High voltage direct current (HVDC) systems controlled by genetic algorithms based fuzzy logic control

Journal of Electrical and Electronics Engineering Research Vol. 4(2), pp. 21-32, November, 2012 Available online at http://www.academicjournals.org/JEEER

DOI: 10.5897/JEEER12.042

ISSN 2141 – 2367 ©2012 Academic Journals

Full Length Research Paper

High voltage direct current (HVDC) systems controlled

by genetic algorithms based fuzzy logic control

Y. A. Mobarak

1,2

1

Electrical Engineering Department, Faculty of Engineering, Aswan University, Aswan, Egypt.

2

Electrical Engineering Department, Faculty of Engineering, Rabigh, King Abdul-Aziz University, Kingdom of Saudi

Arabia. E-mail: [email protected].

Accepted 22 November, 2012

The design methods of fuzzy logic controls (FLC's) based genetic algorithms (GA's) are used to get an

optimized and additional control signal to the high voltage direct current (HVDC) systems, through

genetic algorithms. The optimal values for the gain factors associated with each of the two fuzzy logic

controller inputs and its output is achieved without changing the membership functions or the rule base

of the fuzzy logic controller itself. This paper proposes the different methods of using genetic algorithms

in the design of fuzzy logic controller's optimal inputs and output called genetic algorithm based fuzzy

logic control. The implementation of genetic algorithms in designing an optimal PI-fuzzy logic controller

for an HVDC system, applying the new proposed technique is introduced. The results of designing an

optimal genetic algorithms based PI-fuzzy logic controller (GA-PI-Fuzzy) are compared with those

obtained using the PI-fuzzy logic controller (PI-Fuzzy) and those obtained using genetic algorithm based

fixed element control (GA-FEC). In designing the PI-fuzzy logic controller, two factors are used the scaling

factor (or the normalized space of variables) and the gain factor (or the actual space of variables).

Key words: High voltage direct current (HVDC) system, power system, genetic algorithm, fuzzy logic control.

INTRODUCTION

Applications of fuzzy system need expert knowledge that

can transform it into fuzzy rules. Sometimes it may be

difficult to transform the expert knowledge into fuzzy

rules; addition to the expert knowledge may not be

available (Refaat et al., 2003). So, Refaat deals with

generating fuzzy rules from system input-output data and

its applications for nonlinear function approximation and

systems identification. Hiyama et al. (1995) developed a

coordinated fuzzy logic control series capacitor module

and power system stabilizers (PSS) to enhance stability

of power system. This scheme has been applied to

switched series capacitors in order to improve the overall

stability of the electric power system. Toliyat et al. (1996)

presented an augmented fuzzy logic power system

stabilizer by the modification of the terminal voltage

feedback signal to the excitation system as a function of

the accelerating power on the unit. Metwally and Malik

(1996) presented an application of a fuzzy logic stabilizer

to a multi-machine power system. This scheme has used

machine speed deviation and accelerating power as input

signals. The results showed that this scheme has the

ability to damp both modes of oscillations effectively. A

novel state feedback controller for power system

stabilizers based on fuzzy logic is developed by

El-Sherbiny et al. (1997).

The scheme improved the dynamic performance of

power systems. They indicated the superiority of the

proposed fuzzy logic controls (FLC) based controller over

the fixed elements controllers. Another study was given in

(El-Sadek et al., 2001, 2003) for a certain schemes of the

high voltage direct current (HVDC) control. Dash et al.

(1995) presented an application of a fuzzy logic based

control to the stabilizer loop of static VAR compensator

for

improving

system

damping

during

transient

disturbance. They used the fuzzy variable structure with

accurate mathematical model of the system. Tuning of

the proportional-integral-derivative (PID) power system

stabilizer using fuzzy logic control is developed by

El-Metwally (2000). He added an initial condition based

fuzzy logic to tune the power system stabilizer.

22 J. Electrical Electron. Eng. Res.

Application of fuzzy logic control approach to

multi-machine power system is given by Refay (2000). An

augmented fuzzy logic control PSS for transient stability

enhancement is designed by Hosny et al. (2000). They

used the speed deviation and accelerating power signals

as input signals to the fuzzy logic PSS. Most of these

studies were made on linearized models. All of these

papers were devoted to application of such new FLC

control technique for excitation systems of the ac

generators or for static var compensators. The controllers

developed in this paper are implemented based on fuzzy

logic; a method of reasoning, the presence of uncertainty.

Attention is paid to a class of fuzzy logic controllers

named as PI-fuzzy logic controllers. In this class of fuzzy

logic controllers, the parameters to be determined are the

gain/scaling factors, number of inputs, number of fuzzy

sets, rule base matrix, and membership functions

(Reznik, 1997). It is in engineering practice, the optimal

system is generally the goal of controller researchers, the

work, which will be presented in this paper, is an attempt

to undertake a study of the problem of designing an

optimal PI-fuzzy logic controllers (using genetic algorithm

techniques).

The application of GA's to the problem of reactive

power planning, due to the nonlinearity of this problem,

its solution requires advanced mathematical tool and

techniques (Mahdi et al., 2003). The powerful Multi-path

search capabilities demonstrated by GA endorse its

application. Recently, a simple genetic algorithm (Kenji,

1994; Kwang et al., 1995) has been proposed to solve

the var planning problem. GA is a blind search using

probabilistic transition rules. The high capabilities of GA's

have been proven through their performance in many

fields (Ioannis et al., 2003). In particular GA's has been

used in parameter estimation and tuning of power

apparatus and system controllers (Lansberry and

Wozniak et al., 1994; Ju et al., 1996). A new

methodology for solving optimal power flow (Osmana and

Mousa, 2003), this methodology employs the genetic

algorithm GA to obtain a feasible solution subject to

desired load convergence, and to obtain the optimal

solution. On the other hand, there has recently been a

great deal of interest in promising GA (Michalewicz,

1995; Michalewicz and Schoenauer, 1996) and its

application to various disciplines including power system

planning operation and control. Genetic Algorithm for

Power System Stabilizers (GA-PSS) design in a

multi-machine power system (Refaey et al., 2003), the

proposed GA-PSS is to find the best location and optimal

parameters of the power system stabilizers PSS in order

to improve the dynamic and transient stability of a power

system over a wide range of operating conditions.

Genetic algorithms have been used successfully to solve

complex design problems (Goldberg, 1994).

The genetic algorithms, therefore, manipulate the most

promising strings in its search for improved solutions

(Man et al., 1996; Ribeiro et al., 1994; Ghose et al.,

1999). A real valued representation moves the problem

closer to the problem representation, which offers higher

precision with more consistent results across replications

(Hammad et al., 1983). Application of such GA's to HVDC

systems controls is not yet published in the available

literature. This is the aim of this paper. In this paper, real

valued genetic algorithms are used to optimize the

gain/scaling factors of a PI-fuzzy. Combination of GA

control and fuzzy logic control is an idea of suggestion of

this paper. No previous application of such idea was

presented to power systems controls.

STUDIED HIGH VOLTAGE DIRECT CURRENT (HVDC) SYSTEM MODELING

Here a detailed description of the system models used throughout this paper is presented for the different elements that compose the ac/dc system. These models are developed assuming standard per unit normalization, as is typical in power systems studies (El-Sadek et al., 2001). For transient stability, adequate sufficient representations of generators, transformers, and ac lines are used to simulate the ac side of the power network. The dc system is assumed to have current controllers at both converter ends. These controllers are modeled using fixed elements controllers FEC, proportional integral PI type. Furthermore, to allow for a thorough mathematical analysis, the inverter extinction angle (γ) is assumed to be the controlling variable, as suggested in (El-Sadek et al., 2003), instead of the more common firing angle (α) control signal. In this paper the suffix (r) stands for the rectifier side, while (i) stand for the inverter side. The studied system equivalent circuit is shown in Figure 1. It is the equivalent to a two-terminal dc link connected to ac systems at both ends. The link consists of 450 kV dc line, rectifier and inverter converter stations with their control systems and smoothing reactors. The ac system at both ends consists of a short 500 kV-transmission line and a commutation transformer. The static compensators and the filters are represented by lumped shunt capacitor.

AC system network representation

For transient analysis of symmetrical three phase networks, it is adequate to use the (d), (q) components. The latter has the advantage of eliminating the time varying coupling between ac and dc system. As it was shown by Hammad et al. (1983) that the closed loop behavior of the generators rotors dynamics can be ignored in dc links dynamic behavior studies, Thevinens equivalent reactances behind voltage sources (Egr), (Egi) are used to represent the ac systems at both sides of the HVDC link. Then, they are transformed to equivalent Norton’s current sources (Igr), (Igi) in shunt with the equivalent source reactance’s, (Xsyr), (Xsyi) as shown in Figure 1, where: (r) suffix for rectifier and (i) suffix for inverter. The ac lines reactances are included in (Xsyr), (Xsyi) while their series resistance’s (Rsyr), (Rsyi) are connected in series between the current sources and the input commutation transformer. Susceptances of filters, shunt static var compensation SVC's systems and the reactive components of loads are merged together and represented by (Bcr), (Bci). The input ac voltages are (Vr), (Vi). As the transients in the dc network are very fast than those in the ac system, quasi steady state representation of the dc network is sufficient to represent its dynamic behavior. The input currents to

Mobarak 23

Figure 1. Equivalent circuit of the two-terminal dc link connected to ac systems at both ends.

Figure 2. Generalized model for rectifier converters.

the commutation transformers (Ir), (Ii) are the negative of the fictitious currents (Iar), (Iai) shown in Figure 1.

AC system model

The ac system is represented using transient stability models that assume quasi static evolution of bus voltage phasors on the time scale of interest (Hammad et al., 1983). All variables are assumed to be in per unit, unless it is specified otherwise. Referring to Figure 2, Norton's current sources (Igr) and the ac source network current (Iar) and the input currents to dc network represented by (-Iar).

Separation of these two complex equations into four real equations, written in the (d), (q) reference frame of axes with matrix in compacted form, yields:

[

] [ ]

rdq rr r

I

=

A

×

Y









(1) With: T rdq grq grd arq ard

I

=

I

I

−

I

−

I

















(2)

[ ]

T r grd grq rd rq

Y

=



_

E

E

V

V



_

(3) [Arr] the ac network coefficient’s matrix form in rectifier side (

Hammad AE, El-Sadek MZ, Dash PK (1983)

.

The currents sources values are given by:

gr gr syr

E

I

jX

=

(4)

Modeling of the ac system network at the inverter side, Norton’s current sources (Igi) and the ac source network current (Iai) and the input currents to dc network represented by (-Iai) are related through the same relations (1) to (4) but with the (r) suffix is replaced by (i) suffix.

Modeling of the high voltage direct current (HVDC) link components

The dc link consists of the rectifier converter, inverter converter, their control systems, and the dc transmission line. The rectifier and the inverter models are quasi steady state models, which are also valid during transient conditions. The dc voltage (Vcr) at the rectifier side, is related to both the (rms) line to line ac commutating voltage (Ecr), the thyristors firing delay angle (αr), the ac voltage at commutation transformers terminal (Vr) and the rectifier transformer off nominal tap ratio (ar) by the relations:

(

3

2

)

cos

cos

cr cr r r r r

24 J. Electrical Electron. Eng. Res.

Figure 3. PI rectifier current controller

Figure 4. HVDC control criteria the rectifier is allowed to go

into inverter operation for faster recovery after fault condition.

In series with these dc voltage sources, fictitious resistor (Rcr) representing the voltage drop due to commutating reactance (Xcr) (Figure 3), where, (Rcr=3Xcr/π) and (Reqr) representing equivalent resistance of the commutating transformers, while batteries (Dr) account for voltage drop across thyristor valves. (Lr) is the smoothing reactor inductance, while (ar) the off nominal tap ratios of the commutating transformers tap changers as shown in Figure 3 then; the dc voltage at the rectifier terminal (Vdr) is given by:

d dr cr d cr r r

dI

V

V

I R

L

D

dt

=

−

−









−





(6)

A model valid during transient conditions for the inverter converter is similar for that of rectifier. Therefore, the dc voltage at the inverter terminal (Vdi) is given by:

d di ci d ci i i

dI

V

V

I R

L

D

dt

=

−

−









−





(7)

The dc transmission line model is considered as "T" section. The shunt capacitance is not effective for frequencies of importance in the transients of the dc transmission line, so it is neglected and a (R-L) element represents the lines. Noting, that (Vdi) is negative, the line equation is:

d dr di dc d dc

dI

V

V

R I

L

dt

+

=

+













(8)

Adding the two equations (6), (7), and then equating with equation (8), the dc current equation is given by:

(

)

1

cos

cos

d r r r i i i d t t t

dI

a V

a V

I R

D

dt

=

L

α

+

α

−

−

(9) Where: t r dc i

L

=

L

+

L

+

L

t cr dc ci

R

=

R

+

R

+

R

(10) t r i

D

=

D

+

D

Converters controllers modeling

The control system which is recently used by several industrial utilities (El-Sadek et al., 2001, 2003; Hammad et al., 1983), for two terminal systems for rectifier and inverter is used in this study. As the dc link operates with rectifier trying to hold the link current constant and the inverter trying to hold the receiving end voltage constant, constant current CC control is required for rectifier and constant current CC and constant extinction angle CEA control for inverter. Therefore, two loops for each control system are used: constant current (CC) loop and constant extinction angle (CEA) loop. A logic circuit at the delay angle determinator defines the allowed signal for each mode of operation. For rectifier converter, the greater output signal of the two control loops used the determinator to define the thyristors firing delay angles.

On the other hand, the sum of the output of the two control loops of the rectifier constant current CC signal control (Vccr), the constant extinction angle CEA loop (Vcear) and inverter controller constant current CC signal control (Vcci), the constant extinction angle control signal (Vceai) is fed to the determinator of the thyristor firing delay angle by the logic circuit before delay determinator. DC current transducers are assumed of time delays (Tcr), which are represented approximately by simple (1/1+sTcr) transfer functions. PI regulators are used for current regulating as shown in Figure (4), their proportional gains are (Kr), and integrators time constants are (Tr), ac commutator voltage transducers are assumed to have time delays of (Tor), and represented by (1/1+sTor) transfer functions. Current compensation circuit, forward gains are (2Rcr).

The equations can be obtained using Figure 4 for rectifier system controller:

1

1

sr sr d cr cr

I

I

I

T

T

−

=









+

















&

(11)

1

1

or or r or or

E

E

V

T

T

−

=









+

















&

(12)

cos

r

cos

r or or

V

E

α

α

=









−

γ





(13)

Or:

cos

cos

or r r or or

The PI regulators are used for current regulating, and variables from (0 to Eor(cosαlimr+cosγor)), and current compensation unit is limited to (glimr) and equally Eor(cosαlimr+cosγor). The delay angle determinator is changed from range (-1 to 1), as its output is the value of (cosαr) and not (αr). We have two modes of operation; constant current operation CC and constant extinction angle operation CEA control:

(i) For constant extinction angle CEA control (Vcear>Vccr), hence:

2

r cear cr sr

V

_α

=

V

=

R I

(15)

(ii) And constant current CC mode of operation for (Vcear<Vccr), hence: r ccr r er r

V

α

=

V

=

g

−

I K

(16) With: r er r r

K I

g

T

−

=

&

(17)

Similarly, The PI regulators used in the inverter side has a similar control circuit of the rectifier and the equations can be obtained using inverter system controller, and relating through the same relations (11) to (14) but with the (r) suffix replaced by (i) suffix. The PI regulators are used for current regulating, and varies from (0 to

Eoi(cosαlimi+cosγoi)). And current compensation unit is limited to (gliir) and equally Eoi(cosαlimi+cosγoi). The delay angle determinator is changed from range (-1 to 1), as its output is the value of (cosαi) and not (αi). We have two modes of operation; constant current operation CC and constant extinction angle operation CEA control, if the inverter operates in the CEA control mode (Vcci) and (g.i) vanish and if it operates at the CC mode (Vceai).

i cci ceai

V

_α

=

V

+

V

(18) (i) For constant extinction angle CEA control:

2

ceai ci si

V

=

R I

(19)

(ii) And for constant current CC and constant extinction angle CEA mode of control: cci i ei i

V

=

g

−

I K

(20) With: _i i ei i

K I

g

T

−

=

&

(21)

High voltage direct current (HVDC) line model

The dc line is simulated using a R-L circuit, and the HVDC controllers are modeled to replicate the simple control scheme shown in Figure 5. Voltage-dependant current-order limit (VDCOL) can be introduced into this model by representing the controller current order as a nonlinear function of the ac converter voltages. This will be represented by assuming voltage dependence of the current order settings in the converter current controllers depicted below.

Mobarak 25

Figure 5. Detailed fixed elements HVDC systems converter

controller.

Interface of AC/DC systems

For simplifying the analysis two terminal asynchronous dc links will be considered. The ac voltages at these terminals represented in the (d), (q)-rotating frames of axes. The phase angles of the ac currents on the rectifier side and the inverter side with respect to the ac network axis (d), (q) are (θr-φr) and (θi-φi) respectively and the equations are obtained:

(

)

cos

rd r d r r

I

=

a I

θ

−

φ

(22)

(

)

sin

rq r d r r

I

=

a I

θ

−

φ

(23)

(

)

cos

id i d i i

I

=

a I

θ

−

φ

(24)

(

)

sin

iq i d i i

I

=

a I

θ

−

φ

(25)

The interface is mathematically performed at each integration step by equating the four components of the currents. Equations (22) to (25) with the four corresponding components of (Iar,, Iai): (Iard, Iarq), (Iaid, Iaiq) resulting from the ac network equations. The dc link is usually represented as loads at the ac network terminals. The real and reactive powers are given by:

dcr dr d

P

=

V I

(26)

tan

dcr dcr r

Q

=

P

φ

(27) dci di d

P

=

V I

(28)

tan

dci dci i

Q

=

P

φ

(29) With: 1

2

cos

ci d

cos

i i i

R I

V

γ

−

α

=





−









180

i i

β

=

−

α

(30)

26 J. Electrical Electron. Eng. Res.

Figure 6. Genetic Algorithm based PI-Fuzzy logic controller (GA-PI-Fuzzy SF) design (Scaling Factors Technique) Inverter side.

i i i

µ

=

β

−

γ

Where: (βi), (µi) are inverter ignition and overlap angles, and (φr), (φi) are the phase angles difference between voltages and currents. The power factor is determined for voltages and currents are given by:

cos

cos

dr r r r cr d r cr r r

V

a V

R I

E

a V

α

φ

=

=





−









(31)

cos

cos

di i i i ci d i ci i i

V

a V

R I

E

a V

α

φ

=

=





−









(32)

The ac/dc interface is performed through equating the ac currents at the ac voltages of the commutating transformers. The ac voltages at these terminals represented in the (d-q) rotating frames of axes.

FIXED ELEMENTS CONTROLS FIXED ELEMENTS CONTROLLERS (FEC) SYSTEMS

The HVDC system is actually controlled by FEC. Figure 6 shows the elements of a recent converter controller. The following are the significant aspects of the FEC system:

(a) The rectifier is provided with a constant current CC control and the α limit control. The minimum α reference is set at about (5o) so that sufficient positive voltage across the valve exists at the time of firing, to ensure successful commutation. In the current control

mode, a closed loop regulator controls the firing angle and hence the dc voltages are controlled to maintain the direct current equals to the current order. Tap changer control of the converter transformer brings α within the range of (8o _{to 20}o_).

(b) The inverter is provided with a constant extinction angle CEA control and a constant current CC control. The extinction angle γ is regulated to a value of about (15o). This value represents a tradeoff between acceptable var consumption and a low risk of commutation failure. While CEA control is the norm, there are variations which include voltage control and ignition angle β control. Tap changer control is used to bring the value of γ close to the desired range of (15o to 20o).

(c) Under normal condition, the rectifier is on CC mode and the inverter is on CEA control mode. If there is a reduction in ac voltage at the rectifier end, the rectifier firing angle decreases until it hits the αmin limit.

(d) To ensure satisfactory operation and equipment safety, several limits such as: minimum current limit, and voltage dependent current order limit VDCOL, should be provided to the controller. (e) Additional signal called (Io) is used to augment the controller stability.

(f) Possibility of addition of new signals such as the fuzzy logic signal, artificial neural network signal, neuro-fuzzy signal, and genetic algorithms signals.

(g) Use of local and master remoted controller between sending and receiving ends of the dc system, to coordinate their functions. (h) The controller should generate directly (cosα) and (cosγ) and not (α and γ).

The control has to satisfy the condition that the voltage integral (2XcId) is available between α and (π-γ). The direct current and the commutating voltage vary with changes in operating conditions. With extinction angle equal to a set value (γo) and (Xc). The control

Mobarak 27

Figure 7. HVDC system parameters responses after disturbances of inverter ac voltage (Vi=20%) with (PI-Fuzzy, GA-FEC, and GA-PI-Fuzzy SF (scaling factor)) controller systems.

system consists of three units: the first unit giving a dc output proportional to the direct current; the second giving an output proportional to (Eo cosγo); and the third giving an alternating voltage proportional to the commutating voltage but with a phase lag of (90o_{). The three outputs are added, and a firing pulse is generated} when the sum passes through zero. An additional signal Vcc=K(Iord

-Id) is generated, where (Io) current order; (Id) actual direct line current; (K) gain of CC control. The error (Io-Id) is amplified only when (Id) is less than (Io) that is, when (Io-Id)>0, when (Id) is greater than (Io), the amplifier output is clamped to zero, and the converter operates on CEA control while, when (Io-Id)>0, it operates on CC control.

GENETIC ALGORITHMS BASED PI-FUZZY (GA-PI-FUZZY)

Tuning of the fuzzy logic controller is more difficult and sophisticated than that of the conventional PID controllers. This is because the fuzzy logic controller is an extremely flexible system, whose behavior is determined by a large number of parameters defining the membership functions, rule base, and the scaling factors. Adaptation of the values of the gain factors is a new proposed technique in this paper, which is simple to implement, produces better performance, and needs less CPU time. The identification of parameters in any type of fuzzy logic controllers can be viewed as an optimization problem, finding parameter values that optimize the fuzzy logic controller based on a given evaluation criteria. The most recent successful techniques in optimization are the genetic and the evolutionary algorithms.

Evolutionary computations in both types binary valued and real valued cover efficiently a wide range of optimization problems; they are used in this paper. In GA tuning of the fuzzy logic controller for optimal performance, one of the following methods can be used: (a) Adapting the membership functions parameters of both the input and the output variables (shape, location, and/or width).

(b) Adapting the matrix rule base (decision table).

(c) Adapting the membership functions parameters of the input variables while the output membership functions parameters are fixed.

(d) Adapting the membership functions parameters of the output variables while the input membership functions parameters are fixed.

(e) Adapting the values of the gain factors (scaling factors in case of using normalized space of variables).

The last method (e) is used in this study. In designing the genetic algorithm based PI-fuzzy logic controller two techniques are used: (a) The scaling factor of variables, called (GA-PI-Fuzzy SF), and (b) The gain factor of variables is called (GA-PI-Fuzzy GF).

Genetic algorithm based PI-Fuzzy scaling factors of variables (GA-PI-Fuzzy SF) for high voltage direct current (HVDC) system control

This is the proposed technique in this paper where it is simple to implement, produces better performance, and needs less CPU computation time than the previous methods as shown in Figure 7. Figure 7 shows the block diagram of the genetic algorithm based fuzzy scaling factors of variables GA-PI-Fuzzy SF, in which we will use the scaling factors of variables, the parameters of the real valued genetic algorithm used are as shown in Table (1), and the same fitness function.

The convergence of the best of fitness values of Ke, K∆e, and K∆u is obtained by using genetic algorithm and tabulated in Table 1.

We notice that all of the gain factors Ke, K∆e, and K∆u have values which are easy to be practically implemented in the sense that they are not very small or not very big values, it was found before that the values for Ke and K∆e are very small while the value of K∆u is large. Those obtained values were difficult to be implemented practically.

Genetic algorithm based PI-Fuzzy gain factors of variables (GA-PI-Fuzzy GF) for high voltage direct current (HVDC) system control

The structure of the genetic algorithm based PI-fuzzy logic controller as shown in Figure 7. The block diagram of the control

28 J. Electrical Electron. Eng. Res.

Table 1. The parameters of the real valued for genetic algorithm based PI-fuzzy scaling factor of

variables (GA-PI-Fuzzy SF) techniques.

Parameters Inputs Best solution obtained

Population size 40.0 Best fitness value 3.116

Maximum generations 400.0 Generation 115.0

Subpopulations 2.0 Gain factors Ke 0.00049

Generation gap 0.8 Gain factors K∆e 0.00205

Sampling period in second 0.001 Gain factors K∆u 350.0

Table 2. The parameters of the real valued for genetic algorithm based PI-fuzzy gain factor of variables

(GA-PI-Fuzzy GF) techniques.

Parameters Input Best solution obtained

Population size 40 Best fitness value 810550

Maximum generations 2500 Generation 1850

Subpopulations 2.0 Gain factors Ke 0.2638

Generation gap 0.8 Gain factors K∆e 0.1052

Sampling period in second 0.001 Gain factors K∆u 2.663

system, in which the genetic algorithm will adapt only the values of the gain factors on the bases of evaluating the performance of the control system while the fuzzy logic controller will preserve the same characteristics described above. This is a new proposed technique, in which we will use the gain factors of variables, the parameters of the used real-valued genetic algorithm are listed below. The fitness function f(x) to be minimized by the genetic algorithm is described by:

( )

2 0 0 n n s k k

f

x

α

e

β

te

δ

t

= =

=

∑

+

∑

+

(33)

Where: e is the dc current error, ts is the settling time, and α, β, and δ are the weighting factors.

The convergence of the best of fitness values of Ke, K∆e, and K∆u is obtained by using genetic algorithm. The results obtained are shown in Table (2). We notice that the values for Ke and K∆e are very small while the value of K∆u is large. These values are difficult to be implemented practically.

RESULTS AND DISCUSSION

The rectifier and inverter controllers transient system

performance with genetic algorithm based fuzzy logic

controls use scaling factors (GA-PI-Fuzzy SF) and gain

factors (GA-PI-Fuzzy GF) applied to HVDC converters

controllers. Performance of HVDC power systems, dc

currents and reflections on ac side real powers are

studied, besides rectifier firing angles and inverters

extinction angles variations are clarified. The system is

studied after several transient impacts such as: sudden

ac side voltage dips, and partial var compensation

switching. Afterwards, a comparative study of these

results with those obtained with fuzzy logic control

PI-Fuzzy and Genetic algorithm based fixed elements

controls GA-FEC are performed based on control quality

indices with the time domain performance specifications

of the system step response.

High

voltage

direct

current

(HVDC)

system

performance with GA-PI-Fuzzy SF control signals

A disturbance of 20% step voltage in the inverter ac

voltage is firstly considered. Results are shown in Figure

8, the output dc current is given in Figure 8a, and the

response of the error signal in rectifier side is depicted in

Figure 8b. The response of the rectifier firing delay angle

appears in Figure 8c while that of the inverter extinctions

angle is depicted in Figure 8d and shows clear damping

of the dc current oscillations, with fast settling times to the

initial value at 0.22 s. The error signal shows less first

overshoots and less undershoots, with fast settling of the

error signal (0.22 s) instead of (0.280 s) with PI-Fuzzy

application, and instead of 0.225 s with GA-FEC

application. An advance in the response is recorded with

rapid settling to steady-state values. The results are

obtained with PI-Fuzzy, with GA-FEC, and with

GA-PI-Fuzzy SF controllers. It is being noted that the

steady-state error is decreased from 0.0026 to 0.00112 upon

using the GA-PI-Fuzzy SF. Examination of the figure

depicts decrease in the maximum overshoot from

Mobarak 29

Figure 8. HVDC system parameters responses after disturbances of inverter ac voltage (Vi=20%) with (PI-Fuzzy,

GA-FEC, and GA-PI-Fuzzy SF (scaling factor)) controller systems. (A) DC link current (Idc); (B) Error signal in rectifier side (Ier); (C) Rectifier firing delay angle (α); (D) Inverter extinction angle (γ).

8.67 to 5.40% upon using the GA-PI-Fuzzy SF controller.

Another set of response figures showing the effect of

partial loss of static var compensation at the ac inverter

commutation

transformer

side

on

the

system

performance, are shown in Figure 9. They are obtained

with PI-Fuzzy controls, with GA-FEC controls, and with

the GA-PI-Fuzzy SF controllers. A 50% step variations in

B

ci

is made for 100 ms, then they recovered to its original

value (B

ci

=3.5 pu). The settling time with PI-Fuzzy only

was 0.290 s, while it becomes 0.235 s with the with

GA-PI-Fuzzy SF controls. Regarding of that figure depicts

decrease in the maximum overshoot from 9.15 to 5.70%

upon using the GA-PI-Fuzzy SF controller.

High

voltage

direct

current

(HVDC)

system

performance with GA-PI-Fuzzy GF control signals

A disturbance of 20% step voltage in the inverter ac

voltage is firstly considered. Results are shown in Figure

10. Illustrating Figure 10a shows clear damping of the dc

current oscillations, with fast settling times to the initial

value at 0.215 s. The error signal plot in Figure 10b

shows less first overshoots and less undershoots, with

fast settling of the error signal (0.215 s) instead of (0.280

s) without GA-PI-Fuzzy GF application. Figure 10c,d

shows modifications in the response of the firing delay

angle and extinction angle of the rectifier and inverter,

respectively. An advance in the response is recorded with

rapid settling to steady-state values.

Another set of response effect of partial loss of static

var compensation at the ac inverter commutation

transformer side on the system performance, are shown

in Figure 11. A 50% step variations in B

ci

is made for 100

ms, then they recovered to its original value (B

ci

=3.5pu).

The error signal shows less first overshoots, with fast

settling of the error signal (0.290 s) instead of (0.215 s)

without GA-PI-Fuzzy GF application.

Comparative study between gain factor (GF), and

scaling factor (SF) techniques

Comparison of the system performance parameters

A

B

C

_D

α ( d e g re e ) γ (d e g re e ) Ier ( p .u ) Idc ( p .u )

30 J. Electrical Electron. Eng. Res.

Figure 9. HVDC system parameters responses after disturbances of inverter SVC compensation

partial switching (Bci=50%) with (PI-Fuzzy, GA-FEC, and GA-PI-Fuzzy SF (Scalling factor)) controller systems. (A) Rectifier firing delay angle(α); (B) Inverter extinction angle (γ).

Figure 10. HVDC system parameters responses after disturbances of inverter ac voltage (Vi=20%) with

(PI-Fuzzy, GA-FEC, and GA-PI-Fuzzy SF (scaling factor)) controller systems. (A) DC link current (Idc); (B) Error signal in rectifier side (Ier); (C) Rectifier firing delay angle (α); (D) Inverter extinction angle (γ).

A Time in sec B Time in sec Time (s) _{Time (s)} Time (s) _{Time (s)}

B

A

_B

C

_D

Time in sec Time in sec Time in sec Time in sec Time (s) _{Time (s)} Time (s) Time (s) γ (d e g re e ) α ( d e g re e ) α ( d e g re e ) γ (d e g re e ) Ier ( p .u ) Idc ( p .u )

Mobarak 31

Figure 11. HVDC system parameters responses after disturbances of inverter SVC compensation partial

switching (Bci=50%) with (PI-Fuzzy, GA-FEC, and GA-PI-Fuzzy GF (gain factor)) controller systems (A) Rectifier firing delay angle(α); (B) Inverter extinction angle (γ).

Table 3. Control quality factors performance of GA-PI-Fuzzy logic controller comparison between gain

factors GF, and scaling factors SF.

Parameter ac voltage dips Partial svc switching

GF SF GF SF Ke 0.2638 0.000494 0.2638 0.000494 K∆e 0.1052 0.00205 0.1052 0.00205 K∆u 2.663 350 2.663 350 tr (s) 0.110 0.115 0.115 0.1e20 ts (s) 0.215 0.220 0.115 0.235 OS% 4.62 5.40 4.87 5.70 ess 0.00084 0.00112 0.00089 0.00119

indices upon using optimal PI-fuzzy for gain, and scaling

factors of variables PI-fuzzy logic controller are listed in

Table 3 using the best of fitness values of K

e

, and K

∆e

,

obtained by using genetic algorithm and applying a 20%

voltage disturbance of inverter ac voltage input, and

partial loss of static var compensation.

Conclusions

In this paper, we proposed auto-tuning method for

PI-fuzzy logic controller inputs and outputs based on genetic

algorithms optimization. The proposed technique has

been applied to the design of two terminal HVDC system

controllers. The design method depends on automatically

choosing the values of the gain factors associated with

the input and output variables of the PI-fuzzy logic

controller while the structure of the fuzzy logic controller

itself is fixed. Simulation results demonstrate the

efficiency of the proposed technique, compared to the

traditional methods of designing controllers. Even in the

case of applying disturbance input, the GA-PI-fuzzy logic

controller could adapt itself and cancel the effect of the

disturbance signal without needing to be returned. The

proposed technique has the advantage that its gain

values can be implemented practically.

The GA-PI-fuzzy logic controller shows better

performance than the optimal PI-fuzzy logic controller

does. There are a direct relationship between the input

gain/scaling factors and the universe of discourse of the

input variables, while there is a reverse relationship

between the output gain/scaling factors and the universe

of discourse of the output variables. The genetic-based

PI-fuzzy logic controller, using gain factors of variables,

shows better performance than the genetic based

PI-fuzzy logic controller, using scaling factors of variables,

does.

We notice that the values for K

e

, K

∆e

, and K

∆u

have

A

Time in sec

B

Time in sec Time (s) _{Time (s)} Time (s) _{Time (s)}

B

α ( d e g re e ) γ (d e g re e )

32 J. Electrical Electron. Eng. Res.

acceptable values. These values are easy to be

implemented practically. Also, the GA based unity gain

factor

PI-fuzzy

logic

controller

has

a

faster

responsiveness to disturbance input, than the gain

factors and the scaling factors technique.

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