 100 100 1

G4 Bus 6 53.0 52.7 5

Table 9

Consumer demands with different TCSC maximum compensation levels

Load demand

(MW)

Compensation of TCSC

0% 10% 20%

Bus 4 107.6 106.7 105.7

Bus 5 116.2 115.6 115.0

Bus 9 5 5 5

Bus 10 20.8 21.7 22.8

Bus 11 21.7 20.8 19.7

Bus 12 26.0 26.0 26.0

Bus 13 5.0 5.0 5.0

Bus 14 29.4 30.5 31.6

4.3.2. Impacts on individual suppliers and consumers

The changes in individual consumer’s demand and

supplier’s output at different level of TCSC compensation

are shown in Tables 8 and 9. Because generator 2 and 3

reached their maximum output limits, their outputs remain

constant unaffected by TCSC. Load demands at bus 9 and

13 are at their minimum limits by 20% compensation.

Demand at bus 13 is increased at higher level of TCSC

compensation while the demand at bus 9 remains at its

minimum value throughout.

In this study, a consumer’s welfare is the amount of benefit

the consumer received from using the power, minus the

expense incurred in purchasing the power. Similarly, a

supplier’s welfare is the amount of revenue received from

selling the power, minus the cost of supplying the power. The

individual welfare of each market participant at different

level of TCSC compensation may be computed and are listed

in Tables 10 and 11. Except those buses where generation or

consumption have reached the limits, the change in welfare

of market participants have the same trend as the changes in

generation and demand shown in Tables 8 and 9.

Although, the generation at bus 2 and 3 hit their

maximum limits (100 MW), their individual welfare keeps

20% 40% 60% 70%

0.9 1.7 2.6 3.0

1584 1590 1594 1596

2997 3012 3025 3031

1413 1421 1429 1432

348 350 351 352

331 332 334 335

17.1 17.2 17.1 17.1

0% 40% 60% 70%

5.5 95.4 95.8 95.9

00 100 100 100

00 100 100 100

2.3 54.1 55.2 55.7

40% 60% 70%

106.4 107.3 107.8

115.1 115.4 115.6

5 5 5

24.8 25.6 26.1

17.1 16.0 15.4

25.9 25.9 25.9

5.7 8.1 9.2

32.4 30.5 29.5

Table 11

Consumer welfare ($/h) with different TCSC compensation levels

Bus No Compensation of TCSC

0% 10% 20% 40% 60% 70%

Bus 4 203.5 201.7 199.9 202.6 202.9 203.2

Bus 5 233.8 233.0 232.2 232.4 231.1 230.6

Bus 9 K14.0 K14.3 K14.6 K16.3 K16.3 K16.3

Bus 10 23.8 25.2 26.8 26.6 26.5 26.6

Bus 11 21.9 20.8 19.4 14.7 12.8 12.0

Bus 12 40.7 41.0 41.2 40.3 40.1 39.9

Bus 13 3.1 3.7 4.4 7.1 10.2 11.8

Bus 14 46.3 49.1 52.1 51.2 46.7 44.5

Table 10

Generator welfare ($/h) with different TCSC compensation levels

Bus no. Compensation of TCSC

0% 10% 20% 40% 60% 70%

Bus 1 223.8 223.5 223.3 222.9 224.6 225.3

Bus 2 128.9 129.1 129.3 128.3 130.1 130.8

Bus 3 84.3 84.4 84.6 83.6 85.6 86.4

Bus 6 104.6 103.1 101.6 108.8 113.2 115.2


changing at different TCSC compensation levels. This is

due to the change in spot prices incurred. The negative value

for the consumer welfare at bus 9 is due to the minimum

load demand limit. If this constraint is removed by setting

this minimum limits to zero, the study results show that the

load demand at bus 9 reduces to zero.

Thus, it is seen that the benefits to individual supplier and

consumer are not uniformly distributed and some participants

may actually face reduction in their welfare/profit. Although

TCSC will always provide overall benefit to the system as a

whole, some market participants benefit more and others

benefit less. It is reasonable that those who benefit more should

bear the cost of FACTS devices in proportion to their benefit.

This concept is being considered for further investigation.

4.3.3. Effects on spot prices

The spot prices at generator buses and load buses with the

levels of TCSC compensation are shown in Figs. 3 and 4,

2

3

2

45

6 78

91011

12 13 14

G3

G2

G4

G5

G1

13

45 6

7

89

10 11

12

1318

14

15 16

1719 20

D1 D2 D3

1

Fig. 2. Modified IEEE 14-bus system diagram.

respectively. The general effect of TCSC on spot prices that it

reduces the higher spot prices and increases the lower spot

prices towards the mean value becomes apparent from these

figures. The highest spot price at bus 13 is reduced most thus

reducing the load demand at this bus. Similarly, the lowest

spot price at bus 6 is raised most thus increasing the generator

output at bus 6.

It may be worth noticing that before 20% compensation

of TCSC, the power transfer is redistributed throughout the

transmission network so as to make loads at bus 10 and 14

increase. That contributes to the increase of social benefit

although the total generation and the consumption decrease

and the total real power losses increase. After 20%

compensation level, the transmission line 17 (between

bus 9 and bus 14) and transmission line 11 (between bus 4

and bus 9) reach their maximum transfer limits and line 13

became un-congested. It drives the spot price at bus 9 and 14

0 10 20 30 40 50 60 70 804.8

5.0

5.2

5.4

5.6

5.8

bus1bus2bus3bus6

Rea

l Pow

er S

pot P

rice

(U

S$/W

M-h

r)

TCSC Compensation level

Fig. 3. Spot prices at generator buses at different level of TCSC

compensation.

0 10 20 30 40 50 60 70 806

7

8

9

10

11

bus4 bus5 bus9 bus10 bus11 bus12 bus13 bus14

Rea

l Pow

er S

pot P

rice

(U

S$/M

W-h

r)

TCSC Compensation level

Fig. 4. Spot prices at load buses at different level of TCSC compensation.


higher and spot price at bus 10 lower, compared to those

cases at other compensation levels of TCSC. Thus, it is not

easy to establish precise relationships between the spot

prices and the levels of compensation. Simulation studies

like this would be necessary to view such impacts.

5. Conclusions

Simulation studies on the effects of TCSC on the

operation of spot price power market have been presented

in this paper using a modified IEEE 14-bus system.

A suitable formulation of TCSC cost is established and

Table A-1

Generator data

Gen.No. Bus no. P (MW) Q (MVar)

Max. Min. Max.

1 1 100 20 40

2 2 500 100 50

3 3 500 100 40

4 6 100 20 24

5 8 – – 24

Generation costZC2P2G CC1PG CC0. Note: generator 5 at bus 8 supplies reactiv

Table A-2

Demand data

Demand no. Bus no. pf (lag) P (MW) Q

Max. Min. M

1 4 0.9 200 50 20

2 5 0.9 200 50 20

3 9 0.9 100 5 20

4 10 0.9 100 5 20

5 11 0.9 100 5 20

6 12 0.9 100 5 20

7 13 0.9 100 5 20

8 14 0.9 100 5 20

Consumer benefitZC2P2D CC1PD CC0

included in the objective function. Heuristic method has

been used to determine the locations of TCSC devices with

the objective to maximize the social benefit. It is seen that

with its ability to redistribute power flow in the network,

TCSC can influence the loads and generation at different

buses to achieve significant increase in the social benefit.

Inclusion of TCSC makes the spot price at generator

buses and load buses move towards the average value. In

this way, the impact of TCSC is to enhance total benefit and

reduce the waste of social benefit.

TCSC may affect the welfare gained by individual

participant in different way. Because the use of TCSC

influences the spot price at different buses differently, some

participants benefit more and some benefit less.

Though, the use of TCSC in a market can make it more

efficient, it is not easy to establish direct relationships

between the amount of compensation and various market

quantities. However, simulation can be used to assess the

impacts of TCSC on the desired quantities. The increase in

benefits from using TCSC may not be very high at low

levels of demand and generation. Simulation studies over

extended periods of time would be necessary to evaluate the

overall benefit over long periods of time to evaluate the

actual feasibility of TCSC in an actual system.

Appendix A

Modified IEEE 14-bus System Data. Tables A-1–A-4.

Cost coefficients

Min. C2 C1 C0

K40 0.0245 1 0

K40 0.0351 1 0

K40 0.0389 1 0

K6 0.0372 1 0

K6 – – –

e power only.

(MVar) Cost coefficients

ax. Min. C2 C1 C0

0 K200 K0.015 10 0

0 K200 K0.015 10 0

0 K200 K0.010 5 0

0 K200 K0.015 10 0

0 K200 K0.015 10 0

0 K200 K0.018 12 0

0 K200 K0.018 12 0

0 K200 K0.018 12 0

Table A-4

Modified IEEE 14-bus system line rating


(MVA)

1 1 2 292.41

2 2 3 292.41

3 2 4 292.41

4 1 5 292.41

5 2 5 292.41

6 3 4 292.41

7 4 5 292.41

8 5 6 42.25

9 4 7 42.25

10 7 8 25.0

11 4 9 16.0

12 7 9 42.25

13 9 10 25.0

14 6 11 25.0

15 6 12 25.0

16 6 13 25.0

17 9 14 25.0

18 10 11 25.0

19 12 13 25.0

20 13 14 25.0

Table A-3

Bus data

Bus no. Max. voltage

magnitude (pu)

Min. voltage

magnitude (pu)

1–14 1.1 0.97


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G.B. Shrestha (IEEE S-88, M-90, SM-92) received B.E. (Honours) degree

in Electrical Engineering from Jadavpur University (India) in 1975, MBA

from University of Hawaii in 1985, MS in Electrical Power Engineering

from RPI in 1986, and PhD in Electrical Engineering from Virginia Tech in

1990. Presently he is an Assoc. Prof. at Nanyang Technological University,

Singapore. His main area of interest is power system operation and

planning.

Wang Feng (IEEE S-99) obtained his B.E. from Hohai University,

Nanjing, China in 1994. After working for several years as a development

engineer for EMS (Energy Management System) and DTS (Dispatch

Training Simulator) in Nanjing Automation Research Institute (NARI), he

is pursuing his postgraduate degree at Nanyang Technological University,

Singapore.

Effects of series compensation on spot price power markets

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