Maximum Power Point Tracking techniques for photovoltaic systems: A comprehensive review and comparative analysis

Renewable and Sustainable Energy Reviews 52 (2015) 1504–1518

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Maximum Power Point Tracking techniques for photovoltaic systems: A comprehensive review and comparative analysis S. Lyden n, M.E. Haque School of Engineering and ICT, University of Tasmania, Australia

art ic l e i nf o

a b s t r a c t

Article history: Received 28 January 2015 Received in revised form 27 May 2015 Accepted 29 July 2015

Maximum Power Point Tracking (MPPT) is an important concern in Photovoltaic (PV) systems. As PV systems have a high cost of energy it is essential that they are operated to extract the maximum possible power at all times. However, under non-uniform environmental conditions, which frequently arise in the outdoor environment, many MPPT techniques will fail to track the global peak power. This review paper discusses conventional MPPT techniques designed to operate under uniform environmental conditions and highlights why these techniques fail under non-uniform conditions. Following this, techniques designed specifically to operate under non-uniform environmental conditions are analysed and compared. Simulation results which compare the performance of the common Perturb and Observe (P&O) method, the Particle Swarm Optimisation (PSO) and the Simulated Annealing (SA) MPPT approaches under non-uniform environmental conditions are also presented. The research presented in this review indicates that there is no single technique which can achieve reliable global MPPT with low cost and complexity and be easily adapted to different PV systems. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Maximum Power Point Tracking Partial Shading Conditions Photovoltaic cells

Contents 1. 2. 3.

4.

5.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1505 Criteria to assess global maximum power extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1506 Conventional MPPT approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1506 3.1. Perturb and Observe/Hill Climbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1506 3.2. Incremental Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1508 3.3. Maximum power point estimation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1508 3.4. Artificial intelligence techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1508 3.5. MPPT based on output parameters and single sensor approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1509 3.6. Other MPPT techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1509 MPPT approaches to address partial shading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1509 4.1. Extension of conventional MPPT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1510 4.1.1. Periodic reset and periodic curve scanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1510 4.1.2. Widen search range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1510 4.1.3. Two-stage methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1510 4.2. Techniques based on observations of the I–V and P–V characteristics under PSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1511 4.3. GMPPT techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1511 4.3.1. Line search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1511 4.3.2. Artificial intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1511 4.3.3. Chaos search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1512 4.3.4. Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1512 Power Electronics based approaches to address partial shading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1512 5.1. Distributed MPPT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1512 5.2. Monitoring bypass diode voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1513

Corresponding author. E-mail addresses: [email protected] (S. Lyden), [email protected] (M.E. Haque).

http://dx.doi.org/10.1016/j.rser.2015.07.172 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

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5.3. Differential power processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Power Electronics equaliser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Operating Photovoltaic systems efficiently involves ensuring that the maximum possible energy is extracted from the system at all times. However, the maximum power available may vary rapidly due to changing environmental conditions and shadow from objects in the environment. The passage of clouds over a PV system will cause a change in the irradiance on a panel and subsequently, determining the maximum power is a timevarying problem. To enable maximum power production under changing environmental conditions Maximum Power Point Tracking techniques are proposed which will track to the optimal power point. Several limitations exist with these techniques, particularly under non-uniform environmental conditions. Other techniques designed to achieve the same goal include Maximum Power Point Estimation (MPPE) techniques, such as [1–4] which rely on the use of models of the PV cells. Generally these techniques are defined for uniform conditions so may fail to track the Global MPP (GMPP) during non-uniform environmental conditions. PV systems are made up of a number of individual PV cells that are connected in series to form strings, and then in parallel to form modules [5,6]. Multiple modules can be connected in series and/or parallel combinations to further boost the voltage and current and form PV arrays. When the cells are all exposed to the same environmental conditions, in terms of irradiance

and cell temperature, they exhibit identical characteristics which are simply scaled to give the overall current–voltage (I– V) and power–voltage (P–V) characteristics for a system. Sample I–V and P–V characteristics under uniform conditions for three series-connected modules are given in Fig. 1. If the cells are exposed to non-uniform environmental conditions, which may arise due to some cells being shaded by objects in the environment, the I–V and P–V characteristics become more complex. Shaded cells have a lower capacity than their series-connected counterparts and, as such, could limit the power producing capability of an entire string. To avoid this effect, and to reduce the risk of hot spot formation and damage to the shaded cell, bypass diodes are often installed across either individual cells or substrings to provide an alternative path for the current [5,7]. In the presence of bypass diodes, the I–V and P–V characteristics become more complex and will potentially exhibit several local peaks. For three series-connected modules, the corresponding I–V and P–V characteristics under non-uniform conditions are shown in Fig. 2. The effective utilisation of PV systems is an area that has attracted the attention of the international community. Studies are completed in many countries around the world exploring the potential available solar resource and ways to effectively utilise this. A small subset of these studies is described below. A study into the potential utilisation of wind and solar energy in India

Fig. 1. PV module characteristics for three modules in series with uniform irradiance 1000 W/m2 and uniform temperature 25 1C (a) I–V and (b) P–V.

Fig. 2. Partial shading characteristics for three modules in series with irradiances 1000 W/m2, 700 W/m2, 300 W/m2, and temperature 25 1C, (a) I–V and (b) P–V.

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highlights that the available solar energy in this region is 5000 trillion kW h per year [8]. This large available energy has the potential to be utilised in the presence of increasing electricity costs. In 2013, India has a PV capacity of over 1430 MW accounting for 6% of the renewable energy generation [8]. The integration of renewable sources such as wind and solar are considered in a study of the European Union (EU) for their capability to provide flexibility in the network [9]. By exploring a region composed up of many different countries, specific factors to specific regions that affect the network flexibility can be explored. Additionally, the solar utilisation and availability within each country can be quite different. Germany and Spain are the two countries in the EU which are leading the way with PV integration and research with an installed capacity making up over 51% of the installed capacity in the EU in 2013 [10]. Further studies in the EU investigate the potential for PV systems in Finland, a country where traditionally, due to the high latitude of the country, PV systems have not been utilised [11]. Despite the high latitude of the country it experiences a level of irradiance similar to Germany which is one of the leaders in PV integration. The benefits of cooperation between regions as described with respect to the EU include reducing the potential ramp rates experienced by each country [9]. A study completed in the UAE, explores how the angle of tilt and orientation of the panels for this particular area can improve the solar yield [12]. Studies have been completed in other regions exploring the same idea which highlights that the same principles apply in selecting the optimal tilt and orientation; however, these values can vary considerably from region to region. Saudi Arabia lies in the ‘sun belt’ and experiences high levels of irradiance between 4.479 kW h/m2 and 7.004 kW h/m2 depending on the geographical location [13]. This significant available energy could be well utilised in PV systems and is being increasingly integrated in the Saudi Arabian grid to minimise environmental and health issues and with falling prices to generate electricity from PV systems. In developing countries including China, the importance of developing solar power resources as the electricity network is further developed is attracting increased attention [14]. Solar utilisation in China takes the form of PV in addition to direct methods of utilising the energy including using solar energy for heating buildings and water. In 2007 the PV energy available in China was 1200 MW which is a significant amount. Due to the large geographical area of China, different zones can be defined based on their solar potential. Approximately 67% of China lies in a zone with a large amount of solar potential [14]. Recent figures from Australia indicate that nearly 15% of all residential dwellings have a PV system installed [15]. These studies have highlighted that the integration and utilisation of PV systems around the world is becoming increasingly important as each country tries to move away from fossil fuel based energy sources and promote clean energy and sustainability. While each region will have different irradiance conditions, all regions have the capability to produce power from PV systems. All PV systems, regardless of where they are situated in the world are limited by the same P–V characteristics under uniform and non-uniform conditions. For this reason developing an effective MPPT method is of great importance for the further effective utilisation of PV systems around the world. A variety of MPPT and MPPE techniques have been proposed in the literature [16–20]. Many MPPT methods are designed to work in uniform irradiance conditions [16,17]. Recent developments in MPPT approaches focus on designing methods to achieve MPPT under Partial Shading Conditions (PSC) [18]. The impact of varying the system configuration and other methods to mitigate the effects of PSC and improve the performance under PSC have also been described [19]. The effects of measurement noise, bias and the optimisation of parameters is also explored in the literature

[21–25]. Additionally, it is essential that converters are designed appropriately to guarantee tracking feasibility [26]. The review presented in this paper is different as it also provides consideration of the Power Electronics (PE) based approaches to mitigate PV power maximisation issues under PSC, in addition to identifying how conventional MPPT approaches fail and highlighting newer techniques designed to work under PSC. Additionally, this paper presents simulation results comparing the performance of the common Perturb and Observe MPPT method, against two strategies design to achieve Global MPPT (GMPPT). The strategies considered are Particle Swarm Optimisation and Simulated Annealing, which are both developed in the context of achieving GMPPT. Section 2 will define criteria to assess the global maximum power extraction approaches. Section 3 will discuss conventional MPPT approaches and why these frequently fail under PSC. In Section 4, MPPT approaches to address partial shading, including the enhancement of conventional techniques and methods specifically designed for PSC, are discussed. Section 5 explores the PE based approaches. Simulation results comparing the performance of the P&O, PSO and SA based MPPT methods are described in Section 6. Section 7 provides a discussion and comparison of the techniques based upon the criteria established in Section 2, and Section 8 provides conclusions.

2. Criteria to assess global maximum power extraction Real environmental conditions for a PV system may involve rapidly changing irradiance and non-uniform distribution of temperature and irradiance across the cells due to shadow from objects or due to internal mismatch between the modules [27,28]. Additionally, over time cell degradation effects may change how the system operates [29]. These conditions result in the need for a method that can extract the absolute maximum power under these potentially highly variable and non-uniform conditions. Based on the characteristics of real environmental conditions the following list of criteria for the techniques assessed in this paper are developed.
Differentiation between global and local maxima, or ability to locate the global maxima.
Performance speed, that is, how quickly a MPP is found.
Speed of response under a change in environmental conditions.
Oscillations in steady-state.
Dependence on the electrical parameters of the PV panel or system-specific parameters.
Cost and complexity of the implementation. Each technique reviewed in this paper will be assessed based on its performance against the given criteria to determine the suitability of the technique for application in real environmental conditions. These criteria indicate if the technique can be considered as a universal global maximum power extraction technique which is easily adaptable to other systems.

3. Conventional MPPT approaches In this section conventional MPPT algorithms designed primarily to track the MPP under uniform environmental conditions are discussed. 3.1. Perturb and Observe/Hill Climbing The Perturb and Observe (P&O) and Hill Climbing (HC) methods are very similar as both require a perturbation of some control variable to

S. Lyden, M.E. Haque / Renewable and Sustainable Energy Reviews 52 (2015) 1504–1518

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Fig. 3. P&O flowchart.

determine the direction of tracking. The control variable could be the voltage, current or duty ratio [30]. The HC technique uses a perturbation in the duty ratio of the converter [16,31], while the P&O technique typically uses a perturbation in the voltage [16,32]. Current perturbation is rarely used because it has a slow transient response under changes in irradiance and may be affected by noise in the signal [30]. Both techniques combine information about the direction of the perturbation and the corresponding change in power that has occurred with that perturbation. At the MPP the derivative of the power with respect to the voltage should be zero, greater than zero on the left of the MPP and less than zero on the right of the MPP as indicated in (1). The flowchart of the P&O technique based on a voltage perturbation is given in Fig. 3. dP 40 dV dP ¼0 dV dP o0 dV

left of

MPP ð1Þ

at MPP right of

MPP

In stable environmental conditions these approaches remain within close proximity of the MPP [33,34], however, when rapid changes in irradiance occur, the methods may become confused and track in the wrong direction initially [35–37]. The P&O and HC methods are commonly used MPPT techniques as they are easy to implement, simple and low cost [31,33,34,36]. Additionally, their operation does not rely on knowledge of the PV module characteristics [25,36]. Drawbacks of the approach include that it has either slow convergence or large oscillations depending on the choice of step size, oscillations in steady-state regardless of the step size, and poor performance under rapid changes in irradiance [31,33,34,36–38]. Some enhancements suggested in the literature to improve the performance of the P&O method are outlined below. This is not an exhaustive review of all improvements made to the P&O method, but encapsulates the major contributions. The P&O and HC techniques cannot differentiate between the change in power that arises as a result of the perturbation and the change in power that results from a change in the environmental conditions which can lead to tracking in the wrong direction after a change in irradiance has occurred [35]. Under PSC the techniques will become trapped at the first located maxima, which may be a local maxima, until another change in conditions occurs [39]. Variable step-size P&O techniques are often proposed to reduce the transient and steady-state performance trade-off [31,37,40]. Variable step-size implementations often rely on system dependent constants which drastically affect the performance. Some implementations avoid this limitation for example by using the

Fig. 4. IncCond flowchart.

rate of change of the PV system power with a PI controller to develop an adaptive perturbation [33]. To avoid tracking in the wrong direction, the dP-P&O technique has been proposed which takes an additional measurement in the middle of the sample period to isolate the effect of the perturbation from the change in environmental conditions [34,41]. Another approach to avoid the P&O technique deviating from the correct perturbation direction in the case of fast changing irradiance includes defining an appropriate update frequency to reduce the likelihood of tracking in the wrong direction under dynamic conditions [42]. An adaptive step size can be used with the dP-P&O technique to further enhance the tracking speed and ensure tracking in the correct direction [43]. To enhance the tracking speed it is also possible to combine the P&O technique with model predictive control [44]. The Generalised P&O (GPO) method has also been proposed as a way to reduce the susceptibility of the technique to becoming trapped at a power curve trap which occurs due to measurement noise [21]. This approach involves comparing the most recently measured power to a scaled stored power measurement, which may not be from the previous iteration.

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While the issues of the trade-off between steady-state dynamics and tracking speed, and the tendency to track in the wrong direction under fast irradiance changes are fairly well addressed in the literature, the technique is rarely successfully modified to guarantee GMPPT. Extension of the technique to improve performance under PSC includes the three points incremental P&O (3PI-P&O) which uses a comparison of three points to determine the next required perturbation direction [45]. However, this will not guarantee GMPPT.

3.2. Incremental Conductance The Incremental Conductance (IncCond) is derived from the same basis as the HC and P&O techniques, but is based on a comparison of how the voltage and current change. Eq. (2) equates the derivative of the power with respect to the voltage with the incremental and instantaneous voltage and current components. The flowchart of the IncCond method is shown in Fig. 4. dP dðIV Þ dI ΔI ¼ ¼ I þ V:  I þ V: dV dV dV ΔV

ð2Þ

Eq. (2) leads to the conditions for the IncCond algorithm as given in (3). ΔI I ΔV 4
V ΔI I ΔV ¼
V ΔI o
I V ΔV

left of MPP at MPP

ð3Þ

right of MPP

According to [46], as the IncCond and P&O techniques are built on the same operational principle and have very similar performances, the IncCond technique should be treated as a different implementation of the P&O technique rather than as a technique in its own right. Consequently, the IncCond technique is affected by the same factors as the P&O technique including a trade-off between steady-state oscillations and tracking speed, and inability to distinguish between global and local maxima. Variable step-size IncCond technique implementations are often presented [47,48] and IncCond approaches using direct control to simplify the system are also often implemented [49]. It is suggested that the IncCond technique has improved robustness to measurement noise, when compared to the P&O technique, due to the control decision being dependent on two distinct variables [24]. Further enhancements include the PI-INC tracking which reduces the tracking delay that may occur when operating on the left hand side of the MPP location due to the sensitivity of the Incremental Conductance [50]. Other approaches involved combining the IncCond technique with an MPP locus based technique to accelerate tracking [51]. 3.3. Maximum power point estimation techniques MPPE techniques rely on models and approximations of key characteristics of the I–V and P–V characteristics of PV cells to provide an estimated MPP location based on some measurement. The simplest form of MPPE relies on relating either the shortcircuit current or the open-circuit voltage to the MPP current and voltage respectively via a linear equation. The constants of proportionality k1 and k2 are usually between 0.71 and 0.78, and between 0.78 and 0.92, respectively [16]. Eq. (4) gives the opencircuit voltage relationship and (5) gives the short-circuit current relationship. V mpp  k1 V oc

ð4Þ

I mpp  k2 I sc

ð5Þ

These techniques provide a very basic approximation of the MPP. Under PSC, k1 and k2 will no longer be representative of the ratio of the MPP quantities to the measured quantities, and as the cells degrade the accuracy of these techniques will reduce [52]. The performance of the fractional open-circuit voltage technique under low power conditions has been improved by allowing an adjustable sample time and sample period that depend on the power being produced [53]. MPPE techniques with added complexity require the sampling of additional points to provide an estimation of the MPP location. Six measurement (I–V) pairs can be used to provide an approximation of the I–V characteristics under uniform conditions, which then allows the MPP location to be predicted in the IVMPPE technique [4]. Estimation of the I–V curves based on modelling to predict the MPP location in uniform conditions has been explored [3], as well as applying empirical relationships with a single sensor approach to determine the MPP [2]. A robust analytical relationship for determining the MPP has also been proposed based upon the Single Diode Model (SDM) [1]. Another collection of techniques which use estimation to determine the MPP location include those that rely on the definition of the MPP locus [51,54–56]. The I–V characteristics including the MPP locus are shown in Fig. 5. These techniques often use a linear approximation of the MPP locus to reduce the complexity or use two linear approximations, one for high irradiance and the other for low irradiance [54]. Power losses may occur when obtaining measurements for use in the MPP locus technique, such as in cases where the short-circuit current or open-circuit voltage need to be measured [55]. In all the estimation techniques, the basic foundation is for a PV cell under uniform conditions. This means that the models and equations will be unable to accurately model the MPP location under non-uniform environmental conditions.

3.4. Artificial intelligence techniques A variety of artificial intelligence techniques have been proposed to deal with uniform environmental conditions MPPT in PV systems including Fuzzy Logic and Neural Network based approaches. Fuzzy Logic Control (FLC) based approaches to the MPPT problem can be classified as those that use fuzzy logic to determine a variable step size for techniques such as P&O [31,40,57], or those that use a fuzzy model-based approach [58–63]. The Takagi-Sugeno fuzzy system is often used in preference to Mamdani as it requires fewer rules and coefficients and can be implemented with less complexity [58,61,63]. FLC MPPT approaches are limited in their application as they rely on system specific parameters. If these parameters are not optimised appropriately for the given system, the effectiveness of MPPT will be reduced. Additionally, these techniques are generally not designed to enable GMPPT. Artificial Neural Networks (ANN) provide a mechanism through which the environmental conditions that the PV system

Fig. 5. MPP locus three series connected modules with uniform irradiance.

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experiences can be used to predict the operational point which corresponds to the MPP. ANN are trained on some set of data, which should be representative of the conditions that will be experienced. However, over time the cells will degrade and the non-linear mapping achieved by the ANN will no longer be representative of the MPP location [64]. For this reason, ANN techniques are often combined with conventional MPPT to enhance their accuracy and improve the speed of techniques such as IncCond [64] and P&O [60]. In most MPPT applications the ANN is trained on weather data, which may be difficult to measure [60,65]. ANFIS based techniques combine the advantages of fuzzy systems and ANN and have been trained using weather inputs to determine the MPP location using a five layer network [66]. 3.5. MPPT based on output parameters and single sensor approaches To reduce the cost of MPPT implementation several singlesensor approaches are proposed in the literature. Many of these applications rely on using the output parameters of the converter, such as the voltage or current, as a quantity to maximise or balance to achieve MPPT [67,68]. In the case that tracking is achieved by maximising the output load current or voltage, MPPT involves maximising the converter output which may not necessarily coincide with the MPP of the PV system itself due to the efficiency of the converter [67]. Another approach defines an empirical current based on the measured voltage and known duty cycle of a dc–dc converter for battery charger applications with the Incremental Resistance (INR) MPPT technique [69]. The INR technique is simply the dual of the IncCond technique [70]. A single voltage sensor can be used to take a measurement across a capacitive load and using a defined function, based on the derivative of the power with respect to time, provide a sign to indicate the direction of tracking [23]. Maximising the load current to achieve MPPT for a multi-channel system, that is, a system consisting of multiple PV modules which can be controlled independently, can be accomplished using a single current sensor [71]. This technique reduces considerably the number of sensors and Analogue to Digital Converters (ADCs) required in the realisation of a process very similar to the Distributed MPPT techniques addressed in Section 5.1. In all considered output and single sensor approaches, the cost and complexity may be reduced when compared to other conventional MPPT techniques. Frequently these techniques will maximise the power from the converter rather than the power from the PV system. 3.6. Other MPPT techniques Other MPPT techniques which work under uniform conditions include approaches that rely on Sliding Mode Control (SMC), Ripple Correlation Control (RCC) or Extremum Seeking Control (ESC), parabolic curve prediction, linear search and iteration methods, variable perturbation frequencies, variable inductors and the β-method. These approaches will be briefly considered in this section. A variety of MPPT approaches that utilise SMC are proposed in the literature [63,72–75]. Generally, SMC applications require an appropriately defined sliding surface [75] which may not be optimal under PSC. Various MPPT techniques are utilised with SMC including a TS fuzzy MPPT method [63], a current-based P&O MPPT method [74] and a dynamic optimal voltage estimator to predict the MPP voltage [72]. To minimise the modelling of the system required, a self-optimisation process can be integrated with a SMC based MPPT method such that the gradient does not need to be measured or evaluated [73]. RCC is frequently used in PV MPPT systems as it utilises the switching ripple which is present when switching converters are

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used [76–78]. This switching ripple acts like an artificial perturbation and, replicating the P&O technique, observation can be achieved by using an integrator to drive the signal error to zero [78]. The RCC approach can therefore perform MPPT like the P&O technique but without having oscillations around the MPP. Discrete implementations of the RCC method also exist [76]. ESC approaches are similar to RCC but require a dither signal to be used. Adaptive ESC (AESC) approaches enhance ESC by using knowledge of the system model [79]. A Lyapunov-based switching scheme can enable the ESC approach to converge to the MPP by reducing the perturbation in the neighbourhood of the MPP rather than converging to a limit cycle [80]. ESC approaches can also be used to perform fault diagnosis [81]. Parabolic curve prediction based MPPT methods use the three most recent duty cycles and the relevant power to define a parabolic curve which is renewed until the MPP is located [82]. The parabolic curve is used to predict the next duty cycle that should be sampled to allow the method to converge to the MPP. As three working points are considered, the method is more robust when compared to techniques such as P&O which only provide a comparison between two working points. Additionally, the technique can converge quickly and does not exhibit oscillations around the MPP. The Bisection Search Theorem (BST) has been extended to the PV MPPT problem and allows the MPP to be located by reducing the size of the considered interval until the maximum can be determined [83]. A linear-prediction technique that extends the Newton Iteration Method by using a left and right tangent can be applied to improve searching [84]. This technique enables the MPP to be tracked rapidly without requiring a step-size reference. The steepest descent and centred differentiation methods can also be used to perform MPPT [85]. In this technique, perturbations are stopped once the MPP is reached to avoid oscillations. A change in environmental conditions which will reinitialise tracking is detected by measuring either the resistance or conductance to sense when a change has occurred. Utilising a variable perturbation frequency in addition to a variable step size ensures that the perturbation frequency is higher when the step size is small and lower when the step size is large [86]. The approach ensures that when large steps are taken, the system has sufficient time to settle before the next perturbation is applied to avoid tracking in the wrong direction. Additionally, it encourages a good trade-off between tracking speed and efficiency. A variable inductor approach utilising a buck converter is designed on the basis that the inductance will decrease with increasing current (and in turn increasing irradiance) to enable the MPPT to be located [87]. The β-method is also often used for MPPT and relies upon an intermediate variable called β given by (6). At the optimal point, the parameter β should remain constant, so the β-method works to drive this parameter to a reference value [88].   I β ¼ ln pv
c  V pv ð6Þ V pv q , q is the electron charge ð1:6  10
19 CÞ, A is the diode where, c ¼ AkTN s ideality factor, k is the Boltzmann constant ð1:38  10
23 J=1KÞ, T is the temperature on absolute scale ð1KÞ, and N s is the number of series connected cells.

4. MPPT approaches to address partial shading PSC arise when the irradiance across a PV module varies, leading to increased non-linearity in the P–V and I–V characteristics. The conditions lead to multiple local maxima existing in the

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P–V characteristic which can confuse conventional MPPT techniques as they cannot distinguish between local and global maxima. Other conditions such as cell ageing or degradation, the presence of dust on the surface of the cells and defects in manufacturing can also produce similar complexity in the P–V characteristic. MPPT approaches that can distinguish between local and global maxima need to be applied in cases of PSC to improve the power output of the system. A variety of techniques have been proposed including Particle Swarm Optimisation (PSO), Dividing Rectangles (DIRECT), Fibonacci search, Chaos search and approaches based on comprehensive studies of the I–V and P–V characteristics under PSC. In some cases conventional MPPT techniques are modified using simple strategies to improve their performance under PSC. These methods include performing a periodic reset or periodic curve scan, increasing the searching interval or using two-stage tracking approaches. Section 4.1 considers approaches used to improve the performance of conventional MPPT techniques when applied to systems experiencing PSC. Section 4.2 describes techniques built upon observations of the characteristics under PSC and Section 4.3 describes GMPPT techniques specifically designed to operate under PSC.

representative of the location of the GMPP and energy losses will occur in the measurement process. Periodic reset and curve scanning techniques generally improve the performance of conventional MPPT techniques with minimal increase in implementation complexity and cost. However, these techniques cannot guarantee GMPPT at all times.

4.1.2. Widen search range Another very simple approach that can improve the tracking of conventional MPPT methods under PSC involves extending the searching range of these techniques [31,90,93,94] or identifying optimal regions within which to search [81,95]. ESC can be enhanced by defining regions within which the local optimisation strategy can be applied to locate the GMPP [95]. Widening the search range however, adds to the time required to search for the GMPP and could lead to considerable power losses during tracking. Searching first on the left and then on the right of the located optimum in order to locate the GMPP has also been shown to improve MPPT performance [96]. In some cases, this may still lead to most of the P–V characteristic needing to be swept to ensure GMPPT.

4.1. Extension of conventional MPPT In this section, approaches to improve the performance of conventional MPPT techniques under PSC will be explored, including periodic reset and curve scanning, widening the search range and two-stage approaches. One common limitation of these approaches is that GMPPT cannot be guaranteed at all times.

4.1.1. Periodic reset and periodic curve scanning A very simple enhancement that is often made to conventional MPPT techniques involves a periodic reset of the operating point to improve the probability that the system will locate the GMPP. A periodic reset, with the 3PI-P&O technique, will reduce the likelihood that the algorithm will become trapped at a local maxima [45]. This periodic reset moves the system to a random operating point and occurs every 5–10 min, but cannot guarantee GMPPT. A periodic search, completed every 1–15 min, can be combined with P&O to obtain exact MPPT [89]. This method works by progressively drawing more power from the dc–dc converter until the GMPP is reached. Once the GMPP is located the algorithm uses the P&O method to remain at this point until the next global search is initiated. Other techniques perform a periodic sweep of the entire I–V characteristics to identify the GMPP exactly. This could be achieved by taking a very fast measurement of the I–V characteristic to locate the GMPP [90]. Due to the speed of the sweep, the power loss during it is minimal. The P–V curve is can be periodically scanned leading to GMPP [52] and a switched impedance circuit can be used to perform an I–V curve trace [91]. One disadvantage of sweeping the entire I–V or P–V curve is that power losses occur during the sweep process and there are some regions of the curve where the MPP is unlikely to be located. Additionally, extra circuit components such as switches, capacitors and resistors are often required in these implementations [91]. Using a reconfigurable switched capacitor dc–dc converter a scan of the P–V curve to determine the resistance at the MPP can be performed every three minutes to define a suitable resistance for GMPP [92]. In some cases, a curve sweep can also be performed to enhance the performance of the fractional open-circuit voltage or short-circuit current techniques by defining a more suitable constant of proportionality for use in the current environmental conditions [16]. The approach will improve performance initially, but the changing environmental conditions may quickly lead to this constant no longer being

4.1.3. Two-stage methods A variety of two-stage methods are proposed in the literature to improve the performance of conventional MPPT techniques under PSC [48,91,96,97]. These techniques typically use some process in the first stage to move the operating point near to the predicted GMPP and then converge to this point using a conventional MPPT technique (typically P&O or IncCond) in the second stage. A linear function which moves the operating point when PSC are detected can be defined for a system and combined with variable step-size IncCond in the second stage to provide exact tracking of the GMPP [48]. The technique is simple and can be easily implemented in existing PV installations to enhance MPPT tracking under nonuniform conditions. An I–V curve trace using a switched impedance circuit, consisting of a capacitor in parallel with a resistor, can be adopted to locate the GMPP when PSC are detected [91]. In the second stage conventional techniques are used to track the MPP exactly. One disadvantage of this technique is that it requires additional circuit components in its realisation and the power available from the system is reduced during the I–V curve trace. Several authors define a load line based on an equivalent resistance (proportional to the ratio of the open-circuit voltage to the short-circuit current) to move the operating point in the first stage and then use another MPPT technique in the second stage [91,96–98]. In some operating conditions, the load line may lead to tracking of a local peak, so [96] proposes a global search around the local peak and updating of the load line coefficients based on the GMPP location. The load line method requires online monitoring of both the open-circuit voltage and short-circuit current which means that there will be a periodic loss of power when these measurements are taken. The variable step-size P&O method has also been combined with the fractional open-circuit voltage technique [99]. When a large change in current is observed, the technique will automatically adjust the operating point to improve performance under PSC. Two-stage methods improve the performance of conventional MPPT methods with very small increases in implementation complexity and cost. However, the methods are shown in fail in some conditions and can lead to increased tracking time or a reduction in the power available when determining the load line.

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4.2. Techniques based on observations of the I–V and P–V characteristics under PSC Some authors have provided a comprehensive study of the I–V and P–V characteristics under PSC and extended this to observations which can be used to govern a GMPPT technique [100,101]. The observations of [101] indicate that the separation of MPPs is approximately 80% of the open-circuit voltage of the module and that on either side of the GMPP the MPPs decrease in magnitude. The technique based on the observations of [101] uses conventional MPPT to track the MPP and uses a global peak search process to search the relevant areas of the P–V curve to locate all MPPs until the GMPP is detected. By performing the search in this way, the entire P–V curve does not need to be considered reducing the search time required considerably. A similar approach exists which involves sweeping the P–V curve based on key characteristics [100]. By performing a sweep using key characteristics, the portion of the P–V curve that needs to be searched is reduced improving the tracking performance. Auxiliary curves are defined based on the fact that the change in voltage or current along these curves is much faster than the change occurring along the I–V curve, enabling effective MPP searching to occur. Techniques based on observations of the I–V and P–V characteristics of PV systems under PSC can offer improved tracking performance as the searching range is refined. However, these techniques increase the cost and complexity of conventional MPPT slightly, and may involve the temporary tracking of a local MPP. 4.3. GMPPT techniques This section will address techniques which have been specifically designed to handle tracking the GMPP under non-uniform environmental conditions. The techniques considered include line search methods such as DIRECT and Fibonacci search, artificial intelligence approaches, Chaos search, and Simulated Annealing.

[104-109]. PSO approaches are modelled on the basis of birds flocking and fish schooling and use a collection of particles to collectively solve a problem. Each particle's position is updated based on its best position and the best overall position enabling the particles to converge to a global solution. Typically, PSO is applied to time-invariant problems, so mechanisms to detect a change in environmental conditions and reinitialise the global tracking are essential for PV systems [108]. PSO search requires several parameters to be defined including the momentum factor, speed determining constants and the number of agents [104]. The randomness in the method can be reduced by removing the random parameters leading to fewer parameters and improved performance [109]. The flowchart of the PSO method is shown in Fig. 6. The particles position at the next step is given by (7) where, xki is the previous particle position, xki þ 1 is the new particle position, kþ1 and Φi is the particle's new velocity. kþ1

xki þ 1 ¼ xki þ Φi

ð7Þ

The particle's velocity is calculated based on the particle's previous velocity, the difference between the particle's current position and its best position, and the difference between the global best position and the particle's current position. The particle velocity is calculated using (8), where ω is the inertia weight, c1 ; c2 are the acceleration coefficients, r 1 ; r 2 A U ð0; 1Þ are random numbers, P best; i is the best position of particle i, and Gbest is the best position of all particles in the population.     ð8Þ Φki þ 1 ¼ ωΦki þ c1 r1 P best;i
xki þ c2 r2 Gbest
xki The PSO technique is combined with a Gravitation Search Algorithm to minimise oscillations in steady-state for uniform operating conditions when a change in irradiance occurs [110]. This method exhibits superior performance in tracking to the MPP, with the absence of oscillations in steady-state, when compared to each of the algorithms applied independently. A technique based

4.3.1. Line search Several line search MPPT methods have been proposed to deal with PSC including DIRECT [102], and Fibonacci search [93,103]. Line search algorithms work by restricting and shifting an interval to locate the optimal interval within which the optimum point lies and then converging to this point [93]. The DIRECT method is based on progressively making the searching interval smaller based on the values of samples within the interval and a condition used to determine which interval is the most promising to hold the optimum value [102]. As the P–V characteristic of the PV module can be verified to be a Lipschitz function, the DIRECT method can be used and in most cases will lead to GMPPT. For the Fibonacci search method, the length of the interval considered is determined based on the numbers in the Fibonacci sequence [93,103]. Generally, to make this approach suitable for PSC, it is necessary to define a condition which detects when PSC have occurred [93] to enable the method to reinitialise. Line search methods can enable GMPPT under most conditions with relatively simple test conditions. However, in some cases the techniques will converge to a local MPP and the techniques usually depend on the use of special conditions to detect when PSC have occurred. Depending on the initial parameters used the method may not converge to the GMPP.

4.3.2. Artificial intelligence The main artificial intelligence approach explored in the literature for dealing with the PSC problem is Particle Swarm Optimisation (PSO)

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Fig. 6. Flowchart of the PSO method for GMPPT.

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on a colony of flashing fireflies has been proposed for GMPPT which exhibits superior performance to PSO [111]. The firefly algorithm is inspired by the behaviour of flashing fireflies when attracting a mate. The algorithm is based on the idea that the fireflies will move towards the brightest firefly when brightness corresponds to the power on the P–V curve. PSO generally has good performance in tracking the GMPP under PSC. However, in some cases if the initial particle positions are not selected appropriately, the method may converge to a local solution [104]. Additionally, the performance is strongly related to the values selected for the system constants.

4.3.3. Chaos search A chaotic search approach, which uses dual-carriers to improve the performance, has also been applied to the GMPPT searching process [112]. In the search process a logistic mapping is selected and an additional function is used to map the chaos generators. The chaotic search can operate well under partial shading and unpredictable environmental conditions. As chaotic behaviour appears random, but can be shown to be deterministic, a chaotic search will have superior performance to a completely random search which makes this technique appropriate for improving MPPT performance under PSC. The implementation requires no extra circuit components, however is more complex than conventional MPPT techniques.

4.3.4. Simulated Annealing The Simulated Annealing (SA) MPPT approach is based on the annealing process that is used in metallurgy [113,114]. Essentially, SA represents a random search process that is guided by a temperature parameter and is capable of accepting a worse operating point under certain conditions. By accepting a worse operating point the SA algorithm is able to explore the search space fully and leads to improved tracking to the GMPP. SA based GMPPT approaches require a cooling function to be defined which will guide the search process. A common cooling function used is the geometric cooling schedule given in (9) where, T k is the new temperature, T k
1 is the previous temperature, and α o 1 is the cooling constant. Typically the cooling constant takes a value between 0.8 and 0.99 [113,115–117]. T k ¼ αT k
1

ð9Þ

The Simulated Annealing algorithm has been applied to SA MPPT in uniform conditions [118] and under non-uniform conditions [119] and exhibits good performance in locating a global maxima. The flowchart of the SA algorithm as implemented in [119] is shown in Fig. 7.

5. Power Electronics based approaches to address partial shading Power Electronics (PE) approaches to the partial shading issues in PV systems act by using PE circuits to either control the flow of power or enable individual MPPT at cell, string or module level. The key techniques to be discussed in this section include monitoring the bypass diode voltages to infer shading [120], applying differential power processing [121], using the principal of power electronics equaliser [122] and Distributed MPPT (DMPPT) [39,123–127]. Additionally, changes to the PV system architecture and converter topology can improve performance under PSC such as using the Total-Cross-Tied (TCT) and BridgeLinked (BL) configurations to improve energy yield [19,128,129].

Fig. 7. Flowchart of the SA method for GMPPT.

5.1. Distributed MPPT Distributed MPPT (DMPPT) involves each cell, string or module having its own dc–dc converter and MPPT control [126,127]. This enables the MPPT control to move away from a centralised approach where a single MPP can be tracked, to enable each sub-unit of the system to operate at its own MPP. Centralised and Distributed MPPT architectures are shown in Fig. 8(a) and (b), respectively. The level of granularity results in an increase in power, but is also accompanied by an increase in cost [126,127]. In determining a suitable level of granularity it is essential to determine the power gain for the cost expended. Usually, simple conventional MPPT techniques are used in the power converters for DMPPT including P&O [39,123] and IncCond [130] which means that internally to the unit mismatch cannot be addressed. For instance, if DMPPT is applied at the module level, and there are 36 cells in series with two bypass diodes within the module, any shading within the module itself will not be addressed by the implementation [125] (except in the case of a sub-module implementation such as [35]). However, the technique can still substantially improve the power yield from large PV systems exposed to PSC. Another advantage of the technique is that it increases the reliability, as the failure of a single module or converter will not result in the entire system failing [126]. An analogue technique designed for DMPPT referred to as the Technique based on the Equalisation of the Output operating

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Fig. 8. Comparison of Centralised, distributed and differential MPPT architectures, (a) Centralised, (b) Distributed, (c) Differential.

points in correspondence of the forced Displacement of the Input operating points of two identical PV systems (TEODI) has also been proposed [131]. This technique relies upon having two identical sub-modules and adjusting either the current drawn for parallelconnected modules or the voltage for series-connected modules and using the difference to determine how to shift the duty cycle of each module to move towards the MPP. The limitation of this technique is that it can only be applied to identical sub-modules that experience identical environmental conditions.

5.2. Monitoring bypass diode voltages PSC can, in general, be detected by considering the bypass diode voltages in a system that uses Module Integrated Converters (MIC) [120]. When the relevant string of PV cells is not shaded, the bypass diode should be inactive, however when shading occurs it will become active and exhibit a voltage drop. By monitoring the voltages of the bypass diodes it is possible to infer when PSC has occurred. When a shading condition is detected, the technique initialises a global search process which scans the entire P–V curve (or sections of the curve that are located at multiples of the rated string voltage) to locate the global maxima. One limitation of the technique is that in some cases local maxima may arise without a change in bypass diode voltage which limits the effectiveness of the technique under all conditions. Additionally, this technique can only be applied to systems where the string voltages are accessible and can be measured.

5.3. Differential power processing In the differential power processing (DPP) model for achieving maximum power extraction, converters are placed between adjacent PV modules [121] as shown in Fig. 8(c). These converters supply the current difference that exists between the current at the MPP of the two modules and the converter is only active if there is a difference in the power producing capability of the two adjacent modules. Local MPPT between the modules is achieved by applying conventional MPPT techniques, in this case P&O. By placing the differential converters between the modules the conversion losses and cost can be minimised and series PV modules can be seen to produce more power under PSC. One key advantage of DPP rather than a dedicated converter for each module is that at low levels of mismatch conventional approaches may perform better than DMPPT [132]. DPP approaches allow GMPPT to occur with lower power losses as only the power difference must be processed. Conventional MPPT methods are applied with DPP approaches, so mismatch internal to the module will not be accounted for.

5.4. Power Electronics equaliser The PE equaliser approach to GMPPT involves a topology in which series connected cells can be operated with different voltages and currents according to the Power Independence Principle (PIP) [122]. PE equaliser approaches transfer the power from non-shaded modules to shaded modules to enable all modules to act at their MPP and exhibit an equal power level across the system [133]. Inductive storage elements can be charged by the non-shaded cells and then connected in parallel to the shaded cells to redistribute the energy between the cells [122]. Implementation of this topology requires a suitably sized inductor, and several switches. Capacitors can also be used to store the energy from the non-shaded modules [133].

6. Simulation results The P&O, PSO and SA based MPPT methods are assessed using a simulation model in this section. The PV system is based on eight series-connected modules which experience authentic shading conditions defined by real irradiance data and analysis of the shading of the modules based on an obstacle placed in the environment. Each technique is assessed with two sets of irradiance data. The first set is highly variable and represents a typical autumn day in Tasmania, Australia. The second set has a very slowly varying irradiance and represents a typical spring day in Tasmania. In total, 58 min of the variable data set correspond to when the system experiences shading and 18 min of the clear day irradiance set. The P&O method is implemented with a step size of 0.75 V, and an initial voltage of 10 V. A perturbation is applied every 0.05 s. The PSO method is implemented with three particles and with parameters ω ¼ 0:4, c1 ¼ 1:2, c2 ¼ 1:6 obtained from [107]. The method cycles through the particles and the current particle's voltage is applied to the system every 0.05 s. The SA algorithm is implemented with an initial temperature of 25 1C, final temperature 0.2 1C, temperature update constant of 0.8 and with the temperature update applied every four samples. The sampling time used is 0.2 s corresponding to t¼0 s the random voltage selected, t¼ 0.05 s the algorithm compares the current operating point with the previous best operating point and decides to remain at the new point or return to the previous best operating point for the remainder of the sample time. The time to the MPP for each technique for the variable and clear irradiance profiles is summarised in Table 1, and Table 2, respectively. For the SA algorithm, this time to converge refers to the time taken for the algorithm to track to near the final operating point without accepting any future operating points which are at a considerably lower power and far from the final

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Table 1 Time to MPP – Variable day irradiance profile.

Average (s) Standard deviation (s) Minimum (s) Maximum (s)

P&O

PSO

SA

6.0 0.9 4.8 8.3

3.6 1.8 0.35 10.0

2.9 1.6 0.2 7.4

Table 2 Time to MPP – Clear day irradiance profile.

Average (s) Standard deviation (s) Minimum (s) Maximum (s)

P&O

PSO

SA

7.24 0.76 5.85 8.35

1.64 0.51 0.65 2.6

2.5 1.73 0.2 7.0

Table 3 Performance in converging to the GMPP – Variable day irradiance profile.

1% convergence (%) 2% convergence (%) 3% convergence (%) 4% convergence (%) 5% convergence (%) Converged to other MPP with similar power (%) Not converged (%)

7. Discussion

P&O

PSO

SA

48.3 50.0 50.0 50.0 50.0 6.9 43.1

58.6 60.3 63.8 63.8 67.2 12.1 20.7

37.9 56.9 67.2 75.9 79.3 8.6 12.1

Table 4 Performance in converging to the GMPP – Clear day irradiance profile.

1% convergence (%) 2% convergence (%) 3% convergence (%) 4% convergence (%) 5% convergence (%) Converged to other MPP with similar power (%) Not converged (%)

when compared with the other techniques for the variable day irradiance profile. The PSO method in some cases did not converge during the testing time for the variable day irradiance profile, however exhibited the best performance of all techniques for the clear day irradiance profile. When the 1% convergence criterion is applied the percentage of cases that converge with the PSO technique is greater than with the other methods. As the convergence criterion is increased to the 5% convergence, the percentage of cases that converge with the SA algorithm increases considerably. The goal of the SA implementation is to converge to the neighbourhood of the GMPP so that a local search could be performed to track the MPP exactly and to follow any transients in the irradiance. These results show that SA algorithm exhibits better performance with respect to converging to the GMPP when compared to the PSO and P&O methods under the two irradiance profiles considered. The key benefit of the SA algorithm is that it has complexity similar to that of the P&O technique, yet can achieve GMPPT, and has fewer variables that need to be retained in memory than the PSO technique.

P&O

PSO

SA

52.9 58.8 58.8 58.8 58.8 5.9 35.3

76.5 76.5 76.5 76.5 76.5 11.8 11.8

52.9 70.6 88.2 88.2 94.1 5.9 0.0

operating point. For the P&O method, the convergence time is the time taken to arrive at the MPP and start oscillating around this point, and for the PSO method it is the time taken for all particles to converge to within 0.02 V of each other. The convergence of each MPP technique is considered in Tables 3 and 4 for the variable and clear irradiance profiles, respectively. Various convergence measures are considered including a 1–5% convergence rating. The convergence rating indicates if the method has converged to within a certain percentage of the known GMPP voltage and power. For instance, the 1% convergence rating gives the number of cases where the method converges to within 1% of the known GMPP voltage and to within 1% of the known GMPP power. The other convergence ratings are defined similarly. In each case, the performance against each convergence rating is expressed as a percentage of the 58 variable and 18 clear irradiance test cases considered that meet that requirement. The operating point is considered to have not converged if it has an error of more than 5% in the final operating point power when compared to the known GMPP power. The results show that the SA algorithm performs best in terms of the average, minimum and maximum time to near the MPP

Table 5 compares the explored MPPT techniques and several common conventional techniques against the criteria established in Section 2. For each technique, one or two references are provided. Note that cost is not included in the table due to difficulty in estimating the likely cost of each PV system implementation. However, the systems described in the PE based approaches and those that require an increase in circuit complexity would generally incur additional costs due to the extra power electronics components required. In Table 5, the ability of the technique to reliably identify the GMPP is indicated by ‘no’ if it will rarely track to the GMPP, ‘likely’ if the technique may converge to the GMPP, and ‘usually’ if the technique can be considered to be a reliable GMPPT technique. The tracking speed is indicated as ‘fast’, ‘slow’ or ‘varies’. Where ‘varies’ is indicated shows a technique where the tracking speed is directly dependent on the choice of parameters, for instance the step size in the P&O method. The presence of steady state oscillations is characterised by ‘no’, ‘sometimes’ and ‘common’. Where ‘sometimes’ is indicated shows a technique which depending on the implementation may exhibit a steady state oscillation. An example of this is applying a periodic reset with the P&O technique. The dependence on system specific parameters is shown by ‘yes’, ‘no’ or ‘sometimes’. The case where ‘sometimes’ is indicated relates to the actual implementation required for two-stage methods. Finally, the implementation is classified based on its complexity as ‘low’, ‘moderate’ or ‘high’. This complexity is based on the characteristics of the technique in terms of number of components required, potential software complexity and the ease with which the technique could be applied in new system. The table clearly shows that no single MPPT technique or approach designed for promoting global maximum power extraction under PSC is able to meet all of the criteria defined within this paper. In general, it can be seen that conventional MPPT techniques are usually plagued by a tendency to track a local maxima and may exhibit oscillatory behaviour around the MPP. Additionally, the simplest of these conventional techniques are limited by the definition of system dependent constants which are no longer representative of the system under PSC. Other conventional techniques designed to achieve MPP, including fuzzy and neural network approaches, add to the complexity of the tracking and may still fail under non-uniform conditions. Attempts to improve conventional tracking performance for GMPPT often increase

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Table 5 Comparison of PV MPPT techniques. Technique

Reliably identify GMPP

Speed Speed under irradiance change

Steady-state oscillations

Dependence on system-specific parameters

Complexity

No

Varies Varies

Common

No

Low

No No No

Varies Varies Fast Fast Fast Fast

Common No No

No Yes Yes

Low Low Low

No No No No No

Fast Fast Fast Fast Fast

Fast Fast Fast Fast Fast

No No No No No

No Yes No Yes No

Low Moderate Moderate Moderate Low

No No No No

Fast Fast Varies Fast

Fast Fast Varies Fast

No No No No

Yes Yes No No

High High Low Moderate

No No No No

Varies Varies Varies Varies

Varies Varies Varies Varies

Sometimes No Sometimes Common

No No Sometimes Yes

Moderate Moderate Moderate Moderate

Likely

Varies Varies

No

Yes

Moderate

Likely Usually Usually Usually

Varies Varies Varies Varies

Sometimes No No No

Yes Yes Yes Yes

Chaos Search [112] Simulated Annealing [119]

Usually Usually

Fast Fast Varies Varies

No No

No No

Moderate Moderate Moderate Moderate/ High Moderate Low/ Moderate

Power Electronics based approaches Bypass diodes method [120] Differential power processing [121] PE equaliser [122] Distributed MPPT [126, 127] TEODI [131]

Usually Usually Usually Usually Usually

Slow Varies Fast Varies Fast

No Sometimes No Sometimes No

No No Yes No Yes

Conventional MPPT techniques Perturb and Observe and Hill Climbing [30,46] Incremental Conductance [42,49] Fractional short-circuit current [134] Fractional open-circuit voltage [53, 135] Ripple Correlation Control [78] MPP locus [54,56] Extremum Seeking Control [79,80] Sliding Mode Control [74,75] Load current/voltage maximisation [67] Fuzzy based [60,136] Neural network based [60,65] Bisection Search [83] Β-method [88] Global MPPT techniques Periodic reset [45] Periodic curve scanning [89,90] Two stage methods [96,97] Two-stage methods (equivalent load line) [97,98] Observations of P–V characteristics [101] Refined P–V curve sweeping [95] Line Search (DIRECT) [102] Line Search (Fibonacci) [93, 103] Particle Swarm Optimisation [108,109]

Varies Varies Varies Varies

Slow Varies Fast Varies Fast

technique complexity and are unable to guarantee GMPPT. PE based approaches are shown to increase the energy yield under PSC but the cost involved in such systems may outweigh the benefit. While some techniques are specifically designed to reliably track to the GMPP, these methods often increase the cost and complexity of the system and frequently rely on system dependent parameters which makes it difficult to adapt the technique to other systems. In anticipation of real environmental conditions it is essential that a GMPPT technique is able to quickly track to the GMPP with minimal implementation complexity. The goals for such a technique would include a satisfactory performance on all of the criteria outlined in Section 2, in particular achieving reliable GMPPT identification rapidly with limited steady-state oscillations, moderate complexity and no dependence on system specific parameters.

8. Conclusion This review has demonstrated that many approaches have been proposed to provide superior operation of PV systems experiencing PSC. In general, conventional MPPT techniques cannot achieve GMPPT without significant modification and techniques designed specifically for this purpose may not always guarantee GMPPT, and may involve additional system dependent constants or circuit

High Moderate High Moderate Moderate

elements. Conventional MPPT methods, those designed for PSC and PE approaches have all been extensively considered. Simulation results have been presented comparing the performance of the P&O, PSO and SA MPPT method in achieving GMPPT for a simple PV system consisting of eight series-connected modules. The results presented in this paper clearly indicate that while an abundance of maximum power extraction strategies have been proposed for PV systems, no single technique can meet all required objectives of a universal global maximum power extraction process.

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