A VSC-HVDC Fuzzy Controller for Improving the Stability of AC/DC Power System

Sheng Li, Jianhua Zhang, Jingfu Shang, Ziping WU,Mingxia Zhou

Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education, North China Electric Power University, Changping District, Beijing 102206, China

Abstract —This paper puts forward an auxiliary fuzzy logic

controller for the Voltage Source Converter based HVDC transmission system, VSC-HVDC, to improve the stability of the AC/ DC system by damping the oscillation effectively after disturbance. The fast control capability of the VSC-HVDC and the process of area mode oscillations are analyzed. No detailed model of the system is required for the design of the proposed control scheme. The controller judges the operation states and the control effect and accordingly adjusts its active power order in an adaptive way by using fuzzy rules, so as to damp out the area mode oscillation. Simulation results on the IEEE 4-generator AC/DC power systems have shown that the controller can enhance the dynamic stability of interconnected power systems effectively and is robust to the variation of system operating conditions and oscillation modes.

Keywords: VSC-HVDC; fuzzy logic control; tie-line oscillation

I. INTRODUCTION Compared with traditional HVDC, voltage source converter

based HVDC ，(VSC-HVDC) has a series of advantages and adds fast control capability to power transmission.

There are dozens of VSC-HVDC project in operation worldwide for different purpose, such as transporting power by wind, connecting asynchronous power systems, deregulated electricity market manipulating, improving power quality, feeding remote passive network and etc. Nowadays, VSC-HVDC has been reported to have the ability to deal with power level as much as 300 kV, 1000MW, which means that VSC-HVDC can be used in not only distribution system but also transmission system. At the same time, with the development of VSC-HVDC operation practice, a lot of research interests have been put on the study of modeling, controller design and influence to the grid connected of VSC-HVDC.

There are three kinds of control strategy for VSC-HVDC. The three control strategy deal with the different state of system.

First is basic steady state control when power system is normal. In [1], the approximately decoupled relationship between the two controlling variables and the two controlled variables of VSC is proposed. An inverse steady state model controller for VSC-HVDC system is proposed. In [2], traditional

proportional integral (PI) controllers of VSC-HVDC in conventional a-b-c coordinates are proposed. In [3], an equivalent continuous-time state space model of VSC-HVDC in the synchronous dq reference frame is presented. The d- and q-axis of VSC model are decoupled using the feed forward compensation method. In [12], an adaptive control strategy to improve dynamic performances of VSC-HVDC systems is presented. The adaptive controller considers parameters uncertainties, which was based on back stepping method.

Second is stability control when power system is interfered by some fault. Power system stability is very important, especially for a large-scale system. In year 2003, a record number of total blackouts happened in North America as well as in large portion of Europe, which affected 50million people and caused huge economy losses. In [5,6] ,controller of VSC is considered to add the damping ability of system

Third is restore control or black start control when the power system connecting the one terminal of VSC-HVDC is dead. In [7,8] ,some restore operation by VSC-HVDC are researched

Further study is needed to explore the benefit the VSC-HVDC technology can bring to power system.

Fuzzy logic control strategy doesn’t depend on the detailed system model and is robust to different operating conditions. In this paper a fuzzy logic controller is developed to damp the oscillation of AC line parallel with VSC-HVDC transmission line.

The rest of the paper is organized as follows. In Section 2, the modeling and main feature of HVDC Light system is presented. In section 3, the mode of area oscillation is discussed and proper input signal for fuzzy damping control is recommended. In section 4, the ancillary damping fuzzy controller is designed. Simulation system and case study results are presented and illustrated in Section 5. At last, Conclusions are drawn in Section 6.

II. VSC-HVDC MODELING AND ITS CHARACTERISTIC

2Cd

2Cd

Xf

dU

2Cd

2Cd

Xf

VSC1 VSC2

AC system1

DC LINE

AC system2

T1

T

Fig.1. Topology of 2-level converter VSC-HVDC Transmission system

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Figure 1 shows the topology of a Six pulse two level two terminal VSC-HVDC Transmission system. VSC1 and VSC2 have the same structure. Xf stands for a high order filter with small capacity. Transformer T provides a interface for power exchanging between the AC system and VSC-HVDC transmission line.

AC system

2Cd

2Cd

Xf

dU

DC system

di

δδ −∠ scUssU δ∠

ss QP ,

sI

cc QP ,

XR

Fig.2. typical VSC diagram

In Fig2, Us is the fundamental component of bus voltage in

AC system side and Uc is the fundamental component of bus voltage of AC side of VSC. δ is the phase angle difference between Us and Uc. X is the equivalent inductance of converter filter and R is the resistance of equivalent loss of VSC. Pc and Qc are active and reactive power respectively transferred from the network to the rectifier. Ud is the DC bus voltage and Id is the current of DC lines.

The following equations indicate the relationships among different variables of the system without loss being considered.

δsinc

cs

XUUP = (1)

c

css

XUUUQ )cos( δ−= (2)

Us=1

P

Q

Smax=0.3

Udcmax=1

Pmax=0.3

Smax=0.6 Smax=0.9

Udcmax=1.4 Udcmax=1.8

Pmax=0.9

Pmax=0.6

Pmax=0.3

Pmax=0.9

Pmax=0.6

A

C

B

D

Fig.3. operation range of VSC

The operation range in function of the capacity of VSC,

Smax the DC cable capacity, Pmax, and the rated DC voltage, Udcmax is shown in the PQ-diagram in Fig.3, Where P and Q expressed in per unit. The formulas (1) and (2) give an

approximation of the power flowing between the converter and the AC network in steady state neglecting the losses.

Suppose three phases are balanced, based on Kirchhoff’s law the following equation indicating the relationships among different variables of the system is obtained.

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

cc

cb

ca

c

b

a

c

b

a

sc

sb

sa

uuu

iii

Riii

dtdL

uuu

(3)

The equation (3) in vector form is as follows ：

Cabcabcabc

Sabc uRidtdiLu ++= (4)

where

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++−++

=)120sin()120sin(

)sin(

2δδ

δ

wtwtwt

mUu dCabc (5)

M and δ are respectively the modulation index and the initial phase angle of modulation wave.

Following equation (6) is obtained by transform equation (4)

)( CabcSabcabcabc uuRidtdiL −+−= (6)

AC voltage and AC current are transformed to voltage and current in the synchronous dq0 reference frame through Park transformation .with the transformation matrix P and P-1

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−+−

=

21

21

21

)3/2sin()3/2sin(sin)3/2cos()3/2cos(cos

32 ππ

ππwtwtwtwtwtwt

P (7)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+−+−−−

−=−

1)3/2sin()3/2cos(1)3/2sin()3/2cos(1sincos

1

ππππ

wtwtwtwt

wtwtP (8)

where ω is the angular frequency of system. After Park transformation, equation (9) in vector form is

obtained

0

1

0000 )(1

dqCdqSdqdqdq I

dtdPPuu

LiLR

dtdi −

−−+−= (9)

It is supposed that system operates symmetrically in the steady-state condition. So there is no zero sequence component when 3 phase are balanced, So equation (10)is obtained from(9)its relationship of balance of voltage [13] is:

⎥⎦

⎤⎢⎣

⎡−⎥⎦

⎤⎢⎣

⎡+⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡−−

−=⎥⎦

⎤⎢⎣

⎡

cq

cd

sq

sd

q

d

q

d

uu

Luu

Lii

RwLwLR

Liis 111 (10)

where s is a differential operator, in the synchronous frame, usd and usq are source voltages, the d and q axis components of

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the respective AC bus voltage in the synchronous frame. id and iq are line currents, ucd and ucq are converter input voltages.

Suppose that the fundamental component of AC bus voltage us is in q-axis. Therefore, usd is equal to 0 while the magnitude of usq is equal to that of us, which will simplify the model (10) as.

⎥⎦

⎤⎢⎣

⎡−⎥⎦

⎤⎢⎣

⎡+⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡−−

−=⎥⎦

⎤⎢⎣

⎡

cq

cd

sqq

d

q

d

uu

LuLii

RwLwLR

Liis 1011 (11)

Equation (1) and (2) show that the VSC can act as a synchronous machine with almost no inertia and therefore, it can control active and reactive power almost instantaneously [9], and almost independently [10]. Also, since it has virtually no inertia, it does not contribute to the short circuit current [9]. By means of Phase Width Modulation (PWM) technology, especially Sinusoidal PWM (SPWM),two degrees of freedom, i.e. phase and amplitude can be acquired. Phase and Amplitude Control (PAC) technology is developed for VSC-HVDC applications [2,11].The VSC can easily interchange active and reactive power with an AC network as well as a synchronous machine.

Deferent basic steady state control is applied in VSC dependent on its role in VSC-HVDC .Usually every terminal of VSC-HVDC has two aspects of control task. For the AC side ,VSC can take AC bus voltage or reactive power as control object. For the DC side , VSC can take DC voltage or active power or DC current as control object. At least one VSC in the VSC-HVDC acts to keep DC voltage stable for providing an normal operation point for the whole VSC-HVDC. To the VSC connected to passive network , Controlling AC bus voltage will be the only object . Basic VSC-HVDC Control mode is shown in and Fig 5

1srefQ

1DCrefU1δ

1M

Fig.4 Basic VSC-HVDC Controller for Terminal 1

2srefQ

2DCrefP2δ

2M

Fig. 5 General VSC-HVDC Controller for Terminal 2

VSC-HVDC brings power system many advantages, including [ 12-16]: (i) IGBT valve can switch off and on immediately. there is no worry about commutation failure problem, (ii) no telecommunication required between two stations of HVDC Light system, (iii) active and reactive power controlled independently. reactive power compensation not required, (iv)only small filter is required to filter high frequency signal from PWM. (v)proper ancillary stability controller of VSC-HVDC design improve the stability level of power system (vi) VSC-HVDC can work as black start source after power

system is outage. In this paper, the research interest is mainly put on the

VSC-HVDC control function for enhance power system stability .

III. AREA MODE OSCILLATION SIGNAL CHOOSING

ADP

DC LINE

BDP

AP BPAC LINE

AREA A AREA B

A1 A2

B1 B2

1VSC 2VSC

ACPΔ

ADPΔΔ

Fig. 6. Two-area power system with AC and VSC-HVDC tie lines

Figure 6 shows Two-area power system with AC and

VSC-HVDC tie lines. The controllability of VSC-HVDC can not only adjust the power flow between the two area in normal steady state , but also damping the oscillation by some disturbance, if proper ancillary damping policy has been made in advance.

There are some phenomena can be observed and taken as evidence to determine that area oscillation happens. For example , the angle and angle speed between the centre of inertia of the two area will change during area oscillation and be taken as input signal of controller in [17], But the two variables are not ideal options to identify area oscillation because they have to depend on some costly communication means to be acquired, and the reliability has to be ensured.

Actually the active power flow of the AC tie line which can be measured locally is a ideal signal and sensitive enough for detecting the oscillation. In Fig 6 , it is assumed VSC2 works in the mode of controlling the power flow of the VSC-HVDC line Under this circumstance , the power of AC tie line to be measured is chosen at the end near Area B because of short distance. To damping oscillation, the change of active power, △PAC and the change speed of active power,△△PAC need to be sent to the ancillary damping controller of VSC2.

IV. VSC-HVDC FUZZY CONTROLLER DESIGN The design of steady state controller for VSC-HVDC system

is mainly based on its mathematical model. However, the ancillary damping controller for VSC-HVDC is easy to be influenced by the external interference of the uncertainty, such as the random fluctuation of the load and disturbance of different faults in the two area. It is important to design the VSC-HVDC controllers to be adaptive for different conditions the system. This paper presents a fuzzy logic ancillary damping control added to a normal steady state controller of VSC-HVDC.

The knowledge based on fuzzy control [18], outperform the linear control in many of the cases exposed before, a reason of this is that the human knowledge adds several types of information and can mix different control strategies that can not

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be added in an analytical control law and do not need an accurate mathematical model.

The Knowledge-based fuzzy control uses the experience and the knowledge of an expert about the system behavior. A kind of Knowledge-based fuzzy control is the rule-based fuzzy control, where the human knowledge is approximated by means of linguistic fuzzy rules in the form if-then, which describes the control action that would be made for a human operator. Due to the nonlinear behavior showed by the converter, to the failed attempt of design a linear control, and supported in the advantage of the fuzzy control exposed before, a nonlinear fuzzy control might be desirable to effectively damping area oscillation, by dynamically adjust the active power reference of the normal steady state controller. The control proposed for the ancillary fuzzy logic controllers is a Mamdani controller, because of it is usually used as feedback controller .The rule base represents a static mapping between the antecedent and the consequent variables.

2srefQ

2dcrefP

Basic VSC-HVDC Controller

for Terminal 2 2δ

2M

Ancillary damping Fuzzy

logic controller

ACPΔ2dcrefPΔ

ACPΔΔ

++

Fig.7 Structure of the controller with the ancillary damping control for

Terminal 2

Fuzzy sets must be defined for each input and output variable, as shown in Fig.5. Five fuzzy subsets are needed for the antecedent error ,For both △PAC and △△PAC, the subsets are: negative big (NB), negative small (NS), zero error(Z), positive small (PS), and positive big (PB). Fig.6. The fuzzy subsets used in the consequent were just like the antecedent

Fig.8. Member fuction of △PAC ,△△PAC and △PDCref

The membership functions in Fig 8 were tuned searching the

minimum error in steady state and the minimum oscillation in steady transitory by trial and error method, by using the toolbox FIS of Matlab. The rule base that represents the knowledge obtained from the behavior of the system is summarized in table I, which was proposed after getting a knowledge about the dynamic and steady state behavior of the system.

Table I

Rule base of ADFC

△PAC, △△PAC NB NS Z PS PB

NB NB NS NS NS Z

NS NS NS NS NS Z

Z NS Z Z Z PS

PS Z PS PS PS PS

PB Z PS PS PS PB

V. CASE STUDIES To validate the established ancillary damping fuzzy control

strategy, simulation studies of the test system shown in Fig. 9 have been done with digital simulation software package PSCAD/EMTDC. The test simulation system is a 4 machine system whose parameter is obtained from [19]. At the steady state, about 700MW power is generated from each of the generators. L7 and L9 stand for two loads on buses 7 and which are 967 MW and 1700MW respectively, and G3 a immense source. A two terminal VSC-HVDC transmission line with rated power 400MW is append to connect bus 7 and bus 9 as tie line. Basic control mode is that VSC1 controls DC active power voltage transmitted and its AC voltage, and VSC2 controls DC voltage and its AC voltage .The ancillary damping fuzzy control function is added to the controller of VSC1. The active power of the lines between bus7 and bus8 is measured as input signal for the ancillary damping fuzzy control to dynamically modulate the DC power reference of VSC1 to damping the oscillation cause by disturbance.

In the simulation test, a three-phase to earth fault at one line between bus 8 and bus 9 is applied at 1s from the beginning and last 80ms, then the fault is cut off. The processes of simulation with and without ancillary fuzzy control are shown below.

G1

L9

1 10

2G2

6 75

8VSC1 VSC2

L7

9 11

4

G3

G4

3

Fig. 9 The IEEE 4-generator AC/DC system

Fig10 shows the change process of the active power of lines

between bus 7 and bus8.

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Fig11 shows the curves of the G1 power angle taking the angle of G3 as reference .

Fig12 shows the curves of the G4 power angle taking the angle of G3 as reference .

The simulation result verifies that the ancillary damping fuzzy controller developed in this paper can effectively damp the oscillation caused by disturbance and enhance the stability of the system.

Fig.10 the active power of lines between bus 7 and bus8

Fig. 11 power angle of G1 taking the angle of G3 as reference图4-5

Fig. 12 power angle of G4 taking the angle of G3 as reference

VI. CONCLUSION VSC-HVDC is an advanced and hopeful transmission

technology and fuzzy control is an effective method used to control nonlinear system without the need to resort to complicated mathematical models. In this paper, an ancillary damping fuzzy control is proposed to change the active power reference dynamically. System stability is improved with the proposed ancillary damping fuzzy control are verified in EMTDC/PSCAD simulation test.

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