Maximum power point tracking of single-ended primary ... - IEEE Xplore

www.ietdl.org Published in IET Power Electronics Received on 18th July 2012 Revised on 25th December 2012 Accepted on 16th January 2013 doi: 10.1049/iet-pel.2012.0416

ISSN 1755-4535

Maximum power point tracking of single-ended primary-inductor converter employing a novel optimisation technique for proportional-integralderivative controller Ahmad El Khateb1, Nasrudin Abd Rahim1, Jeyraj Selvaraj1, Mohammad Nasir Uddin2 1

UM Power Energy Dedicated Advanced Centre (UMPEDAC), University of Malaya, Kuala Lumpur, Malaysia Electrical Engineering Department, Lakehead University, Ontario, Canada E-mail: [email protected]

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Abstract: This study presents an optimisation technique for proportional-integral-derivative (PID) controller to achieve maximum-power-point tracking (MPPT) of single-ended primary-inductor converter (SEPIC). A new weight function is developed to optimise the PID parameters based on gradient-descent (GD) method by adding low-pass filter term. The proposed optimisation method does not stick in the local minima, which happens frequently with the traditional weight function used in GD method, where the low-pass filter term suppresses the noise and smooths the iteration process. The prototype of the proposed optimised PID-based SEPIC converter for photovoltaic inverter applications is built using DSPbased TMS320F28335. The performance of the proposed optimised PID-based MPPT scheme is tested in both simulation and experiment at different operating conditions. A performance comparison of the proposed GD method with the conventional GD PID is also made in real-time. It is found that the proposed optimised PID-based SEPIC converter is superior to the conventional GD PID controller in terms of power transfer and efficiency. Furthermore, the proposed optimised PID controller for two-level inverter can achieve a better total harmonic distortion (THD) level as compared to the multi-level inverter frequently used by researchers for the same purpose.

1

Introduction

Owing to its treatment to both transient and steady-state response, proportional-integral-derivative (PID) controller offers the simplest and most efficient solution to many genuine control problems. Over the years, PID controllers have been widely used in industry for converter control, motor drives and other process controls [1, 2]. The optimisation of the PID controller parameters reduces the error signal significantly and comprehensively controls the converter with maximum-power-point tracking (MPPT) operation while minimising overshoot, settling time, rising time and steady-state error. A huge number of optimisation methods have been introduced for PID parameters tuning in the literature. Particle swarm, Taguchi, Chaos, gradient-descent (GD) and genetic algorithms all improve the steady state and the transient characteristics through the optimisation of the PID parameters [3–6]. However, methods like particle swarm, Taguchi and Chaos have some disadvantages. The particle swarm optimisation has problems of dependency on initial conditions and difficulty in finding the optimal design parameters of the final outputs because of the absence of the derivative. Taguchi optimisation method has difficulty in determining the interactions between parameters, where IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121 doi: 10.1049/iet-pel.2012.0416

the results obtained are only relative and do not exactly indicate what parameter has the highest effect on the performance characteristic value [7]. Chaos is not a derivative-dependent optimisation method. It overcomes the difficulties of the derivative-based methods because it heavily depends on the gradient information but it has an advantage since it avoids falling in local minima [6]. GD optimisation is a reiterative technique that is given a starting point, and follows the negative gradient in order to move the point towards a specific solution, which is hopefully the desired value. GD method is popular for very large-scale problems because it is simple, easy to implement and it is guaranteed to find the minimum through numerous time of iterations as long as it exists [8, 9]. As the GD method is an effective optimisation method for solving the PID parameters problem, this work develops GD-PID controller to search for the optimal PID parameters. The GD method often becomes stuck in local minima, which is the most common problem in this method. Conversely, the improvement on this method by adding filter term to the weighting function suppresses the noise, fasten the process and avoid sticking in the local minima. Therefore the proposed method combines between the simplicity of the original method and the advantages of the additional filter term especially avoiding the local minima. 1111

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www.ietdl.org The main part of the MPPT operation is selecting the proper DC–DC converter. Among all the converters available, both the single-ended primary-inductor converter (SEPIC) and the Ć uk converters provide the choice to have either higher or lower output voltage compared to the input voltage. Furthermore, they have contentious input current and better efficiency compared to buck–boost and fly-back converters [10]. Unlike buck–boost converter, the SEPIC has a non-inverted output, and it uses a series capacitor to isolate input from output [11]. The buck and buck–boost converters have discontinuous input current, which causes more power loss because of input switching. The boost converter usually has higher efficiency than the SEPIC, however, its output voltage is always larger than the input which causes inflexibility in power extraction. Even though there is no general agreement in the literature on which one of the two converters is better; the SEPIC or the Ć uk [12–17], this paper seeks to use the SEPIC converter because of the Ć uk converter inverted output. The MPPT method extracts additional power from photovoltaic (PV) array under specific conditions. It represents an optimal load for PV array, producing opportune voltage for the load. The PV cell yields exponential curves for current and voltage where the maximum power occurs at the curve’s mutual knee [18]. The applied MPPT uses a type of control and logic to look for the knee, which, in turn, allows the SEPIC converter to extract maximum power from the PV array. The tracking method, Perturb and Observe (P&O) [19], provides a new reference signal for the controller and extracts maximum power from the PV array. In [20–25] have been working on integrators for the control of their converters, especially the PI controllers. Integrators eliminate steady-state error but degrade system stability. On the other hand, differentiators with a tiny gain improves system stability. Therefore the use of integrators and differentiators is an integrated process, that is, PID. The PID controller can eliminate the steady-state error as well as improve system stability and settling time if the derivative part has been accurately optimised and selected. Therefore there is a need to formally optimise the PID controller parameters. Furthermore, the optimised PID will decrease the THD level of the output current signal and the cost of the system will also decrease because of fewer switches as compared to multi-level inverter which is mainly used to decrease the total harmonic distortion. Wherefore, if we managed to prove that optimised PID has better THD level than that of multi-level inverters, certainly this will lead us to such an optimised PID for multi-level inverters that will show much better THD levels. This paper introduces a novel optimisation technique of GD method for PID controller applied for MPPT-based SEPIC converter showing that the extracted power using the proposed method is 3.4% more than that power extracted using the conventional GD method. The controller shows a high-precision in current transition and keeps the voltage without any changes in variable-load case, represented in small steady state error, short rising time and small overshoot. As the inverter is used in a PV system, the proposed controller is employed for more-accurate output sine-wave, higher dynamic performance under rapidly varying atmospheric milieu and improved total harmonic distortion as compared to the conventional controlled inverters [20–25]. It is worth noting that PI controller is used in many inverter applications that are suitable for 240 V rms and power more than 1 kW as shown in [20, 26, 27]. 1112 & The Institution of Engineering and Technology 2013

2

Overall system description

The SEPIC converter is supplied from the PV panels, and the output is connected with the single-phase inverter. The output signals of the inverter and the converter are fed back to the respective PID controller. The converter is controlled by the optimised PID controller. The converter’s main function is to increase the level of voltage fed to the inverter. In this work, however, voltage level increases or decreases according to the MPPT scheme. Furthermore, the controller changes the voltage level by changing the duty cycle of the pulse-width modulation (PWM) signal, which tracks the reference signal. The sinusoidal reference signal is compared with the overall output signal, and the error is processed through PID controller which generates PWM signals for the single-phase inverter. The SEPIC’s output signal is, thus, compared with the adaptive reference signal to feed the inverter by the most suitable power. The maximum power transfer operation from the PV array is achieved through optimisation of the PID controller based on a combination of PID parameters tuning and measuring the negative gradient of the step response, which is used to achieve the PID variables; iterations were made by means of changing PID variables until the step response achieved the desired response.

3

Optimisation of the PID parameters

The overall control scheme of the proposed MPPT-based optimised PID control of SEPIC converter is shown in Fig. 1. The tuning of PID parameters can bring them to the region of convergence but cannot guarantee that the optimal solution is achieved. As mentioned in [28], PID tuning cannot achieve exact values for PID parameters, but can ensure their existence around the optimal solution. There are two possibilities when the optimisation is done for out of convergence values: the first is that the optimisation process takes a heavy long time to achieve the optimal solution. The second is that the process goes towards infinity. These two problems can be avoided by the proposed optimisation process. The searching process for the optimal controller parameters kp, ki and kd starts by specifying the lower and upper bounds of the PID parameters and initialising the parameter values using Ziegler–Nichols method [29]. For each iteration, the closed-loop system stability is tested and the values of overshoot, steady-state error, rising time and settling time are calculated. Fig. 2a presents the flowchart of the optimisation process. The weight matrix of the learning process at time k is calculated as shown in (1) Wk = Wk−1 − b

∂F ∂Wk−1

(1)

Where β is the optimising step-size or learning rate. Then, the minimum of the objective function is found when ∂F/∂Wk−1 = 0. From (1), the GD equation updating depends on the integration. Thus, (1) can be expressed as in (2) Wk = −

b ∂F −1 1 − z ∂Wk−1

(2)

The GD learning procedure is presented as a feedback system when the reference signal is set to zero and the output weight is W as shown in Fig. 2b. The system error is assumed to be IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121 doi: 10.1049/iet-pel.2012.0416

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Fig. 1 Overall control scheme for the proposed MPPT-based SEPIC converter for PV inverter applications using DSP TMS320F28335

−∂F/∂Wk−1, which is e(k) = 0 − ∂F/∂Wk−1. The controller purpose is to design zero-error signal in a fast and stable response. Therefore the fine response can be obtained by selecting proper values for PID parameters. The z-transform of the PID controller can be expressed as shown in (3) C(z) = kp +

ki + (1 − z−1 )kd 1 − z−1

(3)

After simplifying the PID controller equation, it becomes as follows

 kp 1 − z−1 + ki + 1 − 2z−1 + z−2 kd C(z) = 1 − z−1

(4)

The GD method with incremental tuning motivated by PID control parameters is derived in (5) 

 ∂F ∂F ∂F − ki − ∂Wk−1 ∂Wk−2 ∂Wk−1   ∂F ∂F ∂F − kd −2 + ∂Wk−1 ∂Wk−2 ∂Wk−3

Wk = Wk−1 − kp

(5)

Small change in weighting can be expressed below DWk = −b

∂F ∂Wk−1

(6)

and Wk = − Fig. 2 Flowchart of the optimisation a Flowchart of GD optimisation method b GD learning procedure as a feedback system IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121 doi: 10.1049/iet-pel.2012.0416

b ∂F −1 1 − z ∂Wk−1

(7)

In this algorithm, we will add a block to suppress high-frequency noise and smooth the iteration process which is low-pass filter. Equation (7) can be rewritten as 1113

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Fig. 3 Step-response iterations for the SEPIC converter

presented in (8) with low-pass filter term Wk = −

b az−1 ∂F −1 1 − z 1 − 2dz−1 + z−2 ∂Wk−1

(8)

Based on the same idea, the PID GD algorithm, with an addition of the filter term, can be obtained as shown in (8) defining ∂F/∂Wk−2 = z−1∂F/∂Wk−1 and ∂F/∂Wk−3 = z−2∂F/ ∂Wk−1. Then Wk = −az−1


k1 − k2 z−1 + k3 z−2 ∂F 
 −1 −1 −2 ∂Wk−1 1−z 1 − 2dz + z

(9)

where k1 = kp + ki + kd, k2 = kp + 2kd and k3 = kd. The best performance of the proposed algorithm depends on selecting a proper combination of the poles and the zeros in (9). The proposed method presents tuning the k1, k2 and k3 using Ziegler–Nichols first. Then, the zeros of the controller are fixed and the parameter α and δ are tuned. Both α and δ should be smaller than one to ensure an asymptotic stability. The GD method often becomes stuck in local minima. Local minimum will lead to ∂F/∂Wk−1 = 0. The update of W will stop at this point. Therefore the process is trapped in the local minimum. In such way, it is possible to avoid local minimum if ΔWk−1 is not equal to zero. However, the proposed optimisation method is more

Fig. 4 Power–voltage (P–V) curves for the prescribed PV array 1114 & The Institution of Engineering and Technology 2013

IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121 doi: 10.1049/iet-pel.2012.0416

www.ietdl.org efficient to avoid local minimum. The weight is stuck only when ∂F/∂Wk−1, ∂F/∂Wk−2, ∂F/∂Wk−3 and ΔWk−1 are all equal to zero referring to (5). Therefore the probability in this case is very small in local minima. The desired response is 340 V DC voltage, which corresponds to 240 V rms sine wave as output of the inverter (experimentally, the output voltage of the SEPIC converter has to be higher than 340 V to generate 240 V rms because of some reasons such as: dead-time, delays in control circuitry,

less than one modulation index, efficiency and voltage droop), but this desired voltage does not always achieve the maximum power, which in variable reference signal can be less or more than 340 V DC where the controller of the inverter can achieve the 240 V rms on the current expense. Fig. 3 shows the iterations of the step response of the closed-loop system, starting with the first response and stopping at the last response. It represents direct implementation for the weighting function described in (9). The first response was obtained

Fig. 5 SEPIC converter’s output a Reference voltage b Output voltage c Output current d Voltage error IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121 doi: 10.1049/iet-pel.2012.0416

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www.ietdl.org using Ziegler–Nichols method, whereas the last response was the desired and the finest response which was obtained via iterations using the proposed PID GD method. In Fig. 3, the optimised PID parameters for the last iteration were: kp = 0.3542, ki = 0.0237 and kd = 0.0018. As mentioned in the introduction, tiny gain in the derivative controller improves the system stability, and consistently in this work the optimised derivative gain was found to be very small, 0.0018. This small value is unobtainable via Ziegler–Nichols method, but neither can it be obtained via GD method alone; subsequently, the proposed method with the filter and tuning should be used. The MPPT algorithm gives a new reference voltage once the variation on irradiation happens. A new set of optimised PID parameters are calculated before the DC/DC converter begins to track the new operating point to guarantee the best performance at each operating point.

4

MPPT control of SEPIC converter

The MPPT control technique is applied to achieve a new reference voltage for the optimised PID controller.

It changes the duty cycle of the PWM signal for the SEPIC converter. The P&O algorithm has a simple structure and requires only a few parameters (i.e. power and voltage), so it is extensively used in many MPPT systems [30–33]. Furthermore, it can easily be applied to any PV panel, regardless of the PV module’s characteristics for the MPPT process. The P&O method periodically perturbs duty cycle and compares instantaneous power with past power (before perturbation). Based on this comparison, the PV voltage determines the direction of the next perturbation. P&O shows that if the power slope increases and the voltage slope increases too, the reference voltage will increase; otherwise, it will decrease. The step-size of the P&O method affects two parameters: accuracy and speed. Accuracy increases when the step-size decreases. However, accuracy leads to slow response when environmental conditions change rapidly. Larger step-sizes mean higher speed for MPPT operation, but this will lead to inaccuracy and larger intrinsic oscillations around the

Fig. 6 SEPIC converter’s output voltage and current of a Non-optimised b Optimised PID controller at variable load condition 1116 & The Institution of Engineering and Technology 2013

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Fig. 7 Inverter’s output voltage, current and voltage error signals with the proposed control scheme at variable load condition

maximum power point in steady state. Step sizes should, thus, be chosen well to achieve high speed and accuracy. Two types of simulations for the MPPT converter were applied using MATLAB/Simulink. The first simulation used the characteristic equations for the PV array given in [34], whereas the second one used the solar-cell module given in Simulink. The MPPT algorithm was built via (.m) file and linked with Simulink. The SEPIC circuit was built via SimPower toolbox. Fig. 4 shows the curves for power against voltage, at 25 and 50oC, for radiation variations, from 250 to 1000 W/m2. For simulation purpose, the PV-cell values and the number of PV arrays were taken according to the experimental setup as detailed in the next paragraph. Fig. 5a shows the reference voltage signal tracking the maximum power. The relation between Figs. 4 and 5b can now be easily determined. Hence, it is evident that the maximum power occurs around 330 V.

5 5.1

Simulation and experimental results Simulation results

A simulation was applied on MATLAB/Simulink to verify the practical implementation of the proposed SEPIC controller for single-phase inverter. Fig. 5a presents the reference signal for the SEPIC’s output, where it tracks the maximum power. The voltage and current output signals of the MPPT-based optimised PID controller at a constant load condition are shown in Figs. 5b and c. It is noticeable that the signals were not smooth; instead they carried a component of the maximum power between voltage and current. The voltage range changed from 320 to 360 V. The IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121 doi: 10.1049/iet-pel.2012.0416

voltage signal (Fig. 5b) is similar to the reference signal (Fig. 5a), while the error signal approached zero as Fig. 5d shows. Figs. 6a and b are the results of the variable load condition. Fig. 6a shows voltage and current of SEPIC output, using non-optimised PID controller. It is clear that the output is presenting disturbance at each load change for both voltage and current signals. The SEPIC output signals of the optimised PID controller are presented in Fig. 6b, which gives smooth transition for the current signal and zero transition for the voltage signal. The optimised PWM signal can achieve two things for the inverter; first, it produces a smooth error-free sine-wave. Second, it achieves a smooth transition for the current signal and constant transition for voltage signal in variable-load case. The smooth transition saves the load from destruction by high-voltage pulses or disturbances. Fig. 7 shows the inverter output voltage, current and error signal, for variable loads. The many variations in Fig. 5 clearly disappeared in Fig. 7. They were cured by the PID controller of the single-phase inverter. Furthermore, the transition in Fig. 7 appeared only in current signal, not in voltage signal.

5.2

Experimental results

The experimental setup for the real-time implementation of the MPPT SEPIC converter is shown in Fig. 8. An array of 19 series ‘PV-AE125MF5N’ solar modules was built to generate 330 VDC voltage. Then, the PV array was connected to the SEPIC converter, which uses controlled PWM generated by ‘TMS320F28335’ DSP with 10 kHz 1117

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Fig. 8 Real-time implementation of the MPPT SEPIC converter a Photovoltaic array setup b Experiment implementation of the SEPIC single-phase inverter

Table 2 Inverter specifications Parameter

Value

Table 1 PV-AE125MF5N solar module Parameter maximum power warranted power rated current rated voltage short circuit current open circuit voltage

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Value 125 W 118.8 W 7.23 A 17.3 V 7.9 A 21.8 V

S 1 − S4 LA CA, CB RL voltage transducer current transducer kp-inv ki-inv kd-inv

IGBT, 600 V, GT50J325 3 mH, 14 A SMP 240 μF, 330 VAC 50 Ω, 500 W LEM LV 25-P LEM LA 25-NP 578 990.72 0.0279013

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www.ietdl.org carrier wave. Two 0.5 mH inductors were chosen to keep the operating of the converter in continuous conduction mode. Input capacitor C1 and output capacitor C2 were 470 and 2200 μF, respectively. Table 1 shows the details of the PV-AE125MF5N module, whereas Table 2 shows the PV inverter specifications and its controller parameters. In Table 2, S1 − S4 express the switches of the inverters. LA, CA and CB are the inductor and the capacitors of the filter circuit, while RL belongs to the load. kp-inv, ki-inv, and kd-inv are the PID parameters for the controller used in the inverter’s PWM. The experiment results are divided into three stages. The first stage shows the performance of the proposed optimised PID controller using different irradiation conditions as presented in Fig. 9. The second stage shown in Fig. 10 presents the effectiveness of the proposed method in exploiting power from the PV array over about 2 h with 2 kW power consumption load. The third stage shows the experimental results for the inverter presenting the sine wave signal and the total harmonic distortion illustrated in Fig. 11. The experimental system is tested under different step response operating conditions. Fig. 9a shows the result of the proposed optimised PID controller. In each operating

condition, the maximum power is attained in a relatively short time and has a small oscillation in steady state. Moreover, when the weather conditions change, the proposed controller forces the power to move directly to the new operating point. The responses in Fig. 9a confirm the effectiveness of the proposed controller over the conventional GD optimisation of PID controller shown in Fig. 9b. It is observed that the maximum power in the proposed controller is obtained faster and has smaller oscillation than that obtained using conventional GD optimisation. Fig. 10 clarifies the relation between the exploited power for the SEPIC converter using the proposed optimisation method for the PID controller and the normal GD method. Although the calculated average exploited power using the conventional GD method was 1.734 kW, the average exploited power using the proposed method was 1.795 kW. This power excluded the converter efficiency. As shown in Fig. 10, it is very close to 98% in higher irradiation conditions, and it remains above 92% even for lower conditions. From the aforementioned measurements, it is clear that the exploited power using the proposed GD (with filter term) is higher 3.4% than the power exploited using the scheme of the conventional GD method. The optimisation method has been applied to the inverter’s PID controller. Fig. 11a shows the experimental waveforms of the inverter voltage and current for unity power factor load while Fig. 11b illustrates the robustness of the proposed controller under 0.766 lagging power factor load. The modulation index used is 0.8 referring to [26]. THD measurements for the proposed inverter are measured using FLUKE 43B Power Quality Analyzer. The THD is shown in Fig. 11b, which is measured corresponding to Fig. 11a. The results of the optimised PID SEPIC inverter are compared with those of the conventional controller in terms of THD. In [26], five-level with PI controller was applied to obtain 6.8% THD. That will consume more switches because of multi-level. Also, the use of the PI controller does not achieve low-enough THD even with the use of multi-level topology. Multi-string five-level achieved 5.7% THD in [27], but this value is still far away from 4.5% THD which is achieved here. Furthermore, eight IGBTs were used to build the multi-string five-level inverter. In [22, 23], buck converter was used to adjust the tracking for the maximum power. That will lose around half of the input power because of discrete input current in case of direct connection with PV array. In case of capacitor connection to avoid losing power, the capacitors face a life time issue.

Fig. 9 Step response of the a Proposed b Conventional GD PID-based SEPIC converter IET Power Electron., 2013, Vol. 6, Iss. 6, pp. 1111–1121 doi: 10.1049/iet-pel.2012.0416

Fig. 10 Exploited power of the proposed GD PID against conventional GD PID 1119

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Fig. 11 Experimental results for inverter output a Voltage and current for unity power factor load b Voltage and current for 0.766 lagging power factor load c THD measurement of Fig. 11a

In this paper, four IGBTs were used to implement the inverter, 4.5% THD was achieved, continuous input current and tracking for the maximum power using SEPIC was attained, all via optimisation for the PID controller.

6

Conclusion

A novel optimised PID controller of SEPIC MPPT-based converter has been presented in this paper. The control scheme has been implemented in real-time using DSP board TMS320F28335. The proposed GD method has been compared with the conventional GD optimisation method in terms of system response and input power exploitation. The performance of the improved GD optimisation method was found better than the conventional GD method without filter term. Experimental results indicated that the proposed control scheme provided power transfer 3.4% more than the control scheme of the conventional GD optimisation. Furthermore, the proposed GD does not stick in the local 1120 & The Institution of Engineering and Technology 2013

minima where the low-pass filter term suppresses the noise and smooths the iteration process.

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