Design and Implementation of Three-phase Grid-connected Two-stage Module Integrated Converter

Frank Chen Qian Zhang Ahmadreza Amirahmadi Issa Batarseh

Department of Electrical & Computer Engineering University of Central Florida

Orlando, USA Frankchen@eecs.ucf.edu

Abstract—This paper presents a high efficiency module integrated inverter (MIC) with both stages ZVS operation for three phase grid tied photovoltaic system. LLC resonant dc-dc converter is employed in the first stage to track the maximum power of PV panel. A novel and simple soft switching scheme without adding auxiliary components is proposed for three phase for the second stage. Meanwhile, modeling and control strategy of three phase four-wire DC/AC converter are also discussed. In addition, a dedicated Center Points Iteration (CPI) MPPT algorithm for LLC resonant topology is applied to quickly tracking the maximum power. In addition, the capacitance of DC-link is also investigated because DC-link capacitor plays an important role for dual-stage MIC. Finally, a 400 watts prototype has been built and tested. The peak efficiency of the whole system prototype has been measured, which is up to 96%, 98.2% in the first stage, and 98.3% in the second stage, respectively.

I. INTRODUCTION

With the strict limitation for Global emissions of carbon dioxide (CO2), solar energy is a renewable resource that is increasingly harvested around the World by PV solar panel [1]-[2]. The deployment of grid-tied PV systems has rapidly increased over the last few years, fueled by decreasing cost of installation, increased cost of fossil fuels, and increased public appetite for clean and renewable energy sources. Currently, the MIC system offers “plug and play” concept and greatly optimizes the energy yield. With these advantages, the MIC concept has become the trend for the future PV system development but challenges remain in terms of cost, reliability and stability for the grid connection. General speaking, the MIC topologies can be classified into three different arrangements according to the paper [1]: 1) MIC with a dc link; 2) MIC with a pseudo dc link; 3) MIC without a dc link. MIC with a dc link is the most popular architecture with a boost dc-dc converter cascaded by a dc-ac converter, that is a main research direction for modulate integrated grid-tied converter for photovoltaic system application. So, MIC with a dc link is discussed in this paper to seek good both stages with high efficiency and low cost. Since LLC resonant topology has many merits over wide input voltage range, high efficiency and ZVS/ZCS features, which is already widely used in industrial application. Thus, LLC resonant converter is employed for the first stage to achieve high efficiency, and tacking the maximum power point of each PV panel [3]-[6]. In another aspect, three-phase four-wire ZVS dc-ac converter is built with high efficiency for the second stage. And a novel control scheme is proposed

without increasing external components. Thanks ZVS in both stages, so the overall peak efficiency can reach 96%. This paper is organized as follows. In Section II, configuration of two stage three phase grid-tie inverter system is described. A control strategy for overall system is discussed in Section III. Section IV described modeling and hybrid control of three phase DC/AC converter. CPI MPPT algorithm for resonant LLC topology will be presented in Section V. Section VI illustrates the capacitance calculation of DC-link capacitor. Experimental results are verified through a 400 watts prototype that is shown in Section VII. The conclusion and future work are given at the end.

II. CONFIGURATION OF TWO-STAGE THREE-PHASE GRID-TIE INVERTER SYSTEM

Full bridge LLC resonant converter is employed for the first stage to achieve high efficiency, and tracking the maximum power point of each PV panel. Due to high DC-link voltage for two stages MIC, typically 400V, the voltage doublers circuit is used in the secondary side of LLC resonant converter. In addition, three-phase ZVS DC/AC converter in the second stage of MIC is proposed to achieve high efficiency. The parasitic capacitor of the MOSFET is used to form a resonant tank with high frequency inductor (L1) to operate its current with bi-direction by controlling main switches of half bridge. The proposed high efficiency MIC with both stages ZVS is composed of a LLC resonant dc-dc step up converter and three phase four-wire soft switching dc-ac converter, which is shown in Fig. 1.

Vin

Fig. 1. Two-stage three-phase four-wire grid-tie inverter system

The operation mode of each phase in the second stage can be regarded as identical, because three-phase four-wire DC/AC converter is decoupled causing by neutral wire connection between grid and neutral point of bus voltage. Thus, the operation principle in single phase DC/AC converter how to achieve ZVS is illustrated in Fig.2 as an example of operation mode for three-phase four-wire DC/AC converter.

978-1-4673-4916-1/13/$31.00 ©2013 IEEE

The detail description of operation mode for DC/AC converter is analyzed as below. The theoretical waveform of one phase DC/AC converter during interval is shown in Fig.3. Interval 1 [t0-t1] Prior to t0, S1 is off and S2 is still turned on. We are assuming that the current direction from right to left through L is already changed at t0. Then S2 is turned off. The voltage across the parasitic C2 in S2 starts ramping due to current charge. Consequently, the voltage across S1 is decreasing with voltge across S2 increase. This mode is end once the voltage across S1 reaches to zero. Interval 2 [t1-t2] The body diode of S1 will be naturally conducted at t1. Since then, S1 is turned on with ZVS. And the current flow decays linearly from right to left due to the provision that Vd/2 subtracts output voltage across L1. This mode is end while the current is equal to zero. Interval 3 [t2-t3] The current direction through L is changed from left to right again because of S1 conduction. The main power is delivered in this mode. Interval 4 [t3-t4] At t3, S1 is turned off. The parasitic capacitor C1 of MOSFET is charging due to the action of the inductor’s current; and C2 is discharging in this interval. Once voltage across C2 drops to zero, the parasitic body

diode of MOSFET S2 is naturally turned on because the current direction through L does not change. Interval 5 [t4-t5] Continuing from the previous interval 4, the parasitic body diode of S2 keeps conduction. Thus ZVS condition for S2 switching on is already created. The length of this interval is determined by when S2 is turned on. Generally, this interval is very short. Once S2 turns on, this interval is end. Interval 6 [t5-t6] S2 is turned on under ZVS condition at t5. The current through S2 is gradually decreasing due to the fact that Vd/2 plus output voltage across L. Consequently, the energy stored in the inductor is transferred to the load in this mode. Meanwhile, the current through body diode of S2 will switch to the branch of the MOSFET’s very small on-resistance. Therefore, the conduction loss is also reduced in this interval. Interval 7 [t6-t0] following the previous interval 6, the current through S2 continues to decay. The current direction will be changed in case the current decays to zero. Since then the current through S2 is toward another direction from up to bottom as shown in Fig. 2 to create ZVS condition for S1. The interval 7 is end while the current through S2 reaches to the threshold negative current. Then the new cycle starts again.

Fig.2 Operation mode of single phase DC/AC converter Interval 1: [t0-t1], Interval 2: [t1-t2], Interval 3: [t2-t3], Interval 4: [t3-t4],Interval 5: [t4-t5], Interval 6: [t5-t6], Interval 7: [t6-t0]

Fig.3 the theoretic waveform of one phase DC/AC converter

III. SYSTEM CONTROL DESCRIPTION

A full-digital approach is adopted for the control the double stage three-phase 4-wire inverter PV system, as shown in Fig.4. The PV voltage Vpv and current ipv are both sensed for calculating the instantaneous PV power Ppv. The MPPT function block generates a reference to changing switching frequency then to regulate power in dc-dc stage to tracking the maximum power output. Bus voltage of DC link is detected to compare the reference, the polarity of the error determines how much current need to inject, increase or reduce. For example, if the irradiance is increasing, bus

voltage goes up because DC-DC stage is running with MPPT function. While the UDC is greater than the Uref, in order to keep bus voltage stable, the stage of inverter should inject more current to grid. Otherwise, the irradiance is reducing; inverter needs to reduce current injection to grid. Injecting current to grid is also sensed, through d/q transformation, the active current is following the Id

*, the output value of the DC link regulator, as a reference of the output current injection of the inverter stage. The reactive current is assumed to zero after d/q transformation based on the consideration of PF equals to 1, no phase shift condition.

Fig.4 Overall control diagram of two stages three-phase grid-tie inverter system

IV. MODELING AND CONTROL OF THREE-PHASE FOUR-WIRE

GRID-CONNECTED INVERTER

A. Average model of three-phase 4-wire inverter with LCL filter

The scheme of a three-phase four-wire voltage source inverter (VSI) connected to the grid through an LCL filter is redrawn as shown in Fig.5. The series resistances of the inductors and capacitors have been neglected in order to simplify the derivation of average model. Fig.6 shows an average model of three-phase four-wire DC/AC converter, which may be obtained by neglecting the high frequency components of both the dc voltage and the ac phase currents. According to Kirchhoff’s current &voltage law, the differential equation to illustrate current and voltage as shown in Fig.5 can be expressed by

Fig.5 Three-phase four-wire DC/AC grid-connected converter

(1)

(2)

(3)

(4)

In the steady state, the grid phase currents i2a, i2b, and i2c are controlled to be sinusoidal and in phase with the corresponding grid phase voltages Vga,Vgb and Vgc which can be expressed as cos coscos (5)

Where Vm and ω are the amplitude of the phase voltage and angular frequency of the power source, respectively. The model in the stationary coordinates can be transformed into a synchronous reference frame by the transformation matrix T (Park’s transformation) as follows:

cos cos cossin sin sin (6)

By averaging the inverter legs, Fig.6 shows the whole averaged model of the inverter after transformation into the synchronize three-phase frame can be obtained; and the equations of the averaged model are expressed by (7)-(10). 0 0 (7)

0 0 (8)

0 0 (9)

(10)

Fig.6. Average model in the synchronize three-phase frame

B. Hybrid Control Scheme for Three-phase Four-wire DC/AC Converter

Peak current control is usually implemented using the analog circuits to turn ON and OFF the inverter switches when the current reaches the expected boundaries. The analog circuits have the problem of reliability and they also decrease the power density of the micro-inverter. Another method to implement the peak current control is to predict the required switching time using the calculation inside the controller. The required Ton and Toff of the switches can be predicted in order to change the current between the desired boundaries. The problem of this method is accumulated error caused by the change in the inverter parameters. A new method of ZVS BCM current control is proposed which is a combination of hardware reset and predictive control and is referred to as Hybrid control. Hybrid control doesn’t require external components can be completely implemented using the advanced features of DSPs designed for power electronics applications. By taking advantage of the DSP’s internal comparator, PWM period can be reset whenever the inductor current reaches the required boundary. Turn-ON or Turn-OFF duration can be predicted using the calculation inside the DSP. Fig. 7 shows this hybrid control method.

Fig. 7. Hybrid BCM Current Control

Fig. 8. Reset Boundary of Hybrid BCM Current Control

As shown in Fig.8, turn-on time is defined as the time required to keep the upper switch ON and make the inductor current reach from the lower limit to the upper limit. T-on is calculated according to the equation (11). Turn-off time is defined as the required time which lower switch should stay ON to make the inductor current reach from the upper limit to the lower limit. T-off is calculated according to the equation (12). Switching frequency is derived using the T-on and T-off expressions according to the equation (13).

(11)

(12)

(13)

The implementation of Hybrid BCM current control is shown in Fig. 9. This control method requires accurate sensing of the inductor peak current. Since the inductor current includes both the switching frequency and the line frequency it is bulky to measure it with a single current transformer. However it can easily be sensed with a high frequency current transformer and a low frequency current sensor chip. This current sensing approach reduces the size of current measurement component. These high and low frequency components are separately sensed from the capacitor and the output line and then added together to produce the inductor current. For each phase only one comparator and a PWM generator are needed to produce the switching signals. Since all the controller parts are located inside the DSP chip the propagation delay is very short for this control method.

Fig. 9. DSP Implementation of Hybrid BCM Current Control

V. MPPT ALGORITHM IN DC-DC STAGE

The topology of the LLC converter is illustrated in Fig. 1 as the first stage of the whole system. The input voltage of resonant tank is a square-wave E generated by switches S1-S4 and Vin provided by the PV panel. Although state functions

can be provided to calculate an accurate voltage gain of in

o

VV

, it is usually cumbersome due to the complex interaction between the resonant components. Fourier analysis can be used to convert the square-wave signal into a set of odd harmonic components with the expression is as follows:

∑∞

=

=…3,1

sin k]/)tkω[sin(4VEkπ

(14)

Thus classical ac-circuit analysis can be applied for each harmonic component in (15) as follow [8],

(15)

Where ; ; ; /

and (k)Vo refers to the kth order harmonic components of the output voltage. fs refers to switching frequency of the full bridge; Rac refers to the equivalent load resistance at the primary side of the transformer, and n refers to the turns ratio of the transformer. Thus the voltage gain M can be calculated with equation (16) [8].

M VV M, 16

Based on (16), the normalized gain (Mn=M/2n) vs frequency (fn=fs/fr) waveforms under varying load for LLC can be calculated and illustrated in Fig. 10, where Pn refers to normalized output power. To ensure the ZVS of LLC converter, the operation frequency should be constrained in inductive zone as shown in Fig. 10 [9][10].

Fig. 10 Normalized gain vs frequency waveforms under various load for

LLC In the two-stage micro-inverter, the output of DC/DC stage is connected with the input of DC/AC stage. Conventionally, to ensure normal operation of the DC/AC inverter, the DC link voltage is required to be a constant Vref. Considering the power balance in the LLC converter,

orefooinin IVIVIV == (17) The relationship of input voltage, input current and normalized switching frequency could be calculated based on equations (14-17). The results are plotted in Fig. 11 below.

Fig. 11. LLC converter 3D relationship of input voltage, input current and

normalized switching frequency based on Vo=Vref

Due to the complex interaction between the LLC resonant components, the relationship between Vin and fn is nonlinear and non-explicit. Moreover, the nonlinearity in PV module characteristics exacerbates the complexity of power control with the frequency parameter. Thus simulation instead of direct calculation of the LLC micro-inverter was used to demonstrate the power curves as shown in Fig. 12 (with simulation Fr=140kHz). The initial frequency of the LLC micro-inverter is very high due to the soft start function, generally 3-4 times resonant frequency Fr. Fig.12 illustrates P-F curves while the irradiance of the PV Panel is varying at the initial frequency 280KHz. As shown in Fig. 12, the power difference nearby initial frequency is almost constant. Therefore, the conventional P&O or INC MPPT algorithm is hardly to apply for LLC resonant converter [4] [5]. In order to solve this problem, a novel center point iteration algorithm is

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.5

1

1.5

2

2.5

3

3.5

4

0

0.5

1

1.5

25 10 15 20 25 30 35 40 45 50 55

0

2

4

6

8

10

12

proposed in Fig.13. The flowchart of the MPPT technique is illustrated as Fig. 14. The control parameter is the switching frequency. As shown in Fig. 13, the whole frequency region is firstly divided into 4 parts: part 1: F(1)~F(4), part 2: F(4)~F(3), part 3: F(3)~F(5), part 4: F(5)~F(2).Considering the inductive zone of LLC converter as illustrated in Fig. 5-right, the initial boundary frequencies are set as: F(1)=0.5Fr, F(2)=2Fr, where Fr refers to the LLC resonant frequency and can be calculated by

Fig. 12. P-F curves of LLC micro-inverter connected to a PV panel with

varying irradiance

Fig. 13. P-F curves of LLC micro-inverter connected to a PV panel with

varying irradiance with CPI MPPT algorithm

: (a)Proposed MPPT iterations

(b)Overall flowchart of MPPT

(c)Detail flowchart of the proposed MPPT

Fig. 14. Application of the proposed MPPT on the LLC micro-inverter: (a)Proposed MPPT iterations (b)Overall flowchart of MPPT (c)Detail flowchart of the proposed MPPT

VI. DC-LINK CAPACITOR CALCULATION

The system between DC/DC stage and DC/AC stage is decoupling due to the role of DC link capacitor, which simplifies the controller design for both stages. Electrical capacitor is usually used in the dc link, but the life of electrical capacitor is a major concern. Because of three-phase DC/AC converter in the second stage, the value of the dc-link capacitor should not be choosing very large based on the power rating specification of MIC. Thus the reliability of whole system will be significantly improved if the electrical capacitor of DC-link is replaced by a film capacitor. Though the capacitance value of DC-link based on the Qualitative Analysis is not large in three phase balance system, the condition of grid should be analyzed and considered grid-tied system while MIC is connected with grid. How much capacitance does the DC-link capacitor need is determined by many factors, such as the voltage variations of capacitor, grid voltage dips &surges and response time for disturbance? Generally, these factors can be classified into steady conditions and dynamic conditions of MIC according to the specification. Overall analysis of these factors for PV application, the worst condition to calculate the capacitance of DC-link is the fact that only one phase is still running for three phase electrical power system. Therefore, the capacitance calculation of DC-link capacitor can be simplified as a single phase. From the output power of grid side, we can get the instantaneous power: 2 (18)

Where √2 sin : the instantaneous voltage of grid √2 sin : the instantaneous current connected to grid ω: the grid angular frequency

80 100 120 140 160 180 200 220 240 260 280 3000

50

100

150

200

250

300

Similarly assuming no power loss in the Dget the instantaneous generated power of Pbe expressed by . Then based o

Fig.15. Simplified block diagram of two

Therefore, according to the energy balancpower and output power can be calculated b2 ,Regarding the maximum output power 400rating of each phase has 133 watts. And (Udc) is selected as 400V with voltage rippl

∆ =39.2uF

VII. EXPERIMENTAL RESUL

A two-stage prototype of three-phase MIC to the specification: input voltage frommaximum out power 400W and AC grid The renewable source is a PV simulator, Agmodel E4360A. Low voltage MOSFET withLLC resonant topology is used for the ficonverter. The second stage is a threevoltage source inverter that connects the dthrough an inductance of 600uH. Thereference is 400V and the grid voltage110√2 . The control algorithms for the implemented by two digital signal prDSPIC33FJ16GS504 and STM32F103C8, AC stage and DC-DC stage respectively.applied to communicate between two DSPthe measurement waveforms at DC-DCinductor current waveform of three-phase Dis shown in Fig.17. Fig.18 shows CPI Mperformance in the LLC resonant DC-DC st

ir

vQ2

vQ3

Fig.16. the experimental waveform in DC-D

DC/DC stage, we PV panel that can on Fig.15 we get,

(19)

o-stage

ce between input by.

, ∆ (20)

0 watts, the power DC-link voltage

le (∆u) 20V. (21)

LTS

is built according m 25V to 38V,

voltage 110Vac. gilent Technology h on-resistance in irst stage DC-DC e-phase four-wire dc bus to the grid dc-bus voltage e peak value is while system are

rocessors (DSPs) employed in DC-. SPI function is Ps. Fig.16 shows

C stage; and the DC-AC converter

MPPT algorithm’s tage.

DC stage

Fig.17. the inductor current wavefo

Fig.18. Center Points Iteration MPPT alg

Fig.19 shows the experimental wavconnected with grid. The regulator to keep bus voltage constant while involved. As shown in Fig.19, the gradually increasing with the irradpanel.

Dc link voltage Grid voltage

Inject current

Implementation MAlgorithm and DC

Fig.19. The experimental waveform of overa

50 100 150 200 250 3000.9

0.92

0.94

0.96

0.98

1

input power (W)

effici

ency

Fig.20 efficiency measurement

Efficiency is measured individuallyin Fig.20 and in Fig.21, respectivelseen that the peak efficiency at e98.3%, respectively.

orm in DC-AC stage

orithm in the whole system

veform of overall system of DC-link is employed CPI MPPT algorithm is inject current to grid is

diance escalation of PV

DC/DC OffMPPT C link control

all system with grid-connected

0 350 400 450

Vin=25VVin=30VVin=35V

t in DC/DC stage

y at each stage, as shown ly. From figure it can be ach stage is 98.2% and

0 50 100 150 200 250 300 350 40092

94

96

98

100

Power (W)

Effi

cie

ncy

(%)

Fig. 21.efficiency measurement in DC/AC stage

VIII. CONCLUSIONS

High efficiency three-phase four-wire grid-connected inverter system with two-stage ZVS MIC is proposed and verified by experimental results based on a 400W test bed: the peak efficiency is measured at 98.2%, 98.3% in DC/DC stage and DC/AC stage, respectively. Operation mode of ZVS three-phase DC-AC converter is also illustrated. Average modeling and hybrid control in DC-AC stage, MPPT algorithm in DC-DC stage are both analyzed and discussed. DC-link capacitor plays a key role in the dual stage system; the capacitor’s value is calculated at the worst condition. The film capacitor can be used due to three phase system based on the specification that will increase life time of the whole system.

REFERENCES [1] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, “A review of single-

phase grid-connected inverters for photovoltaic modules,” IEEE Trans. Ind. Appl., vol. 41, no. 5, pp. 1292–1306, Sep.–Oct. 2005

[2] M. Liserre, T. Sauter and J. Y. Hung, "Future Energy Systems: Integrating Renewable Energy Sources into the Smart Power Grid Through Industrial Electronics," Industrial Electronics Magazine, IEEE, vol. 4, pp. 18-37, 2010.

[3] L. Zhigang, G. Rong, L. Jun and A. Q. Huang, "A High-Efficiency PV Module-Integrated DC/DC Converter for PV Energy Harvest in FREEDM Systems," Power Electronics, IEEE Transactions on, vol. 26, pp. 897-909, 2011.

[4] A. Conesa, G. Velasco, H. Martinez and M. Roman, "LCLC resonant converter as maximum power point tracker in PV systems," in Power Electronics and Applications, 2009. EPE '09. 13th European Conference on, 2009, pp. 1-9.

[5] X. Fang, H. Hu, Z. J. Shen and I. Batarseh, "Operation Mode Analysis and Peak Gain Approximation of the LLC Resonant Converter," Power Electronics, IEEE Transactions on, vol. 27, pp. 1985-1995, 2012.

[6] G. Ivensky, S. Bronshtein and A. Abramovitz, "Approximate Analysis of Resonant LLC DC-DC Converter," Power Electronics, IEEE Transactions on, vol. 26, pp. 3274-3284, 2011.

[7] R. Li, Z. Ma, and D. Xu, "A ZVS grid-connected three-phase inverter, "Power Electronics, IEEE Transactions on, vol. 27, pp. 3595-3604, 2012.

[8] H. Hong, "FHA-based voltage gain function with harmonic compensation for LLC resonant converter," in Applied Power Electronics Conference and Exposition (APEC), 2010 Twenty-Fifth Annual IEEE, 2010, pp. 1770-1777.

[9] R. Beiranvand, B. Rashidian, M. R. Zolghadri and S. M. H. Alavi, "A Design Procedure for Optimizing the LLC Resonant Converter as a Wide Output Range Voltage Source," Power Electronics, IEEE Transactions on, vol. 27, pp. 3749-3763, 2012.

[10] L. Zhigang, G. Rong, L. Jun and A. Q. Huang, "A High-Efficiency PV Module-Integrated DC/DC Converter for PV Energy Harvest in FREEDM Systems," Power Electronics, IEEE Transactions on, vol. 26, pp. 897-909, 2011.