Multi-loop control algorithms for Seamless Transition of Grid-connected Inverter

Qin Lei

ECE department, Michigan State University

East Lansing, MI, USA leiqin@msu.edu

Shuitao Yang ECE department,

Zhengjiang University Hangzhou, Zhejiang, PRC

styang@msu.edu

Fang Z. Peng ECE department,

Michigan State University East Lansing, MI, USA fzpeng@egr.msu.edu

Abstract-The grid-connected inverter works as a controlled current source in grid-connected mode, while operates as a controlled voltage source in standalone mode. So in case of utility faults or intentional islanding, the inverter has to change its control strategy from current control to voltage control. This paper first proposed a multi-loop voltage controller with capacitor differential voltage feedback inner loop and voltage reference feedforward for standlone system especially designed to maintain the voltage continuity and decrease the dynamic response time in transition. However, the turn-off characteristics of the SSR which is used as switch here makes the transition last for a long time up to half a cycle. So in order to force the grid currents through the SSR switches to decrease to zero at much less time and make the voltage fluctuates within permissible levels during SSRs turn-off period, the voltage control based voltage amplitude regulation, instantaneous voltage regulation algorithms and current control based zero current regulation algorithms have been adopted in transition. After disconnection from the grid, the inverter will recover its voltage to a rated level. Simulation and experiments are carried out to verigy the proposed controllers and algorithms.

I. INTRODUCTION

In the transition from grid-connected to standalone operation, Solid State Relay (SSR) is used in this paper as the switch between DG and grid which can not turn off right after the driving signal has been removed until the current drops to zero. In order to keep the output voltage less distorted, it is preferred to force the current falling down to zero as soon as possible. Generally, the inductor current could be driven to zero by establishing a negative voltage [1] on it or by controlling the current to be zero directly. Fig. 1 shows the system configuration for transition. A multi-loop voltage controller with capacitor differential voltage feedback inner loop and voltage reference feedforward has been adopted for standalone system and a current controller with grid voltage feedforward has been chosen for grid-connected system. Based on these, some new control strategies for transition have been analyzed in this paper. Simulations and experiments have been carried out to verify the operation principle and features.

II. CONTROL STRATEGY FOR STANDALONE AND GRID CONNECTED SYSTEM

A. Multi-loop controller for standalone system For standalone system, a multi-loop voltage controller with capacitor current feedback as inner loop can eliminate the output LC filter resonant peak to increase stability in load disturbance and enhance dynamic performance [2]. Compared to inductor current feedback, it has lower gain for distortion load current hence has better disturbance rejection capability. However, it has high requirement for the accuracy and dynamic performance of the current sensor because capacitor current is small-scale. So capacitor voltage differential feedback is utilized in this paper [3] to replace capacitor current feedback as shown in Fig.2, which saves a high quality required current sensor. In addition, considering the grid-connected to standalone transition performance, only a PI controller would make the initial output voltage be zero, hence make it discontinuous to the previous voltage. In order to overcome this limitation, a reference voltage feed-forward synchronized with grid is proposed to maintain the waveform continuity and also boost dynamic response. Fig. 3 shows the step response for the closed-loop transfer function with and without voltage reference feedforward. It can be verified that adding a feedforward can boost the dynamic response which is beneficial in transition. Also, a single proportional controller is selected to replace PI controller in order to reduce the harmonics in the waveform which will be analyzed as follows. The output voltage-to-reference voltage and output voltage-to-load current transfer function can be expressed as follows:

_ _

2

2

( ) ( ) ( )(1 )

( ) 1

( ) 1

s

s s

s s

o vo vref ref vo io osT

vrefsT sT

f f f f d v

f fosT sT

f f f f d v

v s G s v G s iK e v

L C s R C K e s K eL s R

iL C s R C K e s K e

−

− −

− −

= ⋅ − ⋅ =+

+ + + ++

−+ + + +

(1)

Fig. 4 compares the bode diagrams for voltage closed-loop transfer function with P and PI controller. By only using a P controller can damp the amplitude peak rise in PI controller between 60HZ and 900 HZ to zero hence reduces the

978-1-4244-4783-1/10/$25.00 ©2010 IEEE 844

T 1 2ms= i

T 2 5ms= i

Fig. 3 Step response of the closed loop transfer function

(a)with voltage feedforward (b)without voltage feedforward

harmonic components. Also with feedforward, when Kv=0.3, the steady state error is within 0.07%, but without feedforward loop, the steady state is 10% even when vK rises up to 9. Obviously that feedforward path enhances the steady-state performance and system stability.

80−

60−

40−

20−

0

g(

)

1 10 100 1 103× 1 104× 1 105×

150−

100−

50−

0

Fig. 4. Bode diagrams of _ ( )vo vrefG s with P or PI controller

B. Current controller for grid-connected system A convertional proporitional-integrator (PI) controller along with a capacitor voltage ov feed-forward compensator has been used here for grid-connected operation[4-5], as shown in Fig.5 (a). Capacitor voltage feed-forward is employed to reduce the effect of the grid voltage and to increase dynamic response. Fig.5 (b) shows the simplified control block diagram. Without considering the grid

,f fL RfC

Grid

SSR

dcV dcC a

cb

iv ovLi

1S 3S 5S

4S 6S 2S Transformer (1:2)

gi

,g gL r

Fig. 1. System configuration for transition from grid-connected to standalone system

1fC s

iv 1f fL s R+

oiLi ci ov

ov

vKov

refv 0gvssTe−

dK s

Augmented Control Plant gv1gL s

gi

Fig. 2. Voltage control block diagram for standalone system

845

( )iref igG s_

( )vg igZ s_

f (Hz)

Mag

nitu

de (d

B)

( )iref igG s_

( )vg igZ s_

f (Hz)

Phas

e(de

g)

Fig.6. Bode diagrams of ( )iref igG s_ and ( )vg igZ s_

impedance, the closed-loop transfer function of the grid current can be obtained as:

( ) ( ) ( ) ( ) ( )

( ) ( )

_ _

3

2 2

g iref ig ref vg ig g

p i f fref g

f p i f p i

I s G s I s Z s V sK s K L C s

I s V sL s K s K L s K s K

= − +

= −+ + + +

(2)

The bode plot of closed loop transfer function is shown in Fig. 6. It has small tracking error and high distortion rejection. With considering Zg,, the closed-loop transfer function of the grid current can be rewritten as:

( ) ( ) ( ) ( ) ( )

( )

( )

_ _

4 3 2

3

4 3 2

g iref ig ref vg ig g

p iref

f g f f f g f p i

f fg

f g f f f g f p i

I s G s I s Z s V sK s K

I sL L C s L C r s L s K s K

L C sV s

L L C s L C r s L s K s K

′ ′= − =+

+ + + +

−+ + + +

(3)

Compared to previous case, there will be an additional second-order transfer function ( )aG s in the control loop,

2

2 2 2a

1( )1 2

na

g f f g n nG s

L C s C r s s sω

ξ ω ω= =

+ + + + (4)

,where n g f a g f g1/ L C , r C / Lω = ξ = .If the line impedance

is high inductive, gr is relatively small, then the aG (s) in (4)

will be ‘‘under-damping’’, which may cause the instability. So the compensator parameter has been chosen accordingly to adjust the steady-state error and system stability margin.

III. PRINCIPLE AND ANALYSIS OF TRANSFER STRATEGIES

A. Voltage control based transfer strategies The voltage amplitude regulation, and instantaneous

voltage regulation [6] are both based on applying voltage control strategy in transition time. Fig. 7 shows the voltage and current phasor diagram for above two strategies. Voltage amplitude regulation method represses the current by increasing or decreasing voltage amplitude while keep phase the same in the transition. Once the grid current is force to decrease to zero, the SSR are turned off and the reference output voltage is recovered to the rated value. It takes less time to complete the transfer process hence minimize the voltage distortion. Instantaneous voltage regulation is to generate a constant voltage difference holding a fixed ratio to the initial grid current at transition start, which can settle the transition time to a fixed value. The detailed equations between transition time tΔ and other parameters are shown

iv 1fL s

ov

ip

KKs

+

gi

refiPWMK

fC s

gimvLi

Cig gL s r+

gv

ov ov

(a) Grid current control with voltage feedforward

Lv 1fL s

ip

KKs

+

gi

refi Li2

11g f f gL C s C r s+ +

fC s

gi

gv

(b)Simplified control block diagram

Fig. 5. Current control block diagram for grid-connected system

846

in Table.1. The variables used are defined as: sv -- grid phase voltage; 1ov -- initial inverter output phase voltage; 2ov --regulated inverter output phase voltage; gi --grid side phase current; 0t --the moment that the drive signal of SSR is given;

Lv --grid side inductor regulated voltage; bV --pre-set voltage drop on the inductor.

B. Current control based transfer strategies The principle of zero current regulation is to retain the current control mode in transition but change the current reference to zero. After the current drops to zero, SSR will turn off and the system shifts to voltage control. Due to the delay of zero current sensing, there is a blank time between disconnection and control mode shift in which voltage is out of control. However, the zero current regulation dynamic response depends on the step response time of current control loop, which is shorter than the time for voltage control loop, thus it gets better dynamic performance. However, this method doesn’t rely on the grid side voltage and also don’t need to sense the voltage accurately. So it is preferred in grid voltage short circuit or highly disturbed case.

IV. SIMULATION AND EXPERIMENTAL RESULT

The system parameter in the simulation and experiment is: 377 / , 10 , 85 , 200 , 1 ,

50 , 0.1 , 0.1 , 20sw sm dc f

f g g ref

rad s f kHZ V V V V L mHC uF L mH r I A

ω = = = = == = = Ω =

Assume grid absorbs current from inverter. Fig. 8 (a) (b) (c) show the simulation results for the three strategies respectively. The current reference in grid-connected mode is set to be 20A. In Fig.8 (a), the inverter output voltage reference is set to be 0.8 times of the grid voltage in the transition. According to the equations in table I, the transition time is calculated to be 0.2ms. The total transition time is 0.8ms by adding the caculated value and voltage loop step response rising time 0.6ms, which is coincident with the simulation results.

sv2ov

gisv

(a)

sv2ov

gisv

(b)

sv

sv2ov

gisv

(c)

Fig. 8. Simulation results for grid voltage Vs, inverter output voltage Vo2, grid side current ig in transition using different strategy (a) voltage amplitude

regulation (b) voltage instantaneous value regulation (c) zero current regulation

gI•

2oV•

sV•

2LV•

1LV•

1oV•

0

2oV•

sV•

2LV•

1LV•

1oV•

ϕ

X

gI•

θ

sV '•

gI '•

2oV '•

2LV•

Fig. 7.Phasor diagram at (a)Voltage amplitude regulation (b) Instantaneous voltage regulation

Table I. Equations for voltage, current and transition time 2

02 22

00

1

−= − = = =

−

+ + + = = = = =

g s o L

g g g gmg sm m L o s g

g sm o m

g gg sm s b L b L

b

i v v v t

di i L IVoltage Amplitude Re gulation I sin( t ) V sin( t ) V sin( t ) v v v L t

dt di / dt V V

L i ( t )Ins tan tan ous Voltage Re gulation I sin( t ) V sin( t ) v v v V kv ( t ) t Co

V k

Δ

ω ω ω Δ

ω θ ω θ Δω

ns tan t

847

In Fig.8 (b), the constant voltage difference is 20V, so the transition time is fixed at 1ms as calculated, which is the same as simulation result. In Fig. 8 (c), as mentioned before current regulation method has relatively small transition time but bigger voltage distortion. Fig. 9 shows the experimental results for voltage instantaneous value regulation and zero current regulation and Fig. 10 shows the picture of experiment hardware. The three upper sinusoidal waveforms are the inverter output voltage and the three lower ones are the current before the load (load are connected in parallel with capacitor on the grid side). So the current after the transition is equal to the load current which is not zero as simulated one. The green one is the grid outage signal, which also indicates the time that the SSR off signal is sent out. From the experimental waveforms, it can be seen that the voltage distortion and transition time are both in a reasonable range. Voltage control based regulation will last for longer time than current control based strategy, while the current

abv bcv cav

ai bi

(a)

abv bcv cav

ai bi

(b) Fig. 9. Experiment results for inverter output line to line voltage and phase

current in transition using two strategies (a) Instantaneous voltage regulation (b)Zero Current regulation

Fig. 10. Experiment hardware prototype

control one may cause a relatively big voltage amplitude and phase change. Voltage based algorithms are used when the grid maintain its voltage after transition and current based algorithm is used when grid voltage is highly distorted.

V. CONCLUSION

This paper proposes the multi-loop voltage controller with reference feedforward strategy for standalone system in order to obtain good stiffness and dynamic performance in transition. Also voltage based and current control based algorithm are adopted in transition to force the current to decrease to zero at a short time. The simulation and experimental results show that the proposed controller and algorithms can provide seamless transfers between the two operating modes for the inverter, avoiding the temporarily uncontrolled output voltage. It can be valuable for grid-connected inverters such as PV and fuel cell generation system.

REFERENCE [1] Guoqiao Shen, Dehong Xu and Danji Xi, “Novel seamless transfer

strategies for fuel cell inverters from grid-tied mode to off-grid mode,” Applied Power Electronics Conference and Exposition, 2005. APEC 2005. Twentieth Annual IEEE, Volume 1, 6-10 March 2005 Page(s):109 - 113 Vol. 1.

[2] Abdel-Rahim, N.M. and Quaicoe, J.E., “Analysis and design of a multiple feedback loop control strategy for single-phase voltage-source UPS inverters,” Power Electronics, IEEE Transactions, on Volume 11, Issue 4 July 1996 Page(s):532 – 541.

[3] Shuitao Yang, Xinping Ding, Jinyun Liu and Zhaoming Qian, “Analysis and Design of a Cost-Effective Voltage Feedback Control Strategy for EPS Inverters,” Power Electronics Specialists Conference, 2007. PESC 2007. IEEE 17-21 June 2007 Page(s):477 – 482.

[4] D. M. Brod and D. W. Novotny, “Current control of VSI-PWM inverters,” IEEE Trans. Ind. Appl., vol. IA-21, no.4, pp. 562–570, Jul./Aug. 1985.

[5] M. P. Kazmierkowski and L. Malesani, “Current control technique for three-phase voltage-source PWM converters: A survey,” IEEE Trans. Ind. Electron., vol. 45, no. 5, pp.691–703, Oct. 1998.

[6] Guoqiao Shen, Dehong Xu and Xiaoming Yuan, “Instantaneous Voltage Regulated Seamless Transfer Control Strategy for Utility-interconnected Fuel cell Inverters with an LCL-filter,”Power Electronics and Motion Control Conference, 2006.IPEMC 2006. CES/IEEE 5th International, Volume 3,14-16 Aug. 2006 Page(s):1- 5

848