PLL-less single stage grid-connected photovoltaic inverter with rapid maximum power point tracking

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ScienceDirect Solar Energy 97 (2013) 285–292 www.elsevier.com/locate/solener

PLL-less single stage grid-connected photovoltaic inverter with rapid maximum power point tracking K.M. Tsang a, W.L. Chan a, X. Tang b,⇑ a

Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong Special Administrative Region b College of electrical and information engineering, Changsha University of Science and Technology, Hunan, China Received 3 March 2013; received in revised form 19 July 2013; accepted 15 August 2013

Communicated by: Associate Editor Elias Stefanakos

Abstract This paper presents a systematic way of designing control scheme for a grid-connected photovoltaic (PV) inverter featuring rapid maximum power point tracking (MPPT) and grid current shaping without using any phase-locked loop (PLL) circuitry. A simple integral controller has been designed for the tracking of the maximum power point of a PV array based on the extremum seeking control method to provide a reference PV output current for the grid interface. For the grid-connected inverter, two current loop controllers have been designed. One of the current loop controllers is designed to shape the inverter output current while the other current control loop is to follow the reference received from the maximum power point tracking algorithm and to provide a reference inverter output current for the PV inverter without largely disturbing the maximum power point of the PV array. Four power switches are used to achieve three output levels and MPPT. Moreover, it is unnecessary to use any energy storage such as rechargeable battery. Experimental results are included to demonstrate the effectiveness of the tracking and control scheme. Ó 2013 Elsevier Ltd. All rights reserved. Keywords: Photovoltaic; Three-level grid-connected inverter; Maximum power point tracking; Grid current shaping

1. Introduction Because of dramatic increase in energy consumption for the last decades, resources and environmental problem are emerging (Sulaiman et al., 2012). Fossil fuel reserves are running out and the environmental impact of the emissions from their combustion is undesirable. It is necessary to reduce carbon emissions and environmental pollutions. Solar energy is an alternative energy gaining increased interests from governments, industry and academia because it is green and sustainable (Liu et al., 2011). The early stage of photovoltaic development was directly toward space applications, for which cost was not a major concern (Taherbaneh et al., 2011). Recently, efficiency in the range of 20–25% has been achieved ⇑ Corresponding author. Tel.: +86 13574187596.

E-mail addresses: [email protected] (K.M. Tsang), eewlchan@ polyu.edu.hk (W.L. Chan), [email protected] (X. Tang). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.08.017

in crystalline silicon-based solar cells while thin-film solar cells could reach 20%. Ultra high efficiencies of over 40% have been achieved in multi-junction cells. In fact, the PV market is growing rapidly, and the price is constantly decreasing (Razykov et al., 2011). One of the most popular standalone applications of the PV energy utilization is water pumping system driven by an electric motor. However, grid-connected applications have experienced strong development over the past few years (Vighetti et al., 2012). Solar electricity generation using building-integrated photovoltaics (BIPV) Liu et al., 2012 can assist in reducing commercial building loads and offering peak-shaving benefits on top of the on-site generation of electricity. The role of grid-connected BIPV in reducing the load demands of a large and urban commercial building located in a warm climate in Spain was reported in Castro et al. (2005). For commercially available PV systems, individual solar cells are connected in series and parallel to form modules to deliver required levels of DC power. It is also necessary to

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use inverter (Wu et al., 2012) if AC power, such as grid-tied system, is needed. Voltage and current changes are expected at the DC side of the inverter. As reported in Dua et al. (2013), the inverter interface is essential to connecting renewable energy sources to the grid. The interface has two main functions: extracting the maximum amount of power from the PV modules and conversion of DC power to an appropriate form of AC power for the grid connection. The current from the PV generator changes with the solar radiation and temperature conditions and PV modules present a non-linear current–voltage curve, so for each solar radiation and temperature conditions there exists an optimum working load which leads to extract the maximum power from the PV modules (Gao et al., 2013). Tracking the maximum power point (MPP) Moradi et al., 2013 of a PV module is an essential task in a PV control system because it maximizes the power output of the PV system for a given set of conditions (Kouchaki et al., 2013). Current control is a key element to obtain the maximum power output of PV systems besides finding the MPP. A repetitive controller can track a sinusoidal reference theoretically. However, there is the trade-off between tracking accuracy and system stability (Mastromauro et al., 2012). The one-cycle control is simple and costeffective but the control performance is sensitive to the user-defined constants (Mario et al., 2008). In this paper, the maximum power point tracking (MPPT) for PV array has been designed to synchronize with the control scheme of the grid-tied interface without using any PLL circuitry (Letting et al., 2012) as supply voltage feedforward control has been employed. The current regulators are designed taking into considerations of the PV module and grid specifications. The hardware requirement is not demanding. Only four power switches are required to achieve three output levels (Khemissi et al., 2013) and MPPT. Moreover, it is unnecessary to use any energy storage such as rechargeable battery. Although three-level inverter has been employed in this paper, other multi-level inverter (Tsang and Chan, 2012) could also be used. Experimental results are included to demonstrate the effectiveness of the grid interface in maximum power point tracking and output current shaping (Tang et al., 2012). 2. PV grid interface Fig. 1 shows a schematic diagram for the PV grid interface. To extract maximum power from the PV array, the current ip drawn from the PV array has to be maintained to a steady value because the power extracted will be lower if the current drawn is above or below the current at the maximum power point. A low-pass LC filter is attached to the PV array such that the current drawn from the PV array will have small ripples and close to maximum power can be extracted from the PV array at all time. If the interface is driven by pulse width modulation (PWM) signal, the state averaging dynamics of the interface can be described as:

RL

vs

ip

L1

ic S1

L2 S2

ig vp

C

vg

vc

S3

S4

Fig. 1. A schematic diagram for the PV grid interface.

L1 i_p ¼ vp  vc C v_ c ¼ ip  ic L2 i_g ¼ vg  vs

ð1Þ

vg ¼ dvc ic ¼ dig where L1 is the inductor connected to the PV panel, L2 is the inductor connected to the grid, vc is the voltage across the capacitor C, ic is the discharging current from the capacitor, ig is the current entering the grid, vg is the output voltage of the inverter, d is the duty ratio for the inverter bridge and vs is the grid voltage, respectively. d takes on the value between 1 and 1. If d = 0.5, the switches S1 and S4 will be on for half a switching cycle followed by S1 and S4 on for half a switching cycle. If d = 0.5, the switches S2 and S3 will be on for half a switching cycle followed by S3 and S4 on for half a switching cycle. When S1 and S4 are on, the inverter output vg = vc. When S1 and S2 are on, the output vg = 0. If d2 = 0.5, the switches S2 and S3 will be on for half a switching cycle followed by S3 and S4 on for half a switching cycle. When S2 and S3 are on, the inverter output vg = vc. When S3 and S4 are on, the output vg = 0. If S1, S2, S3 and S4 are switching in this configuration, a three-level inverter can be realized using only four switches. 2.1. Grid current control If the dynamics of the capacitor voltage vc is very much slower than the dynamics of the inverter output current ig, the capacitor voltage can be regarded as constant and from (1) the dynamics of the inverter output current can be approximated as: L2 i_g ¼ dU m  vs

ð2Þ

where Um is the nominal capacitor voltage at the steady state. Consider the addition of a feedforward controller of the form: GF ðsÞ ¼

1 vc

and a proportional controller of the form:

ð3Þ

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current control loop is inherently unstable because of the very poorly damped LC filer in the input stage of the grid interface. The error voltage between the PV output voltage and the capacitor voltage is fed back to the input side in order to stabilize the control loop. The feedback gain controller is given by: GD2 ðsÞ ¼ K D2

Fig. 2. Block diagram for the grid current control loop.

GPI1 ðsÞ ¼ K P 1

ð4Þ

where KP1 is a constant to form a closed-loop control process. The purpose of adding the feedforward controller is to cancel the effect of vs on the inverter output current ig and the proportional controller forces the inverter output current ig to follow a reference output current igr (Tsang and Chan, 2006). Fig. 2 shows the block diagram of the current control loop. If the model is the true representation of the process, the closed-loop transfer function can be approximated as: I g ðsÞ K P 1U m ¼ I gr ðsÞ L2 s þ K P 1 U m

ð5Þ

Fig. 3a shows the block diagram of the PV current control loop. At the steady state, the PV output current ip will be equal to the capacitor discharge current ic. Assuming there is no power loss: vp ip ¼ V rms igðrmsÞ

xig L2 Um

and the required duty ratio can be obtained as: vs d ¼ K P 1 ðigr  ig Þ þ vc

ð6Þ

ð7Þ

(a)

2.2. PV array current control loop From (1) the PV array current ip will be equal to the capacitor discharge current ic at the steady state. Controlling ic indirectly controls ip and ic itself is affected by the grid current ig. From (1), the PV array current, the discharge current and the capacitor voltage dynamics can be described by: L1 i_p ¼ vp  vc C v_ c ¼ ip  ic

(b)

ð8Þ

ic ¼ dig For the PV current control loop, it has to generate a reference current igr which indirectly generates a capacitor discharging current ic for the regulation of the capacitor voltage and the PV output current. The reference inverter output current is set to be in phase and of the same shape as the grid voltage such that the output of the inverter will have the least effect on the current harmonics of the grid. An integral controller K I2 GI2 ðsÞ ¼ ð9Þ s is included in the control loop such that the PV output current will be equal to the required current at the steady state. The PV

ð11Þ

where Vrms and ig(rms) are the root-mean-squared value of the grid voltage vs and inverter output current ig respectively. If the dynamics of the PV current control loop is set to be very much slower than the grid current control loop, the inverter output current ig quickly follows igr and the gain from the magnitude of igr to ic in the PV current control loop can be approximated to VUrms . A steady m state approximation of the PV current control loop is shown in Fig. 3b. Here vs and d are regarded as output disturbances to the PV output current and they are excluded

If the bandwidth of the grid current control loop is set to xig and xig has to be lower than the switching frequency of the interface, the required controller gain can be obtained as: KP1 ¼

ð10Þ

(c) Fig. 3. Block diagram for the PV current control loop.

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from the plot. As the grid voltage is used to derive the required inverter output current, it can be regarded as external disturbance to the PV output current control loop. One simple way to reduce its effect on the PV output current is to set the bandwidth of the PV current control loop to be very much lower than the grid supply frequency such that the effect of the supply voltage on the PV current control loop will be substantially attenuated by the lowpass characteristic of the control loop. The closed-loop characteristic equation can be approximated as: DðsÞ ¼ LCs3 þ

V rms K D2 L 2 V rms K I2 s þsþ Um Um

ð12Þ

If one of the poles is placed at: s¼

V rms K I2 Um

ð13Þ

and extracted from (12), the resulted second order polynomial becomes: LCs2 þ

V rms L ðK D2  K I2 CÞs Um 2

þ

K I2 ð1  V rmsUK2 I2 L ðK D2  K I2 CÞÞs þ V rms Um m

K I2 s þ V rms Um

¼0

ð14Þ

If: V 2rms K I2 L ðK D2  K I2 CÞ  1 U 2m

ð15Þ

(13) can further be approximated as: LCs2 þ

V rms L ðK D2  K I2 CÞs þ 1 ¼ 0 Um

ð16Þ

The undamped natural frequency for (16) is given by: rffiffiffiffiffiffiffi 1 xip ¼ ð17Þ LC and the damping ratio for (16) is given by: fip ¼

V rms ðK D2  K I2 CÞ 2Cxip U m

ð18Þ

Based on (13), (17), and (18), the dominant characteristic of the PV current control loop can easily be set by KD2 and KI2. Notice that Vrms is taken as the nominal rms voltage of the supply grid. Fig. 3c shows the connection diagram for the two current controllers and the derivation of the duty ratio d from the control loops.

maximum power under varying irradiance. An improvement on the constant voltage method uses the open circuit voltage to estimate the maximum power output voltage while the short circuit current method uses the short circuit current to estimate the maximum power output current. Perturb and observe method searches for the maximum power point by changing the PV voltage or current and detecting the change in PV output power. The step size for the search affects the rate of convergence of the tracking. Also, the method may fail under the rapidly changing atmospheric conditions (Petrone et al., 2011). A faster searching technique for the PV array can be realized using the extremum seeking control (Heydari-doostabad et al., 2013). From the power versus current PV characteristic curve, four cases can be distinguished. If DP > 0 and Dip > 0, where DP is the change of power and Dip is the change of current from the PV array, the maximum power point can be obtained in increasing ip. If DP < 0 and Dip < 0, the maximum power point can be obtained in increasing ip. If DP > 0 and Dip < 0, the maximum power point can be obtained in decreasing ip. If DP < 0 and Dip > 0, the maximum power point can be obtained in decreasing ip. Fig. 4 shows the extremum seeking control block diagram in realizing the four distinguished cases for the MPPT of PV array. Instead of a sinusoidal perturbation (Letting et al., 2012), a disturbance on the PV array current of the form:  pt DI ¼ asgn sin ð19Þ T where a is the magnitude of the disturbance and T is the duration for either positive or negative half cycle, is added to the control loop to persistently excite the seeking procedure. For the same magnitude of perturbation a, the square wave perturbation converges faster than the sinusoidal perturbation because the sum of changes in half cycle of oscillation for a square waveform is larger than a sinusoidal waveform. In theory, the control loop is stable for any value of Kmppt > 0. As the extremum seeking control involves the derivative of the power, low-pass filtering of the raw power is required in order to remove the unwanted high frequency noise in the approximate derivative signal. The

3. Rapid maximum power point tracking There are a number of different approaches for maximum power point tracking (MPPT) Shaiek et al., 2013. They are the constant voltage method, open circuit voltage method, short circuit method, perturb and observe method and the incremental conductance method. The constant voltage method is the simplest method but it has been commented that the method could only collect about 80% of the available

Fig. 4. Block diagram for the maximum power point tracking control loop.

K.M. Tsang et al. / Solar Energy 97 (2013) 285–292

ip

filter will introduce phase shift or time delay in the filtered signal and this will affect the stability of the control loop especially for large value of Kmppt. If the time delay of filter, magnitude and frequency of current disturbance, and the gain of the PV array are taken into account, a reasonable gain for the integral controller can be taken as: K mppt ¼

2 sT aV oc

The speed of convergence can be set by a, T and Kmppt. 4. PV simulator To test the performance of the maximum power point tracking control loop, current tracking and current shaping of the grid-connected inverter, a PV simulator with open circuit voltage of 600 V and short-circuited current of 5 A was built in connecting 200 V 6 A DII6A2 diodes in series and a constant current source was connected to the diodes as shown in Fig. 5. Different amplitudes of current were injected into the simulator at 25 °C and the output characteristics were collected. Fig. 6a and b show the voltage against the current and the voltage against delivered power respectively. The maximum power points were also highlighted for different amplitudes of constant current source. Clearly, the characteristics of the PV simulator and the real PV array are very similar. The constant current source of the PV simulator could be regarded as the short-circuited current of a PV array. A plot of the maximum power point against the short-circuited current is shown in Fig. 7. A quadratic equation of the form: P mp ¼ 11:81I 2sc þ 226:8I sc

constant current source Isc

ð20Þ

where Voc is the open circuit voltage for the PV array and s is the approximate time delay of filter. The magnitude of the disturbance a has to be sufficiently large such that the power level with positive and negative disturbances can clearly be identified and sufficiently small such that the output power will not be too fluctuated. The frequency of the disturbance has to be selected to a value such that the transient of the change of power for a step change in the current can be fully captured within half cycle of the excitation. The required PV array current can be obtained as: Z dP DI ipr ¼ DI þ K mppt dt ð21Þ dt a

ð22Þ

is well fitted to the data set where Pmp is the maximum power delivered and Isc is the short-circuited current of the simulator. Fig. 7 also shows the fitted curve superimposed on the collected data and a very close approximation has been obtained and an estimate of the maximum power at some other operating points can easily be obtained from (22). 5. Implementation of the PV grid interface To demonstrate the effectiveness of the proposed grid interface, an experimental setup was built to handle 50 Hz 220 Vrms supply. Power MOSFETs, SPP17N80C3, were used to realize

289

vp

Fig. 5. A PV simulator.

the switches of the inverter. The inductors were chosen as L1 = 7.66 mH and L2 = 0.82 mH and the capacitor used was C = 3300 lF. The switching frequency for the PWM was set to 31.25 kHz. An industrial PC was used to sample all required variables and to implement the control loops. The sampling frequency was set to 10 kHz. From the characteristic curve of the simulator, the nominal capacitor voltage Um was set to 450 V which was around the voltage at maximum power when the short-circuited current was half rated. If the bandwidth of the grid current control loop was set to 1 kHz, from (6) the required controller gain became: K P 1 ¼ 0:0114

ð23Þ

For the PV current control loop, the bandwidth was set to 2.5 Hz and the damping ratio was set to 1 such that the PV current control loop and the capacitor voltage dynamics would be very much slower than the grid current control loop. The 50 Hz signal and its higher harmonics entering the PV current control loop would also be substantially attenuated by the loop dynamics. From (13): K I2 ¼ 32:13

ð24Þ

if the dominant pole was place at 5p. From (18): K D2 ¼ 2:79

ð25Þ

With (24) and (25), the closed-loop poles of (12) were situated at 19.49, 113.89 and 279.95 and the dominant pole characteristics was very close to the specified value 5. To test the performance of the current tracking of the PV current control loop and the delivering of power to the grid, the PV simulator was connected to the input of the interface and the constant current source was set to 4 A. The reference PV output current was fixed at 3.55 A. Fig. 8 shows the performance of the control scheme. The PV output voltage was rather steady and the mean output voltage was 473 V. The inverter output current had the same shape of the grid voltage and it was also in phase with the grid voltage. The mean PV output current was 3.48 A. Because of the ripples in the PV output current, the average delivered power was only around 95% of the available maximum power. This clearly demonstrated the effectiveness of the interface in conveying power from the PV panel to the grid. Fig. 9 shows the

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K.M. Tsang et al. / Solar Energy 97 (2013) 285–292 6 Isc = 5A

5 Isc = 4A

Current (A)

4 Isc = 3A

3 Isc = 2A

2 Isc = 1A

1 Isc = 0.5A

0

0

100

200

300

400

500

600

700

Voltage (V)

(a) Simulator output current against output voltage 2500

Vmp = 494V Imp = 4.46A

2000

Power (W)

Isc = 5A Vmp = 486V Imp = 3.55A

1500 Isc = 4A

Vmp = 468V Imp = 2.67A

1000

Isc = 3A

500

Isc = 1A

0

Vmp = 445V Imp = 1.79A

Isc = 2A

IV = 0.5A

0

100

200

300

Vmp = 416V Imp = 0.87A Vmp = 380V Imp = 0.44A

400

500

600

700

Voltage (V)

(b) Simulator output power against output voltage Fig. 6. Characteristic curves of the PV simulator at 25 °C. 2500

2000

1500

1000

500

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Fig. 7. Relationship between maximum power point and the short circuited current at 25 °C.

performance of the interface if the filtering capacitor was removed. As the reference PV output current was fixed at 3.55 A and the action of the current controllers were fast, the control system experienced limit cycle oscillations. There were large variations in the PV output voltage and the PV output current. The limit cycle oscillation also affected the inverter output current. The extracted power was less than

50% of the available maximum power. Even though the inverter output current was in phase with the phase voltage, it composed of a lot of high order harmonics. This clearly demonstrated that the input stage LC filtering was required in order to improve the average power extracted from the PV panel. Even though the limit cycle oscillations can be removed in slowing down the two current controllers, this will affect the grid current tracking and the speed of MPPT. The implementation of the extremum seeking control loop was on the same hardware and also sampling at 10 kHz. As derivative of power with respect to time was required, a linear phase finite impulse response differentiator with 51 coefficients and a passband up to 100 Hz and stopband starting from 250 Hz had been implemented to obtain the derivative of power. The time delay introduced by the differentiator was s = 0.0025 s. For the amplitude of excitation, a was set to roughly 2% of the maximum short-circuited current of the PV simulator such that it would be large enough to detect the difference and small enough to not disturb the system too much. In this example, it was set to a = 0.1 A. For the setting of the duration of excitation, it had to be long enough for the transient to settle down. As the bandwidth of the input cur-

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steady-state response of the inverter which was shown in Fig. 10d showed that the inverter output current was of the same shape and in phase with the grid voltage. 6. Conclusions A systematic approach of designing controllers for maximum power point tracking, current tracking and shaping for grid-connected PV inverter were presented. The effectiveness of the proposed controller setting in maximum power point tracking was clearly demonstrated. Experimental results also demonstrated that the grid interface together with the current loop controllers effectively conveyed the power from the PV array to the grid because Channel 1 - PV output voltage

700

Channel 2 – PV output current

600

Channel 3 – Grid voltage 500

rent tracking loop was set to 2.5 Hz, the transient of the current would die down in around 0.25 s. In this example, the duration T was set to 0.25 s. As the open circuit voltage Voc of the PV simulator was around 600 V, from (20) the gain of extremum seeking control loop became Kmppt = 53.33. The maximum power point tracking control was then combined with the current tracking controllers to form a complete system. Fig. 10 shows the tracking performance of the whole system. The short-circuited current was set to 5 A and the available maximum power was 2203 W. The initial PV output current was zero. Fig. 10a and b showed that the PV output voltage gradually reduced to around 478 V and the PV output increased to 4.28 A. Fig. 10c showed that the maximum power point was tracked in about 20 s. The

400 300 200 100 0

0

5

10

15

20

25

30

35

40

Time (s)

(a) PV output voltage 5 4.5 4 3.5

Current (A)

Fig. 8. Tracking performance of the inverter interface.

Voltage (V)

Channel 4 – Inverter output current

3 2.5 2 1.5 1 0.5 0

0

5

10

15

20

25

30

35

40

Time (s)

(b) PV output current 2500

Power (W)

2000

1500

1000

500

Channel 1 - PV output voltage Channel 2 – PV output current Channel 3 – Grid voltage Channel 4 – Inverter output current

Fig. 9. Tracking performance of the inverter interface without filtering capacitor.

0

extracted power maximum power

0

5

10

15

20

25

30

35

40

Time (s)

(c) Extracted power Fig. 10. Tracking performance of extremum seeking control and current shaping controllers.

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K.M. Tsang et al. / Solar Energy 97 (2013) 285–292 15 10

Current (A)

5 0 -5 -10 -15

0

5

10

15

20

25

30

35

40

Time (s)

(d) Inverter output current

Channel 1 - PV output voltage Channel 2 – PV output current Channel 3 – Grid voltage Channel 4 – Inverter output current

(e) Steady-state outputs Fig. 10. (continued)

the output current of the inverter was in phase and of the same shape as the grid voltage. Acknowledgment The authors gratefully acknowledge the support of the Hong Kong Polytechnic University. The authors gratefully acknowledge the support of the national natural science foundation of china (No. 51277013) and Scientific Research Fund of Hunan Provincial Education Department (No.13K055) too. References Castro, M., Delgado, A., Argul, F.J., Colmenar, A., Yeves, F., Peire, J., 2005. Grid-connected PV buildings: analysis of future scenarios with an example of Southern Spain. Solar Energy 79 (1), 86–95. Dua, Yang, Lu, Dylan Dah-Chuan, James, Geoffrey, Cornforth, David J., 2013. Modeling and analysis of current harmonic distortion from grid connected PV inverters under different operating conditions. Solar Energy 94, 182–194.

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