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Indirect DC-Link Voltage Control of Two-Stage Single-Phase PV Inverter Feng Gao, Ding Li, Poh Chiang Loh, Yi Tang and Peng Wang

School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore gaofeng@ieee.org

Abstract ─ This paper presents a novel indirect dc-link voltage control scheme for the application of grid-tied two-stage single-phase photovoltaic conversion system. Unlike the traditional control method for grid-tied inverters where the dc-link voltage is always directly sensed to regulate the output current, the proposed scheme eliminates the dc-link voltage sensing unit but does not downgrade the inverter overall performance. The proposed scheme can be easily extended to control the multi-string configuration without any extra control complexity needed. Simulation verifications prove the effectiveness of the proposed control scheme. Index Terms ─ Grid-tied inverter, indirect dc-link voltage control, photovoltaic, single-phase inverter.

three-phase inversion system. The dc-link voltage ripple would consequently induce the suboptimal operation around maximum power point even after the proper

(a)

I.

INTRODUCTION

(b) Fig. 1: Topological illustration of (a) single-stage or (b) two-stage single-phase PV inverter.

Renewable power (e.g. wind and solar energy) generation as the effective supplementary in traditional power generation systems has being drawn great attentions on both industrial applications and innovations to fulfill the rapidly expanded market which was generally stimulated by government regulations under the consideration of environmental issues. Among the renewable energy transformation devices, photovoltaic (PV) panel is one of the most promising sources since it can convert solar energy to electricity directly, which when fed into AC power network, an inverter with the maximum power point tracking (MPPT) capability should be connected to convert dc voltage generated by PV panel to sinusoidal ac voltage. The types of PV inverters can be broadly classified as grid-tied and off-grid inverters, where the single-phase grid-tied PV inverters that generally provide the residential electricity from PV panels occupy the largest PV inverter market. To date, the single-phase grid-tied PV inverter has been constructed using either single-stage or two-stage topology [1-8] as illustrated in Fig. 1, where the single-stage topology (Fig. 1(a)) presents the most reliable and cost effective solution but with the operational limitation of minimum PV voltage being larger than the peak ac grid voltage in order to avoid the over-modulation operation resulting in the large series connection of PV panels which is unwanted from the optimal operation point of view and can be attenuated by connecting to a line frequency transformer (bulky and less efficient). Meanwhile the ac output power ripple which has double fundamental frequency oscillation unavoidably introduces the double-line-frequency voltage ripple unlike the balanced

ΔV

(a)

ΔV

(b) Fig. 2: General illustration of (a) P-V curve and (b) I-V curve generated by PV panel with dotted line showing the near optimal operation range of single-stage single-phase PV inverter.

978-1-4244-2893-9/09/$25.00 2009 IEEE

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operation of maximum power point tracking as illustrated by the dotted line in Fig. 2. To minimize the dc voltage ripple and then enhance the solar energy transfer efficiency, a large value dc-link capacitor is normally employed, which however cannot fully eliminate this problem and leads to the increase of system size and cost. Alternatively, a two-stage solution as shown in Fig. 1(b) consisting of dc-dc boost converter and dc-ac inverter can operate in a large range of PV voltage ensuring the proper PV energy conversion under wide operational range. Moreover, the inserted dc-dc converter decouples the direct connection of PV panel and ac output so that the ac output power ripple will not induce the double-line-frequency ripple of PV voltage. The MPPT efficiency can then be enhanced by using a relatively small input capacitor Cf to just attenuate the high frequency input voltage ripple in the dc-dc voltage conversion. Using a dc-dc converter in front, the efficiency of whole inverter would decrease since more passive and active components are involved in the energy processing when compared to the single-stage topology but when considering the improved MPPT efficiency and wide operation range the two-stage solution is superior to the single-stage inverter. To control the grid-tied inverters, it is necessary for both single-stage and two-stage inverters to measure the dc-link voltage and control it to follow the preset dc-link voltage reference [1, 2]. To do that, a voltage sensor is required to measure the dc-link voltage directly and monitor any undesirable voltage change. In the two-stage topology, two voltage sensors will be used if the MPPT is performed in the dc-dc converter. An alternative method is to track the MPP in ac side by observing the dc-link voltage change [9, 10] which however would unavoidably leads to the long time MPPT operation before reaching the steady state. To reduce the overall system cost and meanwhile maintain the high MPPT efficiency of two-stage PV inverter, this paper proposes an indirect method to control the dc-link voltage so that the dc-link measurement unit can be removed without influencing the ac output quality. This paper first analyzes the design principle of dc capacitance which in Section V would be further assumed to verify the performance of proposed control scheme. And then the overall control strategy including the proposed indirect dc-link voltage control is fully investigated. Matlab simulations of two-stage single-phase PV inverter are performed to verify the effectiveness of the proposed indirect dc-link voltage control scheme. II. CAPACITANCE DESIGN OF TWO-STAGE GRID-TIED PV INVERTER To comparatively reduce dc capacitance, the dc-link capacitor should be selected by ignoring the strict requirement of double-line-frequency dc-link voltage ripple found in single-stage PV inverter so that the non-electrolytic capacitor can to some extent be assumed in

Fig. 3: Waveform illustration of output power, dc-link voltage and grid voltage in one fundamental period.

two-stage inverter especially in low-power application with the benefits of enhanced life time and reduced system size and cost [11, 12]. Before start to address the proposed control strategy, the dc-link capacitance and input filter capacitance will first be mathematically designed respectively to keep the voltage ripples under the expected operational range without inducing any damage and large PV voltage variation. A. Calculation of DC-Link Capacitance In unity power factor operation of PV inverter (intended in most PV applications), the output power Pac has a double-line-frequency oscillation as shown in the upper part of Fig. 3, whose peak value is exactly double input power 2PPV. The double-line-frequency oscillation of output power will unavoidably induce the same double-line-frequency ripple of dc-link voltage Vdc as shown in the middle part of Fig. 3. To carefully illustrate the inherent principle of double-line-frequency voltage ripple, Fig. 3 is assumed as an example to explain, where once Pac is larger than PPV at the instant of π/4 of one line frequency cycle meaning that the dc-link capacitor starts to discharge energy to fulfill the additional output requirement, the dc-link voltage Vdc will then begin to drop from the maximum value Vmax till the minimum value Vmin at the instant of 3π/4 during which output power Pac starts to reduce to equal PPV from the instant of π/2. After that, input power will charge up dc-link voltage since now less power is sent out to grid. The dc-link voltage will rise up from minimum value to maximum value in quarter of fundamental period. The amplitude of double-line-frequency dc-link voltage ripple can be calculated by considering the energy balance at the dc-link [13] where,

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ΔE =

1 2 2 Cdc (Vmax Vmin ) = 2

∫

3π

4×ω f

π

( Pac PPV )dt

(1)

4×ω f

1 Pac = vac × iac = Vac I ac (1 cos(2ω f t )) (2) 2 PPV = VPV × I PV (3) Where, Vac and Iac represent the amplitude of ac output voltage and current, respectively. IPV and VPV are the total output current and voltage of PV string assumed to be constant in a two-stage PV inverter. Assuming a lossless system, the amplitude of ac output current Iac should be derived as: I ac = 2 PPV Vac (4) Therefore, equation (1) can be rewritten as: P 1 2 2 (5) Cdc (Vmax Vmin ) = PV ωf 2

Cdc = PPV PPV ΔV = ω f Vave ΔV ω f Vave Cdc

(6)

Obviously, from (6) the amplitude of double-line-frequency dc-link voltage ripple V = Vmax Vmin is mainly determined by the dc-link capacitance, predefined dc-link voltage and input power from PV panel which is also directly related to the ac output current when the inverter is connected to grid. Therefore, the dc-link capacitance can be minimized as long as the dc-link voltage is below the predetermined safe operation limit and higher than the grid voltage under the maximum power operation condition. Similar to the finding in single-phase power factor correction [12], a noted feature in determining Vmin in two-stage PV inverter is that Vmin is unnecessary to keep higher than the amplitude of grid voltage as long as there is no overlap between the dc-link voltage and grid voltage as shown in Fig. 3. B. Calculation of Input Filter Capacitance The input filter Cf is inserted to reduce the power oscillation by keeping the PV voltage constant in theory. In practice, the large current ripple of dc inductor Ldc (small inductor is normally assumed in high frequency switching converter to reduce the system cost and size) will lead to the significant voltage oscillation in PV panel similar as illustrated in Fig. 2(b) when input capacitance filter is not connected. With a small filter capacitor added, the voltage ripple across PV panel can be reduced significantly. Mathematical derivations presented below illustrate the relationship between PV voltage ripple and filter capacitance in the dc-dc boost stage of PV inverter. Due to the nonlinear characteristics of V-I curve in Fig. 2(b) the PV panel can be treated as either a current source when operation point locates in the left hand of MPP or a voltage source when operation point locates in the right hand of MPP. To simplify the calculation process, the nonlinear characteristics of PV output is first ignored.

Instead, the PV panel is treated as a current source in the following analysis. Secondly, the analysis assumes the boost converter operate in continuous conduction mode (CCM). Therefore, the capacitor voltage ripple (also PV panel voltage ripple in Fig. 1(b)) VPV can be simply derived using the energy balance theory as stated in the last subsection. 2 T 2 DT 2VPV (VPV × Δi )dt = C f ΔVPV VPV = 0 4 Ldc (7) 2 DT VPV ΔVPV = 4C f Ldc Where, D is the conduction duty ratio of boost converter and T represents the switching period. i refers to the current difference between input current from PV (constant as assumed) and inductor current iLdc. The amplitude of iLdc can be calculated as DTVdc/L and due to the linear rising and dropping characteristics of iLdc the integration in (7) can then be simply calculated to derive either the input voltage ripple or the filter capacitance needed under particular operation conditions.

∫

III. CONTROL STRATEGY OF TWO-STAGE SINGLE-PHASE GRID-TIED PV INVERTER In the presented topology, the current controlled boost converter performs the MPP tracking function and the current controlled H-bridge outputs the expected sinusoidal current meanwhile controls the dc-link voltage. Unlike the traditional dc-link voltage control in which the measured dc-link voltage compares to the reference voltage and then the error signal passes through a Proportional-Integral (PI) controller to acquire the proper compensation value for output current reference [1, 2], this paper proposes an indirect control method to regulate the dc-link voltage without measuring the dc-link voltage directly so as to reduce the total system cost. In principle, the overall control diagram is illustrated in Fig. 4, where the control block can be divided into two parts. The first is the MPPT function and the corresponding current control of boost converter. Another is the output current control of single-phase inverter with compensation current added for regulating the dc-link voltage. The detailed illustration for these two control sections are presented below. A. Current Based Maximum Power Point Tracking and Control of Boost Converter This paper assumes a current based MPPT method to track the maximum power point and generate the corresponding current reference IPV-ref to control the boost converter. For fast tracking purpose, a current based P&O method with reference holding function is employed. Doing so, the MPPT can operate fast and immune to the unavoidable current ripple induced by the voltage ripple which always exists in the physical elements as illustrated

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in (7). Unlike the MPPT control in single-stage inverter [14], the adopted MPPT does not generate oscillation around MPP at steady state thanks to both the two-stage configuration and ripple-free operation of reference holding function which does not respond to tiny power variations. Along with the adjustment of IPV for tracking MPP, the boost converter is controlled by only following the change of IPV without considering the output voltage value as traditional converters. In practice, the generated IPV-ref compares to the sensed ILdc not IPV since the small ripple current of IPV (expected) results that the gain of PI controller is high and consequently induces the instability problem. Alternatively, the comparative large current ripple of Ldc can reduce both the gain requirement of PI controller as defined in (8) and the risk of instability and then the practical PV current will follow the reference current rapidly and accurately. 1 GPI ( s ) = K p + Ki (8) s

B. Phase-Locked-Loop and Single-Phase Output Current Control A single-phase phase-locked-loop (PLL) with a transport delay block to generate orthogonal system is assumed to synchronize the output current by calculating the phase angle θ of grid voltage. Additionally, the amplitude and frequency of grid voltage can be calculated to monitor the grid variation. A well-known proportional-resonant (PR) controller suitable for single-phase inverter operation is employed in this paper to control the output current as illustrated in Fig. 4. The PR controller defined as (9) has been verified that it can track the current reference Iref with zero steady-state

error [15]. s (9) 2 s + ω0 Using PR controller can also avoid the stationary frame to synchronous frame transformation which is usually difficult in single-phase system. GPR ( s ) = K p + K i

2

C. Indirect DC-Link Voltage Regulation Based on the power balance theory, the compensation current IComp for regulating dc-link voltage is in fact the compensation for power loss inside the two-stage inverter. Assuming a lossless system, the generated DC power from PV panels should be completely converted to AC power. Therefore, the amplitude of ac current reference can be simply derived as (4). Meanwhile, the dc-link voltage control becomes insignificant because the PV system has limited input power unlike the case of motor drive which draws power from unlimited power grid. However, in practice the losses of two-stage PV inverter will continuously decrease the dc-link voltage to the unaccepted value if the compensation current is not added. Traditionally, the compensation current is produced by directly regulating the dc-link voltage which compares the measured voltage to reference value and then pass through a PI controller to get the compensation current. Alternatively, this paper proposes an indirect method to regulate the dc-link voltage so that the dc-link voltage sensing unit can be eliminated. In fact, the sinusoidal reference generated by the PR controller referring to Ref in Fig. 4 can reflect the change of dc-link voltage. Specifically, when dc-link voltage is lower than the peak ac voltage, over-modulation condition would appear in the normalized Ref. On the other hand, when dc-link voltage is too high, the H-bridge would operate in

+

×

×

2PPV Ua

Fig. 4: Overall control diagram of the two-stage PV inverter.

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Fig. 5: Indirect control diagram of dc-link voltage using hysteresis control.

the low modulation condition implying the peak value of normalized Ref being much smaller than unity. Both situations are intended to be avoided and can be regulated by controlling the modulation reference Ref. Since only the amplitude of Ref is concerned in the dc-link voltage control, a simplified PLL block which only calculates RefPeak is employed, where the phase angle for calculating amplitude in simplified PLL can directly employ θ that has been produced for synchronizing the output sinusoidal current. Doing so, the calculation burden has not been increased much. Due to the double-line-frequency voltage ripple, RefPeak demonstrates the similar double-line-frequency oscillation around the reference value of RefPeak’. The compensation current IComp for attenuating the error between RefPeak’ and RefPeak can then be derived by using a PI controller with small upper and lower limits similar as adopted in tradition methods. Small upper and lower limits can prevent the output current distortion generated by the dc-link voltage control. Carefully observing the function of PI controller, it is revealed that the PI controller can be replaced by a simpler hysteresis controller (HC) as illustrated in Fig. 5, where IComp only has two alternative values. When RefPeak reaches the lower limit (highest dc-link voltage), a small value (zero or positive) is produced by HC which is used to decrease the dc-link voltage by increasing the output current. When RefPeak reaches the upper limit (lowest dc-link voltage), a small negative value is produced to reduce the output current and consequently increase dc-link voltage. In addition to the simplicity, a drawback of HC in dc-link voltage regulation is that the dc-link voltage oscillates between upper and lower limits fast and will not

reach stable since the compensation current is constant and the capacitor charging and discharging process in Fig. 3 will not be equal in final. To reduce switching losses, the indirect dc-link voltage reference RefPeak’ can be variable according to the generated input power so that at low power operation referring to the low irradiation level condition the dc-link voltage can be kept as low as possible with small double-line-frequency ripple as well according to (6). Alternatively, at high power operation (high irradiation level) condition RefPeak’ will be adjusted to decrease accordingly to keep the dc-link voltage with increased double-line-frequency ripple band still slightly larger than grid voltage. IV. EXTENSION TO MULTI-STRING IMPLEMENTATION Besides the illustrated implementation for centralized or single-string PV panel configuration in Fig. 1(b), the proposed control method can also be simply extended to multi-string PV implementation. Since the front-end dc-dc boost converter can operate independently to track MPP and regulate current, the extension to multi-string implementation can then be simply configured as shown in Fig. 6, where multiple dc-dc converters are connected in parallel and the communication between dc-dc converters and dc-ac inverter is only the generated power from each converter through independent MPP tracking. The ac output current reference is then calculated using the total generated power. When the communication speed between microcontrollers is adequate, multiple standard and plug-and-play dc-dc converters can be designed with their own microcontrollers and an independent inverter is designed to transform dc power to ac grid providing a wide freedom of system construction and reducing the requirement for calculation speed in each converter and inverter. An issue that should be considered in multi-string implementation is the dc-link capacitance when connecting multiple dc-dc converters. Since the output power directly determines the voltage ripple of dc-link, a predefined dc-link capacitance should be selected in accordance with the inverter power rating. V. SIMULATION VERIFICATIONS

Fig. 6: Illustration of multi-string configuration.

To verify the effectiveness of proposed control scheme in the two-stage PV inverter topology shown in Fig. 1(b), the PV panel was intentionally treated as a voltage-controlled current source in which the change of PV current strictly follows the non-linear curve shown in Fig. 2(b) in Matlab simulations. Using the Matlab modeling method in [16], the characteristics of modeled single PV panel are demonstrated in Table I under the conditions of irradiation level, 800W/m2 and temperature, 25C. A centralized PV model made of 26 PV panels with maximum power of 1254W under 800W/m2 irradiation level is then used to

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TABLE I. CHARACTERISTICS OF SINGLE PV PANEL MODELED IN MATLAB SIMULATIONS. Number of series connected cells, Ns Number of series connected cells, Np Short-circuit current, ISC Open-circuit voltage, VOP Maximum power, Pmax 36 1 3.04 A 20.8 V 48.2454 W

1254.5 1254 1253.5 225 220 215 5.8 5.7

evaluate the performance of two-stage single-phase PV inverter controlled by the proposed indirect dc-link voltage control scheme. The two-stage PV inverter was constructed in Matlab\PLECS simulation using Cf = 100F, Ldc = 0.5mH, Cdc = 100F and Lac = 10mH. The switching frequencies of both boost converter and H-bridge is 20 kHz. The generated power is fed into a single-phase ac grid with its fundamental frequency of 50Hz and amplitude of 325V. Fig. 7 shows the simulated results under steady state operation when irradiation level is 800W/m2, where the two-stage PV inverter operated at the maximum power point after the successful MPPT process. It is observed that the output power of PV panel has small ripple band of less than 1W which is induced by the voltage ripple of around 3V and the related current ripple of less than 0.1A as respectively reflected by the second and third waveforms in Fig. 7. Such small input ripple verifies the effectiveness of input filter and is in accordance with the mathematical calculation of (7). The reference holding function in MPPT detects the change of power ripple. Once the power ripple is kept in the accepted value, the current reference will not be changed so that the MPPT can maintain the smooth operation of boost converter at steady state without the continuous perturbation of reference current as traditional P&O MPPT method. Consequently, the output power will maintain unchanged as reflected by the smooth current waveform of Ig and the dc-link voltage Vdc keeps at the predefined value of 325/0.9 with double-line-frequency ripple around, where 0.9 is the normalized modulation depth of Refpeak’ in Fig. 4. In fact, the dc-link voltage varies within the range of around 316V and 423V matching well with equation (6). Both infer that the indirect dc-link voltage regulation works well under steady state operation and will not lose the control of dc-link voltage. Fig. 8 shows the transit performance of two-stage PV inverter with indirect dc-link voltage control. At 0.1s, the PV output power increases due to the sudden irradiation change from 800W/m2 to 1000W/m2 and the MPPT stabilizes at 0.2s with very small power ripple as shown in Fig. 8. And to keep a low dc-link voltage at low power operation and ensure the correct modulation at high power operation, Refpeak’ decreases from 0.9 to 0.87 when irradiation level changes. Because the amplitude of output current reference is mainly derived from the input power as presented in (4) and the output current can track its steadily

5.6 450 375 300 10 0 -10 0 10 20 Time(ms) 30 40 50

Fig. 7: Simulated steady state operation of two-stage single-phase PV inverter. TOP to BOTTOM: generated PV power; PV voltage; VPV, PV current, IPV; dc-link voltage, Vdc; inverter output current, Ig.

1600 1400 1200 250

200 8 6 4 500 400 300 10 0 -10 0 100 200 300 Time(ms) 400 500 600

Fig. 8: Simulated transit operation of two-stage single-phase PV inverter. TOP to BOTTOM: generated PV power; PV voltage; VPV, PV current, IPV; dc-link voltage, Vdc; inverter output current, Ig.

increased reference rapidly with the fine-tuned PR controller, the dc-link voltage at transit-state therefore will not rise or drop significantly with a recovery process from 0.1s to 0.3s in Fig. 8 mainly because of the reconstruction of compensation current from transient state to steady state. Well setting the control parameters, the transit operation will neither reduce output quality nor lose the dc-link voltage control. It is also noted that the dc-link voltage ripple is smaller at low output current condition matching with the analysis of (6) again. VI. CONCLUSION This paper proposes the indirect dc-link voltage control

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scheme for two-stage single-phase PV inverter to reduce system size and cost. With careful design, the dc capacitance can be reduced by allowing the large double-line-frequency voltage ripple and the whole inverter will still be stable. The overall control strategy for both boost converter and single-phase inverter is presented and the indirect dc-link voltage control is mainly analyzed. Simulation results verify the effectiveness of proposed control scheme. REFERENCE

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