2005 IEEE St. Petersburg PowerTechSt. Petersburg, Russia, June 27-30, 2005

Abstract — This paper describes the development of a control

system and control strategies capable of governing multiple flexible AC transmission system (FACTS) devices in coordination with load shedding. The main purpose of the presented coordinated control system is to remove overloads caused by lines’ outages in transmission network. The proposed control system is based on linearized expressions in steady state. Therefore they do not require intensive computations. A simulation model of the control system is suitable for real time implementation. It constantly monitors power flows and generates appropriate control signals to each load and FACTS device in order to maintain acceptable power flow levels. It has been interfaced with load flow software to test its effectiveness through non-linear simulations using the 14 bus IEEE test power system as the study case. The results obtained are presented.

Index Terms — Load shedding, FACTS devices, coordinated power flow control, sensitivity analysis.

I. INTRODUCTION t present there is no doubt about economical justification of parallel operation of power plants as component parts of electric power systems and parallel operation of

power systems as component parts of power interconnections. However, the growing size of power systems and the electric industry deregulation complicate their control. At the same time the risk of occurrence and avalanche-like development of emergencies also increases. That is why emergency control plays a more and more important part in prevention of emergencies, termination of their cascade development and restoration of normal operation of EPS. Taking into account the high speed of emergency processes, such a control must be largely automatic. There are several forms of emergency control actions for enhancement of steady-state, voltage and transient stability [1]–[4]: • Generator tripping;

The study was supported by the Grant of Russian Leading Scientific School #2234.2003.8.

P. V. Etingov is with Energy Systems Institute, 130, Lermontov str, 664033 Irkutsk, Russia (e-mail: etingov@isem.sei.irk.ru). The presented work was performed during an invited stay at Ecole Polytechnique Fédérale de Lausanne (EPFL).

A. Oudalov is with ABB Switzerland Ltd., 1, Segelhof, 5400 Baden-Dättwil, Switzerland (e-mail: alexandre.oudalov@ch.abb.com)

N. I. Voropai is with Energy Systems Institute, 130, Lermontov str, 664033 Irkutsk, Russia (e-mail: voropai@isem.sei.irk.ru).

A.J. Germond and R. Cherkaoui are with EPFL, 1015 Lausanne, Switzerland (e-mail: alain.germond@epfl.ch).

• Load shedding; • Steam turbine fast-valving/generation runback; • Reactor/capacitor switching; • HVDC link rapid power ramping; • Transient excitation boosting; • Dynamic braking; • System separation.

Some of the emergency control methods, such as tripping of thermal units, are “heroic” in nature and may impose significant stress on equipment [2].

Recently, new ability in power system control appeared with the advent of flexible ac transmission systems (FACTS) technology. FACTS technology allows practically complete utilization of the capacity of transmission elements up to their limits and provides the different kinds of devices, which are making it possible to redirect power in real-time and provide virtually instantaneous responses to transmission system disturbances [5]. There are plenty of publications considering application of FACTS devices to power system including application of FACTS devices as emergency control means [5]–[7]. However, the problem of coordination and combined application of conventional emergency control actions and FACTS devices has not been fully investigated. There are just several publications which attempt to study this problem [8], [9].

In the paper we propose some new view to the problem of coordination of load shedding as conventional emergency control action and FACTS devices. We considered application of two types of FACTS devices: Thyristor Controlled Series Capacitor (TCSC) [6] and Thyristor Controlled Phase Shifting Transformer (TCPST) [7]. The basic schemes of the TCSC and TCPST are presented in Figs. 1–2.

Fig. 1. The basic scheme of the TCSC.

Coordinated emergency control of load shedding and FACTS devices

Pavel Etingov, Member, IEEE, Alexandre Oudalov, Nikolai Voropai, Senior Member, IEEE, Alain Germond, Member, IEEE, and Rachid Cherkaoui

A

Fig. 2. The basic scheme of the TCPST.

II. METHODOLOGY

A. The concept of sensitivity analysis The methodology based on the sensitivity analysis [10] was

extended to find out an intercoupling between variations of setpoints of different FACTS devices and volume of load shedding with variation of active power flow in transmission network. A simple but sufficiently accurate relationship could be derived for computation the control actions (volume of load shedding and setpoints of FACTS devices) in order to meet the required power flows in postemergency state.

The control variables are the volumes of load shedding and the setpoints of FACTS devices. The controlled quantities are the active power flows in transmission lines. If we look at any pair FACTS–line or Load–line in a power system, a direct control effect of control action on power flows can be expressed as following:

( )FACTSline SettingfP = and ( )loadline PfP ∆= where SettingFACTS is a direct control variable of any FACTS device (e.g. line reactance, phase shift angle, etc.) and loadP∆ is volume of load shedding. Below we consider the application of sensitivity analyses by the example of FACTS devices.

For any pair FACTS-line the above mentioned non-linear relationships can be decomposed in two parts. The first part is the linear coefficient of influence kinf and the second part is the non-linear regulation characteristic of FACTS device [11].

It means that at first, we initialize the level of violation of controlled quantity (power flow) and find the required change of the indirect control variable of FACTS (the power flow through FACTS device) to remove that violation. Then, for a known level of power flow through FACTS device we find out the value of direct control variable (line reactance for TCSC and phase shift angle for TCPST), which is required to provide those indirect control variables.

B. Coefficients of influence of FACTS For each FACTS device multiple load flow were computed

with different values of direct control variables. The coefficients were estimated of influence by a relationship between the variation of active power flow in the controlled transmission line j – jlineP∆ and the variation of active power

flow through the FACTS device i – iFACTSP∆ [11].

inew

FACTSiFACTS

jnew

linejline

iFACTS

jlinejFACTS PP

PPPP

ki −

−=

∆

∆= 0

0

, (1)

where jlineP0 is the value of active power flow in the

controlled line j before changing the setpoint of FACTS i,

jnew

lineP is the value of active power flow in the same line after

changing the setpoint of FACTS i, iFACTSP0 is the value of active power flow in the line with FACTS i before changing its setpoint, and i

newFACTSP is the value of active power flow in

the line with FACTS i after changing its setpoint. Hereafter in the section simulation results, we will describe

details of acquisition of different types of coefficients of influence for power flows. We utilize the IEEE 14 bus test power system for a calculation of different coefficients of influence. In Figs 3–4 the examples of relationships

)( iTSPSTj

TCPST fki

α= and )( iTCSCj

TCSC xfki

∆= are presented.

As may be seen from the figures, these relationships are linear and do not depend on the value of setpoints of FACTS. Therefore we could make an assumption that the value of kinf is practically constant for a given network topology.

Fig.3. The relationships )( iTSPST

jTCPST fk

iα= for lines 1-2, 1-5, 2-5, 2-3, 2-4,

3-4, 4-5. The TCPST is in the line 2-5.

Fig.4. The relationships )( iTCSC

jTCSC xfk

i∆= for lines 1-2, 1-5, 2-5, 2-3, 2-4,

3-4, 4-5. The TCSC is in the line 2-5.

C. Regulation characteristics of FACTS Regulation characteristic numerically links together the

effect of FACTS control variable on the controlled parameters (power flows) in the transmission lines where the FACTS is located. Thus, regulation characteristics help to transform a required amount of power flow in the FACTS device, for a modification of power flow in the controlled line, into the real setpoint of FACTS device such as a reactance or a phase shift angle of FACTS devices [11].

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

-1 -0.8 -0.6 -0.4 -0.2 0

∆xTCSC2-5·100, %

KTC

SC 2

-5 1_5

2_32_42_53_44_51_2

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

-30 -20 -10 0 10 20 3

αTCPST 2-5, grad

KTC

PST

2-5

1_52_32_42_53_44_51_2

1) TCSC The regulation characteristic of the TCSC for active power

flow represents the effect of the variation of control variable of the TCSC ∆xTCSC on the active power in the line with that TCSC ∆PTCSC. Fig. 5 shows the regulation characteristics of the TCSC for different power system operation conditions. The best approximation of this characteristic is provided by a quadratic function [6], but as we can see from these figures that in most analyzed cases the quadratic term was relatively small. Therefore, it is possible to linearize the regulation characteristic of the TCSC. Fig. 6 presents the regulation characteristic of the TCSC 2-5 for different operation conditions. The gradient of regulation characteristic of TCSC depends on operation conditions of power system (Fig. 6) and it could be calculated as:

iTCSC

iTCSCiTCSC x

P∆∆

=β (2)

However, there is a linear relationship between the gradient of regulation characteristic and the initial active power flow in the TCSC 0

iTCSCP (fig.7).

Therefore we can formulate the following relationship:

0

1

iTCSCPP

x iTCSC

iTCSCi

∆=∆

γ, (3)

where 0iTCSC

PiTCSC

iTCSCβ

γ =

Fig.5. Regulation characteristic of the TCSC 2-5 for active power flow: a) base mode; b) heavy mode (Kload=2).

Fig.6. Regulation characteristic of the TCSC 2-5 for different operation conditions.

Fig.7. Relation between the gradient of regulation characteristic and initial active power flow in the TCSC 2-5. 2) TCPST

The regulation characteristic of the TCPST for active power flow is a relationship between the variation of active power flow in that TCPST ∆PTCPST and the variation of its control variable ∆αTCPST. In Fig.8 the regulation characteristics of the TCPST are shown. The gradient of regulation characteristic of TCPST for active power flow unlike TCSC does not depend on operation conditions of power system and it could be calculated as:

iTCPST

iTCPSTiTCPST

Pα

β∆∆

= (4)

Fig.8. Regulation characteristic of the TCPST for active power flow: (a) TCPST 2-5 (b) TCPST 3-4.

D. Coefficients of influence of load By analogy with coefficients of influence of the FACTS

devices we can formulate the following equation for coefficients of influence of the load i on the line j:

inew

loadiload

jnew

linejline

iload

jlinejload PP

PPPP

ki −

−=

∆

∆= 0

0

, (5)

where jlineP0 is initial value of active power flow in the

controlled line j ; jnew

lineP is value of active power flow in the

controlled line j after load i shedding (changing); iloadP0 is

-150 -100 -50

0 50

100 150

-40 -20 0 20 40

αTCPST 3-4, grad

∆P T

CPS

T 3-

4, M

W

(b)

-200

-150

-100

-50

0

50

100

150

200

250

-40 -20 0 20 40

αTCPST 2-5, grad

∆P T

CPS

T 2-

5, M

W

-70

-60

-50

-40

-30

-20

-10

0

0 10 20 30 40 50 60 70 80

PTCSC, MW

β

γ

-5

0

5

10

15

20

25

30

-0.5 -0.4 -0.3 -0.2 -0.1 0 ∆x·100, %

base1.520,7∆

P TC

SC 2

-5, M

W

-0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0-10

0

10

20

30

40

50

60

70

∆P T

CSC

2-5, M

W

∆x·100, %

Quadratic approximation ∆PTCSC=28,9 ∆x2 -45,9∆x-0,1

Linear approximation ∆PTCSC=-69,9∆x-2,6

(b)

-0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0-5

0

5

10

15

20

25

30

∆x·100, %

∆P T

CSC

2-5, M

W

Linear approximation ∆PTCSC=-33,3∆x-1.02

Quadratic approximation ∆PTCSC=10 ∆x2 -24,9∆x-0,1

(a)

(a)

initial value of active power of the load i; inew

loadP is value of active power of the load i after its changing. Fig. 9 shows the relationships between the coefficients of influence of load on power flow in the main lines in test power system ( j

loadik ) and the changes of load 3 and 4

( iloadP∆ ).

Fig.9. The relationships )( iload

jload Pfk

i∆= to the lines 1-2, 1-5, 2-5, 2-3,

2-4, 3-4, 4-5.

E. Emergency Control strategy. 1) Control strategy to the TCPST

In case of overload of the line j ( max

0linejlinejline PPP −=∆ ), the control action for the

TCPST device i can be calculated as:

ij

TCPST

jlinejline

ij

TCPST

jlineiTCPST

iik

PP

kP

ββα

⋅

−=

⋅

∆=∆ max

0

(6)

This equation does not observe the appearance of congestions in other transmission lines after the control action. Therefore we wrote the following system of inequalities on the basis of (6):

iTCPSTij

TCPSTjlinejline ikPP αβ ∆⋅⋅≤− max

0 , Mj K1= (7)

where M is a number of controlled lines, jlineP max is the

maximal admissible value of active power flow in the controlled line j.

Using the principle of superposition of control actions of several controllers we can deduce an equation (7) for a more general case with several TCPST devices:

∑=

∆⋅⋅≤−TCPST

i

N

iiTCPSTi

jTCPSTjlinejline kPP

1max

0 αβ , (8)

Mj K1= Moreover, there are following regulation constraints:

maxmin iTCPSTiTCPSTiTCPSTiTCPST αααα ≤∆+≤ , (9)

TCPSTNi K1=

where NTCPST is a number of TCPST devices, miniTCPSTα and

maxiTCPSTα are the minimal and maximal values of phase shift

angle of ith TCPST. 2) Control strategy for the TCSC

We can formulate the system of inequalities for TCSC devices by analogy with the (8) and (9) for TCPST devices:

∑=

∆⋅⋅⋅≤−TCSC

i

N

iiTCSCiTCSCi

jTCSCjlinejline xPkPP

1

0max

0 γ , (10)

Mj K1=

maxmin iTCSCiTCSCiTCSCiTCSC xxxx ≤∆+≤ , (11)

TCSCNi K1=

where NTCSC is a number of TCSC devices, miniTCSCx and

maxiTCSCx are the maximal and minimal values of reactance

compensation of ith TCPST. 3) Control strategy for the load shedding.

If we have overload jlineP∆ on the line j, the volume of

load i that must be shed can be calculated as:

jload

jlinej

load

jlinejlineiload

iikP

k

PPP

∆=

−=∆ max

0

(12)

A minimization of the total outage cost caused by the Load Shedding is chosen as objective function:

( ) i

N

iiloadiloadP

CostPPCostload

iLoad

⋅∆=∆ ∑=

Σ∆ 1min , (13)

where iCost is the outage cost of the load i, $/MW, Nload is a number of the loads available to shed.

The optimizing variables iloadP∆ are subjected to the following inequalities constraints:

01

max0 ≤∆⋅−− ∑

=

load

i

N

iiload

jloadjlinejline PkPP , Mj K1= (14)

iloadiload PP max∆≤∆ , loadNi K1= (15)

where M is a number of controlled lines; iloadP max∆ is the maximal volume of the load i shedding. 4) Coordinated control strategy for the load shedding and FACTS devises.

Finally we can formulate the optimization problem to finding coordinated control actions on the basis of equations (8–15).

( ) i

N

iiloadiloadP

CostPPCostload

iLoad

⋅∆=∆ ∑=

Σ∆ 1min

subject to

ΣΣΣ∆+∆+∆≤− jjj

ngloadsheddijlinejline TCSCTCPSTPPPPP max

0 , (16)

Mj K1= where

∑=

Σ∆⋅=∆

load

l

N

llload

jloadngloadsheddi PkP

1

∑=

Σ ∆⋅⋅=∆TCPST

m

N

mmTCPSTm

jTCPSTTCPST kP

1

αβ

-0.6 -0.4 -0.2

0 0.2 0.4 0.6 0.8

-150 -100 -50 0 50 100 150 200 ∆Pload3, MW

Klo

ad

1_52_32_42_53_44_51_2

∑=

Σ ∆⋅⋅⋅=∆TCSC

n

N

nnTCPSTnTCSCn

jTCSCTCSC xPkP

1

0γ

subject to following engineering constraints:

lloadlload PP max∆≤∆

maxmin mTCPSTmTCPSTmTCPSTmTCPST αααα ≤∆+≤

maxmin nTCSCnTCSCnTCSCnTCSC xxxx ≤∆+≤

loadNl K1= , TCPSTNm K1= , TCSCNn K1= Obviously that control actions of FACTS devices do not

cost anything. Therefore, the algorithm first tries to remove the overloads by coordinated actions of FACTS devices. In case of insufficiency of FACTS devices the algorithm uses in addition the load shedding. The proposed technique allows finding the optimal volume of load shedding (with minimal total outage cost) taking into account the effect of FACTS devices. 5) Emergency control structure

Fig. 10 shows the proposed emergency control structure. It consists of the following main blocks: the measuring system, the knowledge base, the inference block and the power flow calculation block.

The knowledge base contains the information about coefficients of influence of loads and FACTS devices for all dangerous outages in power system, parameters of regulation characteristic of FACTS devices, cost of outage of loads (consumers), engineering constraints, lines thermal and stability limits. The values of coefficients of influence and parameters of regulation characteristic remain practically constant for different generation-load profiles of the power system consequently preliminary trained knowledge base is able to give an adequate information. However if the

measuring system provides the data of current operating condition of power system it makes sense to correct (update) the knowledge base on-line.

Information about disturbance comes to the inference block. Then the inference block calculates the emergency control actions by using (13), (16) and (17) based on the measurements of pre-fault conditions and the information provided by knowledge base. Moreover it is possible to make a verification of control action in the power flow calculation block in other words it checks the possibility of existence of post-emergency state obtained after application of control action. Finally coordinated optimal control action transfers to the loads and FACTS devices.

III. TEST RESULTS

A. Description of the test power system The Matpower package for Matlab™ has been used for

power flow solving [12]. A special procedure was created to calculate the values of coefficients of influence and parameters of regulation characteristics. Also, a calculation program for the coordinated emergency control actions was developed on the basis of proposed technique by using Matlab Optimization Toolbox.

The studies were carried out on the IEEE 14 bus test power system (Fig. 11).

It contains two distinct areas: the first one with a lack of production is in vicinity of the buses 3, 4, 5 and the second one with a surplus production is in vicinity of the buses 1 and 2.

The transmission lines, which connect these areas, are intensively loaded in the maximum load period. Therefore tripping even the one of these lines is a strong disturbance, which can result in a large overload in the network and even leads to the loss of the power system stability.

We considered different power system operation conditions in this study. Parameters of some of them are presented in Table I. We supposed that FACTS devices (TCPST or TCSC) are installed in the lines 2–5 and 3–4 and the loads number 3, 4, 9, 13 and 14 are available for shedding.

1 1.06 pu

2 1.04 pu

3 1.01 pu

232 MW 0 MVR

73.2 MW

70.8 MW

4 1.02 pu

56.2 MW 54.5 MW

23.4 MW

23.7 MW

0 MW 23 MVR

94 MW 19 MVR

40 MW 42 MVR

22 MW 13 MVR

5 1.02 pu

41.5 MW

40.6 MW

61.2 MW

61.7 MW 48 MW -4 MVR

7 1.06 pu

28.1 MW

28.1 MW

8

1.08 pu

0.0 MW 0.0 MW

0 MW 18 MVR

9 1.06 pu

28.1 MW 28.1 MW

16.1 MW

16.1 MW

29 MW 17 MVR

6 1.07 pu

44.1 MW

44.1 MW 8 MW 2 MVR

0 MW

13 MVR

75.5 MW

72.8 MW

12 1.06 pu

7.8 MW

7.7 MW

13 1.05 pu

1.6 MW

1.6 MW 6 MW 2 MVR

17.7 MW

17.5 MW

11 1.06 pu

7.4 MW

7.3 MW

11 MW 8 MVR

4 MW 2 MVR

10 1.05 pu

5.2 MW 5.2 MW

9 MW 6 MVR 3.8 MW

3.8 MW

14 1.04 pu

5.7 MW 5.6 MW

15 MW

5 MVR

9.4 MW

9.3 MW

14 MW

6 MVR

76.3 MW

78.4 MW

(17)

Fig. 11. IEEE 14 bus test power system.

POWER FLOW

CALCULATION BLOCK

Measurements

Current operating conditions

Pline, Pload, Pgen

Correction and

updating

Disturbance

TRANSIENT STABILITY BLOCK

Control action

Load shedding

Generator tripping

FACTS control

KNOWLEDGE BASE

System configuration

kinf 1

kinf N …

FAC

TSs

kinf 1

kinf N …

Load

s

kinf 1

kinf N …

Gen

erat

ors

kinf 1

kinf N …

FAC

TSs

kinf 1

kinf N …

Load

s

kinf 1

kinf N …

Gen

erat

ors

kinf 1

kinf 1 …

FAC

TSs

kinf 1

kinf N …

Load

s

kinf 1

kinf N …

Gen

erat

ors

Pmax 1

Pmax N …

Ther

mal

Pmax 1

Pmax N …

Stab

ility

Line’s limits Coefficients of

Load shedding

Generator tripping cost

INFERENCE BLOCK

∆α 1

∆x N …

FAC

TSs

∆Pload 1

∆Pload N …

Load

s

∆Pgen 1

∆Pgen N …

Gen

erat

ors

Line 1

Line N …

Emer

genc

y ou

tage

of e

lem

ent

Trans

Trans …

Gen 1

Gen N …

Control action

verification

Control action verification

Fig. 10. Emergency control structure.

At the beginning we have calculated the coefficients of influence of loads and FACTS devices on the transmission network and parameters of regulation characteristics of FACTS devices. Tables II–IV show the values of coefficients of influence and gradient of regulation characteristic of TCPST 2–5 and TCSC 2–5 on the lines 1–5 and 2–3 depending on the operation conditions of power system. One can see that the values of coefficients of influence are practically independent of operation conditions and constant. The values of coefficients of influence for TCPST deviate from average value in case of high phase shifter angle αTCPST (±15 degree and more). However normally TCPST devices operate in the range of αTCPST =±5…7 degree because of operating constrains (operating under high angles results in overloading the line with installed TCPST). Therefore it is possible to use constant coefficients of influence of FACTS in most cases. Though obviously that if there are available measurements we can update all parameters on-line. Table V shows the calculated average values of coefficients of influence to the transmission network.

Then, the list of main disturbances (line outages) was formed on the basis of the analysis of test power system. In the same way as for normal power system operation conditions the coefficients of influence of loads and FACTS devices and the gradients of regulation characteristics of FACTS devices were calculated for each emergency situation. Table VI presents the values of kinf and β of TCPST 2–5 for different line outages.

After we have found all required numerical data a number of different simulations were carried out to evaluate the proposed emergency control algorithm. Coordinated control actions for different line outages in different power system operation conditions were calculated and analyzed.

These studies have shown the proper operation of the proposed technique. Let us present an example of emergency control algorithm’s operation in detail.

B. Example of emergency control algorithm’s operation (outage of the line 4–5, operation conditions – Mode 3(Table I))

In the case of the emergency outage of line 4–5 we have two heavy overloaded lines 2–4 and 2–3 (Fig. 12). In Table

VII the values of coefficients of influence for this emergency are presented. Several possible scenarios are considered. 1. There are no FACTS devices, only load shedding is

available. 1.1. All loads have the same cost of shedding, i.e.

Cost3=Cost4=Cost9=Cost13=1 $/MW; We used the symbol “$” as a symbol of some conventional units.

1.2. Cost3=2 $/MW; Cost4=Cost9=Cost13=1 $/MW. 1.3. Cost3=3 $/MW; Cost4=Cost9=Cost13=1 $/MW. 1.4. Cost3=6 $/MW; Cost4=Cost9=Cost13=1 $/MW. 1.5. Cost3=1 $/MW; Cost4=2 $/MW; Cost9=Cost13=1

$/MW. 1.6. Cost3=1 $/MW; Cost4=2 $/MW; Cost9=2 $/MW;

Cost13=1 $/MW. 2. TCPST device are installed in the line 2–5.

Cost3=Cost4=Cost9=Cost13=1 $/MW. 3. TCSC device are installed in the line 2–5.

Cost3=Cost4=Cost9=Cost13=1 $/MW. 4. TCPST devices are installed in the lines 2–5 and 3–4.

Cost3=Cost4=Cost9=Cost13=1 $/MW. The following volumes of maximum load shedding were

specified: ∆Ploadmax3=100 MW, ∆Ploadmax4=50 MW, ∆Ploadmax9=40 MW, ∆Ploadmax13=20 MW. And FACTS devices have the following working range: –15°<αTCPST2–5<+15°; –15°<αTCPST3–4<+15°; 0 %<∆xTCSC2–5<40 %

The calculated optimal solutions for considered scenarios are shown in the Table VIII. At the beginning take a look at the first scenario when FACTS devices are not installed.

In the case 1.1 the following optimal solution was obtained: in order to unload lines 2–4, 2–3 it is necessary to shed the loads number 3 and 4 (∆Pload3 = 37.7 MW, ∆Pload4 = 38.9 MW). Cost of load shedding is 76.5 $ and the total amount is 76.5 MW. This solution corresponds to a solution with minimum total amount of load shedding.

In the case 1.2 we have the same solution as in the previous case. It could be explained that the load 3 has high influence on overloading lines and this solution is economically feasible regardless of the fact that the cost of load 3 shedding is two time more expensive.

In the case 1.3 the optimal solution is ∆Pload3 = 18 MW, ∆Pload4 = 50 MW; ∆Pload9 = 40 MW. Total cost of load shedding is 144 $ and the total amount is 108 MW. As may be seen, the total amount of load shedding is much higher than in the first case. This effect has the following explanation: the shedding of the load 3 (the load with higher influence on

TABLE I PARAMETERS OF CONSIDERED POWER SYSTEM OPERATION CONDITIONS

Mode 1 (base) Mode 2 (kload=0,7)

Mode 3 (kload=1,5)

Mode 4 (kload=2,0) Element

P Q P Q P Q P Q Generator

1 2 3 6 8

Load 2 3 4 5 6 9

10 11 12 13 14

232.53 40.00 0.00 0.00 0.00

21.70 94.20 47.80 7.60 11.20 29.50 9.00 3.50 6.10 13.50 14.90

-22.03 32.54 20.15 50.00 28.2

12.70 19.00 3.90 1.80 7.50 16.60 5.80 1.80 1.60 5.80 5.60

148.00 40.00 0.00 0.00 0.00

15.19 65.94 33.46 5.32 7.84

20.65 6.30 2.45 4.27 9.45

10.43

-5.90 8.05 -0.77 39.3616.48

8.89 13.302.73 1.26 5.25 11.624.06 1.26 1.12 4.06 3.92

211.52 200.00

0.00 0.00 0.00

32.55

141.30 71.70 11.40 16.80 44.25 13.50 5.25 9.15

20.25 22.35

-4.77 30.70 60.00 50.00 60.00

19.05 28.50 5.85 2.70

11.25 24.90 8.70 2.70 2.40 8.70 8.40

234.12200.0060.00 0.00 50.00

43.40

188.4095.60 15.20 22.40 59.00 18.00 7.00 12.20 27.00 29.80

-7.48 45.73 68.88

104.64 40.00

25.40 38.00 7.80 3.60 15.00 33.20 11.60 3.60 3.20 11.60 11.20

1 1.06 pu

2 1.04 pu

3 1.01 pu

217 MW -18 Mvar

139.1 MW

130.8 MW

4 0.99 pu

136.0 MW

126.2 MW

10.5 MW

10.8 MW

0 MW 75 Mvar 141 MW

29 Mvar

200 MW 45 Mvar

33 MW 19 Mvar

5 1.03 pu

36.1 MW

35.4 MW

0.0 MW 0.0 MW

72 MW 6 Mvar

7 1.01 pu

27.8 MW

27.8 MW

0 MW 37 Mvar

0.98 pu

27.8 MW

27.8 MW

15.8 MW

15.8 MW 6 1.07 pu

90.9 MW 90.9 MW

11 MW 3 Mvar

76 Mvar

69.2 MW

66.9 MW

73.8 MW

71.9 MW

17 MW 11 Mvar

71.9 MW

73.8 MW

139%

136% A MVA

Fig. 12. Outage of line 4–5.

overloaded lines) is very expensive. Therefore it is economically feasible to shed the loads with smaller influence on the overloading lines, but with lower costs.

Fig. 13 illustrates graphically the efficiency of control actions. In Fig. 13(а) is shown the comparison of different control action according to total amount of load shedding and Fig. 13(b) presents the comparison of economic feasibility of calculated optimal control actions and control action with minimum amount of load shedding (obtained in case 1.1).

In the second scenario the following solution was achieved: ∆Pload3 = 39 MW; ∆Pload4 = 25 MW α TCPST2-5= -12.3°. The cost of the load shedding is 64 $ and the total amount is 64 MW. Thus in the case of the application of the TCPST 2–5 we decrease the amount of required load shedding by 16 % in comparison with the first scenario (case 1.1).

In the third scenario the application of the TCSC 2–5 instead of TCPST demonstrates smaller efficiency because of constraint of line reactance compensation.

In the fourth case the following solution was achieved: ∆Pload3 = 60.4 MW; α TCPST2-5= -12.7°; α TCPST3-4= -2.41°. The cost of the load shedding is 60.4 $ and the total amount is 60.4 MW. Thus in the case of the application of the coordinated multiple FACTS devices, we decrease the amount of required load shedding by 22 % in comparison with the first case.

The illustration of the efficiency of FACTS devices as emergency control means is shown in Fig.14. We can see that the combined application of the load shedding and the FACTS devices allow to decrease the financial damage to consumers.

0

50

100

150

1.1 1.2 1.3 1.4 1.5 1.6

load 3 load 4 load 9 load 13

50100150200250

1.1 1.2 1.3 1.4 1.5 1.6

min total amount of load shedding optimal solution

Fig.13. Comparison of different load shedding scenarios: a) according to total amount of load shedding; b) according to economic feasibility.

50556065707580

Without FACTS TCSC 2-5 TCPST 2-5 TCPST 2-5 &TCPST 3-4

Fig.14. Illustration of the efficiency of FACTS devices’ application.

TABLE II THE VALUE OF KINF TCPST 2–5 DEPENDING ON OPERATION CONDITIONS.

TCPST 2–5 Line 1-5 Line 2-3

Alfa Case 1 Case 2 Case 3 Case 4 Case 1 Case 2 Case 3 Case 4-15 -0.34 -0.34 -0.33 -0.33 -0.18 -0.19 -0.19 -0.19 -10 -0.35 -0.35 -0.35 -0.35 -0.19 -0.19 -0.19 -0.19 -5 -0.36 -0.36 -0.36 -0.36 -0.20 -0.20 -0.20 -0.20 -2 -0.37 -0.37 -0.36 -0.37 -0.20 -0.20 -0.20 -0.20 2 -0.38 -0.38 -0.37 -0.38 -0.20 -0.20 -0.21 -0.21 5 -0.39 -0.39 -0.38 -0.38 -0.21 -0.21 -0.21 -0.21 10 -0.40 -0.40 -0.39 -0.40 -0.22 -0.21 -0.22 -0.22 15 -0.41 -0.41 -0.41 -0.41 -0.22 -0.22 -0.22 -0.22

TABLE III THE VALUE OF KINF TCSC 2–5 DEPENDING ON OPERATION CONDITIONS.

TCSC 2–5 Line 1-5 Line 2-3

∆x, % Case 1 Case 2 Case 3 Case 4 Case 1 Case 2 Case 3 Case 446 -0.377 -0.379 -0.363 -0.362 -0.192 -0.190 -0.191 -0.19440 -0.378 -0.379 -0.364 -0.364 -0.193 -0.191 -0.193 -0.19635 -0.378 -0.379 -0.365 -0.365 -0.194 -0.192 -0.194 -0.19723 -0.378 -0.380 -0.367 -0.367 -0.196 -0.194 -0.197 -0.20017 -0.379 -0.380 -0.368 -0.368 -0.197 -0.194 -0.198 -0.20112 -0.379 -0.380 -0.369 -0.369 -0.198 -0.195 -0.199 -0.2026 -0.379 -0.380 -0.370 -0.370 -0.198 -0.195 -0.200 -0.2032 -0.380 -0.381 -0.371 -0.371 -0.198 -0.195 -0.200 -0.203

TABLE IV THE VALUE OF β TCPST 2–5 AND TCSC 2–5 DEPENDING ON OPERATION

CONDITIONSTCPST

2–5 TCSC

2–5 Alfa Case 1 Case 2 Case 3 Case 4 ∆x, % Case 1 Case 2 Case 3 Case 4-15 -6.07 -6.50 -6.43 -6.39 46 -191 -123 -369 -408 -10 -6.14 -6.46 -6.40 -6.36 40 -189 -126 -358 -392 -5 -6.38 -6.40 -6.36 -6.32 35 -180 -122 -338 -368 -2 -6.34 -6.37 -6.33 -6.29 23 -168 -115 -312 -339 2 -6.29 -6.31 -6.29 -6.25 17 -163 -112 -303 -328 5 -6.25 -6.27 -6.25 -6.21 12 -158 -109 -293 -317 10 -6.29 -6.18 -6.18 -6.14 6 -149 -103 -276 -298 15 -6.21 -6.09 -6.09 -6.05 2 -145 -100 -267 -288

TABLE V THE VALUES OF COEFFICIENTS OF INFLUENCE (NO LINE OUTAGES)

Line TCPST 2–5

TCSC 2–5

TCPST 3–4

TCSC 3–4

Load 3

Load 4

Load 9

Load 13

Load 14

1–2 1–5 2–3 2–4 2–5 3–4 4–5

0.40 -0.36 -0.20 -0.42 1.00 -0.18 -0.53

0.40 -0.37 -0.20 -0.42 1.00 -0.18 -0.53

0.20 -0.26 1.11 -0.53 -0.39 1.00 0.55

0.20 -0.26 1.09 -0.53 -0.38 1.00 0.55

0.85 0.29 0.60 0.15 0.07 -0.45 -0.31

0.75 0.37 0.18 0.33 0.21 0.16 -0.49

0.75 0.39 0.17 0.30 0.25 0.15 -0.23

0.73 0.42 0.15 0.28 0.28 0.13 0.03

0.76 0.41 0.16 0.30 0.27 0.15 -0.12

TABLE VI THE VALUES OF KINF AND β OF TCPST 2–5 FOR DIFFERENT OUTAGES

Line Outage of line β 1–2 1–5 2–3 2–4 2–5 3–4 4–5 1–2

(1 circuit) -6.1 0.35 -0.32 -0.22 -0.46 1.00 -0.20 -0.58

1–2 -5.0 – 0.03 -0.32 -0.68 1.00 -0.30 -0.911–5 -5.2 0.02 – -0.32 -0.66 1.00 -0.28 -0.812–3 -5.8 0.47 -0.44 – -0.55 1.00 0.00 -0.432–4 -5.2 0.63 -0.58 -0.39 – 1.00 -0.34 -0.322–5 – – – – – – – – 3–4 -5.9 0.47 -0.45 0.00 -0.56 1.00 – -0.484–5 -4.6 0.77 -0.77 -0.09 -0.17 1.00 -0.08 –

TABLE VII THE VALUES OF COEFFICIENTS OF INFLUENCE (OUTAGE OF LINE 4–5)

Line TCPST 2–5

TCSC 2–5

TCPST 3–4

TCSC 3–4 Load 3 Load 4 Load 9 Load 13

1–2 1–5 2–3 2–4 2–5 3–4 4–5

0.77 -0.77 -0.09 -0.17 1.00 -0.08

0

0.78 -0.77 -0.09 -0.17 1.00 -0.08

0

0.05 -0.09 1.10 -0.96 -0.13 1.00

0

0.05 -0.09 1.09 -0.96 -0.13 1.00

0

0.98 0.20 0.70 0.33 -0.08 -0.38

0

0.96 0.23 0.33 0.62 -0.04 0.29

0

0.86 0.33 0.26 0.44 0.12 0.23

0

0.73 0.42 0.14 0.26 0.28 0.12

0

Tota

l cos

t of l

oad

shed

ding

, $

Scenario

Tota

l am

ount

of l

oad

shed

ding

, MW

To

tal c

ost o

f loa

d sh

eddi

ng, $

Scenario

(b)

(a)

TABLE VIII LIST OF CALCULATED CONTROL ACTIONS

Scenario Load 3 Load 4 Load 9 Load13 Cost TCPST

2–5 TCSC 2–5

TCPST 3–4

1

1.1 1.2 1.3 1.4 1.5 1.6

37.7 37.7 18 14

57.5 100

38.9 38.9 50 50 0 7

0 0

40 40 40 0

0 0 0

20 0 0

76.6 114.3 144 194 97.5 114

– – – – – –

– – – – – –

– – – – – –

2 39 25 – – 64 –12.3° – – 3 38 35 – – 73 – 40% – 4 60 – – – 60 –12.7° – –2.41°

IV. CONCLUSIONS This paper presents the coordinated emergency control

system for limitation overloading in the transmission network by using load shedding combined with multiple FACTS devices, which is based on the sensitivity analysis and linear optimization techniques. The conclusions of the paper can be summarized as follows: • The proposed emergency control system and its control

strategies can be successfully used for the coordination of load shedding as well as for load shedding combined with control of multiple FACTS devices to limit lines’ overloads and prevent power system instability caused by the outages of lines;

• The proposed emergency control strategy allows choosing optimal selection of load shedding to limit lines’ overloads taking into account the cost of consumers’ outages;

• The simulations have shown that FACTS devices are effective tools for emergency control. Application of FACTS devices combined with load shedding decreases the amount of required load shedding and so allows to reduce the financial damage to consumers;

• The performance of TCPST is higher than the performance of TCSC, which could be explained by a meshed network topology (presence of many parallel paths) and the small operational range of TCSC.

V. REFERENCES [1] G. Trudel, S. Bernard, G. Scott, “Hydro-Quebec's defence plan against

extreme contingencies,” IEEE Transactions on Power Systems, Vol. 14, No. 3, 1999, pp. 958 – 965.

[2] P. Kundur, G.K. Morison,L. Wang, “Techniques for on-line transient stability assessment and control,” in Proc. of the IEEE Power Engineering Society Winter Meeting, Vol.1, Jan. 23-27, 2000 pp. 46-51.

[3] N.I. Voropai, D.N. Efimov, P.V. Etingov, “Coordination of electric power system emergency control in a market environment,” in Proc. Of the IFAC Symp. On Power Plants and Power Syst. Contr., Seoul, Korea, Sept. 15-19, 2003, pp. 131-136.

[4] N.I. Voropai, “Emergency operation control and congestion management problems in Russia’s electric power systems: a conceptual view,” in Proc. Of the Int. Workshop Liberalization and Modernization of Power Systems: Congestion Management Problems,” Irkutsk, Russia, August 11-14, 2003, pp. 85-89.

[5] N.H. Hingorany, “Flexible AC Transmission System”, IEEE Spectrum, April 1993, pp.40-45;

[6] M. Noroozian, G. Anderson, “Power Flow Control by Use of Controllable Series Components”, IEEE Trans. Power Delivery, Vol.8, No.3, pp.1420-1429, July 1993;

[7] M. Iravani, “Application of Static Phase Shifters in Power Systems”, IEEE Trans. Power Delivery, Vol.9, No.3, pp.1600-1608, July 1994;

[8] M.Y. Vaiman, I.M. Vaiman, “Preventive actions for power system stability preservation”, in Proc. of the WESCON’96, Anaheim, Oct. 22-24, 1996, pp. 153 – 158.

[9] F.M. El-Kady, “Contingency analysis in the presence of series FACTS in power systems”, in Proc. of the IEEE Transmission and Distribution Conference, Atlanta, Vol. 1, 28 Oct.-2 Nov., 2001, pp. 241–246.

[10] A. Oudalov, R. Cherkaoui, A.J. Germond, M. Emery, “Coordinated power flow control by multiple FACTS devices”, in Proc. of the IEEE Power Tech 2003 Conference , Bologna, Italy, June 23-26, pp. 48-52

[11] A. Oudalov, R. Cherkaoui, A.J. Germond, “Coordinated control of multiple series FACTS devices”, in Proc. of the Power System Automation and Control Conference (PSAC’99), Bled, Slovenia, pp. 71-77;

[12] MATPOWER 2.0 User’s Manual, Power Systems Engineering Research Center (PSERC), School of Electrical Engineering, Cornell University, Ithaca, NY 14853, www.pserc.cornell.edu/matpower/

VI. BIOGRAPHIES Pavel V. Etingov (M’05) is a senior researcher at the Energy Systems Institute of the Russian Academy of Science, Irkutsk, Russia. He was born in 1976 in Irkutsk. He graduated with honors from the Irkutsk State Technical University specializing in electrical engineering in 1997. He was a fellow at the Swiss Federal Institute of Technology in 2000-2001. P.V. Etingov received his PhD degree in 2003 from the Energy Systems Institute of the

Russian Academy of Science. His research interests include stability analysis of electric power systems, emergency control, FACTS devices and application of artificial intelligence to power systems.

Alexandre Oudalov received his M.Sc. degree in electrical engineering from the Technical State University of Novosibirsk, Russia in 1993 and his PhD degree in 2003 from the Swiss Federal Institute of Technology of Lausanne (EPFL), Switzerland. Since 2004 he is a research engineer at ABB Switzerland Ltd. His research interests include modern power technologies, FACTS devices and automatic control.

Nikolai I. Voropai (M’1996, SM’1998) is Director of the Energy Systems Institute (Siberian Energy Institute until 1997) of the Russian Academy of Science, Irkutsk, Russia. He is also Professor at Irkutsk State Technical University. He was born in Belarus in 1943. He graduated from Leningrad (St. Petersburg) Polytechnic Institute in 1966 and has been with the Siberian Energy Institute since. N.I.Voropai received his degree of Candidate of Technical Sciences at the Leningrad Polytechnic Institute

in 1974, and Doctor of Technical Sciences at the Siberian Energy Institute in 1990. His research interests include: modeling of power systems; operation and dynamic performance of large interconnections; reliability, security and restoration of power systems; development of national, international and intercontinental electric power grids. N.I.Voropai is a member of CIGRE, a Senior Member of IEEE, and a member of PES. He is the Chairman of the IEEE Power Engineering Russian Chapter.

Alain J. Germond is a professor at the Swiss Federal Institute of Technology in Lausanne (EPFL). He is Director of the Electric Power Systems Laboratory. He was born in 1943, and obtained his engineer’s degree in 1966, and PhD degree in 1975 from EPFL.He worked with Systems Control in Palo Alto, and with ATEL in Switzerland before becoming full time professor at EPFL in 1985.His research interests include power system stability, optimisation, and

application of artificial intelligence to power systems. Alain Germond is a member of CIGRE and of IEEE.

Rachid Cherkaoui received the M.Sc. and the Ph.D. degrees in electrical engineering in 1983 and 1992, respectively, from the Swiss Federal Institute of Technology (EPFL). He is now Senior Scientist at the electrical power systems laboratory (LRE) of EPFL. His research interests are in power and distribution systems analysis and control. He is the head of the research group “Optimisation & Simulation” at LRE.