Control of Grid-Connected Voltage Source Inverter with LCL Filter

Suzan Eren, Alireza Bakhshai, Praveen Jain Department of Electrical and Computer Engineering

Queen’s University Kingston, Ontario, Canada

Abstract—This paper presents a control scheme for a grid-connected three-phase voltage source inverter with an LCL filter, which is suited for renewable energy applications. The proposed method has the following properties: fast tracking, optimized dynamics, grid disturbance rejection, and active resonance damping. The controller is based on an augmented linear quadratic regulation (LQR) scheme, which is optimized based on a weighted cost function. The LQR controller is augmented to include two complex conjugate poles at the grid frequency for sinusoidal voltage disturbance rejection upon connection to the grid. Furthermore, this control scheme actively damps the resonance introduced into the closed-loop system through the third-order LCL filter. Finally, the current reference is found by calculating the instantaneous power, which allows for faster power tracking compared to using the technique of measuring average power. Results verify the validity of the proposed control scheme.

I. INTRODUCTION Renewable energy is a sustainable solution to the global

energy crisis, which is being caused by diminishing fossil fuel reserves, energy security concerns, and pollution. However, to reach the consumer, renewable energy sources should be connected to the utility grid. This brings with it certain challenges, such as meeting increasingly strict grid connection standards like IEEE 1547, which place emphasis on the quality of the current injected into the grid. Other challenges include maximizing power delivery, increasing reliability, and decreasing cost.

Renewable energy sources are connected to the grid through power converters. Controlling grid-connected power converters is challenging and presents a number of control issues. The proportional integral (PI) controller is the conventionally used control method for this application, and its sluggish speed prevents it from efficiently transferring the produced power. Also, as renewable energy sources become more widespread, it is increasingly imperative that the power transferred from the source to the grid is a clean signal free of noise and distortion. To achieve these objectives, a control scheme is required that is tailored to this application.

First-order L filters are typically used for the grid-connected voltage source inverters used in this application.

These filters need a large inductor in order to filter out the switching harmonics at the output of the inverter to an acceptable degree. Using a third-order LCL filter increases the attenuation of the switching harmonics threefold. Thus, the LCL filter is less bulky and has better filtering capabilities. However, LCL filter has resonant behavior around its resonant frequency. A passive or active damping scheme is required to restore stability to the closed-loop control system. Since passive damping is lossy, active damping techniques introduced by the controller are more attractive.

Several innovative control schemes for grid-connected voltage source inverters have been proposed in the literature to address the aforementioned challenges, of which [1]-[6] are a few. In [1] a robust control strategy is proposed for load voltage regulation in grid-connected inverters that use an LCL filter. In this paper a multi-loop current controller is designed to decouple the current and voltage control dynamics. The use of a very complicated control algorithm is the drawback of the proposed controller. In [2] a modified current controller based on the PR control approach is proposed to improve the performance of the closed-loop system against current harmonic. Although the proposed technique is able to handle the current harmonics, the speed of the controller is limited against load changes. In [3], an active damping method is introduced for a grid-connected rectifier. The experimental results show satisfactory damping and stable operation. However, the bandwidth of the controller is limited against load changes.

The proposed system is described in Section II. This section includes information about the system model used to design the controller, the proposed control scheme for the grid-connected voltage source inverter with an LCL filter, and the method used to generate the current reference. Results are given in Section III, which is followed by the conclusion in Section IV.

II. PROPOSED METHOD

A. System Model The system model used to analyze and design the proposed

system is shown in Fig. 1. This figure shows a voltage source inverter connected to the point-of-common-coupling (PCC) on

978-1-4577-1216-6/12/$26.00 ©2012 IEEE 1516

the grid through an LCL filter. The system model is represented by the following equations:

diinv

dt=

1L1

(e - R1iinv - vo ) (1)

digdt

=1L2

(vo - R2ig - vPCC ) (2)

dvo

dt=

1Co

(iinv - ig ) (3)

L1R1e vPCC

iinv ig

Inverter

L2R2vo

Co

Figure 1. System Model with LCL Filter.

B. Proposed Control Scheme The proposed controller is a state feedback controller,

which has been optimized using linear quadratic regulation (LQR). Additionally, the state feedback is augmented to include a term for the grid disturbance (i.e., the voltage at the PCC) at the grid frequency of 60 Hz. This is achieved by adding two complex conjugate poles at the grid frequency to the state feedback controller.

By optimizing the coefficients of the state feedback controller, an optimal controller can be achieved, which can steer the system from one point to another on an optimal trajectory by minimizing the energy of the controlled output and minimizing the energy of the control signal. An LQR optimized state feedback controller operates by minimizing a quadratic cost function, represented by the following equation:

J = z(t)

2+ ρ u(t)

2dt

0

∞

(4)

The proposed augmented state space matrix, which is used to design the controller, is represented by the following equation:

X•

Q•

= Aaugmented

XQ

+ BaugmentedU +Waugmented (5)

where Q =

q1

q2

represents the augmented states and

Waugmented represents the disturbance caused by the voltage at the PCC.

Given that the voltage at the point of common coupling can be seen as a disturbance, state feedback control under a constant input disturbance can be addressed by defining a new state vector. Two resonant poles are placed at the grid frequency. Thus, there is infinite gain and disturbance rejection at that frequency, which ensures perfect tracking.

Let:

q = s

s 2 + ωn2 y (6)

And let:

q1 = q

q2 = q•

1

(7)

Thus, the augmented state space matrix can be written as the following:

PCCc

g

inv

n

c

g

inv

vL

e

L

L

qqvii

LLR

CC

LLR

LLR

qqvii

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛−

+

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

−

+

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

−−−

−

−−

−−

=

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

000

10

1000

1

01010000

00011

0010

0010

2

1

1

2

1

2

11

1

22

2

11

1

2

1

ω

(8)

C. Controller Current Reference Conventionally, the average output power of the voltage

source inverter is measured, and used to calculate the reference current for the controller. Since average power is measured through integration, this introduces a delay into the control loop. The proposed control scheme is able to avoid this delay by using instantaneous power values in order to calculate the reference current. The current reference is calculated using the following equation:

iref = p* (t)

vPCC

(9)

where vPCC is the voltage at the point of common coupling and p*(t) is given by:

p(t) = V sin(ωt)I sin(ωt +θ ) (10)

and given that,

P = 1

2VI cos θ( ) (11)

Q = 1

2VI sin θ( ) (12)

then (10) can be rewritten as:

p(t) = P[1− cos(2ωt)]+ Q sin(2ωt) (13)

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By supplying the desired average real output power to (11), the current reference can be found through (9). In this control scheme the desired average output power can be found by placing a DC-link controller to keep the voltage across the DC-link capacitor constant. When this voltage is constant, all of the input power is transferred to the voltage source inverter. The average reactive output power is chosen according to the voltage regulation needs of the grid.

III. RESULTS The proposed control scheme has been validated using

simulation and experimental setups.

A. Simulation Results The PSIM software has been used to obtain these

simulation results. Figure 3 shows the transient response of the proposed controller against the step change in the active power. According to this figure, the grid current has a very high quality and the controller shows very fast response. Figure 4 illustrates the tracking error of the inverter output current. Figure 5 depicts the transient response of the proposed controller against step changes in the active and reactive power. According to this figure, the controller can effectively control the phase of the grid current based on the required reactive power.

B. Experimental Results

A TMS320F28335 eZdsp board has been used to obtain these experimental results. This DSP board is a floating-point DSP, which offers a very flexible environment for advanced calculations. This DSP has a 12-bit ADC with a sequencer that is able to convert multiple analog signals sequentially. It also has 6 EPWM (Enhanced PWM) modules, which can produce the desired PWM signals with a very high degree of flexibility.

Figure 6 shows the preliminary experimental results of the proposed controller. In this figure, the output voltage of the inverter and the output current of the inverter are shown.

IV. CONCLUSION

This paper presents a novel control scheme for a grid-connected three-phase voltage source inverter. The proposed control loop includes an instantaneous power-based current

reference generator, which does not introduce a delay into the control loop, as does the conventional average power-based current reference generation. The three-phase VSI is connected to the grid through an LCL filter, which is not only less bulky than the conventional L filter, but also has greater switching harmonic output mitigation. The control method consists of an optimal state feedback controller, which provides fast tracking. It also provides active damping to deal with the resonance created by the LCL filter due to its optimal pole placement. Additionally, the state feedback controller is augmented with two complex conjugate poles at the grid frequency to reject the sinusoidal disturbance caused by the voltage at the point of common coupling. This work has significant real-world application, since renewable energy sources are the subject of increased attention and the grid connection or renewable energy sources will be subject to increasingly strict regulations.

REFERENCES [1] Mohamed, Y.A.-R.I.; , "Mitigation of Dynamic, Unbalanced, and

Harmonic Voltage Disturbances Using Grid-Connected Inverters With LCL Filter," Industrial Electronics, IEEE Transactions on , vol.58, no.9, pp.3914-3924, Sept. 2011.

[2] Guoqiao Shen; Xuancai Zhu; Jun Zhang; Dehong Xu; , "A New Feedback Method for PR Current Control of LCL-Filter-Based Grid-Connected Inverter," Industrial Electronics, IEEE Transactions on , vol.57, no.6, pp.2033-2041, June 2010.

[3] Bierhoff, M.H.; Fuchs, F.W.; , "Active Damping for Three-Phase PWM Rectifiers With High-Order Line-Side Filters," Industrial Electronics, IEEE Transactions on , vol.56, no.2, pp.371-379, Feb. 2009.

[4] [4] Ricchiuto, D.; Liserre, M.; Kerekes, T.; Teodorescu, R.; Blaabjerg, F.; , "Robustness analysis of active damping methods for an inverter connected to the grid with an LCL-filter," Energy Conversion Congress and Exposition (ECCE), 2011 IEEE , vol., no., pp.2028-2035, 17-22 Sept. 2011

[5] F. Gao and M. R. Iravani, “A Control Strategy for a Distributed Generation Unit in Grid-Connected and Autonomous Modes of Operation,” IEEE Transactions on Power Delivery, pp. 850-859, Vol. 23, No. 2, April 2008.

[6] Marwali, M.N.; Min Dai; Keyhani, A., "Robust stability analysis of voltage and current control for distributed generation systems," Energy Conversion, IEEE Transactions on , vol.21, no.2, pp. 516-526, June 2006.

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ci

ai

ref,av

ref,bv

θ

*ai*bi

bi

ref,cv

*ci

cav gai

cbv gbi

ccv gci

Figure 2. Grid-Connected Three-Phase Voltage Source Inverter with Proposed Control Scheme.

0

-10

-20

10

Ig

0

-10-20

10

20

Iinv

0.2 0.3 0.4Time (s)

0

1000

2000

W

0

0.5

1

1.5

2

2.5

3

Pref_pu pref

0.28 0.3 0.32 0.34Time (s)

0

-10

-20

10

Iref Iinv

(a) (b)

Figure 3. Transient response of the proposed controller against a step change in active power reference, (a) grid current, inverter output current, and output power, (b) instantaneous and average power reference, reference and actual inverter current.

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0

-0.5

-1

0.5

1

1.5

2

Ve

0.26 0.28 0.3 0.32 0.34 0.36Time (s)

0

-10

-20

10

Iref Iinv

0

-100

-200

-300

100

200

300

Vg Iinv

0 0.1 0.2 0.3 0.4 0.5Time (s)

0

-500

500

1000

1500

2000

W

(a) (b)

Figure 4. Transient response of the proposed controller against a step change in active power reference, (a) tracking error of the inverter current (b) inverter output current and grid voltage.

0

-200

200

Vg Iinv*10

0-1

1234

pref

0.1 0.2 0.3 0.4Time (s)

0

-10

10

20

Ve

0

-10-20

10

20

Iinv Iref

0-1

1234

pref

0.1 0.2 0.3 0.4Time (s)

0

-5

5

Ve

(a) (b)

Figure 5. Transient response of the proposed controller against step changes in active and reactive power reference, (a) grid voltage, inverter output current, and instantaneous power, (b) tracking error of the output current.

(a) (b)

Figure 6. Experimental results: (a) Inverter output voltage and output current, (b) Inverter output current.

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