Optimal Neuro-Fuzzy External Controller for a STATCOM in the 12-Bus Benchmark Power System

Paper Id: TPWRD-00465-2006

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Abstract—An optimal neuro-fuzzy external controller is

designed in this paper for a Static Compensator in the 12-bus

benchmark power system. The controller provides an auxiliary

reference signal for the STATCOM in such a way that it

improves the damping of the rotor speed deviations of its

neighboring generators. A Mamdani fuzzy rule base constitutes

the core of the controller. A heuristic dynamic programming

based approach is used to further train the controller and enable

it to provide nonlinear optimal control at different operating

conditions of the power system. Simulation results are provided

that indicate the proposed neuro-fuzzy external controller is more

effective than a linear external controller for damping out the

speed deviations of the generators. In addition, the two

controllers are compared in terms of the control effort generated

by each one during various disturbances and the proposed neuro-

fuzzy controller proves to be more effective with smaller control

effort.

Index Terms—Neuro-fuzzy systems, Optimal control, Static

compensator, Supervisory level control, Adaptive critic designs.

I. INTRODUCTION

TATIC Compensators (STATCOMs) are power

electronics based flexible ac transmission system (FACTS)

devices that are connected in parallel to the power network and

can control the voltage at the point of common coupling (PCC)

[1]. Regulating the voltage at the PCC during slow changes to

the power system and/or controlling the active/reactive power

exchange with the network are some of the most common main

control objectives for this device [1], [2]. However, many

researchers have investigated the possibility of enhancing the

damping capabilities of the STATCOM by providing an

external additional control loop that sends an auxiliary control

signal to the STATCOM in order to control it from a

Manuscript received August 6, 2006. Financial support by the National

Science Foundation (NSF), USA under grants ECS #0400657 and ECS #0348221, and from the Duke Power Company, Charlotte, North Carolina, USA, for this research is gratefully acknowledged.

R.G. Harley and S. Mohagheghi are with the Intelligent Power Infrastructure Consortium (IPIC) in the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0250 USA (e-mail: [email protected], [email protected]). Ronald Harley is also a Professor Emeritus at the University of KwaZulu-Natal, South Africa.

G.K. Venayagamoorthy is with the Real-Time Power and Intelligent Systems Laboratory, Department of Electrical and Computer Engineering, University of Missouri-Rolla, MO 65409-0249 USA (email: [email protected]).

supervisory level.

Most of these proposed external controllers employ a linear

control scheme, in the form of a simple proportional gain or a

PI controller. Hingorani and Gyugyi [1] proposed a PI based

external control structure for the STATCOM that enables it to

increase the damping of the power system. Patil et al. [3]

designed a linear controller that provides auxiliary control

signals to the line voltage control loop of a STATCOM

connected to a single machine infinite bus. By applying this

auxiliary signal to the line voltage reference of the

STATCOM, it is able to damp out the torsional oscillations in

the power system more effectively. Also, Mathur and Karma

[2] designed a linear external controller for a STATCOM to

improve the damping of the low frequency power oscillations

in the power system.

The inherent disadvantage of the linear external control

schemes, i.e., being dependent on the operating conditions of

the power system, is not as critical for the STATCOM external

control as it is in the case of its internal controller. This is due

to the fact that the external controller does not normally have a

role in the main quasi steady state control objective of the

STATCOM. Rather, it is designed to improve the damping

capabilities of the STATCOM during the transients and/or

dynamic disturbances. However, the efficacy of the linear

external controller can still be affected by a change in the

operating conditions of the power system or its topology. As

the complexities of the power system to which the STATCOM

is connected increases, linear control schemes become less

efficient in achieving the desired supervisory level control

objectives.

Some external controllers have been proposed that

incorporate nonlinear or intelligent control schemes. Farsangi

et al. [4] designed a H∞ robust controller to improve the

transient stability of a 4-bus 2-generator power system. Yixin

et al. [5] designed a fixed structure fuzzy logic based external

controller for damping out the inter-area oscillations in a two-

area multimachine power system. Qu and Chen [6] reported

the successful application of a fuzzy logic based external

controller, with a fixed structure, for a STATCOM in a similar

application. However, these nonlinear control schemes have

some disadvantages associated with them as well. Any

nonlinear external control scheme requires a mathematical

model of the power system, which is tedious to derive. On the

other hand, fuzzy logic based external controllers with fixed

Optimal Neuro-Fuzzy External Controller for a STATCOM in the 12-Bus Benchmark Power

System Salman Mohagheghi, Student Member, IEEE, Ganesh K. Venayagamoorthy, Senior Member, IEEE

Ronald G. Harley, Fellow, IEEE

S


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parameters lose their efficacy as the dimensions of the power

system increases, since there is no guarantee that a heuristic

rule base, according to a human expert, can provide an optimal

performance.

The powerful and well established theory of optimal control and dynamic programming can be used as an alternative. While mathematically proven to provide an optimal control policy, this technique has its own disadvantages. Solving the dynamic programming algorithm in most of the cases is not feasible. Even a numerical solution requires overwhelming computational efforts, which increases exponentially as the size of the problem increases (curse of dimensionality). These restrictive conditions lead the solution to a suboptimal control scheme with limited look-ahead policies [7]. The complexity level is even further exacerbated when moving from finite horizon to infinite horizon problems, while also considering the stochastic effects, model imperfections and the presence of the external disturbances.

Adaptive critic designs (ACD) based controllers [8] can overcome the above mentioned problems. These are powerful techniques designed to perform approximate dynamic programming (ADP) in the presence of noise and uncertainties, even in non-stationary cases and provide optimal control over the infinite horizon of the problem [8]. Such controllers do not need prior information of the plant to be controlled and can be trained online without any large amount of offline data.

This paper uses the ACD theory to implement an optimal neural network based fuzzy (neuro-fuzzy) external controller for a STATCOM connected to the 12-bus benchmark power system [15]. The proposed controller uses the Action dependent heuristic dynamic programming (ADHDP) method which is a member of the ACD family, in order to provide nonlinear optimal control.

The structure of the multimachine power system and the conventional linear external control scheme, used as the basis of comparison with the proposed neuro-fuzzy, appear in Section II of the paper. Section III summarizes some of the key concepts behind ACD based controllers. The structure of the proposed STATCOM neuro-fuzzy external controller is explained in Section IV. Section V provides the details of the training process required for the proposed controller. Simulation results are provided in Section VI in order to compare the effectiveness of the proposed neuro-fuzzy external controller with that of the conventional external controller during large scale disturbances. Finally, the conclusion is given in Section VII.

II. ADAPTIVE CRITIC DESIGNS

Adaptive Critic Designs (ACDs) were first introduced by Werbos in [9] and later in [10], and by Widrow in the early 70’s [11]. Werbos later on proposed a family of ADP designs [12]. These are neural network based techniques capable of optimizing a measure of utility or goal satisfaction, over multiple time periods into the future, in a nonlinear environment under conditions of noise and uncertainty; in other words they perform maximization/minimization of a predefined utility function over time [13], [14].

A utility function U(t) along with an appropriate choice of a discount factor should be defined for the ACD neurocontroller. At each time step t, plant outputs (a set of measured variables) X(t) are fed into the controller, which in turn generates a policy (control signal A(t)) in a way that it optimizes the expected value of a user-defined utility function over the infinite horizon time of the problem, which is known as the cost-to-go function J given by Bellman’s equation of dynamic programming [13] as follows:

∑∞

=

+=0

)()(k

kktUtJ γ (1)

where U(.) is the utility function and γ is a discount factor for finite horizon problems (0<γ<1). A discount factor of zero uses the present value of the utility function as the optimization objective (same as the minimization of one step ahead error), while a discount factor of unity considers all the future values of the utility function equally important and is most suitable for the infinite horizon problems.

The Critic neural network accomplishes the task of dynamic programming by approximating the true cost-to-go function with no prior knowledge of the system. Moreover, it avoids the curse of dimensionality that occurs in some cases of classical dynamic programming based optimal control [13].

Essentially, ACD based controllers are based on three different mathematical theories: approximate dynamic programming, optimal control and reinforcement learning. Two major categories of the ACD family include the model based ACD designs, where a model of the plant to be controlled is required in order to train the controller, and the Action Dependent ACD (ADACD) designs, which is a model free approach. The Action Dependent HDP-based (ADHDP) ACD neuro-fuzzy controller proposed in this paper includes two different parts:

• Critic network; a neural network trained to approximate the cost-to-go function J required for optimization;

• Fuzzy logic controller; which functions as a controller and is trained to provide the optimum control signals to the STATCOM, resulting in minimization/maximization of the function J over the time horizon of the problem.

III. STATCOM IN THE 12-BUS BENCHMARK POWER SYSTEM

Figure 1 illustrates the schematic diagram of the 12-bus

power system with a STATCOM. The power system is a 12-

bus 3-generator network that is designed for evaluating the

effects of FACTS devices at the transmission level [15]. The

uncompensated system has low voltages at buses 4 and 5 [15].

Preliminary simulation results by the authors showed that

installing a STATCOM at bus 4 can drastically improve the

voltage profile of the whole network [24]. The details of the

STATCOM internal control structure is provided in Appendix

A.

A. STATCOM External Control

The external controller provides an auxiliary control signal

for the line voltage controller (PIV) reference signal (Fig. 1).

The control objective of the external controller is to provide


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additional damping for the two generators neighboring the

STATCOM, i.e., generators 3 and 4. Generator 2 is close to

the infinite bus and the simulation results indicate that it is not

significantly affected by the STATCOM.

Fig. 1. Schematic diagram of the 12-bus power system with a STATCOM.

It is known that an active Var compensator with suitable

internal/external controller can improve the dynamic stability

of the power system it is connected to [16]. In its simplest

form, this can be a bang-bang control scheme, where the

compensator injects/withdraws reactive power into the

network in response to the oscillations in the active power (or

load angle). During the time that the transmission line active

power and the load angle are increasing, reactive power

injection into the network causes an increase in the PCC

voltage which opposes the change in the active power and the

load angle. Similarly, a decrease in the active power and load

angle can be compensated by withdrawing reactive power

from the network and therefore decreasing the voltage [1].

Although this control procedure is effective in damping out the

line active power flow and the load angle variations, it causes

voltage deviations at the network buses. However, during large

scale disturbances, where maintaining the system stability is of

the highest priority, these voltage fluctuations can be ignored.

Although care should be taken that at none of the buses the

voltage falls outside the acceptable range, which is normally

[0.95, 1.05] p.u.

Since measuring and analyzing the speed deviations of the

generators are simpler and more practical than the line active

power flows or the generator load angles, speed deviations of

generators 3 and 4, ∆ω3 and ∆ω4 are selected respectively as

the main inputs to the external controller. An increase in the

load angle δ of any generator (and therefore the active power

flow of the neighboring lines) is caused by an increase in the

corresponding generator’s speed with respect to the steady

state rotor speed and vice versa.

B. Linear External Controller

Generators 3 and 4 have inertia constants of 3.0 and 5.0

MW.s/MVA respectively, which result in the local swings with

frequencies of approximately 1 Hz for generator 3 and 0.8 Hz

for generator 4. The fact that generators 3 and 4 oscillate at

different frequencies complicates the external control scheme,

since the auxiliary control signal which is suitable for

generator 3 for example, might at times exacerbate the

dynamic oscillations of the rotor of generator 4 and vice versa.

It was reported in [17] that a linear control scheme as shown in

Fig. 2 can improve the dynamic stability of the two generators.

However, due to the nonlinear nature of the power system, the

performance of the linear external controller in Fig. 2 is widely

affected by a change in the power system configurations or the

operating conditions [17]. Nevertheless, the parameters of the

controller are fine tuned at a single operating point in order to

give the “best” overall performance.

Fig. 2. Schematic diagram of the STATCOM linear external controller.

C. Alternative Solution: Neuro-Fuzzy Systems

In the nonlinear non-stationary power system in Fig. 1, the

level of complexity to establish a relationship between the

inputs (the auxiliary reference signal to the STATCOM) and

the outputs (rotor speed of the two generators ω3 and ω4) is too

high for a linear controller. This is specifically causing

difficulty for a conventional control scheme due to the fact that

the oscillations on generators 3 and 4 are out of phase. This

problem can be solved by using an intelligent control scheme,

in which the controller exerts a control action while watching

its effect on the overall performance of the power system. An

ACD based neuro-fuzzy controller is an excellent candidate

for such a control scheme, since:

• the relatively low number of inputs and outputs allows the creation of an effective fuzzy rule base for the controller;

• introduction of neural networks enables the controller to perform in an optimal way by evaluating the effects of its control actions on the response of the power system, and updating the controller parameters accordingly.

Applications of connectionist learning systems such as

artificial neural networks to adaptively adjust the parameters

of fuzzy systems have been discussed in the literature [18]-

[20]. In a typical neuro-fuzzy system, the parameters of the

fuzzy controller, such as the membership functions and the

consequent rules, are considered as the synaptic weights of a

connectionist learning system. Neural network based learning

techniques are then applied in order to adjust these parameters

based on the performance of the system. Figure 3 illustrates

the schematic diagram of the neuro-fuzzy controller for the

STATCOM, with the fuzzy membership functions and the

fuzzy min/max operators as the nonlinear activation functions


4

of the neurons.

Fig. 3. Schematic diagram of the neuro-fuzzy external controller.

IV. ACD NEURO-FUZZY EXTERNAL CONTROLLER

STRUCTURE

Figure 4 shows the schematic diagram of the proposed

STATCOM neuro-fuzzy external controller. It is an adaptive

critic designs based fuzzy controller which is capable of

providing near optimal results in the presence of noise and

uncertainty in a nonlinear system, such as the power system

shown in Fig. 1.

The entire system of Figs. 1 to 4 is simulated in the PSCAD/EMTDC® environment. A simulation step size of 50

µs is selected, while the sampling time for training the controller is 2.0 ms (500 Hz).

Fig. 4. Schematic diagram of the STATCOM ACD based neuro-fuzzy

external controller.

The plant in Fig. 4 consists of the multimachine power

system in Fig. 1, the STATCOM and the PIDC controller. The

input to the plant is the modulation index ma generated by the

PIV controller and its output X(t) is the vector of the speed

deviations of generators 3 and 4. The proposed external

controller consists of two main components: the neuro-fuzzy

controller (Fig. 3) and a Critic neural network, which is trained

to approximate the cost-to-go function J (Fig. 4).

A. Neuro-Fuzzy Controller

The heart of the neuro-fuzzy controller is the fuzzy

inference system. A first order Takagi-Sugeno fuzzy model is

used for implementing the controller, which is a special case of

the Mamdani model [19]. The input to the fuzzy controller is

the vector of the selected states of the power system as in (2):

TtttX )](),([)( 43 ωω ∆∆= . (2)

The neuro-fuzzy controller in return generates a control

signal ∆Vref, which is added to the line voltage reference of the

local PIV controller (Fig. 1). At steady state, the PIV has a line

voltage reference of 1.0 p.u. Therefore, the output of the

neuro-fuzzy controller is clamped at ±0.05 p.u., such that the

voltage at bus 4 does not fall outside the acceptable range of

[0.95, 1.05] p.u.

Five membership functions are considered in Fig. 3 for the

rotor speed deviations of each generator, which are associated

with the fuzzy terms Negative Big, Negative Small, Zero,

Positive Small and Positive Big; while the output variable ∆Vref

has seven fuzzy membership functions associated with it,

namely Negative Big, Negative Medium, Negative Small, Zero,

Positive Small, Positive Medium and Positive Big. The rule

base implemented for the neuro-fuzzy controller is shown in

Table I. TABLE I. NEURO-FUZZY CONTROLLER RULE BASE.

Input Fuzzy Variables

∆ω4

NB NS Z PS PB

∆ω3

NB PB PM PM PS Z

NS PM PM PS Z NS

Z PM PS Z NS NM

PS PS Z NS NM NM

PB Z NS NM NM NB

Gaussian membership functions are used for each fuzzy

input variable. The membership degree of variable x in the

fuzzy set Aj can be expressed as [19]:

−−=

2

2

1exp)(

j

j

A

mxx

j σµ

, (3)

where mj and σj are the corresponding center and the width of the fuzzy set respectively. Singleton fuzzy sets are assigned to the fuzzy output variable, where the membership degree at a certain singleton point zj is unity, but zero otherwise:

=

=othrwise

zzz

j

B j 0

1)(µ . (4)

The Mamdani min-max method is employed for the fuzzy

inference mechanism and the centroid method is applied for

defuzzification of the fuzzy output variable [19]. Therefore,

the crisp output of the controller can be expressed as Equation

(5):

∑

∑=∆

j

j

j

jj

refw

zw

tV

.

)( , (5)

where wj is the firing strength of the jth rule.

B. Critic network

The parameters of the neuro-fuzzy controller are derived in

such a way that it performs well over a range of operating

conditions and during different faults. This is also partly

ensured by the inherent robustness of the fuzzy controller.

However, the performance is yet far from optimal and

therefore, the controller is further trained so that it can perform

optimal control of the plant over the infinite horizon of the

problem. The coefficients of the fuzzy output variable, i.e., the


5

singleton parameters zj are considered to be the adaptive

parameters of the fuzzy controller. An adaptive critic designs

based approach is applied in order to provide appropriate

training signals for the neuro-fuzzy controller. A Critic

network is trained in order to learn the cost-to-go function

associated with the power system. In other words, it evaluates

how well the neuro-fuzzy controller is doing from moment to

moment. Once sufficiently trained, the Critic network can in

turn provide the appropriate training signal for the fuzzy

controller.

The utility function for the Critic network is comprised of

two terms (decomposed utility function):

)()()( 21 tUtUtU += , (5)

where:

|)2()1()(|)( 3331 −∆+−∆+∆= ttttU ωωω , (6)

|)2()1()(|)( 4442 −∆+−∆+∆= ttttU ωωω . (7)

The two terms are necessary because the rotors of

generators 3 and 4 have different swings and therefore, the

STATCOM should try to improve the performance of both

generators at the same time. The cost-to-go function estimated

by the Critic network is:

∑

∞

=

+=0

)(.)(i

iitUtJ γ , (8)

This can be further simplified as:

∑ ∑∑

∞

= ==

=

+=

0

2

1

2

1

)()(.)(i k

k

k

k

itJitUtJ γ . (9)

Two sub-Critic networks are therefore used, where each one

learns one part of the cost-to-go function. Utility function

decomposition speeds up the process of Critic network

learning, since each sub-Critic is estimating a simpler function

[21]. Figure 5 shows the schematic diagram of the Critic

network. It consists of two separate multilayer perceptron

(MLP) neural networks [22], with 10 neurons in the hidden

layer of each one and the same input from the Action network,

i.e., the neuro-fuzzy controller. The hyperbolic tangent is used

as the activation function of the hidden neurons.

Fig. 5. Schematic diagram of the STATCOM Critic network.

V. NEURO-FUZZY CONTROLLER TRAINING

A. Critic Network Training

A period of forced training is carried out for training the

Critic network. During this stage, pseudorandom binary signal

(PRBS) disturbances are added to the STATCOM voltage

reference Vref from an external source (switches S1 and S2 in

Fig. 6 are in position 1).

Fig. 6. STATCOM neuro-fuzzy external controller training.

The PRBS disturbance applied to the system should be

generated in such a way that it excites the natural frequencies

of the power system. The frequency of the PRBS disturbance

is therefore heuristically chosen as a combination of 0.5, 1 and

2 Hz which are close to the natural frequencies of the power

system, with the total PRBS signal magnitude limited to ±5%

of the value of Vref at steady state [27]. The neuro-fuzzy

controller tries to force the plant to follow the reference by

injecting the required amount of reactive power into the

network. The resultant deviations in the values of the power

system states in (2) along with ∆Vref are now fed into the Critic

network, which goes through backpropagation training to

update its synaptic weight matrices. The training procedure for

the Critic network is discussed in more detail in the authors’

previous work [23].

The Critic network training starts with a low discount factor

of 0.2, which is gradually increased to 0.8 as the training

proceeds. This will help the weights of the Critic network

converge faster [17]. Moreover, an annealing learning rate

scheme is used in which the Critic network training starts with

a learning rate of about 0.1, and gradually decreases to a value

of 0.005. This ensures that during the initial training stages the

Critic network adapts itself to the plant dynamics quickly, but

as the learning process continues, the Critic network does not

have drastic reactions to sudden changes in the plant dynamics.

In this way the Critic network does not forget the previously

learned information. Critic network training is repeated at

various operating conditions until a reasonable accuracy is

achieved.

B. Neuro-Fuzzy Controller Training

The ACD based neuro-fuzzy controller optimizes the

overall cost over the time horizon of the problem (minimizing


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the function J in (8)) by providing an optimal control input to

the plant. In order for the controller to be able to minimize the

cost-to-go function over the infinite horizon of the problem, it

should be trained with the following error signal:

)()()( * tJtJte −= , (10)

where J*(t) is the desired value for the cost-to-go function,

which in the case of dealing with deviation signals is zero. The

mean-squared error function in (11) is used as the error

function for executing the backpropagation algorithm:

)(

2

1)( 2

tetE ×= . (11)

A gradient descent learning algorithm is applied for

adjusting the values of the coefficients of the fuzzy output

variable, i.e., the singleton parameters zj, where each

parameter is updated in the negative direction of the gradient

of the objective function E(t) as follows:

)(

)()()1(

tz

tEtztz

j

jj∂

∂−=+ η , (12)

where η is the learning rate which is considered to be 0.005 in

this study. The partial derivative of the objective function with

respect to any parameter can be derived using the following

chain rule:

)(

)(

)(

)(

)(

)(

)(

)(

tz

tV

tV

tJ

tJ

tE

tz

tE

j

ref

refj ∂

∆∂×

∆∂

∂×

∂

∂=

∂

∂. (13)

The first term in (13) is equal to J(t) and the second term

can be derived by backpropagating constant 1.0 through the

neuroidentifier [17]. The last term in (13) can also be

simplified as follows:

∑∆×

=∂

∆∂

j

j

refj

j

ref

w

tVw

tz

tV )(

)(

)(.

(14)

In this study only the singleton parameters zj of the neuro-

fuzzy controller are updated. It is also possible to apply a full

updating scheme where the parameters of the input

membership functions in (3) are adaptively adjusted as well.

However, a partial updating scheme is used here which

considers all the parameters of the input fuzzy membership

functions to be constant throughout the simulation. This

approach is adopted since it is less computationally intensive.

Moreover, the parameters of the input fuzzy sets are derived

after closely studying the performance of the two generators

during various natural faults applied to the system.

The ACD neuro-fuzzy controller is trained by the cost

function defined in (8) using the update formula in (12)-(13),

so that its output coefficients are adjusted for optimum

performance. The fuzzy controller is trained online during the

actual performance of the power system. At this stage the

fuzzy controller is controlling the plant (switches S1 and S2 in

Fig. 6 are in position 2). Various faults and disturbances are

applied to the power network and the resultant error signal

derived in (10) is used for updating the parameters zj of the

output fuzzy sets.

VI. SIMULATION RESULTS

Several tests are now carried out in order to evaluate the

effectiveness of the proposed neuro-fuzzy external controller

and compare its performance with the linear external controller

for the STATCOM, as well as the case where the STATCOM

has no external controllers.

A. Case Study 1: Short Circuit along the Transmission Line 3-

4

A 100 ms three phase short circuit is now applied to the

middle of one of the parallel transmission lines connecting the

STATCOM to generator 3. Figures 7 and 8 show the

effectiveness of the proposed neuro-fuzzy controller in

damping out the rotor speed oscillations and indicate that the

proposed neuro-fuzzy controller manages to improve the

dynamic damping of both generators, even though the rotors of

the two machines have different, and opposing at times,

excursions.

1 2 3 4 5 6 7 8375

375.5

376

376.5

377

377.5

378

378.5

Time (sec)

Gen

era

tor

3 R

oto

r S

peed

(ra

d/s

ec)

No External Control

Linear Controller

Neuro-fuzzy Controller

Fig. 7. Rotor speed deviations of generator 3 during case study 1.

1 2 3 4 5 6 7 8 9376

376.5

377

377.5

378

378.5

Time (sec)

Gen

era

tor

4 R

oto

r S

peed

(ra

d/s

ec)

No External Control

Linear Controller




7

B. Case Study 2: Short Circuit along the Transmission Line 7-

8

With the transmission line 3-4 remaining disconnected after

the fault is cleared, a 100 ms three phase short circuit is now

applied to the transmission line connecting buses 7 and 8. This

section of the power system is relatively weak and sensitive to

disturbances. Figure 9 illustrates the effectiveness of the

neuro-fuzzy external controller in restoring the system back to

the steady state condition. It shows that the linear controller,

which was trained at a different operating condition, cannot

respond effectively to the rotor speed deviations of generator

4. Figure 10 emphasizes the fact that the STATCOM,

externally controlled by the neuro-fuzzy controller, injects less

initial reactive power into the network when responding to the

fault. Simulation results indicate that the STATCOM

controlled by the neuro-fuzzy controller reduces the peak

reactive power injection by almost 14 MVar. Based on a

typical conservative price of 50$/kVar, this reduction results in

approximate savings of $700,000.

It should be noted that during the normal steady state

operation of the power system the STATCOM already injects

about 290 MVar in order to maintain the desired voltage

profile across the power system. It is normally customary for a

STATCOM to have a safety margin in terms of reactive

power, so that it is able to respond to different loading

conditions and/or disturbances. Clearly the amount of this

safety margin is case dependent and is decided by the design

engineers. The main objective of this paper is to show that an

intelligently controlled STATCOM is able to use less reactive

power from the device safety margin in order to respond to

different faults and improve the dynamic stability of the

system. Figure 10 clearly shows that a STATCOM with 24%

safety margin equipped with a neuro-fuzzy external controller

can respond well to the fault, whereas a STATCOM with a

linear external controller, even with 29% safety margin, cannot

respond to the fault in the same manner.

1 2 3 4 5 6 7

376.4

376.6

376.8

377

377.2

377.4

377.6

377.8

378

Time (sec)

Gen

era

tor

4 R

oto

r S

peed

(ra

d/s

ec)

No External Control

Linear Controller



1 2 3 4 5 6 7 8250

300

350

400

Time (sec)

Reacti

ve P

ow

er

Inje

cte

d b

y t

he S

TA

TC

OM

(M

Var)

No External Control

Linear Controller


Fig. 10. Reactive power injected by the STATCOM during case study 2.

Figure 11 shows the voltage at bus 4 during the transient

and it clearly shows that both external control schemes limit

the voltage within the acceptable range of ±0.05 p.u. This

voltage deviation is normally allowed during dynamic and

transient disturbances [1].

1 2 3 4 5 60.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

Time (sec)

Vo

ltag

e a

t P

CC

(p

.u)

No External Control

Linear External Controller

Neuro-fuzzy External Controller



No External Control

Fig. 11. Voltage at bus 4 in Fig. 1 during case study 2.

It should be noted that although the STATCOM external

control scheme proposed in this paper is effective in damping

out the line active power flow and the generator speed

oscillations during disturbances, it causes temporary voltage

deviations at the network buses, specifically at bus 4 where the

STATCOM is connected. However, during large scale

disturbances, maintaining the system stability and improving

the power system damping is normally a high priority, and as

long as the voltage fluctuations that occur for a short duration

of time are within the acceptable range of [0.95,1.05] p.u.,

there can be a tradeoff between the rotor speed and the line

voltage.

Examples of changing the line voltage reference (or the

reactive power reference) of a shunt FACTS device during

transient and dynamic disturbances has been shown for a

STATCOM in [1], [2], and for a Static Var Compensator


8

(SVC) in [28].

C. Case Study 3: Transmission Line 2-5 Switch On/Off

In a different type of disturbance, the transmission line

connecting buses 2 and 5 is disconnected and is switched back

into the power system after 3 seconds. Figure 12 shows the

superiority of the proposed neuro-fuzzy external controller in

damping out the rotor speed deviations fast. Once again, Fig.

13 emphasizes the fact that the neuro-fuzzy external controller

reduces the amount of three-phase reactive power injected by

the STATCOM and therefore its overall cost. Also, Fig. 14

illustrates the voltage at the PCC (Fig. 1) during the fault.

1 2 3 4 5 6 7 8375

375.5

376

376.5

377

377.5

378

378.5

379

379.5

380

Time (sec)

Gen

era

tor

3 R

oto

r S

peed

(ra

d/s

ec)

Linear Controller

No External Control



1 2 3 4 5 6 7150

200

250

300

350

400

450

500

550

Time (sec)

Reacti

ve P

ow

er

Inje

cte

d b

y t

he S

TA

TC

OM

(M

Var)

Linear Controller

No External Control


Fig. 13. Reactive power injected by the STATCOM during case study 3.

D. Performance Measurement

In this section, the performance of the neuro-fuzzy external

controller is compared with the linear external controller and

the uncompensated power system. A performance index is

defined for each case study 1-3 as in (15): 1

1

2

,4

1

2

,3

1

2

,2

111.

−

===

∆+∆+∆= ∑∑∑

N

k

k

N

k

k

N

k

kiNNN

IP ωωω,

(15)

where ∆ωj,k represents the kth sample of the rotor speed

deviations of the jth generator and index i represents the ith case

study. During each fault/disturbance applied to the system, 100

samples (N) are taken from each rotor speed during the first 10

sec of simulation. The overall performance index of each

controller is derived according to the performance indices P.Ii,

obtained from various case studies, as in (16):

1

.

1.

−

= ∑

i iIPIP , (16)

1 2 3 4 5 6 7

0.96

0.98

1

1.02

1.04

1.06

1.08

Time (sec)

Vo

ltag

e a

t P

CC

(p

.u)

No External Control





No External Control

Fig. 14. Voltage at bus 4 in Fig. 1 during case study 3.

Table II summarizes the results. In the last row of the Table

the overall performance indices are normalized based on the

overall performance index of the uncompensated system. This

shows that the neuro-fuzzy controller improves the

performance of the power system by almost 40% during large

scale disturbances. TABLE II. PERFORMANCE INDICES OF THE NEURO-FUZZY AND THE LINEAR

EXTERNAL CONTROLLERS FOR THE STATCOM.

TYPE OF TEST NO

EXTERNAL

CONTROL

LINEAR

EXTERNAL

CONTROLLER

NEURO-FUZZY

EXTERNAL

CONTROLLER

SHORT CIRCUIT ALONG

THE TRANSMISSION LINE

2-5 1.98 2.32 2.64

SHORT CIRCUIT ALONG


3-4 0.98 1.25 1.68

SHORT CIRCUIT ALONG


7-8 1.24 1.57 2.12

TRANSMISSION LINE 2-5

SWITCH ON/OFF 0.57 0.53 0.67

TRANSMISSION LINE 4-6

OUTAGE 1.26 1.58 1.76

OVERALL

PERFORMANCE INDEX 0.204 0.227 0.285

NORMALIZED OVERALL

PERFORMANCE INDEX 1.0 1.112 1.397


9

VII. PRACTICAL CONSIDERATIONS

A. Hardware Implementation

The proposed ACD based neuro-fuzzy controller can be

implemented on a DSP board. Venayagamoorthy et al. [25],

[27] have successfully implemented a neurocontroller on a

turbogenerator. The authors have also reported successful

implementation of a fuzzy controller for a STATCOM in a

multimachine power system [26]. The controller, built on a

DSP board, sends the control signals to the power system

which is implemented on a Real-Time Digital Simulator

(RTDS).

B. Real-Time Development of Neuro-Fuzzy Controller

Essentially, the training process of the fuzzy system is of

the greatest importance and delicacy. This is due to the fact

that the training stages of the Critic network can be conducted

offline; however, the training process of the fuzzy controller

should be executed online while it is controlling the plant.

In a real power system, applying the PRBS disturbances for

training the neuro-fuzzy controller might not be desirable or

practical. In such cases, training data can be obtained from the

normal operation of the power system, as the network is

exposed to natural changes to its operating condition and/or

configuration, as well as possible large scale faults. Clearly,

the Critic network should be trained first. Once its weights

have converged, the fuzzy controller can undergo training. In

this way the controller parameters will take a longer time to

converge, but this will not cause any problems for the power

system, since:

• The initial parameters of the fuzzy controller (the

membership function and the consequent parameters) are

derived in a way that it stabilizes the power system. At

worst case, the fuzzy controller acts as a nonlinear gain

scheduling controller which is yet more effective than a PI

controller [26].

• A Critic network with its weights converged, is guaranteed

to provide optimal training signals to the controller [13].

It is possible in this case to define an adaptive learning rate

parameter for the controller, which is increased when a change

occurs in the value of its inputs and is a small number when

the input values are almost constant. This prevents the

controller weights/parameters from forgetting the previously

learned information.

C. Installment Cost

Implementing a neuro-fuzzy controller like the one

proposed in this paper requires a larger amount of capital

investment compared to a PI controller. However, it should be

noted that the installment cost of a DSP based neuro-fuzzy

controller for a STATCOM is negligible compared to the

capital investment required for the FACTS device itself.

Moreover, the neuro-fuzzy controller improves the overall

performance of the system by reducing the amount of reactive

power injected by the STATCOM, which in turn reduces the

ratings of the inverter switches and hence its cost.

VIII. CONCLUSIONS

An optimal neuro-fuzzy controller has been designed in this

paper for external control of a STATCOM connected to the

12-bus benchmark power system. Based on the speed

deviations on the generators neighboring the STATCOM, the

external controller generates an auxiliary control signal, which

is applied to the line voltage reference signal of the

STATCOM in order to improve the dynamic stability of the

power system during large scale disturbances. Using adaptive

critic designs theory, the neuro-fuzzy controller is able to

provide nonlinear optimal control over the infinite horizon of

the problem, with no need to any mathematical model of the

power system or the STATCOM. Reinforcement learning is

applied for training the external controller, which makes it

largely insensitive to the size of the power system.

Simulation results have been provided that indicate that the

proposed neuro-fuzzy external controller is more effective than

a linear based technique for damping the speed deviations of

the generators neighboring the STATCOM. Moreover, it

achieves this with smaller amounts of reactive power injected

by the STATCOM as a result of the faults, which in turn could

lead to a smaller STATCOM size and therefore savings on the

cost of the FACTS device if it were to have a secondary

function of providing system damping.

APPENDIX A- STATCOM INTERNAL CONTROLLER

The STATCOM considered in this study is a voltage source

inverter (VSI) type. It is essentially a voltage source inverter

that is connected to the power system through a step-up

transformer. The internal controller of the STATCOM is

shown in Fig. 15. It consists of two PI controllers for

regulating the line voltage at the PCC (PIV) and the dc link

voltage inside the STATCOM (PIDC). The deviations in the

line voltage ∆V and the dc link voltage ∆Vdc are passed

through these two separate PI controllers in order to determine

the inverter modulation index ma and the phase shift α

respectively. These signals are fed into the PWM module that

in turn generates the firing pulses applied to the STATCOM

switches. This control scheme was found to be effective in

responding to small scale as well as large scale disturbances in

the power system.

Fig. 15. STATCOM internal control scheme.


10

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[1] N.G. Hingorani and L. Gyugyi, Understanding FACTS- Concepts and

Technology of Flexible AC Transmission Systems, New Jersey: IEEE Press, 1999, ISBN 0-7803-3455-8, pp 135-208.

[2] M. Mathur and R.K. Varma, Thyristor-Based FACTS Controllers for

Electrical Transmission Systems, New York: Wiley- IEEE Press, 2002, ISBN 0-4712-0643-1.

[3] K.V. Patil, J. Senthil, J. Jiang and R.M. Mathur, “Application of STATCOM for Damping Torsional Oscillations in Series Compensated AC Systems”, IEEE Trans. Energy Conversion, vol. 13, no. 3, pp 237-243, Sept. 1998.

[4] M.M. Farsangi, Y.H. Song and Y.Z. Sun, “Supplementary Control Design of SVC and STATCOM Using H∞ Optimal Robust Control”, in Proc. International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, April 2000, pp 355-360.

[5] N. Yixin, M.L. On, H. Zhenyu, C. Shousun and Z. Baolin, “Fuzzy Logic Damping Controller for FACTS Devices in Interconnected Power Systems”, in Proc. IEEE International Symposium on Circuits and Systems, vol. 5, May 1999, pp 591-594.

[6] S. Qu and C. Chen, “Low Frequency Damping by STATCOM with a Fuzzy Supplementary Controller”, in Proc. International Conference on Power System Technology, vol. 1, October 2002, pp 67-70.

[7] D.P. Bertsekas, Dynamic Programming and Optimal Control, Massachusetts: Athena Scientific, pp 269-359, 2000.

[8] P.J. Werbos, “Tutorial on Neurocontrol, Control Theory and Related Techniques: From Backpropagation to Brain-Like Intelligent Systems”, Tutorial Presented at the 12th Int. Conf. on Mathematical and Computer Modeling and Scientific Computing (ICMCM & SC), Chicago, IL, USA, August 2-4, 1999.

[9] P. Werbos, Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences, Ph.D. Thesis, Committee on Applied Mathematics, Harvard U., 1974.

[10] P. Werbos, The Roots of Backpropagation: From Ordered Derivatives

to Neural Networks and Political Forecasting, Wiley, ISBN 0-471-59897-6, 1994.

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Cybernetics, vol. 3, no. 5, pp 455-465, 1973. [12] P.J. Werbos, “A Menu of Designs for Reinforcement Learning Over

Time”, Neural Networks for Control, Massachusetts: MIT Press, pp 67-95, 1990.

[13] P.J. Werbos, “New Directions in ACDs: Keys to Intelligent Control and Understanding the Brain”, in Proc. IEEE-INNS-ENNS, vol. 3, July 24-27, 2000, pp 61-66.

[14] D.V. Prokhorov and D.C. Wunsch, II, “Adaptive Critic Designs”, IEEE

Trans. Neural Networks, vol.8, no. 5, pp 997-1007, Sept. 1997. [15] S. Jiang U.D. Annakkage and A.M. Gole, “A Platform for Validation of

FACTS Models”, IEEE Transactions on Power Delivery, vol. 21, no. 1, pp 484-491, Jan. 2006.

[16] T.J.E. Miller, Reactive Power Control in Electric Systems, John Wiley & Sons, 1982, ISBN 0-4718-6933-3.

[17] S. Mohagheghi, “Adaptive Critic Designs Based Neurocontrollers for Local and Wide Area Control of a Multimachine Power System with a Static Compensator”, PhD Thesis, School of Electrical and Computer Engineering, Georgia Institute of Technology, August 2006.

[18] M. Figueiredo and F. Gomide, “Design of Fuzzy Systems Using Neurofuzzy Networks”, IEEE Trans. Neural Networks, vol. 10, no. 4, pp 815-827, July 1999.

[19] J.S.R. Jang and C.T. Sun, “Neuro-Fuzzy Modeling and Control”, Proceedings of the IEEE, vol. 83, no. 3, pp 378-405, March 1995.

[20] C.T. Lin and C.S.G. Lee, “Reinforcement Structure/Parameter Learning for Neural-Network-Based Fuzzy Logic Control Systems”, IEEE Trans.

Fuzzy Systems, vol. 2, no. 1, pp 46-63, Feb. 1994. [21] G.L. Lendaris and J.C. Neidhoefer, “Guidance in the Use of Adaptive

Critics for Control”, in Handbook of Learning and Approximate

Dynamic Programming, J. Si, A.G. Barto, W.B. Powell and D.C. Wunsch II, Piscataway, NJ, 2004, ISBN 0-471-66054-X, Chapter 4, pp 97-124.

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[23] S. Mohagheghi, Y. del Valle, G.K. Venayagamoorthy and R.G. Harley, “A Proportional-Integrator Type Adaptive Critic Designs Based

Neurocontroller for a Static Compensator in a Multimachine Power System,” IEEE Trans. Industrial Electronics, vol. 54, no. 1, Feb. 2007.

[24] G.K. Venayagamoorthy, Y. del Valle, S. Mohagheghi, W. Qiao, S. Ray, R.G. Harley, D.M. Falcao, G.N. Taranto and T.M.L. Assis, “Effects of a STATCOM, a SCRC and a UPFC on the Dynamic Behavior of a 45 Bus Brazilian Power System”, in Proc. IEEE PES Inaugral Conf. & Expo. in

Africa, Durban, South Africa, July 11-15, 2005, pp 305-312. [25] G.K. Venayagamoorthy, R.G. Harley and D.C. Wunsch II,

“Implementation of Adaptive Critic Based Neurocontrollers for Turbogenerators in a Multimachine Power System”, IEEE Trans.

Neural Networks, vol. 14, no. 5, pp 1047-1064, September 2003. [26] S. Mohagheghi, G.K. Venayagamoorthy, S. Rajagopalan and R.G.

Harley, “Hardware Implementation of a Mamdani Based Fuzzy Logic Controller for a Static Compensator in a Multimachine Power System”, in Proc. IEEE-IAS, Hong Kong, vol. 2, October 2005, pp 1286-1291.

[27] G.K. Venayagamoorthy and R.G. Harley, “A Continually Online Trained Neurocontroller for Excitation and Turbine Control of a Turbogenerator”, IEEE Trans. Energy Conversion, vol. 16, no. 3, pp 261-26, September 2001.

[28] T.J.E. Miller, Reactive Power Control in Electric Systems, John Wiley & Sons, 1982, ISBN 0-4718-6933-3.

Salman Mohagheghi (S’99) received the B.Eng. from University of Tehran, Iran in 1999 and M.Sc. from Sharif University of Technology, Tehran, Iran in 2001, both in Power Electrical Engineering. In 2006 he graduated with PhD in Electrical Engineering from Georgia Institute of Technology, Atlanta GA, where he is currently doing research as a postdoctoral fellow. His research focuses on wide area control in power systems, protective relaying and distributed state estimation.

Ganesh Kumar Venayagamoorthy (S’91, M’97, SM’02) received the B.Eng. (Honors) degree with a first class honors in Electrical and Electronics Engineering from the Abubakar Tafawa Balewa University, Bauchi, Nigeria, and the MScEng and PhD degrees in Electrical Engineering from the University of Natal, Durban, South Africa, in March 1994, April 1999 and February 2002, respectively. He was a Senior Lecturer at the Durban Institute of Technology, South Africa prior to joining the University of Missouri-Rolla (UMR), USA in May 2002. He is currently an Associate Professor of Electrical and Computer and the Director of the Real-Time Power and Intelligent Systems Laboratory at UMR. His research interests are in power systems stability and control, computational intelligence, alternatives sources of energy and evolvable hardware. He has published about 200 papers in refereed journals and international conference proceedings. Dr. Venayagamoorthy is a recipient of the following awards: a 2004 NSF CAREER Award, the 2006 IEEE Power Engineering Society Walter Fee Outstanding Young Engineer Award, the 2006 IEEE St. Louis Section Outstanding Section Member Award, the 2005 IEEE Industry Applications Society (IAS) Outstanding Young Member Award, the 2005 South African Institute of Electrical Engineers (SAIEE) Young Achievers Award, the 2004 IEEE St. Louis Section Outstanding Young Engineer Award, the 2003 International Neural Network Society (INNS) Young Investigator Award, a 2001 IEEE Computational Intelligence Society (CIS) Walter Karplus Summer Research Award and five prize papers with the IEEE Industry IAS and IEEE CIS. He is also a recipient of the 2006 UMR School of Engineering Teaching Excellence Award and the 2005 UMR Faculty Excellence Award. He is an Associate Editor of the IEEE Transactions on Neural Networks. He is a Senior Member of the SAIEE, a Member of INNS, the Institute of Engineering & Technology, UK, and the American Society for Engineering Education (ASEE). He is currently the IEEE St. Louis CIS and IAS Chapter Chairs, the Chair of the Task Force on Intelligent Control Systems and the Secretary of the Intelligent Systems subcommittee of IEEE Power Engineering Society and the Chair of the IEEE CIS Task Force on Power System Applications. Dr. Venayagamoorthy is listed in the 2007 edition of Who’s Who in America.

Ronald G Harley (M’77-SM’86-F’92) received the MScEng degree (cum

laude) in electrical engineering from the University of Pretoria, South Africa

in 1965, and the Ph.D. degree from London University in 1969.

In 1971 he was appointed to the Chair of Electrical Machines and Power

Systems at the University of Natal in Durban, South Africa. At the University

of Natal in South Africa he was a professor of Electrical Engineering for

many years, including the Department Head and Deputy Dean of


11

Engineering. He is currently the Duke Power Company Distinguished

Professor at the Georgia Institute of Technology, Atlanta, USA. His research

interests include the dynamic behavior and condition monitoring of electric

machines, motor drives, power systems and their components, and controlling

them by the use of power electronics and intelligent control algorithms.

Dr. Harley has co-authored some 380 papers in refereed journals and international conferences and three patents. Altogether 10 of the papers attracted prizes from journals and conferences. He is a Fellow of the British IEE, and a Fellow of the IEEE. He is also a Fellow of the Royal Society in South Africa, and a Founder Member of the Academy of Science in South Africa formed in 1994. During 2000 and 2001 he was one of the IEEE Industry Applications Society's six Distinguished Lecturers. He was the Vice-President of Operations of the IEEE Power Electronics Society (2003-2004) and Chair of the Atlanta Chapter of the IEEE Power Engineering Society. He is currently Chair of the Distinguished Lecturers and Regional Speakers program of the IEEE Industry Applications Society. He received the Cyrill Veinott Award in 2005 from the Power Engineering Society for “Outstanding contributions to the field of electromechanical energy conversion”.

Optimal Neuro-Fuzzy External Controller for a STATCOM in the 12-Bus Benchmark Power System

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