2014 International Symposium on Power Electronics, Electrical Drives, Automation and Motion
A PV AC-module based on coupled-inductors boost DC/AC converter M. Coppola, P. Guerriero, F. Di Napoli, S. Daliento, D. Lauria, A. Del Pizzo Department of Electrical Engineering and Information Technologies (DIETI), University of Naples Federico II via Claudio 21, 80125 Naples, Italy e-mail:
[email protected] to generate the ac utility line voltage. These solutions can result in high volume, weight, cost and reduced efficiency, thus being not convenient in distributed applications.
Abstract— In this paper the design and the control of a PV (Photovoltaic) AC-module based on a double coupled-inductors boost topology are discussed. This circuital configuration allows obtaining of the high voltage amplification needed in individual panel applications. The operation principle of the proposed circuit is analyzed and a proper calibration of the PV panel simulation model is performed. The adopted control strategy is based upon sliding control technique in order to exploit its well-known properties of robustness. Furthermore, a Maximum Power Point Tracking (MPPT) approach based on a Incremental Conductance (IC) algorithm is used to track the actual maximum power point. Finally, the numerical results reported in the paper permit to confirm the feasibility of the proposed design and control strategy. Keywords— AC-module, coupled-inductors boost inverter.
I.
individual
PV
An interesting alternative to overcome the latter drawbacks is the employment of coupled-inductors circuit configuration for achieving both high efficiency and high voltage gain [6]-[11]. The solution proposed in this paper is based on single-stage dc-ac power converter employing two coupled-inductors step-up dc-dc converters and modulating their output voltages in a sinusoidal way. This approach [6],[7] is able to reach the desired boost action by means of coupled-inductors [9], [11] while obtaining an higher efficiency w.r.t. conventional circuits.
module,
The proposed double-boost dc-ac converter with coupled-inductors is depicted in Fig. 2. The boost converters produce a dc biased sinusoidal waveform, so that each source generates only a unipolar voltage. The modulation of each converter is 180° out of phase with the other, which maximizes the voltage excursion across the load. The generation of bipolar voltage at output is solved by a push-pull arrangement. Thus, the dc-dc converters need to be current bidirectional.
INTRODUCTION
The main purpose of this work is the optimal integration of photovoltaic energy resources in existing electrical distribution systems. In a conventional PV system many PV modules are connected in series to obtain a dc voltage suitable for ac utility line voltage. In series configuration, mismatch conditions could affect the PV system performance causing a lack of producible power. Usually in small-size applications the PV systems are affected by partial shading due to architectural and/or environmental issues.
The PV AC module control is based upon an adaptive sliding technique where the proper references are provided by a MPPT (Maximum Power Point Tracking) algorithm in order to assure that the input power is closed to the maximum achievable value.
Various approaches based on distributed dc-dc converters [1] or micro-inverter [2]-[5] have been proposed to address these issues by increasing power conversion granurality. The aforementioned topologies allow a dedicated MPP tracking for each module of the PV plant.
The sliding mode control has been selected for its well known properties of robustness against disturbances and modeling uncertainties [9]. The adopted MPPT tracks the actual maximum power point by comparing the global and local conductance according to the conventional IC approach [12]. The incremental conductance value is obtained by a dynamic measurement of the ac voltage fluctuations on the input dc-link capacitor.
This paper is devoted to the design and control of an individual PV module ac generator by using a single-stage dc/ac converter. The main drawback of this latter topology is the possibility of achieving a proper voltage amplification. In fact, the proposed circuit must be able to step-up the low operating voltage of an individual panel to a voltage level suitable for ac grid connected applications (i.e. 400 V).
The paper is organized as follows. The system modeling is presented in section II. Hence, section III derives the control law based upon sliding control technique with optimized MPPT algorithm. Section IV is devoted to verify the validity of the proposed design. Finally, in section V the conclusions will be drawn.
Conventional approaches to obtain the boost action are: a single stage which use an inverter to generate ac utility line voltage by a step-up transformer; a two stage power generation with a boost dc-dc converter as front stage to get the sufficient dc-bus voltage, and an inverter as second stage
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voltage can be obtained as vout1 vout 2
vo
2 Apk sin Zt
(5)
B. PV module The micro-inverter architecture proposed in this paper is intended to be integrated in an individual PV module ac generator. The design procedure of the PV AC-module relies on a numerical simulation exploiting a calibrated circuital model of the PV module. The compact model of the PVmodule is based on the five-parameter single-diode model. This popular model, based on the so-called “superposition principle”, accurately describes the behavior of most PV panels under standard (i.e., non-stressed) operating conditions.
Fig. 1 Schematic circuit of coupled-inductors double-boost dc-ac converter, including copper resistances.
II.
An experimental calibration procedure was performed to characterize a commercial PV-panel, which exhibits a nominal power of 160 Wp, an open-circuit voltage of 36 V and a short circuit current of 6 A at STC. Model input parameters were extracted by analyzing experimental I-V curves. In particular, a simple non-intrusive approach was used to accurately assess the shunt resistance and the global series resistance [13], [14].
SYSTEM MODELING
A. Step-up circuit The ac module shown in Fig. 1 is used to obtain increased voltage gain with respect to the conventional circuit whenever an ac voltage larger than the dc-link voltage is needed (e.g. in grid connected PV power generation). It includes resistors (R1-R4) that account for inductors copper losses, the power MOS switches (M1-M4) and their body diodes (D1-D4).
Fig. 2 shows I-V (a) and P-V (b) curves obtained with the calibrated model at different irradiation levels (500, 750 and 1000 W/m2 respectively).
By referring to the right side circuit of Fig. 1, and neglecting the power losses, the dc voltage gain is
8
Vout1 1 ND (1) Vin 1 D where N=N2/N1 is the winding ratio of the magnetically coupled inductors, while N1 and N2 are the winding turns of the primary and secondary inductors, and D is the duty cycle. The coupling coefficient, k, is considered ideal (k=1). The value of N must be properly chosen to maximize the converter efficiency.
Current [A]
6
(1 N )(2 D 1) (1 D) D then the corresponding voltage gain is Vin
Vdc Apk sin Zt
5
10
(b)
Power [W]
15 20 25 Voltage [V]
30
35
40
@ 500 W/m2 @ 750 W/m2 @ 1000 W/m2
200 150 100 50 0 0
15 20 25 30 35 40 Voltage [V] Fig. 2. a) I-V curves obtained with the calibrated model at different irradiation levels: 1000 (solid line), 750 (dotted line) and 500 W/m2 (dash-dotted line); b) corresponding P-V curves.
(2)
5
10
The different irradiation levels reported in Fig. 2 accomplish with the European standard efficiency.
vo (1 N )(2 D 1) (3) Vin (1 D) D By proper modulation the two converters produce a sinusoidal waveform with a dc bias given by vout1
2
250
Assuming that the two converters of Fig. 1 are 180° out of phase, the output voltage of the coupled inductors inverter can be easily derived as follows
vout1 vout 2
4
0 0
Moreover, the inductance values (L1, L2) are obtained as reported in [11], also accounting for the inductors copper resistance (R1, R2). The total inductance and resistance values are L and R, respectively. These considerations are also valid for the left side circuit in Fig. 1.
vo
@ 500 W/m2 @ 750 W/m2 @ 1000 W/m2
(a)
III.
CONTROL STRATEGY
The boost micro-inverter of Fig. 1 is composed of two coupled inductors step-up dc-dc converters. The operation of the overall system can be better understood by referring to only one side of the circuit (e.g. the right side converter). For this latter, the sliding mode approach proposed in [9] has been
(4)
vout 2 Vdc Apk sin Zt where Vdc is the dc bias voltage at each output, while Apk is the ac voltage amplitude added to Vdc. Thus, the inverter output
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performed.
A. Current control The main purpose of the controllers in Fig. 3 is to make the output current iconv follows as faithfully as possible a sinusoidal reference in phase with the grid voltage.
The first step for modeling the proposed topology of dc-dc converter is the choice of two state space variables. The first one is the output voltage. The second one, since the magnetic flux is not directly measurable, is the current im1, defined as follows, [7]: i1 ®i 1 N ¯1
im1
t Ton t Toff
(6)
where, Ton=DT, Toff=(1-D)T and T=Ton+Toff is the switching time period, N is the turns ratio, as above mentioned, and i1 is the primary winding current. By referring to (6) and Fig. 1, the following relationships can be stated: dim1 vin R1im1 v v R R2 u in out1 1 u 1 i 1 u ° 2 m1 L1 L1 1 N ° dt L1 1 N ® im1 i ° dvout1 1 u conv1 °¯ dt C1 1 N C1
(7)
where . More specifically, u=1 when M1 is ON (M2 OFF); when the M1 is OFF (M2 ON). Using the approach proposed in [6], if the vector x of statevariables error is defined as
> x1 , x2 @
T
ref ª¬im1 I mref1 , vout1 Vout º 1¼ the following standard modeling can be deduced
x
x
x
Ax Bu Az F
(9)
ref T out1
ª¬ I , V defined as in [9].
with z
ref m1
(8)
º¼ , while the matrices A, B, F are Fig. 3. PV AC-module circuit configuration and scheme of the controllers.
The reference value of duty ratio is estimated as: v 1 in vout1 (10) D v 1 N in vout1 According to the variable structure system theory, a sliding surface has to be chosen, within the state variables space, where control functions are discontinuous. The following sliding surface is chosen: (11) S1 x E1 x1 E2 x2 T where T
Assuming that the two converters are 180° out of phase, the output voltage references are defined as
2 Arms sin(Zt D ) 2 (13) 2 Arms ref vout 2 Vdc sin(Zt D ) 2 As suggested in [6], the value of the dc offset (Vdc) is chosen to produce a symmetrical variation of the duty cycle around 0.5. The adopted value is 230 V, and a variation of the duty cycle between 0.3 and 0.7 is expected, so assuring the operation in the linear zone of the dc gain characteristic of the boost inverter. ref vout 1
>E1 , E2 @ .
In the actual case of finite switching frequency, a suitable hysteresis band has to be foreseen and, hence, the control law becomes: 0 if S (x) ! ' (12) u ® ¯1 if S (x) '
Vdc
Instead, Arms and are properly chosen by imposing a unit power factor at the output. Thus, they can be obtained as follows
where the amount of hysteresis in the sliding surface. All the above considerations can be replaced for the left side dc-dc converter of the double boost circuit.
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§ Z Lline Ppvref 2 °A V ¨¨ grid rms °° rms © Vgrid rms ® ° § Z Lline Ppvref · ¸¸ °D arctan ¨¨ 2 © Vgrid rms ¹ ¯°
· ¸¸ ¹
2
(14)
The angular frequency is the ac grid angular frequency (
, f=50 Hz), Lline is the line inductance, Ppvref is the active power reference to be injected in the grid.
be rewritten as
g pv
(22) 0 v pv Otherwise, the sign of the left side of (22) provides information about the position of the operating point respect to MPP according to the following relations
Furthermore, the output current references (see Fig. 3) are defined as ref iout 1
ref iconv iCref1
(15) ref ref iout iconv iCref2 2 The output current reference is the sum of two contributions. The first is in phase with the grid current: ref iconv A sin Zt where A is obtained according to the following relation
ipv 0 v pv vMPP ° g pv v pv ° (23) ® ° g ipv ! 0 v ! v pv MPP ° pv v pv ¯ The MPPT creates a mismatch between the input and the output power in order to charge or discharge the input capacitor. To obtain a variation 'v of the input capacitor voltage, the power reference is set as follows
(16)
( Arms cos D Vgrid rms ) 2 ( Arms sin D ) 2
A
(17) (Z Lline ) 2 The second is the out of phase current through the output capacitor:
'v 2 (24) Cin f MPPT 2 where c is the sign of the left side of (22), Cin is the input capacitance and fMPPT is the frequency of the MPPT iterations. Pref
Arms (18) sin(Zt D S 2) 2 The current references for the sliding mode controllers can be written as follows iCref1
Z C1 2
ref °°im1 ® °i ref °¯ m 2
1 N ref iout1 1 D 1 N ref iout 2 1 D
ipv v pv ipv 'v v pv g pv 'v c
IV.
SIMULATED PERFORMANCES
The ac module of Fig 3 has been designed by considering the key circuital parameters listed in Tab. I. A PV module calibrated model has been used as described in sub-section II.B.
(19)
A set of simulations in PSIM environment have been conducted in order to evaluate the system performance at different irradiation levels (see Fig. 2).
B. MPPT algorithm The adopted MPPT algorithm tracks the actual maximum power point by comparing the global and local conductance according to the conventional IC approach [12] and controls the input capacitor charge by providing to the sliding mode control unit an adaptive power reference Ppvref , which results in an adaptive sliding surface.
TABLE I.
The incremental conductance value is obtained by a dynamic measurement of the PV voltage and current. The dc-ac conversion causes voltage fluctuation on the dc input capacitor at the double of grid frequency, thus the PV steady-state voltage and current can be stated as follows
i pv
ipv
ipv ipv
(20) v pv v pv v pv where, pv, pv are the dc components, while pv, pv are the superimposed alternating components. The derivative of the PV instantaneous power with respect to the operating voltage is
CIRCUIT PARAMETERS
Parameters
Values
Cin
10 mF
C1=C2
22
L
6.4 mH
R
49.7
Lline
5 mH
N
4.4
1
1
7.0055
2
5.0333
Fig. 4 reports the instantaneous PV power, thus demonstrating the optimal MPP tracking of the proposed algorithm. This latter also allows a reduction of the oscillations around the MPP and guarantees a MPPT steady-state efficiency greater than 98.6% in all considered cases.
dPpv
di pv (21) i pv v pv ipv v pv g pv dv pv dv pv where gpv is the differential conductance. It is obtained as the ratio of the amplitude of pv and pv. According to [12], at the MPP, the slope of power-voltage curve is zero, and (21) can
Moreover, the adopted control strategy is able to force the output voltages vout1 and vout2 to follow the desired 180° out of
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Fig. 4. Input photovoltaic power vs time for different irradiation levels 1000 (solid line), 750 (dashed line) and 500 W/m2 (dotted line).
Fig. 6. Grid current at different input power levels (1000 W/m2,solid line; 750 W/m2, dashed line; 500 W/m2, dotted line) compared to the grid voltage (solid gray line).
phase sinusoidal references (eq. 13). The steady-state behavior of the single side voltages is depicted in Fig. 5. It can be seen the good agreement with respect to the desired behavior. In order to verify the effectiveness of the proposed control technique in terms of power efficiency, the performances at different power levels (i.e. at different irradiation levels) are considered in Fig. 6. This latter highlights the comparison among the grid voltage and the grid currents obtained for the aforementioned different cases. The numerical results manifest that the proposed design approach is promising in order to assure suitable power efficiency. In fact, the estimated efficiency of the micro-inverter is greater than 95.6% in all the considered cases. Furthermore, the system has been simulated by changing the irradiation level starting from 1000 W/m2 to 500 W/m2 through 750 W/m2, as shown in Fig. 7 (dotted line). The level step occurs in linear manner in 200 ms. The PV power behavior is also reported in Fig. 7 (solid line). It shows that the proposed control makes sure that the circuit is able to track the MPP also under varying operating conditions. V.
Fig. 7. Input photovoltaic power vs time dynamically changing the irradiation level (solid line). The irradiation behavior is also reported as reference (dotted line).
providing a higher voltage amplification w.r.t. conventional boost inverters. So, it is suitable for individual PV panel grid-tied applications.
CONCLUSIONS
The inverter is controlled by using a sliding mode technique and improved by adding a proper MPPT algorithm, based on the IC approach. This latter is able to control the input capacitor charge by providing dynamically the power reference, thus resulting in an adaptive sliding surface.
The paper has focused the attention on the design and the control of a PV AC-module based on coupled-inductors boost dc-ac converter. The proposed inverter topology features the advantage of
Moreover, the numerical results have highlighted the effectiveness of the proposed control to obtain the desired output voltages and currents in different irradiation conditions. Indeed, the estimated overall power efficiency is always greater than 95.6%, in all the considered cases. Finally, the system behavior in terms of dynamic MPPT efficiency has been analyzed and high performance has been reached even under rapidly varying irradiation. REFERENCES [1]
Fig. 5. Single side output voltages: vout1 (dotted line),vout2 (solid line).
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