A Low Cost Solution to Grid-connected Distributed

A Low Cost Solution to Grid-connected Distributed Generation Inverters Guoqiao Shen1㧘Jun Zhang1, Xuancai Zhu1, and Dehong Xu1 1

Power Electronics Institute, Department of Electrical Engineering, Zhejiang University, China

Abstract- A low cost utility interactive inverter is valuable to the residential PV or fuel cell distributed generations. This paper presents a low cost solution to the single-phase grid-connected inverters, including the inverter topology, filter structure, and the current control methods. The reason for choosing the proposed converter topology is given. A novel current control method using the combinatorial feedback of the grid current and the capacitor voltage is introduced for the inverter, so that a low cost non-damped or slightly damped LCL-filter can be employed to attenuate the switch frequency current ripple and the system can be optimized easily for minimum steady-state error and current harmonic distortions, as well as the system stability. The characteristics of the inverter system with the proposed controller are investigated. Simulations and experimental results on a 5kW fuel cell inverter are provided to verify the proposed solution and its control strategy.

I.

INTRODUCTION

The contribution of a renewable power source to the total power generation becomes more and more important. For low-power applications, like household photovoltaic (PV) panels and fuel cells, the cost of the generation system is an important issue. Since the fuel cell or PV cell delivers dc power, it should be inverted to ac power before being connected with the grid. Therefore, a low cost grid-tied inverter is much valuable to the residential PV and fuel cell distributed generations. Traditionally, L-filter is used as the interface between the grid network and the grid-connected voltage source PWM inverters. In contrast, the alternative LCL form of low-pass filter offers the potential for improved harmonic attenuation with lower total inductance, which is a significant advantage for the system cost and high dynamic performance [1]. However, the systems incorporating LCL filters are of third order, and they require more complex current control strategies to maintain system stability and are more susceptible to interference caused by grid voltage distortion [2]. Due to the LCL-filter resonance, the control loop gain and bandwidth are limited by the requirement for system stability when a PI control method in stationary reference frame is applied [3-4]. It has two main drawbacks: inability of the PI controller to track a sinusoidal reference without steady-state error and poor disturbance rejection capability. Proportional Resonant (PR) controller gained a large

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popularity in recent years in current regulation of grid-tied systems [5]–[6]. It introduces an infinite gain at a selected resonant frequency for eliminating steady-state error or current harmonics at that frequency. However the harmonic compensators of the PR controllers are limited to several low-order current harmonics, due to the system instability when the compensated frequency is out of the bandwidth of the system [7-8]. Passive damping method is often used to maintain the system stability, but it is limited by cost, losses, and degradation of the filter performance [9]. The use of active damping by means of control may seem attractive but it is often limited by a complex tuning procedure of the controllers [10]. This paper proposes a low cost solution for single-phase grid-connected inverters. The reasons for choosing the proposed converter are given. A new current feedback method with the combination of the grid current and capacitor voltage is introduced, so that a non-damped or slightly damped LCL-filter can be used to attenuate the switch frequency current ripple. In this way, the control system with the LCL-filter can be degraded from a third-order function to a first-order one, then a large proportional gain can be selected and a wide bandwidth can be obtained. Its principle is similar to the LCCL control strategy which was presented in [11], but the feedback is easer to be carried out. Consequently, the control system can be optimized easily for minimum steady-state error and current harmonic distortions, as well as the system cost. The characteristics of the inverter system with the proposed controller are investigated. Simulations and Experimental results on a 5kW fuel cell inverter prototype are presented in this paper. II.

SYSTEM TOPOLOGY

In order to select a proper converter topology, the special application must be considered and the overall performance requirements to the inverter are: 1. To deliver a grid current with a high power factor and a low current THD, match the code such as IEEE Std.1547-2003. 2. To be operated in both standalone and grid-tied modes. 3. To have a high efficiency in the whole operation range. 4. Maximum power or long lifetime should be ensured for the PV cells and fuel cells. 5. The cost should be minimized. Because the PV cells and the fuel cells deliver dc power in a wide voltage range and the grid voltage is 220Vrms, the inverter should perform two tasks: The power must be inverted and the

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voltage must be regulated to match both input and output side. These tasks could either be done by connecting an inverter to the green power followed by a 50Hz transformer or by connecting a switch mode DC-DC converter to the green power followed by a grid connected inverter without 50Hz transformer. In order to limit the physical size and the cost of the system, a system topology with a DC-DC converter followed by a half-bridge inverter with an LCL-filter is preferred as in Fig.1. Thus, no 50Hz transformer is used.

Fig. 1. System topology for the grid-connect fuel cell inverter

III.

FILTER OPTIONS AND CHARACTERISTICS

The main three considerations for the design of the LCL-filter are the attenuation at the switching frequency, the current ripple out of the inverter, and the reactive power of the filter. The switching frequency current ripple is caused by the pulsed voltage vi from the inverter due to the PWM control. In Fig.1, The transfer function from vi to grid current i2 is shown in (1). I2 (s) 1 GVi  I 2 ( s ) (1) Vi ( s ) D (1  D ) L2 Cs 3  Ls Here, L L1  L2 , D L1 L . The grid inductance Lg is included in L2, and series resistance of the inductance is neglected. Fig.2 shows the bode plots of the transfer function for different L1 and L2 combinations with a constant total inductance L=3.1mH, and C=12uF. From the equation (1) and Fig. 2, the LCL-filter is shown to be a third-order function with a peak at the resonance frequency, and its phase change rapidly. When C=0, that means the L-filter is used, it is degraded to a first-order function (solid line in Fig.2). For a given frequency above the resonant frequency of the filter, the transfer function GVi-i2(s) gets the minimum amplitude in case =0.5. In other words, for a given switch frequency and a given attenuation requirement, the total inductance value required in LCL-filter is less than that in L-filter, it is minimized when L1=L2=L/2. Generally, less inductance value means lower cost for the system. However, system incorporating LCL filter is of the third order, and there exists a peak amplitude response at the resonant frequency of the LCL-filter. Therefore, it requires more carefully design of current control strategy to maintain system stability. The most popular method is to insert a damping resistor (Rd) in the capacitor shunt branch of the LCL-filter [2], but the filter with a passive damping has less attenuation in the high

frequency region. Fig.3 shows the bode plots of the V-I transfer function from inverter output voltage to grid current for the filters with deferent damping resistors. As shown in Fig.3, the damped filter has more attenuation on the resonant frequency, but it has less attenuation in the high frequency region. This will make the damping filter a serious problem to match the EMI standards for high power converters with a lower switching frequency. IEEE Std.1547-2003 recommended that the harmonics higher than 35th should be limited to be less than 0.3%. Assume that the PWM switching frequency is selected as 10kHz for a 5kW inverter, the switching frequency voltage is about 300V in the inverter output side, more than -72dB additional attenuation is required in the transfer function GVi-I2(s) at the switching frequency to meet the 0.3% current ripple requirement. From Fig.3, the V-I attenuation for non-damped or slight damped filter is more than -72dB, but .with a damping resistor of 5ohm, the V-I attenuation is only -65dB at 10kHz. Hence, for a given switching frequency and required attenuation, when a passive damping is introduced, the size of the filter will be raised, that will result in a decreased system bandwidth and increasing in system cost. Besides, the passive damping can also cause extra power loss that may result in need for more cooling.

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Fig.2. Bode plots of the transfer function of the LCL-filters /GVi-I2(s)

Fig.3. Bode plots of the V-I transfer function of the LCL-filters

IV.

CONTROL STRATEGIES

A.

Conventional Feedback Methods As shown in Fig.4, the inverter current (a) or the grid current (b) is conventionally used as a feedback variable of the current controller to regulate the current injected into the grid.

The use of active damping by means of control, such as the addition of an inner control loop of the capacitor current, may seem attractive, but it is often limited by a complex tuning procedure of the controllers [10], and also the extra cost for the current sensing. B.

Proposed Feedback Method The proposed new control structure is shown in Fig.6, the combination of the grid current (i2) and the capacitor voltage (vc) with a gain of Hv is feed back to the current regulator. Here, the capacitor voltage is ease to be obtained, and it is required for the inverter to run in stand-alone mode. Only one control loop is employed in Fig.6, hence the extra cost is low.

(a)

(b) Fig.4. The conventional current control: (a) with the inverter current feedback (i1) (b) with the grid current feedback (i2)

Then, the V-I characteristics of the LCL-filter will affect the control loop gain of the system, especially at the resonance points of the filter. Fig.5 shows the bode plots of the open-loop transfer function under the conventional current feedback control strategies without current regulators, where the PWM control delay is assumed to be 100s. An amplitude peak exists at the resonant frequency of the LCL-filter, and it will limit the control loop design.

Fig.6. Block diagrams of the proposed current control: under WAC control

Then the feedback current compensated by the capacitor voltage can be expressed as

I f (s)

I 2 ( s )  H v ( s )Vc ( s )

(2)

Here, the capacitor voltage Vc(s) can be derived from the inverter output voltage as

Vc ( s )

1D V (s) D (1  D ) LCs 2  1 i

(3)

From (1) to (3), the transfer function from Vi to If can be derived,

GVi  I f ( s )

I f (s) Vi ( s )

H v ( s )(1  D ) Ls  1 [D (1  D ) LCs 2  1] Ls

(4)

There are three poles in the above third order function. When the voltage compensation gain is selected to satisfy the condition presented as (5)

H v ( s ) D Cs

Then GVi  I f ( s ) has two zeros which can counteract its two

Fig.5. Bode plots of the open-loop transfer function under conventional control without current regulators

If a PI current regulator is used, for the purpose of the system stability, the proportional gain KP is limited due to the peak amplitude existing at the resonant frequency of the non-damped LCL-filter. Hence, the control loop gain for the traditional strategy is quite small, and the system output is not able to track a sinusoidal reference perfectly.

poles. Hence, equation (5) is degraded from third-order to first-order,

GVi  I f ( s )

I f (s) Vi ( s )

1 Ls

(6)

Note that equation (6) is similar to the transfer function of L-filter, so it is easy to optimize the control system for the compensated grid current (If). However, the switching ripple

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current injected into the grid is still attenuated by a third-order LCL-filter. Then, by using the proposed compensated grid current feedback control, the peak amplitude presenting at the resonant frequency of the LCL-filter is no long existing in the control loop gain now. Also, the PI or other current regulator may be applied in the new feedback system, but this time the proportional gain Kp value can be increased to a larger value to increase the system bandwidth and performance. Of course, the RMS current reference in the control should be modified by a current addition of DVc < jZoC , or DVg < jZo C approximately.

resister (0.5¡) in the LCL-filter.

Fig.7 Bode plots of the transfer function under different feedback control interfered by the grid impedance

C.

Design issues of the Current Controllers The characteristics of the proposed compensated grid current feedback method can be demonstrated further by a current control design for the system. Considering the ESR of inductor in LCL-filter, assume a same quality factor for the inductor L1 and L2, the ESR of represented as R1 and R2, then R1 D ( R1  R2 ) (7) With the voltage compensation gain as (5), the two zeros counteract two poles in GV  I ( s ) completely, (6) should be i

f

Fig.8 Bode plots of the transfer function with a slight damping

modified to

I f (s)

1 (8) Vi ( s ) Ls  R1  R2 Actually, the grid impedance which is included in the gird side inductor L2 is not easy to be evaluated exactly. This is a big problem for most of the grid current control strategies. The exact value of D in (5) can not be designed and the ESR of inductor mismatches (7), zeros can not counteract poles completely for GV  I ( s ) . However, with an approximate voltage i f

In case of a weak grid is connected, where the grid impedance is quite large, an estimate of the line inductance and an adjustment of control parameters is necessary, as like most of other control method. Now, a PI current regulator is designed with the proposed control method, as shown in Fig.6. The control loop gain has the form of (10),

compensation gain, the counteracting effect will exist for most of grid impedance values because it is generally quite small compared with the filter inductors. Fig.7 shows the bode plots of the transfer function that is interfered by the grid impedance value: Rg=0.1, Lg=15%L1. The control parameters are given as C=12uF, L1=L2=1.5mH, R1=R2=0.1, D 0.5 , and the grid impedance is ignored. It is shown that the compensated grid current feedback control can decrease the amplitude peak at the LCL-filter resonant frequency in case of mismatched voltage compensation gain to low ESR and inductance values of the grid impedance. The mismatching problem for low impedance grid can be mitigated by a slight damping to the LCL-filter. Then the voltage compensation gain H v ( s) in (5) should be modified to

Here, H(s) is the feedback gain, GPI ( s) is the PI regulator expressed as (11), and GPWM ( s) is the inverter gain is expressed

GVi  I f ( s )

(9).

H v (s)

D Cs Rd Cs  1

(9)

Here, Rd is the damping resister in series with the capacitor of the LCL-filter. Equation (9) is more beneficial to the system control design to suppress the signal interference. Fig.8 shows the bode plots of the transfer function with a small damping

GLp ( s)

I f ( s) Ei ( s)

GPI ( s ) ˜ GPWM ( s ) ˜ GVi o I f ( s ) ˜ H ( s )

as (12), including the switch delay Td. 1 GPI ( s ) K P (1  ) Ti s

G PWM ( s )

Ee  Td s

(10)

(11)

(12) Fig.9 shows the bode plots of the loop transfer function under two different current feedback control, with the system parameters given as: E=370Vdc, H(s)=0.02, Ti=1570, Td =100uS, C=12uF, L1=L2=1.5mH, R1=R2=0.1, Rd=0.5 and D 0.5 . The ESR of the inductor is 0.1¡. PI proportional gain Kp for grid current feedback control is 0.1, and it is 1.5 for the proposed feedback control because the current loop gain has no amplitude peak at LCL-filter resonant frequency. Obviously, the loop gain and the cross-over frequency with new control strategy are much higher than that with conventional control strategies. Comparing above two current feedback controls, the proposed voltage compensated grid current feedback control strategy can provide a larger attenuation for steady-state error and the predominant low order harmonics in the current spectrum.

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VI.

A 5kW DSP controlled prototype is built to verify the proposed control strategy for the grid-connected fuel cell inverter, as shown in Fig 1. In this system, the output voltage of the fuel cell is 80~115V DC. ZVS PSFB DC/DC converter is selected to set-up the output of the fuel cell to ±365Vdc. The other system parameters are the same as in simulation.. Fig.11 shows the experimental results under PI control strategies with 25% current rating. In these figures, (a) shows the results with the grid current i2 feed-back and (b) shows the results with the new feedback method. In case (a), the proportional gain Kp=1.5, but the system output current is slightly unstable, and is markedly lagged to the grid voltage. In the case (b), the proportional gain Kp=2.5, and the system is stable. The new feedback control obtains low current THD comparing to the grid current feedback. As shown in Fig.11, when the grid current I2=5A, the current THD is 14.10% and the third order harmonic current is 12.60% under I2 feedback PI control. The new feedback control has a current THD of 10.44% and up to 8.3% third harmonic at the same time.

Fig.9 Bode plots of the control loop function with different control methods.

V.

EXPERIMENTAL RESULTS

SIMULATION RESULTS

A 5kW grid-connected inverter model is built in PSPICE to verify the proposed control strategy. The input voltage of the inverter is ±370Vdc. The half bridge inverter transfers the energy to a single phase grid. Capacitor voltage compensated grid current feedback is employed as shown in Fig. 6. The grid voltage is 220Vac/50Hz, switching frequency is 16 kHz, the dead time is 2.5us, PWM control delay is 100us. Parameters of the LCL-filter are selected as L1=L2=1.5mH, C=12uF with a damping resister 0.5¡in series. The ESR of the inductor is 0.1 ¡. Fig.10 shows the simulation result under PI control strategies with the new feedback method (t50ms). The PI parameters are: Kp=1.5, Ti=1570. In the beginning, the control method was the proposed feedback control, the output current was stable with good waveform, after the control method changing to grid current feedback control at t=50ms, the output current was oscillated gradually. The simulation result shows that the inverter with the proposed control method has a better grid current waveform.

(a) Ch.1: Grid voltage, 300V/div, Ch.2: Grid current, 18A/div, t: 10ms/div

(b) Ch.1: Grid voltage, 300V/div, Ch.2: Grid current, 18A/div, t: 10ms/div Fig.11 Experimental results @ grid current 5A, (a) with i2 feed-back, Kp=1.5,(b) with proposed feedback Kp=2.5

Fig.10 Simulation result under different control strategies

Fig.12 shows the experimental results under PI control strategies with full current rating. As shown in Fig. 12, when the grid current I2=20A under new feedback PI control, the current

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THD is 3.25%, the third order harmonic current is 2.58%. It has a current THD of 4.30% and up to 5.6% third harmonic with i2 feedback control. The THD can be improved about 1 percent with the proposed control strategy.

close-loop control system can easily optimized for minimum steady-state error and current harmonic distortions. 20.00%

without duc/dt

with duc/dt

17.50% 15.00%

THD

12.50% 10.00% 7.50% 5.00% 2.50% 0.00% 0

5

10

15

20

25

Grid current (A)

Fig.13 Experimental results, THD vs. grid current

ACKNOWLEDGMENT

(a) Ch.1: Grid voltage, 300V/div, Ch.2: Grid current, 45A/div, t: 10ms/div

The authors would like to acknowledge the support of Delta Power Electronics Science and Education Foundation, the support of National High Technology Research and Development of China 863 Program (2007AA05Z243) and the support of the Specialized Research Foundation for the Doctoral Program of Higher Education of China (J20070715). REFERENCES

(b) Ch.1: Grid voltage, 300V/div, Ch.2: Grid current, 45A/div, t: 10ms/div Fig.12 Experimental results @ grid current 20A, (a) with i2 feed-back, Kp=1.5,(b) with proposed feedback Kp=2.5

Fig.13 shows the THD comparison of experimental results between the two control strategies. The higher line is the THD result under PI control strategy grid current i2 feed-back (without duc/dt). The lower line is the THD result under proposed control strategy (with duc/dt). From Fig.13 we can see that with the proposed control strategy the THD can be improved about 1 percent when grid current is larger than 50% rating.

VII. CONCLUSIONS A low cost solution to the single-phase grid-connected inverters is presented in this paper, including the inverter topology, filter structure, as well as a new current feedback control strategy. By the use of the capacitor voltage compensated grid current feedback, the inverter control system can be degraded from third-order to first-order, a low cost non-damped or slightly damped LCL-filter can be applied, the open loop gain and the bandwidth can be increased, so that the

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