Design Algorithm of Grid-side LCL-filter for Three

0 downloads 0 Views 580KB Size Report
Abstract--A design algorithm for grid-side LCL-filter of three- phase voltage source PWM rectifier is presented, which allows to use reduced values of inductance, ...
1

Design Algorithm of Grid-side LCL-filter for Three-phase Voltage Source PWM Rectifier Yibin Tong, Fen Tang, Yao Chen, Fei Zhou, and Xinmin Jin

Abstract--A design algorithm for grid-side LCL-filter of threephase voltage source PWM rectifier is presented, which allows to use reduced values of inductance, improve system dynamic performance and reduce cost compared to traditional L-filter. These advantages are even more attractive in medium and high power applications. In this paper, the design criterion and calculation procedures are introduced in detail. A design example is reported, and the obtained LCL-filter has been realized and tested by simulation and experiments. Experimental results show that the obtained LCL-filter can provide sufficient attenuation of current harmonics and meanwhile ensure a high grid-side power factor. The goodness of this design method is demonstrated. Index Terms--harmonic analysis, LCL-filter, power factor, three-phase voltage source PWM rectifier.

I. INTRODUCTION

T

HREE-PHASE voltage source PWM rectifier (Threephase VSR) is widely used in many applications such as motor drives, battery management and grid-connected generation due to its advantages of full control of both dc-link voltage and AC side power factor, and its capability of nearly instantaneous reversal of power flow[1]- [2]. These converters are usually connected to the grid through a simple L filter to reduce the AC side current harmonic. However, with the increase of power rating, especially in medium and high power applications, switching frequency of three-phase VSR is usually limited. Therefore, in order to meet corresponding harmonic standards, a high value of input inductance is needed, which will not only result in deterioration of system dynamic response, but also bring in a series of problems such as excessively large volume and high cost [3]. Meanwhile, due to the triangle relationship between voltage vectors of three-phase VSR, a higher dc-link voltage is required to guarantee current controllability, which means

Yibin Tong is with the Department of Electrical Engineering, Beijing Jiaotong University, BeiJing 10044 CHINA (e-mail: [email protected]). Fen Tang is with the Department of Electrical Engineering, Beijing Jiaotong University, BeiJing 10044 CHINA (e-mail: [email protected]). Yao Chen is with the Department of Electrical Engineering, Beijing Jiaotong University, BeiJing 10044 CHINA (e-mail: [email protected]). Fei Zhou is with the Department of Electrical Engineering, Beijing Jiaotong University, BeiJing 10044 CHINA (e-mail: [email protected]). Xinmin Jin is with the Department of Electrical Engineering, Beijing Jiaotong University, BeiJing 10044 CHINA (e-mail: [email protected]).

©2008 IEEE.

power semiconductor switches with higher voltage endurance is needed. That is a further increase of cost. Currently, a most effective solution to these problems is to adopt LCL filter instead of traditional L filter[4], as shown in Fig.1, where Q1~Q6 are insulated gate bipolar transistors (IGBTs), Lg indicates grid-side inductor, L indicates rectifierside inductor, Cf indicates filter capacitor, R indicates damping resistor to avoid resonance, C indicates dc-link capacitor, Udc is dc-link voltage, ex is grid phase voltage, ux is rectifier output phase voltage, ix is phase current in rectifierside, igx is phase current in the grid-side, ifx is phase current in the capacitor branch, x=a, b, c. Current reference directions are also denoted in Fig.1. To obtain the same filter performance, the total inductance of LCL filters is much smaller than that of L filters. Thus, it can not only achieve better current dynamic performance and more reasonable value of the dc-side voltage but also reduce the volume and the cost. These advantages are even more attractive in medium and high power applications. However, a poor design of LCL filter can cause a lower attenuation compared to that expected or even an increase of the distortion due to oscillation effects. In recent years, substantial amount of work on the design of LCL filters has been reported. For example, it is shown that the value of filter capacitor Cf depends on the position of sensors in [5]. However, the value of rectifier-side inductor has not been profound discussed. In [6]-[7], active damping algorithms have been proposed to replace damping resistors so as to improve system efficiency. However, the implementation of these algorithms either requires additional sensors or requires complicated calculation. Hence, the damping resistor is still a simple and reliable alternative in the acceptable cost of efficiency. This paper proposes a more complete and concise design method of LCL filters based on thorough analysis of working principle and previous research achievements. The design criterion and calculation procedures are introduced in detail. A grid-side LCL design example of 15kW three-phase VSR is given. The corresponding simulation and experimental waveforms are also reported. Experimental results verify the superiority of this design method. The total inductance of the adopted LCL filter is much smaller as compared to the L filter. Naturally, the development cost decreases. In addition, the total harmonic distortion (THD) of grid-side current is

2

only 3% and the control performance is also guaranteed. Q1 ia L

iga Lg

eb

igb

ib

ec

igc

ic

Q5

ua

+

ub Cf

C

Udc

load

ea

Q3

uc

ifa ifb ifc Q4

Q6

Q2

R

Fig. 1. Power circuit of three-phase voltage source PWM rectifier based on LCL-filter

II. LCL FILTER DESIGN PROCEDURES Using voltage sources to replace grid voltage and rectifier ac-side voltage and ignoring damping resistors, the single phase system topology is obtained in Fig.2. The ratio of the grid-side current harmonic component to the rectifier-side current harmonic component can be arbitrarily tuned via the proper capacitance and inductance selection. A large mount of current harmonic component is by-passed by the capacitor branch. igx

Lg

L

ix

ifx ex

Cf

ux

x=a,b,c

( 2)

2 Z b = E /P

where E is the line-to-line rms voltage and P is the system power. This resistor Zb is known as the base impedance of the system. After inserting the capacitor branch, the position of voltage sensors and current sensors has four combinations, which are shown in Fig.3. If measured current and voltage are also controlled in phase. Then the impedance from the grid-side is different. The equivalent circuit of each combination and the corresponding pu. (per unit) values are discussed in detail as follows: (1) Measuring the voltage vc across the capacitor and the rectifier-side current i Since vc and i are controlled in phase, an equivalent circuit is shown on the right in Fig.3(a), where the equivalent impedance from the grid-side consists of a parallel combination of Cf and the base impedance in series with Lg. All impedances are defined at fundamental frequency as: Xg=ωLg X=ωL Xc=1/ωCf. And the corresponding pu. values are given as: xg=Xg/Zb x=X/Zb xc=Zb/Xc. Thus we can get









= jX + (-jX Z )/(-jX + Z ) ( 3) grid g c b c b Dividing (3) by the base impedance Zb on both sides and neglecting the square term of xc, we get Z

zgrid = Z grid / Z b = jx g + 1/(1 + jxc ) 2 = jxg + (1 − jxc ) /(1 + xc )

Fig. 2. Single phase system topology

A. Rectifier-side Inductor Design Ignore Lg and Cf firstly and assume grid voltage is harmonic-free. The h-th harmonic amplitude of rectifier acside output voltage is u(h) and the h-th harmonic amplitude of rectifier-side current is limited to i(h), where h is the order of the harmonic. Thus the inductance can be given as [8] u ( h) L = max , h = 2,3, (1) hωb i(h) where ωb=2π fb is fundamental angular frequency. i(h) is decided by the corresponding harmonic standard. u(h) changes as the selected pulse width modulation method and the corresponding modulation index change. Currently, space vector pulse width modulation (SVPWM) is commonly used in three-phase PWM rectifiers [9]. The corresponding u(h) can be obtained by Fourier analysis of ux. The detail will be discussed in the following concrete design.

L

B. Filter Capacitor Design Without the capacitor branch, the position of voltage sensors and current sensors has only one combination. Since grid current and grid voltage are controlled in phase, the system is pure resistive. Therefore we can obtain the expression as below

≈ 1 + j ( xg − xc )

( 4)

Which indicates that the circuit from the grid-side is pure resistive if we make xc=xg. (2) Measuring the voltage vc across the capacitor and the grid-side current ig Since vc and ig are controlled in phase, an equivalent circuit is shown on the right in Fig.3(b), where the equivalent impedance from the grid-side consists of the base impedance in series with Lg. The pu. value of the equivalent impedance from the grid-side can be written as (5), and the circuit is inductive. zgrid = 1 + jxg

( 5)

(3) Measuring the grid voltage e and the grid-side current ig Since e and ig are controlled in phase, an equivalent circuit is shown on the right in Fig.3(c), where the circuit from the grid-side is pure resistive. The pu. value of the equivalent impedance from the grid-side can be written as z =1 ( 6) grid (4) Measuring the grid voltage e and the rectifier-side current i From the grid-side, the equivalent impedance is given as

3

v v

v

v

v

= E / I = E /( I + I ) grid g f

are the grid-side current space vector, the capacitor current space vector and the rectifier-side current space vector, v v respectively. I f and I respectively satisfy the following expressions v v E / I = Zb (9) Combining Equations (7)~(9), we get Z grid = − jX c Z b /( Z b − jX g − jX c ) (10)

orientation. Therefore, the method of measuring voltage across the capacitor is seldom used, and the position of voltage sensors is usually at the grid-side. Meanwhile, in order to get better over-current protect of the main switches of rectifier, the current sensors are usually at the rectifier-side. That is to say, the fourth detecting method is usually adopted although the grid-side equivalent circuit is capacitive. If the value of xc is small enough, the decrease of power factor can be ignored. Let P and Q are the active and reactive power absorbed by the system, respectively. According to (11), we can get Q / P = (− jxc ) /1 = Z b / X c = ωb Z b Cf (12)

The pu. value is shown as (11) and the equivalent circuit is shown as Fig.3(d), where the equivalent impedance from the grid-side consists of a parallel combination of Cf and the base impedance. zgrid = Z grid / Z b

Equation (12) indicates that the reactive power can be decreased by a smaller value of Cf. However, the filter components selection of LCL filter need to be considered as a whole. Excess decrease of the value of Cf will result in the increase of the value of grid-side inductance Lg.

Z

(7)

v

v

v

v

where E is the grid voltage space vector, and I g , I f and I

= − jX c /( Z b − jX g − jX c ) = 1/( jxc +

Xg Xc

+ 1)

≈ 1/(jxc + 1) ≈ 1-jxc Lg ~

(11)

L

Lg

VSR

Cf

Cf

Zb

vc

i Control unit

Zgrid

(a) Measuring capacitor voltage vc and rectifier-side current i Lg ~

L

Zb

vc Control unit

Zgrid

(b) Measuring capacitor voltage vc and grid-side current ig Lg ~

L

VSR

Cf

Zb

e

ig Control unit

Zgrid

(c) Measuring the grid voltage e and grid-side current ig Lg ~

L

VSR

Cf e

Cf

Zb

i Control unit

ig (h) = i(h) /(1 − ω 2 Lg Cf )

(13)

where ω =2π fbh. if |ig(h)|=α |i(h)| (0