An Improved Maximum Power Point Tracking

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An Improved Maximum Power Point Tracking Algorithm with Current-Mode Control for Photovoltaic Applications Chee Wei Tan, Tim C. Green, Senior Member, IEEE and Carlos A. Hernandez-Aramburo, Member, IEEE. Department of Electrical and Electronic Engineering, Imperial College London London, United Kingdom. Abstract — An improved perturb-and-observe maximum power point tracking algorithm is presented that incorporates a current compensated converter. In order to achieve fast response and accurate holding of the maximum photovoltaic (PV) power under changing environmental conditions, a variable perturbation step size is adopted. In addition, a control parameter α, is introduced to enhance the tracking sensitivity during abrupt changes of environmental conditions. Instead of directly perturbing the switch duty-cycle, the system operates on the current reference of an inner controller that regulates the PV current. The effects of different values of fixed and variable step sizes are assessed through simulation and the results described. The performance of the new MPPT controller was simulated using the PLECS extension to Simulink. Keywords – Photovoltaic (PV); Maximum Power Point Tracking (MPPT); Perturb and Observe (P&O); Current-Mode Control (CMC).

I. INTRODUCTION Fossil fuels, which are widely used for conventional power generation, have been identified as one of the main contributors to the greenhouse effect. Besides this, the fast developments of industries have made great inroads into the non-renewable fossil fuel and they are now significantly depleted [1]. In order to diminish the environmental impact and slow the depletion of the fossil fuel, the development of alternative energy systems have been brought to the fore. Among the renewable energy sources, solar or photovoltaic (PV) energy has become one of the most promising sources of energy due to the fact that photovoltaic energy is free and environmental friendly. Besides this, PV is scaleable from very small to very large and easy to integrate with existing power converters. There is significant experience within European member countries with PV systems. The ‘Campaign for TakeOff’ launched by European Commission seeks to install a total capacity of 1 GWp PV power by 2010 [2] to promote decentralised electrification in developing countries and in the EU-wide domestic market. In addition to that, the largest PV power plant in the world, which has the plant capacity of 5 MWp, went on stream in August 2004 in Germany [3].

Although the rapid development of photovoltaic materials technology and the increased demands for PV materials have led to a reduction of the PV module costs [4], the capital costs of PV systems are still very high. Therefore, there is a necessity to design a power converter that is not only high in efficiency but also optimises the energy production of the PV material. The power produced by a photovoltaic module is dependent upon the amount of solar irradiance and temperature of the photovoltaic device. The output power of a PV module also varies as a function of its operating point because of the inherent non-linear current-voltage relationship of a typical photovoltaic cell. Therefore, a Maximum Power Point Tracking (MPPT) algorithm is commonly used to maximize the power drawn from PV modules under varying atmospheric conditions. Among the Maximum Power Point Tracking techniques, the Perturb and Observe (P&O) method is the most popular method because of the simplicity of its control structure [5]. However, there have been relatively few studies made of the P&O MPPT algorithm in conditions of a rapidly changing environment such as sudden shadow changes. This paper begins by explaining the electrical characteristic of PV cells and proceeds with a review of available MPPT algorithms. Subsequently, an improved P&O MPPT algorithm that uses a current controlled converter is presented. The algorithm is designed to adapt rapidly by using a variably sized perturbation step applied to the current-mode control (CMC) converter. Further, the effect of using different perturbation step size is described. Finally, the simulation results are discussed and conclusions are drawn. II. ELECTRICAL CHARACTERISTIC OF PV CELLS Fig. 1 shows the equivalent circuit for a PV cell. The output current of the equivalent circuit, I can be expressed as a function of the cell’s voltage V [6],[7]:

I = I L − I D − I sh ⎡ ∴ I = I L − I o ⎢e ⎣⎢

V + I ⋅RS n⋅VT

⎤ V + I ⋅ R S − 1⎥ − R P ⎦⎥

(1) (2)

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PV Current

+

IL

_

ID

Ish Rp

V _

Figure 1. Equivalent circuit of photovoltaic cell

1250 W/m2 1000 W/m2 750 W/m2 500 W/m2 250 W/m2

PV Voltage (V)

where IL, the photocurrent, is a function of cell temperature and solar irradiance. Diode quality factor Boltzmann’s constant (1.381 × 10-23) Electronic charge (1.602 × 10-19 C) Lumped series resistance ( Ω ) Lumped shunt resistance ( Ω )

The PV module characteristic depends on the solar irradiance and the temperature of the photovoltaic module. As the solar irradiance increases, the photocurrent increases while the PV voltage also increases slightly, hence, the power produced by the PV module increases. The open circuit voltage of the PV module decreases with a rise of the PV module temperature. It is, therefore, desirable to keep the PV module temperature low in order to extract the maximum power from the module. The effects of solar irradiance and temperature on the I-V and P-V characteristics of PV module are illustrated in Fig. 2 for the example of a BP.365U, 65-watt multi-crystalline PV module the characteristics of which are presented in Table 1 III. MPPT ALGORITHMS An MPPT algorithm sets a reference value for one of the variables (commonly the duty-cycle but also possibly a current or a voltage) in the power converter that interfaces the PV array to a battery or load. The reference is chosen so that the converter draws the current or imposes the voltage that operates the PV panel at or near the maximum power point (MPP) for the prevailing irradiance and temperature. MPPT techniques can be categorized into off-line and on-line methods. Off-line MPPT techniques require prior information about the PV array and measurements of either the solar irradiance, the short circuit current or the open circuit voltage of the particular PV array [8, 9]. An example is the Constant Voltage MPPT which keeps the operating point near the maximum power point by matching the PV voltage to a fixed reference voltage. This method starts from the assumption that the variations of solar irradiance and temperature cause insignificant changes to the voltage that defines the MPP and

(a) PV Current

PV Power

PV Current (A)

n k q RS RP

PV Power

PV Current (A)

+

PV Power (W)

I

0 °C 25 °C 50 °C 75 °C

PV Power (W)

Rs

100 °C

PV Voltage (V) (b) Figure 2. Simulated I-V and P-V characteristics of a PV module, (a) at constant temperature 25 ºC, (b) at constant solar irradiance 1000 W/m2.

TABLE 1. ELECTRICAL CHARACTERISTICS OF THE 65W MULTICRYSTALLINE PHOTOVOLTAIC MODULE BP 365U AT STC. Parameter Maximum power (Pmax) Voltage at Pmax (Vmpp) Current at Pmax (Impp) Short circuit current, (ISC) Open-circuit voltage (VOC) Temperature coefficient of ISC

Value 65 W 17.6 V 3.69 A 3.99 A 22.1 V (0.065 ± 0.015) %/○C

Temperature coefficient of VOC -(80 ± 10) mV/○C NOCT (Nominal Operating Cell Temperature) 47 ± 2 ○C Standard Test Condition (STC): 1 kW/m2 (1 Sun) at spectral distribution of AM 1.5 and cell temperature of 25 ○C.

that a constant reference voltage is an adequate approximation of the true MPP [10]. On-line MPPT methods are more popular than the off-line methods. This is because these methods are able to track the MPP quickly and do not rely on the knowledge of the PV array characteristics. The on-line MPPT methods include Hill Climbing, Perturb and Observe, Incremental Conductance and hybrid methods. A. P&O MPPT algorithm There have been extensive applications of the P&O MPPT algorithm in various types of PV system [5, 11, 12]. This is because P&O algorithm has a simple control structure and few measured parameters are required for the power tracking. The name of algorithm itself reveals that it operates by periodically

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perturbing the control variable and comparing the instantaneous PV output power after perturbation with that before. It has the advantage of not relying on the PV module characteristics in the MPPT process. The outcome of the PV power comparison together with the PV voltage condition determines the direction of the next perturbation that should be used. B. Incremental Conductance MPPT algorithm The Incremental Conductance MPPT algorithm was developed in [13], and is based on the fact that at the MPP (for any irradiance and temperature), the derivative of the PV output power with respect to the PV voltage is zero. Thus, the PV voltage can be regulated relative to the voltage at the MPP by measuring the incremental conductance, dI/dV and chord conductance, I/V. dP d ( IV ) dI = = I +V dV dV dV

dP at the MPP, =0 dV dP > 0 to the left of the MPP, dV dP < 0 to the right of the MPP dV

(3)

(4)

The result of the computation of (3) and (4) will determine the direction of the required change in the control variable so as to move the PV voltage towards the MPP. This algorithm has the advantage of no oscillation occurs around the MPP in steadystate unlike the continuous perturbations of the P&O algorithm. However, the drawback of this algorithm is the complexity of the design the controller. C. Other MPPT Techniques A novel MPPT technique for PV panels using switching frequency modulation was developed by H. S.-H. Chung et al. [14]. This method has the advantages of not requiring prior knowledge of the PV panel and avoiding sophisticated mathematical computation. However, it requires an external signal to perturb the system and significant care has to be taken to ensure that the small signal introduced into the modulation process is correct. An algorithm for rapid tacking of the MPP in a PV system was presented in [15]. This technique achieves rapid movement toward the MPP but must switch to a conventional MPPT algorithm when the operating point approaches close to the MPP. IV. THE PROPOSED MPPT CONVERTER The proposed MPPT system consists of an improved P&O algorithm which uses adaptive variable step sizes applied to the reference current of a current-controlled DC-DC converter. The

aim of these modifications over the conventional P&O MPPT is to achieve fast response and accurate holding of the MPP under rapidly changing environmental conditions such as sudden changes of shadow. As was observed in Fig. 2(a), the short-circuit current of a PV module is proportional to the solar irradiance. In [8] it was further shown that there is a linear dependence between the current at MPP and short circuit current, IMPP = MC ISC

(5)

where MC is known as the current factor. This suggests that it is the current that should be the controlled variable that is perturbed. Perturbing the duty-cycle or the voltage can cause very large changes in operating point but perturbing the current gives a more useful indication of the sensitivity of the power to the PV operating point. A fast-acting local current control loop adjusts the duty-cycle of the converter to force the module current to follow the reference value indicated by the MPPT algorithm. The configuration of the current-controlled boost DCDC that was selected together with the MPPT is shown in Fig. 3. The process of the proposed MPPT algorithm is illustrated in the flow chart as presented in Fig. 4. The perturbation step, ΔI, is added to the reference current at each iteration of the algorithm: Iref(k) = Iref(k-1) + α∆I

(6)

The size of the step is made dependent on the sensitivity of the PV power to the previous perturbation. The sign of the step is determined by kr, which is the opposite of the sign of the slope in the P-V characteristic curve:

ΔI = kr PPV _ diff

PPV _ diff

PPV = Ppv ( k ) − Ppv ( k −1)

(7) (8)

where Ppv(k) is the present PV power and Ppv(k-1) is the previous measured PV power and kr is a one of four constants for the four possible combination of perturbation direction and Ppv/V slope direction. The values of kr were found by trial and error.. The additional term, α, is included to enable the sensitivity to be enhanced or reduced to achieve both rapid movement toward the MPP following a large change in characteristic and to aid accurate convergence of the MPPT on the true MPP. If the Ppv_diff is larger than the value of ε, the perturbation step size in the control variable will be reduced by multiplying an α less than unity. This avoids overshooting the MPP when approaching the MPP from a region where the Ppv/V curve is steep. In the algorithm, α is characterized into two ranges: 0.003 is used for for Ppv between zero and ½ PMPP and 0.015 for PPV up to PMPP. If the Ppv_diff is less than

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the control limit then α is set to unity.The perturbation cycle is repeated for any changes of environmental conditions to maintain the PV power at MPP.

Vpv Ipv

Iref

MPPT

err

δ

PI

+_

PWM

IL L

Ipv

Diode

Io +

Vpv

IL

+

C

Cin

_

Vo _

PV Array

Figure 3. Configuration of the Current-Mode-Controlled-Boost DC-DC MPPT converter. Start Sense VPV(k) and IPV(k) Calculate

PPV(k) = VPV(k) × IPV(k) Calculate

Ppv_diff = |PPV(k) - PPV(k-1)| Yes Yes

α=

Multiply with

α=

0.015

Yes Yes

No

Ppv > PMPP/2 ?

Multiply with

No

Ppv_diff > ε ?

Bypass

α=1

0.003

Ppv_diff > 0 ?

VPV(k) - VPV(k-1) > 0 ?

No

Yes

conversion because of the large error and lost opportunity to generate power. A smaller perturbation step-size reduces the magnitude of oscillation around the MPP and increases the energy conversion effectiveness once the MPP has been achieved. However, this would only solve the problem at steadystate; it would also lead to slow response under rapidly changing environmental conditions. A small perturbation step-size reduces the error caused by oscillation around the MPP but greater deviation from the MPP occurs under rapid changes of atmospheric conditions because of the slow response. Consequently, there is a trade off between fast tracking and power error in deciding a suitable fixed size of perturbation step. B. Variable Perturbation Step Size In this improved P&O MPPT algorithm, a variable perturbation step size was adopted. The variable step size could be implemented in several ways. Here, the perturbation step size was based on the PV power difference Ppv_diff due to the effect of a change in solar irradiance and temperature. Equation (7) showed that the perturbation step size is automatically tuned according to the PV power difference. Therefore, a large change of solar irradiance or temperature causes a large change in the power produced by PV module and this automatically tunes the control variable ∆I to a larger size to respond faster to the atmospheric changes. During steady-state, the PV power difference is approximately zero, thus Iref is maintained close to the previous value with very small perturbation steps. Although the variable perturbation step-size gives better performance than a fixed step-size, it might hunt wildly during a transient before reaching the steady-state condition. Since the PV power waveform is mostly governed by the PV current under changes of solar irradiance, controlling the inductor current can help to reduce the oscillation in PV power during the transient state.

No

VPV(k) - VPV(k-1) > 0 ?

No

V. SIMULATION RESULTS kr = −k1

kr = k2

kr = k3

kr = −k4

Calculate

∆I = kr (Ppv_diff / Ppv) Iref(k) = [ Iref(k-1) + α∆I ] Return

Figure 4. Flow chart of the improved Perturb and Observe MPPT algorithm.

A. The Effect of Perturbation Step-Size For a given perturbation interval, the larger the perturbation step the faster the PV current can be driven to the MPP. However, the larger the perturbation step-size, the larger are the intrinsic oscillations around the MPP in steady-state. These oscillations can reduce the effectiveness of the PV power

A series of simulations were performed using the PLECS circuit simulator as part of MATLAB/Simulink. The affect of choosing a fixed perturbation step size is shown in Fig. 5(a)-(d), in which an MPPT with four different step sizes was simulated with a PV panel at 25.○C and initially illuminated at 1000 W/m2. After a simulation time of 0.1 s the illumination was decreased to 800.W/m2. These fixed step-sizes were simulated with a duty-cycle controlled (not current-mode-controlled) converter. It is apparent that a large perturbation step size (0.01) creates large oscillations around the MPP. The oscillation reduces as the size of perturbation decreases. However, the settling time required for the tracking process to reach steady-state increases. For the case of a perturbation step size of 0.0001, it takes a long time to reach MPP and the system responds slowly to

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the change of solar irradiance.

PV Power (W)

Cumulative PV Energy (J)

(f) Figure 5. PV power and cumulative energy for fixed step sizes of (a) 0.008, (b) 0.001, (c) 0.0005, (d) 0.0001 and variable step size (e) without CMC and (f) with CMC

t (s)

PV Power (W)

Cumulative PV Energy (J)

(a)

t (s)

PV Power (W)

Cumulative PV Energy (J)

(b)

t (s)

PV Power (W)

Cumulative PV Energy (J)

(c)

t (s)

PV Power (W)

Cumulative PV Energy (J)

(d)

t (s)

PV Power PV Energy

Cumulative PV Energy (J)

PV Power (W)

(e)

t (s)

The variable perturbation step size MPPT was first applied to the duty-cycle controlled converter and the results are presented in Fig. 5(e). It can be seen that the steady-state operating point is held with negligible oscillation and that the transient is fast. There is, however, significant oscillation, or hunting, during the transient. Fig..5(f) show that applying variable step-size MPPT to a current-mode converter gives fast and oscillation-free response during the transient and good holding of the stead-state condition. The performance of MPP tracking affects the total PV energy yield; fast transient response and less oscillation increase the amount of PV energy produced and vice versa. The cumulative PV energy is shown on the right axis of each plot in Fig. 5. In order to verify the accuracy with which the MPP is identified, the converter was simulated with a series of different values of solar irradiance. The solar irradiance is set to change in steps of 100 W/m2 from 1000 to 300.W/m2 at 25ºC. The simulated PV module power under resistance load is illustrated in Fig. 6(a), in which the PV power settles at steady-state in a short period. Moreover, the power extracted by the converter has less ripple and no oscillation at steady-state. Besides that, the controller is able to bring the power operating point back to MPP quickly under each step change of solar irradiance. Fig. 6(b)-(c) illustrate the MPPT process and operation. It can be seen from the I-V and P-V characteristic curves that the operating point moves along the locus of the MPP as the solar irradiance changes. In each step, the MPP is accurately identified and therefore best use is made of the PV panel. IV. CONCLUSION An improved Perturb and Observe MPPT algorithm with a current-mode controlled DC-DC converter has been described. The effect of the perturbation step-size on the energy yield from the PV panel has been examined and one possible way of defining a variable perturbation step size has been explained. It has been demonstrated that the variable perturbation step-size helps to rapidly achieve the MPP in the event of a sudden change of irradiance due perhaps to a shadow. Additionally, a control parameter has been applied to tune the control variable under abrupt changes of environmental conditions. Simulation results show that the system can accurately hold the MPP without oscillation in steady-state and avoids hunting during a transient. ACKNOWLEDGMENT The authors would like to acknowledge Universiti Teknologi Malaysia (UTM) for the financial sponsorship of Mr C.W. Tan during his Ph.D. programme at Imperial College London.

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1000 W/m2

REFERENCES

900 W/m2

[1]

800 W/m2 700 W/m2

[2]

500 W/m2 2

400 W/m

300 W/m2 PV Power PV Energy

[3] [4] [5]

(a) [6] 1000 W/m2

[7] [8]

[9]

300 W/m2

[10] (b) 1000 W/m2

[11] [12]

[13] 300 W/m2

[14] (c) Figure 6. (a) PV module power and energy under a series of values of solar irradiance with the new maximum power point tracking process, (b) I-V characteristic, (c) P-V characteristic.

[15]

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