Control of grid-connected DC-AC Converters in ... - IEEE Xplore

POWER ELECTRONICS CONTROLLERS FOR POWER SYSTEMS

271

Control of grid-connected DC-AC Converters in Distributed Generation: Experimental comparison of different schemes T. Hornik and Q.-C. Zhong Department of Electrical Engineering & Electronics, The University of Liverpool (UK) [email protected] and [email protected]

Abstract— In this paper, different control schemes for gridconnected DC-AC power converters are discussed and compared with experimental results. The voltage controller based on H ∞ and repetitive control techniques is compared with a traditional proportional-integral (PI) controller implemented in synchronously rotating reference frame and a proportional resonant (PR) controller implemented in stationary reference frame, with main focus on harmonics distortion and DC current injection to the utility grid. The result shows that the H ∞ repetitive controller offers significant improvement in waveform quality and current harmonic distortion over conventional PI and PR controllers.

I. I NTRODUCTION Rapidly increasing energy consumption on one side and steadily reducing energy sources and climate changes on the other side highlight importance of DPGS based on renewable energy sources, mainly from wind turbines and photovoltaic panels. Distributed Power Generation Systems (DPGS) provide an alternative to the traditional large centralised facilities, such as coal, nuclear or gas powered power plants, where currently most of the electricity is generated. These systems often convert the raw energy sources into electricity with a level and/or type not suitable to be connected to the main utility grid directly. Following the development of power electronic technology, inverters are used to interface between DPGS and utility grid as they match the characteristics of the DPGS and the requirements of the grid connections. Power electronics improves the performance of the DPGS and provides the DPGS with power system control capabilities, improves power quality and their effect on power system stability [1], [2], [3]. However the rapidly increasing number of the DPGS based on renewable energies highlights their main disadvantages, for example, the natural properties such as uncertainty in the availability of the energy source or the fluctuating nature of the input power (wind speed fluctuation etc.). Moreover, the high penetrations and steadily increasing individual DPGS power ratings must be taken into account during their integration into the power system. As a results, the requirements of grid operators become stricter and stricter, and the DPGS will be required to have power plant characteristics, in the sense that DPGS has to be able to behave as active controllable components in the power system and meet very high

technical standards, such as voltage and frequency control, active and reactive power control, quick responses during transient and dynamic situation in the utility grid, harmonics minimisation etc. Hence the control strategies applied to DPGS become of high interest and need to be further investigated and developed. In this paper, a voltage controller based on H ∞ and repetitive control techniques proposed in [4], [5] is further developed and experimentally tested, with main focus on reducing harmonics distortion and DC current injection to the utility grid. The repetitive control offers an alternative for voltage tracking, as it can deal with a very large number of harmonics simultaneously. The repetitive controller has a high gain at the fundamental and all harmonic frequencies of interest. The principle of repetitive control is that if a system is subject to a periodic disturbance, then the error information from previous cycles, stored in a delay line, can be used to achieve better performance. The repetitive control leads to a very low harmonic distortion for the output voltage even in the presence of nonlinear loads and/or grid distortions. The performance of the voltage controller is experimentally compared with a proportional-integral (PI) controller implemented in the synchronously rotating reference frame and a proportional resonant (PR) controller implemented in the stationary reference frame. The rest of the paper is organised as follows. In Section II the general structure of DPGS based on renewable energy sources is described, a grid controller and its main function and different control structures are discussed and the primary grid operators requirements are briefly summarised. In Section III, the experimental setup is described. This is followed by controller design in Section IV. In Section V, the experimental results are presented and discussed, and finally conclusion are made in section VI. II. OVERVIEW OF DPGS STRUCTURE AND CONTROL The structure of a distributed power generation system depends on the input power nature (wind, solar etc.) and different hardware configurations are possible [6]. Figure 1 shows a general structure of DPGS. The system employs two back-to-back converters with a full-scale power rating. This bidirectional power

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2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP

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converter consists of two conventional pulse-width modulated (PWM) converters and is nowadays one of the most widely used in DPGS integration [1]. The input-side converter, controlled by an input side controller, normally ensures that the maximum power is extracted from the input power source and transmits the information about available power to the grid-side controller. The main objective of the grid-side controller is to interact with the utility grid. The grid-side controller has usually the following tasks: control of active power sent to the grid, control of reactive power transferred between the DPGS and the grid, control of the DC-link voltage, control of power quality and grid synchronisation [7].

the voltage harmonics distortion is almost always less than current distortion [9], more emphasise is on the current assessment. In order to meet these requirements, the controllers used should have very good capability in harmonic rejection. TABLE I M AXIMUM HARMONIC CURRENT DISTORTION Odd harmonics

Maximum harmonic current distortion

< 11th

< 4%

11th − 15th

< 2%

17th − 21th

< 1.5%

23rd − 33rd

< 0.6%

> 33rd

< 0.3%

Transformer Input-side Converter

Grid-side Converter

Output Filter

B. Control schemes for the grid-side converter

Fig. 1.

Input-side controller

Grid-side controller

Maximum power extraction Input–side protection

Power quality Power flow Grid synchronization DC-link voltage

General structure of the Distributed Power Generation Systems

A. Requirements of the grid operators Previously, control and stabilisation of the electricity system were taken care of only by large power station units. However due to the large penetration of DPGS the grid operators issue more strict interconnection requirements, called grid code compliance. The interconnection requirements differ significantly from one country to another. This depends on the properties of each power system as well as the level of the DPGS penetration. Countries with a very low DPGS penetration do not necessarily need to accept strict requirements as countries that have substantial proportion of the DPGS connected to the power system. In general the requirements are intended to ensure that the DPGS have the control and dynamic properties needed for operation of the power system with respect to both short-term and long-term security of supply, voltage quality and power system stability. For example in Denmark, the country with the largest penetration of wind power in the power system, a wind farm has to be able to contribute to control task on the same level as conventional power plants, constrained only by limitation of existing wind conditions [1]. In this paper, the most relevant requirement is the power quality. The power quality assessment is mainly based on total harmonics distortion (THD) and DC current injection. For both wind turbine and photovoltaic arrays connected to the utility grid, the maximum THD of output voltage is 5% (120V −69kV ). Table I shows the maximum current distortion limits [8]. However, as

The basic control structure of grid-side controllers consists of a fast internal current loop, which regulates the grid current, and an external voltage loop, which controls the DC-link voltage [10]. The current loop is responsible for power quality issues and the dc-link voltage controller is designed for balancing the power flow in the system. Such a control structure can be implemented in different reference frames, e.g. the natural frame, the synchronously rotating reference frame or the stationary reference frame. 1) Natural frame control: The general idea of the natural frame control, also called abc control, is to have an individual controller for each grid current. In this paper, a voltage controller for the grid-side converter is developed according to [5], [11], [12] and implemented, with main focus on reducing harmonics injection to the utility grid. The control structure is shown in Figure 2. The system consists of two loops: the internal loop using an H ∞ repetitive voltage controller to track the reference voltage and an external power loop to control the active power P and reactive power Q. In this structure PLL is used to calculate voltage reference Vref . Transformer DC Power source

Grid-side Converter

da

db

dc

Output Filter

ia

ib

ic

uga

Ugc

ugb

PWM Modulation

ua

ub

PLL

θ

uc -

Voltage controller

Fig. 2.

Internal model

Control structure for natural frame

e

-

Vref -

Power controller

Qref Pref


2) Synchronously rotating reference frame control: This is also called the dq frame. Control scheme is shown in Figure 3. It uses abc → dq transformation module to transform the control variables from their natural frame abc to a dq frame, which synchronously rotates with the frequency of the grid voltage. As a result, the control variables are DC signals, which leads to easy control and filtering. The following PI controllers are normally used in this frame: Ki , (1) CP I (s) = Kp + s where Kp and Ki are proportional and integral gains respectively. The dq control can work well on balanced systems, but is not good at correcting unbalanced currents which are a common feature of distribution systems [4]. The performance to reject loworder harmonics is poor [7], [10]. To improve the performance of the PI controller in this structure, cross-coupling terms and voltage feed-forward can be used. Transformer DC Power source

Grid-side Converter

da

db

ia ib ic

dc

CHC (s) =

Kih

h=3,5,7,..

s s2 + (ωh)

2,

(3)

where h is the harmonic order. In order to obtain good performance, the resonant frequency has to be identical to the grid frequency. As reported in [14], this frequency can be adaptively adjusted to follow grid frequency variation. Transformer DC Power source

Grid-side Converter

da

db

dc

PWM Modulation uα

uβ

Output Filter

ia ib ic

PLL αβ

iα

iβ

-

Current controllers

Fig. 4.

ua ub uc

abc

θ

i α* -

i d*

αβ

iβ*

dq

i q*

Control structure for stationary reference frame

ua ub uc

abc

abc dq id

θ

PLL

iq

θ

dq ud

+ +

III. E XPERIMENTAL SETUP

uq

+ +

Fig. 3.

compensator is given by

Output Filter

PWM Modulation

Current controllers

273

id * iq*

Control structure for synchronously rotating reference frame

3) Stationary reference frame control : The stationary reference frame control, also called αβ, is shown in Figure 4. In this case, the grid voltages and currents are transformed into reference frame using abc → αβ transformation. The control variables are sinusoidal, which brings difficulty in designing a controller with the correct gain against frequency characteristic to regulate the fundamental frequency and to reject harmonic components. PI controllers with their pole (infinite gain) at zero-frequency are not best suited to this task and it is unable to eliminate the steady-state error [10]. Proportional resonant (PR) controller is usually used. Such a controller has high gain around the resonant frequency and thus is capable to eliminate the steady-state error [7], [10], [13]. The transfer function of a PR controller is given by s CP R (s) = Kp + Ki 2 , (2) s + ω2 where ω is the angular resonant frequency. In this structure low-order harmonics compensator can be easily implemented to improve the performance of the current controller without influencing its behaviour [7]. The transfer function of the harmonics

The experimental setup, shown in Figure 5, consists of an inverter board, a three-phase LC filter, a three-phase grid interface inductor, a board consisting of voltage and current sensors, a step-up transformer, a dSPACE DS1104 R&D controller board and a ControlDesk software, and MATLAB Simulink/SimPower software package. The inverter board consists of two independent three phase inverters and has the capability to generate PWM voltage from a constant 42V DC voltage source. The generated three-phase voltage is connected to the grid via controlled circuit breaker and step-up transformer. The sampling frequency is 5 kHz and the PWM switching frequency is 15 kHz. IV. C ONTROLLERS DESIGN In this section, three different controllers are designed for the experimental setup after establishing its model. These are a voltage controller based on the H ∞ and repetitive control techniques, a PI controller in the synchronously rotating reference frame and a PR controller in the stationary reference frame. The design of the PI and PR controllers follow the procedures described in [7] and the design of the voltage controller follows the theory described in [4], [5], [11], [12]. In the cases of PI and PR controllers only the current loop is considered. The influence of the DC-link controller, harmonic compensator (PR controller) and feed-forward filtering (PI controller) are omitted.


274

TABLE II PARAMETERS OF THE LCL FILTER parameter

value

parameter

value

Lf

150µH

Rf

0.045Ω

Ltr

60µH

Rtr

0.06Ω

Lg

450µH

Rg

0.135Ω

Cf

22µF

Rd

1Ω

+ VDC -

u

PWM

Sc

inverter uf

Lf

Rf

i1

filter inductor

Lg+Ltr i2

ic

Rg+Rtr

Cf

grid interface inductor and transformer inductance

Vc

Rd

Vg grid

neutral

(a) experimental setup Local Load PCB 2 Measure 1

DC Power source

Grid-side Converter

da

db

Measure 2

Transformer

Output Filter

dc

if

uf

Circuit Breaker

ig u g

be described as

DSpace 1104

(b) block diagram of the experimental setup Fig. 5.

Fig. 6. Single phase representation of the plant. The transfer function of the plant is derived in terms of impedances, where Z1 = sLf + Rf , Z2 = sC1 + Rd f and Z3 = s(Lg + Ltr ) + Rg + Rtr .

Experimental setup

uf Vg

=

The considered plant consists of the grid-side converter, LC filter (Lf and Cf ), grid interface inductor Lg and a transformer. The pulse-width-modulation (PWM) block together with the inverter are modelled with an average voltage approach with the limits of the available dc-link voltage [4].The LC filter, grid interface inductor and the leakage inductance of the transformer (Ltr ) form together an LCL filter. The filter inductors are modelled with a series winding resistance. The transfer function of the plant is derived using the single phase representation of the filter, shown in Figure 6, in terms of impedances, where Z1 = sLf + Rf , Z2 = sC1 f + Rd and Z3 = s(Lg + Ltr ) + Rg + Rtr . The parameters of the LCL filter are given in Table II. The grid side parameters Ltr and Rtr represent the transformer. The pulsewidth-modulation (PWM) block together with the inverter are modelled with an average voltage approach with the limits of the available dc-link voltage [4]. Following the Kirchhoff’s current law (KCL), the relation for currents flowing through the filter is given by i1 − ic − i2 = 0 and using the Kirchhoff’s voltage law (KVL), the voltages can

Z12 Z22

i1 i2

where Z11 = Z1 + Z3 , Z12 = −Z3 , Z21 = Z3 and Z22 = − (Z2 + Z3 ). The transfer function between the grid current and the inverter voltage is HP lant (s) =

A. Model of the plant

Z11 Z21

i2 Z21 = . uf Z12 Z21 − Z11 Z22

(4)

The effect of the grid voltage to the grid current is treated as a disturbance. B. Design of the Proportional-Resonant controller The PR controller is designed using the root locus approach. The closed-loop system transfer function in discrete form is given by CP R (z)HP (z)HD (z) , GCL (z) = 1 + CP R (z)HP (z)HD (z) where CP R (z) and HP (z) are the controller and the plant transfer functions, discretised using c2d MATLAB function from (2) and (4), respectively. The processing delay of the PWM inverter is represented by HD (z) [13]. The root locus of the closed-loop system is shown in Figure 7. The proportional gain Kp = 1.12 is chosen to to obtain a damping ratio of ξ = 0.707. Figure 8 shows the Bode plots of the open-loop system for different integral gain Ki . The integral gain is chosen as Ki = 200 for implementation. Since it has a very high gain at the resonant frequency, this controller has very good capability in reducing the steady-state error. In order


275

Root Locus of the closed-loop system 1 0.6π/T 0.8 0.6

Imaginary Axis

0.5π/T

0.4π/T 0.10.3π/T 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.7π/T 0.8π/T

0.4 0.2 0 -0.2

0.9π/T

0.2π/T

0.1π/T

π/T π/T 0.9π/T

0.1π/T

-0.4 -0.6

0.8π/T

0.2π/T 0.7π/T

-0.8

0.3π/T 0.6π/T

-1 -1

-0.8

-0.6

-0.4

-0.2

0.5π/T 0

0.4π/T 0.2

0.4

0.6

0.8

1

Real Axis

Fig. 7.

Root locus of the closed loop system

to synchronise the inverter with the utility grid, the grid phase calculated in a PLL block is used as the phase reference. No further harmonics compensation is added to the controller. Open-loop Bode Diagram Magnitude (dB)

150

Ki=25 Ki=50 Ki=100 Ki=200

100

50

0 90

Phase (deg)

45 0

1) Plant model in the state space: Assume that the currents of the two inductors and the voltage of the capacitor as state T . The external input variables variables x = i1 i2 Vc (disturbances and references) are the grid voltage Vg and the T reference voltage Vref and the control , w = Vg Vref T w Vg Vref u input is u. Hence = . The output u signals from the plant are the tracking error e = Vref − VC and the current iC . The plant is described by the state equation

-45 -90

x˙ = Ax + B1 w + B2 u

-135 -180 -225 -270 1 10

10

2

10

3

10

4

Frequency (rad/sec)

Fig. 8.

Fig. 9. The block diagram of the H ∞ repetitive control scheme, where P is the transfer function of the plant, C is the transfer function of the stabilising compensator and M is the transfer function of the internal model.

Bode plots of the open-loop system for different Ki

and the output equation D11 C1 e x+ = y= D21 C2 iC ⎡

where

⎢ A=⎣

C. Design of the PI controller According to [7], [15], the PI controller in the synchronously rotating (dq) reference frame is the equivalent of the PR controller in the stationary (αβ) reference frame. Hence the proportional gain Kp and the integral gain Ki are not changed, when the controller transfer function is transformed from the rotating frame to the stationary frame and vice versa. D. Design of the H ∞ repetitive voltage controller The main objective of the voltage controller is to maintain a clean and balanced grid voltage in the presence of non-linear loads and/or grid distortion. The block diagram of the control system, consisting of a plant P , an internal model M and a stabilising compensator C, is shown in Figure 9.

⎡

R

− Lff

0

0

− Lgg − C1 ⎤

1 C

0 B1 = ⎣ − L1g 0 C1 = 0 0 −1 D11 = 0 D21 = 0 According to model M and compensator C system and this

0 0 ⎦, 0 , 1 , 0 ,

R

(5)

D12 D22

− L1f 1 Lg

0

⎡

w u

,

(6)

⎤ ⎥ ⎦, 1 Lf

⎤

B2 = ⎣ 0 ⎦ , 0 C2 = 0 1 0 , D12 = 0 , D22 = 0 .

Figure 9, the controller consists of an internal a stabilising compensator C. The stabilising assures the exponential stability of the entire implies that the error will converge to a small


276

steady-state error. The internal model M is obtained from a lowωc pass filter W(s) = s+ω with ωc = 5000 rad/sec cascaded with c −τd s a delay line e , with τd = τ −

1 = 19.9ms, ωc

(7)

which is slightly less than the fundamental period τ = 20ms. 2) Realisation of the extended plant P˜ : The H ∞ control problem shown in Figure 10 is formulated to minimise the H ∞ norm of the transfer function T z˜w˜ = F l(P˜ , C) from w ˜ = [v1 v2 w]T to z˜. The closed-loop system can be represented in terms of the Laplace transform as z˜ w ˜ = P˜ , u = C y˜, y˜ u where P˜ is the extended plant, and C is the stabilising compensator to be designed.

=

A C1

y2 = iC + µv2 =

A C2

⎤ v1 ⎥ 0 0 B1 B2 ⎢ ⎢ v2 ⎥ ⎣ w ⎦ ξ 0 D11 D12 u A B1 B2 w = µv2 + u C2 D21 D22 ⎤ ⎡ v1 ⎥ 0 0 B1 B2 ⎢ ⎢ v2 ⎥ ⎣ w ⎦ 0 µ D21 D22 u

⎡

(8)

(9)

z1 = W (e + ξv1 ) ⎡

A = ⎣ Bw C1 0

0 Aw Cw

0 Bw ξ 0

z 2 = Wu u =

Au Cu

⎡ ⎤ ⎤ v1 B2 ⎢ v2 ⎥ ⎥ Bw D12 ⎦ ⎢ ⎣ w ⎦ 0 u (10) ⎤ ⎡ v 1 ⎥ 0 0 0 Bu ⎢ ⎢ v2 ⎥ (11) 0 0 0 Du ⎣ w ⎦ u

0 B1 0 Bw D11 0 0

Combining equations from (8) to (11), the extended plant is then represented as ⎤ ⎡ B2 A 0 0 0 0 B1 ⎢ Bw C1 Aw 0 Bw ξ 0 Bw D11 Bw D12 ⎥ ⎥ ⎢ ⎢ 0 0 Au 0 0 0 Bu ⎥ ⎥ ⎢ ⎥ 0 Cw 0 Dw ξ 0 Du D11 0 P˜ = ⎢ ⎥ ⎢ ⎥ ⎢ 0 0 0 D 0 0 C u u ⎥ ⎢ ⎣ C1 0 0 ξ 0 D11 D12 ⎦ C2 0 0 0 µ D21 D22 (12) Fig. 10.

Formulation of the H ∞ control problem

The extended plant P˜ consists of the original plant P together with weighting functions W and Wu and weighting factors ξ and µ. A realisation of W is −ωc ωc Aw Bw = W = Cw 0 1 0 and a realisation of Wu is Wu =

Au Cu

Bu Du

which is frequency-dependent and it can be chosen as a high-pass filter to reduce the controller gain at high frequencies. From the formulation of the H ∞ control problem, Figure 10, the following can be deduced: B2 A B1 w y1 = e + ξv1 = ξv1 + u C1 D11 D12

3) H ∞ controller design: For H ∞ controller design the parameters of the system from Table II are used. The weighting −5000 5000 and functions are chosen as follows: W = 1 0 −5000 1 . The tuning parameters are chosen to Wu = −5 0.001 be ξ = 80 and µ = 0.8. Using theMATLAB hinf syn algorithm, C1 ∞ the H controller C = which nearly minimises the C2 ∞ H norm of the transfer matrix from w ˜ to z˜ is obtained. Using MATLAB c2d algorithm, the discrete controller is then given as follows: 7.9202z(z + 0.03645)(z − 0.3679)(z − 0.4694) , C1 (z) = (z − 0.3099)(z − 0.3679)(z − 0.1353) C2 (z) =

0.26617z(z − 0.8987)(z − 0.3679) . z 2 (z − 0.3099)(z − 0.3679)


4

Current [A]

2 0

#1:2 #1:1

-2 -4

0.00

0.01

0.02

0.03

0.04

0.05

0.04

0.05

Time [sec]

(a) Current error [A]

0.4 0.2 0.0

#1:1

-0.2 -0.4 0.00

0.01

0.02

0.03

Time [sec]

(b) Fig. 11. PR controller: (a) current IA , tracking current reference Iref and (b) tracking error of the controller 4

Current [A]

2

#1:2 #1:1

0 -2 -4

0.00

0.01

0.02

0.03

0.04

0.05

Time [sec]

277

All measurements were taken, when the inverter was connected to the grid. The active power generated by inverter was 75W and reactive power exchange with the grid was 0VAR. This corresponds to a power factor of 1. Half of the active power was consumed by the local resistive load and the other half was transferred to the grid via a step-up transformer. Figure 11(a) shows the output current IA (red) of the PR controller tracking current reference Iref (green) and 11(b) shows tracking error of the controller. The PR controller is capable to eliminate the steady-state error around the resonant frequency and its tracking performance around this frequency is satisfactory. For better performance of the controller, resonant frequency should be all the time identical to the slightly varying grid frequency [14]. The current harmonic distortion was 4.13%, and DC current component was 100.2mA. Figure 12(a) shows the output current IA of the PI controller tracking current reference Iref and 12(b) shows its tracking error. The recorded current distortion was 4.42%. The tracking performance of the PI controller is comparable to PR controller, however current harmonics distortion is slightly higher. The DC current component was 102.3mA. The current and voltage outputs of the H ∞ repetitive controller are shown in 13(a) and 13(b) respectively. Figure 13(c) shows the controller tracking error. The recorded current THD was 2.96% and DC current component was 80.96mA. It is worth highlight the fact that the voltage reference Vref (green), calculated by the power controller, indicate higher distortion, than the actual voltage output (red). The voltage and the current THD together with DC current component for all three different control schemes are summarised in Table III. TABLE III THD AND DC CURRENT INJECTION COMPARISON OF CONTROLLERS

(a)

PERFORMANCE

Current error [A]

0.4 0.2

THD [%]

#1:1

0.0 -0.2 -0.4 0.00

0.01

0.02

0.03

0.04

DC component [mA]

Controller

VA

IA

Vgrid

IA

PI

1.02

4.42

1.91

102.3

PR

1.22

4.13

1.72

100.2

Repetitive

1.22

2.96

1.96

80.96

0.05

Time [sec]

(b)

VI. C ONCLUSION

Fig. 12. PI controller: (a) current IA , tracking current reference Iref and (b) tracking error of the controller

Three different control schemes are implemented for an experimental grid-connected inverter. The result shows that the H ∞ repetitive controller offers significant improvement in terms of waveform quality and current harmonic distortion over the conventional PI and PR controllers. The advantages of the H ∞ voltage repetitive controller, in addition to the independent control of each phase, are better tracking performance, smaller

V. E XPERIMENTAL RESULTS In this section, the experimental results of the three different controllers are presented and compared in terms of the tracking error, current harmonics distortion and DC current injection.


278

4 #1:1 #1:2

Current [A]

2 0 -2 -4

0.00

0.01

0.02

0.03

0.04

0.05

0.04

0.05

0.04

0.05

Time [sec]

(a)

20

#1:1 #1:2

Voltage [V]

10 0 -10 -20

0.00

0.01

0.02

0.03

Time [sec]

(b)

Voltage error [V]

2 1 #1:1

0 -1 -2

0.00

0.01

0.02

0.03

Time [sec]

(c) Fig. 13. H ∞ repetitive voltage controller: (a) current IA , (b) voltage VA tracking reference Vref and (c) tracking error of the controller

DC current component and smaller THD. The disadvantage is that the design is a bit more complicated and the controller is a bit more complex. R EFERENCES [1] Thomas Ackerman (Editor). Wind Power in Power Systems. John Wiley and Sons, Ltd, 2005. [2] F. Blaabjerg, Zhe Chen, and S.B. Kjaer. Power electronics as efficient interface in dispersed power generation systems. Power Electronics, IEEE Transactions on, 19(5):1184–1194, Sept. 2004. [3] Frede Blaabjerg, Florin Iov, Remus Teodorescu, and Zhe Chen. Power electronics in renewable energy systems. Power Electronics and Motion Control Conference, 2006. EPE-PEMC 2006. 12th International, pages 1– 17, Aug. 2006. [4] George Weiss, Qing-Chang Zhong, Tim C. Green, and Jun Liang. H infinity repetitive control of dc-ac converters in microgrids. IEEE Transactions on Power Electronics, 19(1):219–230, 2004.

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