Analysis and comparison of PV configurations and MPPT methods to maximize power under partial shading

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POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell'Informazione

Course of Electrical Engineering

ANALYSIS AND COMPARISON OF PV

CONFIGURATIONS AND MPPT METHODS TO

MAXIMIZE POWER UNDER PARTIAL SHADING

Supervisor: Prof. Luigi Piegari

Master Thesis by: ZHANG WENLI

Student ID Number: 875060

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Abstract

Partial shading is the condition where PV array experiences different levels of irradiations on it, which results significant reduction in output power. To handle this issue, PV modules are connected in various configurations as reported in literatures to improve power attainment under partial shading, and many techniques are put forward to achieve the maximum power point.

This thesis studies the comparison of different PV configurations and MPPT methods to maximize power under partial shading conditions.

After a comprehensive overview of different connection schemes of PV modules, several experiments are carried out on various configurations in Simulink. The superiority of these configurations in distinct operating conditions is demonstrated by comparing their maximum power output, relative power loss and fill factor.

A brief overview of main MPPT techniques is provided and one of them is validated in Simulink under partial shading conditions. An improvement is proposed to the conventional method to enhance its accuracy of maximum power point tracking.

Based on the results obtained, two centralized and distributed PV systems are built in Simulink to compare their performance by simulating the practical output power and the efficiency of the system.

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1 Introduction

Nowadays the big part of energy comes out by using of fossil fuels but issues like the political and economic crisis, environmental pollution, limitation of fossil resources and etc., have revealed the necessity of finding new sources of energy.

As one of the required sources for solving these problems, demand of solar energy is increasing gradually in recent years. Solar energy is so clean and does not produce any greenhouse gases which means environmental and health costs of generating energy will decrease and also the global warming issue can be controlled. One of the other benefits of solar energy is that it is worldwide and available such as almost all countries can use it for generating energy without depending to other countries.

The use of PV cells is one of the most common ways to exploit solar energy and directly convert it to electrical energy. Today, the number of installed cells is rapidly increasing and these cells are used in three different types: stand alone, grid connected and hybrid.

Of course there are still two important barriers in the path of PV cells, relatively expensive cost and low efficiency. The efficiency of PV modules are very low (10-25% in general). On top of that, power attainment from PV modules varies with irradiance and temperature. Thus, throughout the day maximum efficiency cannot be ensured. Besides, PV array lose power continuously when irradiance levels are different on different modules connected. The phenomenon when the respective PV modules on the arrays connected are receiving different irradiance or insolation levels is known as partial shading.

Therefore it is completely necessary to mitigate the effect of partial shading by choosing a suitable PV configuration and deploy accurate methods to extract maximum power of the PV system.

In this thesis, different PV configurations and MPPT methods are taken into consideration to maximize power under partial shading conditions

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2 Photovoltaic System

2.1 Photovoltaic Cell

The Photovoltaic (PV) cell is the main component of PV system which converts solar PV energy into electrical energy. The amount of power generated from the PV cell or module mainly depends on the solar irradiance and temperature.

2.1.1 Solar Irradiance and Cell Temperature

The sun is the most important energy resource present on earth. The solar radiation is the electromagnetic energy emitted by the sun during the nuclear fusion in its core. The solar radiation through the atmosphere is weakened due to scattered and absorption.

Fig.2-1: Solar radiation on the earth’s surface

Tab.2-1. Radiation under different weather conditions

As shown in Fig.2-1, the so-called global radiation is composed by direct radiation, diffuse radiation and albedo radiation. Direct radiation comes directly from the sun without change of direction whereas diffuse radiation is the result of scattering of the sunbeam or reducing the magnitude of the sunbeam due to atmospheric constituents as

Weather Clear Hazy or cloudy Overcast

Global radiation 600 – 1000 W/𝑚2 200 – 400 W/𝑚2 50 – 150 W/𝑚2

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the horizon, only diffusion radiation reaches the earth's surface. Albedo radiation refers to reflected light from the ground and surroundings and corresponds to the ratio of reflected to the incident light at a surface considered, namely albedo. Tab.2-1 shows radiation variation under different weather conditions.

The irradiance variation is considered the main perturbing factor to be faced, because of its unpredictability. Even when the sky is clear, the radiation intensity on the Earth's surface changes continually during a day. Less radiation is available early in the morning or late in the afternoon, as then the radiation has a longer path through the atmosphere and is more strongly attenuated than at midday.

The cell temperature, here indicated as 𝑇, is calculated from the ambient temperature 𝑇_𝑎 given in book [1] by using the nominal operating cell temperature (NOCT):

𝑇 = 𝑇_𝑎+𝑁𝑂𝐶𝑇−20

800 𝐺 (2-1)

It is worth noting that the temperature usually changes quite slowly, so that the temperature value is often considered a constant if the analysed time-window is not very long.

2.1.2 Fundamentals of Photovoltaics

The direct transformation from the solar radiation energy into electrical energy is possible with the photovoltaic effect by using solar cells. Figure below shows the three main parts of a solar cell schematically: the diffused strong n-doped emitter, the space-charge zone and the p-doped base [2].

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Fig.2-2. Structure of a solar cell

Under incident light, a photon with sufficient large energy falls on the surface of the solar cell, penetrates emitters and space-charge zone and is absorbed in the p-doped base. An electron-hole pair is developed due to the absorption. Since electrons are in the minority in the p-base, one calls them minority charge carrier contrary to the holes, which are majority charge carrier here. This electron diffuses in the p-base until it arrives at the boundary of the space-charge zone. The existing strong electrical field in the space-charge zone accelerates the electron and brings it to the emitter side. Thus, a separation of the charge carriers took place. Thereby the electrical field works as separation medium. A prerequisite is that the diffusion length of the electron has to be large enough so that the electron can arrive up to the space-charge zone. In case of too small diffusion length a recombination would occur before reaching the space-charge zone, and, consequently, the energy would be lost. Absorption of a light quantum in the emitter leads again to the formation of an electron-hole pair. According to the strongly doped n-emitter the holes are here the minority charge carrier. With sufficient large diffusion length, the hole reaches the edge of the space-charge zone, is accelerated by the electric field and is brought to the p-base side. If the absorption occurs in the space-charge zone, electrons and holes are immediately separated according to the existing electrical field there. In consequence of the incident light it yields: if concentration of electrons at the n-emitter side is increased, concentration of holes at the p-base side

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connection to the base and recombines with the holes there. Current flow means however power output. This current flow continues so long as the incident light radiation is available. As a result, light radiation is immediately converted into electricity.

The best way to analyze the behavior of the PV generator in a simulation environment is to adopt an equivalent circuit model and relevant equations describing it. In the following, such models are introduced.

2.2 Mathematical Modeling of PV Module

2.2.1 PV Equivalent Circuit

Various electrical equivalents of PV cell are found in literature and the single-diode model is the most widely used model among them. The ideal, practical and simplified models of single-diode PV cell are shown in Fig.2-3(a). Two-diode and bishop models for PV cell are shown in Fig.2-3(b) and Fig.2-3(c). For better accuracy and ease of mathematical calculations to find the values of series and shunt resistances, single-diode model of PV cell is considered. The practical circuit consists of a photo current generator (𝐼𝑝ℎ), a diode (D), a parallel resistance (𝑅𝑝) representing the leakage

current and a series resistance (𝑅𝑠) representing an internal resistance of the PV cell [3].

Iph D Rs Rp Ideal model Simplified model Practical model + V -I (a)

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Iph D2 Rs Rp D1 (b) Iph D Rs Rp Ip (c)

Fig.2-3. Bishop equivalent circuit model of PV cell

The mathematical representation of the I-V characteristics of practical PV cell is given as follows:

I = 𝐼_𝑝ℎ− 𝐼₀[𝑒𝑥𝑝 ( 𝑞

𝑘𝑇𝐴(𝑉 + 𝐼𝑅𝑠)) − 1] − 𝑉+𝐼𝑅𝑠

𝑅𝑝 (2-2)

where 𝐼𝑝ℎ is light generated current, I0 is the cell saturation of dark current, 𝑇 is the

cell’s operating temperature in Kelvin, 𝑘 is the Boltzmann constant (1.381 × 10−23_J/

K), 𝑞 is the electron charge (1.602 × 10−19 C), 𝐴 is diode ideality constant [3]. The photovoltaic current mainly depends on the solar irradiation and temperature given as:

𝐼_𝑝ℎ = [𝐼_𝑠𝑐+ 𝐾_𝐼(𝑇 − 𝑇_𝑟𝑒𝑓)] 𝐺

𝐺𝑛 (2-3)

where 𝐼_𝑠𝑐 is the short circuit current of the cell at 25°C and 1000 W/𝑚2_,_𝐾

𝐼 is the

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The saturation current varies with the cell temperature and it can be expressed as: 𝐼₀ = 𝐼_0,𝑛(𝑇𝑟𝑒𝑓 𝑇 ) 3 𝑒𝑥𝑝 [𝑞𝐸𝑔 𝐴𝑘 ( 1 𝑇𝑟𝑒𝑓− 1 𝑇)] (2-4)

where 𝐼_0,𝑛 is the nominal saturation current, 𝐸_g is the band gap energy of the semiconductor (𝐸g = 1.12 eV for the polycrystalline Si at 25 °C).

RsNs/Np Np Ns IphNp RpNs/Np

Fig.2-4. Equivalent circuit model of PV module

The output power of a typical PV cell is less than 2 W at 0.5 V. In order to produce desired output power, PV cells are connected in series and parallel configuration to build up a module [3]. The equivalent circuit of the PV module arranged in 𝑁𝑝 parallel

and 𝑁_𝑠 series is shown in Fig.2-4. The voltage-current characteristic equation of a PV module is expressed as:

I = 𝑁_𝑝𝐼_𝑝ℎ− 𝑁_𝑝𝐼₀[𝑒𝑥𝑝 ( 𝑞 𝑘𝑇𝐴( 𝑉 𝑁𝑠+ 𝐼𝑅𝑠 𝑁𝑝)) − 1] − 𝑁𝑝 𝑁𝑠𝑉+𝐼𝑅𝑠 𝑅𝑝 (2-5)

2.2.2 Characteristic Curves of PV Module

In the thesis the system concerns the Suntech Power STP245S-20/Wd module, whose parameters are listed in Tab.2-2, its simulink model is shown in Fig.2-5.

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Parameter Variable Value in STC Condition

Short-circuit current 𝐼𝑠𝑐 8.52A

Open-circuit current 𝑈_𝑜𝑐 37.3V

Mpp current 𝐼_𝑚 8.04A

Mpp voltage 𝑈_𝑚 30.5V

Number of cells in series 𝑁𝑠 60

Temperature coefficient of 𝐼_𝑠𝑐 𝐾_𝐼 0.05 %/℃

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The electrical behavior of the PV module is given by the current-voltage and power-voltage curves. Fig.2-6(a) and Fig.2-6(b) shows the characteristic curves of the chosen PV module under standard test condition (STC). Such conditions are defined by the cell temperature 𝑇𝑆𝑇𝐶 = 25℃, irradiation

level 𝐺𝑆𝑇𝐶 = 1000𝑊/𝑚2, and the air mass value 𝐴𝑀 = 1.5.

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Fig.2-6. characteristic curves of the PV module

The I-V characteristic curve shows all the possible working points. It can be observed that the output power does not have a linear behavior, the maximum values of voltage and current are 𝑉𝑜𝑐 and 𝐼𝑠𝑐. The P-V characteristic curve is given by the product of

the current and voltage in each point of the I-V curve. Although the current has its maximum at the short-circuit point, the voltage is zero and thus the power is also zero.

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rectangular point in the above figure). The so-called maximum power point (MPP) represent the working point, at which the solar cell can deliver maximum power for given radiation intensity and temperature.

The quantity of Eq. (2-6) is called Fill Factor. It indicates how far the I-V characteristic curve approximates to a rectangle and represents the quality of the solar panel. Normally the value for crystalline solar cells is about 0.7-0.8.

𝐹𝐹 = (𝑉𝑚∙𝐼𝑚)

(𝑉𝑜𝑐∙𝐼𝑠𝑐) (2-6)

The maximum output power of the cell is then

𝑃_𝑚 = 𝑉_𝑚∙ 𝐼_𝑚 = 𝑉_𝑜𝑐∙ 𝐼_𝑠𝑐∙ 𝐹𝐹 (2-7) Thus, the efficiency of the solar cell, which refers to the ratio of the output electrical energy by the input solar radiation, is defined by the following relation.

𝜂 =𝑉𝑜𝑐∙𝐼𝑠𝑐∙𝐹𝐹

𝑃𝑖𝑛 (2-8)

Where Pin indicates the input solar radiation.

According to Eq. (2-3), the short circuit current of the PV module and solar irradiation are directly proportional to each other. Therefore, the power of the PV module is directly proportional to solar irradiation. When the solar irradiation level decreases, the power of the PV module decreases [3]. I-V and PV characteristics of PV module for different solar irradiation levels at constant temperature (25 °C) are shown in Fig.2-7 and Fig.2-8. According to Fig.2-7, when the solar irradiation increases, the short circuit current of the PV module increases, so the power increases.

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Fig.2-7. I-V characteristic of PV module for different solar irradiation

Fig.2-8. P-V characteristic of PV module for different solar irradiation

According to Eq. (2-4), the short-circuit current of the PV module and temperature are inversely proportional to each other. In other words, the power of the PV module is inversely proportional to solar irradiation. When the temperature increases, the power of the PV module decreases [4]. I-V and P-V characteristics of PV module for different temperatures at constant solar irradiation (1000𝑊/𝑚2) are shown in 9 and Fig.2-10. According to Fig.2-9, when the temperature decreases, the open circuit voltage of the PV module increases, so the power increases.

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Fig.2-9. I-V characteristic of PV module for different temperature

Fig.2-10. P-V characteristic of PV module for different temperature

Figures 2-7 to 2-10 put into evidence the strong dependence of the panel performances on the temperature and the solar irradiance level. The temperature has a significant effect on the open-circuit voltage value, as shown in Fig.2-9 and Fig.2-10. On the contrary, the temperature has a lower effect on the short-circuit current value. The irradiance variation has dual effects on the electrical characteristics with respect to the temperature. In Fig.2-7 and Fig.2-8, the PV module open-circuit voltage is almost independent of the irradiation. On the contrary, the short-circuit current is linearly dependent on the irradiance.

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2.3 Configurations of Grid-tied Photovoltaic Systems

Grid-connected PV systems are traditionally classified by power capacity, which are listed as small-scale, intermediate-scale, and large-scale [5]. PV generators that are less than 50 kW are usually considered as small scale PV systems. A system that can produce more than 1 MW is commonly considered as large-scale or utility-scale, although this category now covers systems up to tens or even hundreds of MW. Systems between these two ranges are designated as intermediate-scale. Recent classification focuses also on voltage levels as low-voltage (LV) and medium-voltage (MV) [6]. Converter topologies used can overlap the above classification. For example, the topology of the classic voltage source inverter (VSI) can be used for the small-scale, medium-scale or large-scale grid integration. The same topology can be utilized for the LV grid connection or MV grid connection through step-up transformers. To have a criterion to clearly distinguish the system architectures and topologies, all grid-tied systems can be classified by the function of maximum power point tracking (MPPT) in terms of centralized MPPT (CMPPT) and distributed MPPT (DMPPT). This classification provides a clear framework for understanding the grid-tied architectures and topologies used for photovoltaic systems [7].

2.3.1 Centralized Maximum Power Point Tracking systems

A PV array comprises modules that are connected in series-parallel combination to meet the input voltage requirement of the centralized power inverter for grid connection, and achieve the desired rated power. The maximum power point tracking in such systems is operated by a centralized inverter at array level. Such structures are referred to as CMMPT systems [8].

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2.3.1.1 Topologies of a PV Array

Figure 2-11 shows the common schematic diagram of PV array configurations. They are simple-series (SS), parallel (P), series-parallel (SP), total-cross-tied (TCT), bridge-link (BL) and honey-comb (HC).

(a) (b) (c)

(d) (e) (f)

Fig.2-11. Schematic diagram of PV array configurations (a)SS, (b)P, (c)SP, (d)TCT, (e)BL, (f)HC

SS configuration is the simple and basic configuration and it is shown in Fig. 2-11(a). The PV modules are connected to each other in a series string and the output is taken across the two ends. While output voltage of this configuration is high, but output

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current is low. Besides, in almost all partial shading conditions SS performs the worst in terms of power loss and power output [9]. Therefore, various configuration schemes are proposed so as to overcome this drawback.

Fig.2-11(b) shows 5×5 P configuration of PV modules. It is also one of the simplest configuration of PV modules. The PV modules are connected in parallel to each other having only 1 module in 1 string. The output is taken parallel across all the PV modules connected. Partial shading has low effect on PV modules in P configuration and it will produce the most power at MPP in all partial shading conditions used. Consequently, the relative power loss is also the lowest as power loss is obtained by finding the difference between MPP when the PV modules are unshaded and that when partially shaded [10]. However, P configuration has a drawback of having high current and low voltage which is not feasible for the application of PV modules.

SP configuration is shown in Fig. 2-11(c). In order to get desired output voltage, all modules are first connected in series form and then these series connection are connected in parallel. SP configuration is usually investigated to be having lower output performance when compared to TCT configuration. Also, partial shading losses is reduced significantly in TCT when compared with SP. Although in most of the cases TCT outperforms SP configuration, SP configuration can perform better than TCT when it comes to row-wise shading pattern, due to the fact that it has more series string to be more susceptible to mismatch losses [11]. In addition, two arrays of PV modules of SP configuration of same array size but different number of rows and columns are investigated in [12]. It shows that when fewer modules are connected in series and more in parallel is more advantageous. Hence, too long a series string in SP is not beneficial in terms of output power attainment.

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which maximizes its array utilization, it outperformances in most of the cases compared with SP configuration [13]. Besides, TCT has lower variation interval of MPP voltage during partial shading condition and it has gained popularity in real world environmental condition. But the large number of cross ties has increased the complexity of the configuration and solving the system mathematically requires large calculation time and computational burden due to its non-linear characteristics [14].

BL configuration is shown in Fig.2-11(e). There is a bridged unit with four modules. Two modules in a bridge are connected in series and then they are connected in parallel. Bridges are linked via cross ties. BL has slightly longer operational lifetime and is less susceptible to electrical mismatch loss than TCT [15]. Under ladder and column-wise shading pattern, BL comes in the second place when maximum power output is evaluated among SP, TCT and BL configurations [16].

HC configuration is shown in Fig.2-11(f). HC is a modified version of BL configuration and its bridge size is variable. HC can actually perform better than TCT when the array is asymmetrically arranged and connected or when number of columns receiving same insolation is more than the number of rows [30]. However, TCT still outperforms HC in most of the cases due to the fact that it has more internal connections which provides more current paths and further prevents reduction of current in the branches.

The summary of the advantages and limitations of the 6 different configurations is listed in Table.2-3.

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Configurations Advantages Limitations

Simple connections Current is too low

SS Minimum amount of wiring Voltage is too high

Very susceptible to aging problems Very prone to mismatch losses

Simple connections Voltage is too low

P Usually has only single power peak Current is too high

High output power, low mismatch loss Not usually used in the PV application

Susceptible to aging problems More multi-peak effect

SP Performs better than TCT during row-wise shading Lower maximum power in most cases when compared to cross ties configurations

Smooth inflexion point

TCT

Less multi-peak effect Very high redundancy High maximum power in most cases Very high wiring loss Long operational lifetime Numerous connections

Good fault tolerance Poor performance in row-wise shading condition Small variation of MPP during partial shading Requires unrealistic number of switches and sensors Adapts well to random shading patterns

High maximum power during unshaded condition High redundancy

BL Slightly longer operational lifetime than TCT High wiring loss

Higher maximum power than TCT when unshaded Lower maximum power than TCT when partial shaded Less multi-peak effect Lower maximum power than TCT in most cases

HC Outperforms TCT with asymmetrical array High wiring loss Outperforms TCT during row-wise shading High redundancy

Tab.2-3. summary of the advantages and limitations of various configurations

2.3.1.2 Topologies of conversion systems

Typical architectures of grid-tied CMPPT systems are shown in Fig.2-12.

Galvanic isolation is required by some grid codes due to the requirement for a grounded system. Figure 2-12(a) shows a three-stage conversion system with galvanic isolation,

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isolation that uses a low frequency transformer at the output stage. Low frequency transformers are bulky and heavy, but are robust and provide galvanic isolation exactly at the point of common coupling. Figure 2-12(c) shows a one-stage conversion system with galvanic isolation that converts the PV array output directly to AC through the PV inverter and low frequency transformer.

The recent grid codes allow ungrounded PV systems, which make use of non-isolated or transformer-less inverters [18]. This depends on the voltage level of the power grid and the power of the PV system. For example, in China non-isolated inverters are allowed when the power of the PV system is lower than 200KW, they have advantages of high efficiency and low price. Without any transformer loss, the system aims for higher efficiency than the isolated counterparts. Two-stage and one-stage conversion systems without galvanic isolation are shown in Fig.2-12(d) and Fig.2-12(e).

Fi lt er A rr ay (a) Fi lt er A rr ay (b) Fi lt er A rr ay (c) Fi lt er A rr ay (d)

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Fi lt er A rr ay (e)

Fig.2-12. Architectures of grid-tied CMPPT systems

In multiple-stage converters, the control of the front end power interface is mainly for maximum power point tracking. While in single-stage operation, the DC/AC inverter must be able to undertake both MPPT and other required grid-tied functions [19]. The single-stage power interface has the advantage of simplicity and aims for higher conversion efficiency than a two-stage solution. However, the DC link configuration in multiple stage conversion distributes the control into two individual tasks and provides flexibility to implement modular DC/DC MPPT units to achieve more effective energy harvesting [20].

2.3.2 Distributed Maximum Power Point Tracking systems

The centralized architecture always results in some shortcomings, such as hotspots issues caused by partial shading cases, power loss due to mismatched conditions and non-flexible system designs etc. [21]. Thus, DMPPT has attracted significant research attention to address the above issues. However, adding converter stage implies adding losses. For this reason, the advantage in terms of efficiency of the MPPT is counterbalanced by added losses and an optimal solution has to be searched.

2.3.2.1 Distributed Maximum Power Point Tracking systems at PV String Level

The string level DMPPT structure is shown in Fig.2-13, with three distributed maximum power point trackers at the individual series/parallel PV string level.

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Fi lt er Fi lt er (a) (b)

Fig.2-13. DMPPT systems at PV string level

The output of each string is modulated by an independent DC/DC converter, which acts as the maximum power point tracker. The DC bus can be linked to either a DC micro grid or an AC grid through a centralized DC/AC inverter. Therefore, the power degradation caused by any mismatch effect at string level is minimized. The DC/DC and DC/AC converters can be either independent units or integrated inside one enclosure. Some commercial systems implement the DC/DC units inside combiner boxes to perform independent string-level MPPT [22].

2.3.2.2 Distributed Maximum Power Point Tracking systems at PV Module Level

The major inherent flaws in the architecture of the PV system mentioned before are the mismatching effects which lead to degradations in performance and multi power peak presence that results in a complicated MPPT realization. In order to overcome the abovementioned drawbacks, the module shown in Fig.2-14, which is composed of a PV panel with a DC/DC converter or a DC/AC converter, is developed to provide a solution to optimize the power harvest from the PV array. The module integrated converters provide independent MPPT operation within each PV module, which allows local optimization and reduces power losses resulted from mismatch and partial shading [23],while adding power losses in the converter stage.

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Fi lt er Fi lt er (a) (b) Fi lt er Fi lt er (c) (d)

Fig.2-14. DMPPT systems at PV module level (a)TCT, (b)SS, (c)TCT, (d)SS

In inverter integrated PV module level DMPPT system, the DC bus can be linked to either DC micro grids or AC grids through a centralized DC/AC inverter. This structure provides an ideal solution to support a DC micro grid. In Fig.2-14(a) integrated converters are connected in parallel onto a common DC bus. This structure has superior performance since the double-line frequency ripple is no longer present in the DC/DC conversion stage. The disadvantages are high voltage conversion ratio, relatively low

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stack structure can allow each module to be operated at a low conversion ratio that allows high conversion efficiency [24]. The drawbacks are that the structure is not as flexible as the parallel configurations and the reliability can be a concern since the series connection cannot be immune to single point failure.

In converter integrated PV module level DMPPT system, the AC bus is directly connected to the AC network. The concept indicates an ideal solution to integrate PV power to form a common AC bus. In Fig.2-14(c) the integrated inverters are connected in parallel, the parallel interconnection completely eliminates the single point failure that is common in series connection. Meanwhile, the system becomes highly modular and flexible since the parallel structure can be easily expanded [25]. Besides the common merits, the direct DC/AC conversion shows the additional advantages of the lowest capacity for a DC/AC grid connection and simple system wiring since DC wiring is integrated at the module section and AC wiring is common for ordinary electricians. The drawback of this system is also clear since the overall system cost is higher than the centralized counterpart, the conversion efficiency is constrained due to the high DC/AC conversion ratio, the MPPT effectiveness is influenced by the impact of double-line frequency ripple in single-phase systems, and harsh outdoor operating environment influences the lifetime and reliability of the electronics [26]. In Fig.2-14(d) the integrated inverters are serially connected to form a common AC bus. Compared to the parallel solution, the DC/AC conversion ratio is lower. The drawbacks are the higher requirement for control and coordination, the inflexibility and single power failure which are common in any series connected system [27].

2.3.3 Topologies of Converters in Grid-tied Photovoltaic Systems

2.3.3.1 Topologies of PV side converters

The PV side converter refers to the DC/DC power stage that connected with the PV generator. The converters are operated by the algorithm of MPPT for the highest solar energy harvesting. The schematics of the non-isolated and isolated topologies are shown in Fig.2-15 and Fig.2-16 including boost, buck, buck-boost DC/DC and

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H-bridge converters. The selection is based on the voltage levels of the PV side and the DC link.

The boost converter topology is shown in Fig.2-15(a). The operation of the converter comprises two states: an ON state in which the inductor storages the energy to supply to the output when the switch is in OFF state. When the transistor is in conduction, it means that is saturated, so the diode anode is short circuited to ground, thus, it is in reverse polarization and behaves as an open circuit. The diode ensures that the discharge current prevenient from the capacitor does not go toward the source but supplies the load. The output voltage, in continuous conduction mode, is given by:

𝑉𝑐 = 𝑉𝑝𝑣⁄(1 − 𝐷) (2-9)

where D is the duty cycle of the converter obtained as the ratio between the ON time and the switching period.

The boost converter should be used if the PV terminal voltage is always lower than the DC link voltage. It is usually selected for the string-level power interface thanks to the claimed advantages for PV applications [28].

The buck converter topology is shown in Fig.2-15(b). The buck converter should be utilized when the input voltage is always higher than the output one [28]. The operation of the converter comprises two states: an ON state in which the switching device allows current flow, transmitting the input energy to the output, the diode is in reverse polarization, it means that is an open circuit. The OFF state is when the transistor behaves as an open circuit isolating the circuit, the current coming from the inductor flows through the diode so the inductance L discharges toward the load. The output voltage, in continuous conduction mode, is given by:

𝑉_𝑐 = 𝑉_𝑝𝑣∙ 𝐷 (2-10) The buck-boost converter using inverting topology is shown in Fig.2-15(c). The operation of the converter comprises two states: when the switch S is in ON the inductor current increases whereas the diode is an open circuit (as in the boost converter), and

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output circuit to the inductor in the OFF state of the transistor. The output voltage is given by the product of the conversion ratios of Eq. (2-9) and Eq. (2-10):

𝑉𝑐 = 𝐷 (1 − 𝐷)⁄ ∙ 𝑉𝑝𝑣 (2-11)

The buck-boost converter should be only considered if the input and output voltage cannot be clearly distinguished as either step-up or step-down with the consideration of the variation of the DC link voltage [29].

The H-bridge bipolar converter topology is shown in Fig.2-15(d). The output voltage is given by:

𝑉𝑐 = 𝑉𝑝𝑣(2𝐷 − 1) (2-12)

The isolated topology is commonly based on H-bridge converter as shown in Fig.2-16(a). Compared with the non-isolated solution, the isolated topology has an electronic barrier between the input and output of the DC-DC converter. This barrier can withstand dangerous voltages from a few hundred volts to several thousand volts. The disadvantage is low efficiency and the package size is bigger than a non-isolated due to the transformer. The isolated H-bridge converter is conventionally utilized for high power level, which satisfy the requirement of the string level solution. It also matches the DC/DC power interface in CMPPT system.

(a) (b)

(c) (d) Fig.2-15. Schematic circuits of non-isolated DC/DC PV side converters

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(a) (b)

(b) (d) Fig.2-16. Schematic circuits of isolated DC/DC PV side converters

2.3.3.2 Topologies of Grid side converters

In applications where the PV is connected to the grid or to an AC load, DC/AC converters are needed to generate a sinusoidal tension at industrial frequency. Figure 2-17 illustrates the common DC/AC topologies used for grid connection, which include the H-bridge circuit for single-phase integration in Fig.2-17(a) and the current source inverter (CSI) or voltage source inverter (VSI) for three-phase integration in Fig.2-17(b).

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(b)

Fig.2-17. Schematic circuits of DC/AC grid side converters

The analysis of H-bridge isolated converter can generally follow the same as the non-isolated buck converter, but it provides the function of galvanic isolation and flexibility to be designed for various conversion ratios thanks with the transformer implementation [30]. The CSI shares the same circuit schematic with the VSI, which is commonly used for motor drives and three phase power supplies. For MV grid integration, step-up transformers can be utilized to boost from LV to MV. The DC link can either be the link between the PV side converter and the grid side converter or the PV terminal, which is defined as one-stage conversion.

2.3.3.3 Topologies of AC Filters

AC filter is required to mitigate the harmonic injection from the grid side converters. Shown in Fig.2-17, the L filter is applied between the grid side converters and grids. Due to causing a long-time response, the system dynamics is poor, but the L filter is simple and robust both for implementation and analysis and has the lowest cost among the three filters. The LC filter shown in Fig.2-18(a) is commonly used in VSI based systems, and its output electrical power quality is better than L filter. Recent studies focus more on the LCL filters, which are shown in Fig.2-18(b).The third order LCL filter is preferred over an L or LC filter due to the 60 dB/decade attenuation of the frequencies above the resonance frequency and the reduction in physical size of the inductor [31].

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(a) (b) Fig.2-18. Schematic circuits of AC filters

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3 Partial shading

3.1 Bypass diode

Shadows from cables, tree tops, surrounding structures or passing clouds may cause partial shading, which is known as the phenomenon when the respective PV modules connected on the array are receiving different irradiance or insolation levels.

In a series connection, the same current flows through each module whereas the total voltage is the sum of the voltage across each cell. When partial shading occurs, the output power at maximum power point (MPP) of the shaded cell is reduced and this causes mismatch in the PV modules [32]. Regarding series connection, although the other unshaded panels can produce their 100 % photocurrents, the amount of current flowing in the circuit can only equal the amount of the current produced by the shaded panels. The rest of the current produced by the unshaded panels will flow into their own diodes, the diodes of the shaded panels are reverse biased by the voltage generated by the other unshaded panels. This causes power dissipation and then “hot spot”: an intolerable effect, which leads to breakdown in the cell p-n junction and in turn to destructions, cell or glass cracking or melting of solder.

One solution to this problem is to connect bypass diode anti-parallel to the cells as shown in Fig.3-1. With the bypass diode, when the voltage becomes negative the diode starts conducting and the voltage on the PV cell is kept around zero. But this further causes the output performance of the PV modules to be affected.

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3.2 Partial shading effect

A simple series model connected with 5 modules is built as shown in Fig.3-2 to find how partial shading affects the output performance of the PV modules with bypass diode. The bypass diode is already added into the cell model package.

Fig.3-2 The simulation model of a series string

The shaded irradiance condition is set as the irradiance level of 200𝑊/𝑚2_{. Fig.3-3}

shows the output characteristics of the series string when one, two, three and four cells of the string are evenly shaded. Because of the partial shading, each PV curve shows 2 MPPs, and each IV curve shows 2 corresponding knee points. The number of shaded cells influences the value of global maximum power point (GMPP) and the position of MPPs.

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(b) 2 cells are shaded

(c) 3 cells are shaded

(d) 4 cells are shaded

Fig.3-3 The simulated PV and IV characteristics of a series string under even shading

Another two conditions are simulated to further study how is the relationship between partial shading and output characteristics. For soft shading condition, the irradiance levels for the five modules of the string are set as 600, 700, 800, 900 and 1000𝑊/𝑚2_.

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shown in Fig.3-4, each PV curve has 5 MPPs, which is equal to the number of different shading irradiance set in the series string. Under soft shading condition, the irradiance difference between cells are small and the gaps between MPPs are also small. On the contrary, the gaps between MPPs under strong shading condition are more significant.

(a) Under soft shading

(b) Under hard shading

Fig.3-4 The simulated PV and IV characteristics of a series string under not uniform shading

A parallel string model connected with 5 modules as shown in Fig.3-5 is simulated under the same conditions as the series connected model. Compared with the series string, the PV and IV curve shows no local maximum power point(LMPP) or local knee point under different partial shading conditions. The value of maximum power also performances better than the GMPP value of series string under partial shading.

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Fig.3-5 The simulation model of a parallel string

(a) 1 cell is shaded

(b) 2 cells are shaded

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(d) 4 cells are shaded

Fig.3-6 The simulated PV and IV characteristics of a series string under even shading

(a) Under soft shading

(b) Under hard shading

Fig.3-7 The simulated PV and IV characteristics of a parallel string under not uniform shading

Consequently, smart MPPT algorithms are needed to be deployed to handle the multiple peaks issue. Apart from MPPT algorithms, effect of partial shading can also be mitigated by choosing a suitable configuration of PV modules.

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3.3 Output characteristic of different topologies under partial

shading conditions

As written in chapter 2, the PV array configurations based on different interconnections of PV modules are Simple-Series (SS), Parallel (P), Series–parallel (SP), Total-Cross-Tied (TCT), Bridge-Linked (BL) and Honey-Comb (HC).

For large PV systems, the selected location should be an open filed without structures or trees around, also if this is not always possible. Anyways, shadows commonly from passing clouds cannot be avoided. Clouds with different shapes and thickness can cause variation in the area and irradiance level of shadows. In this section, 4 shading patterns are presented as:

(A) even row shading comes from the top side of the PV array and goes to bottom at constant speed;

(B) random shading comes from the top side of the PV array and goes to bottom at constant speed;

(C) even column shading comes from the left side of the PV array and goes to right at constant speed;

(D) concentric shading comes from top left of the PV array and goes to bottom right at constant speed.

In each shading pattern the solar irradiance levels are categorized into 4 different groups. Group 1 receives an irradiance of 100 W/m2_{, Group 2 receives an irradiance of 300}

W/m2, Group 3 receives an irradiance of 600 W/m2, Group 4 receives an irradiance of 1000 W/m2 _{respectively. The distribution of the 4 groups in each shading pattern is}

shown in Fig.3-8. Assume that the shadow of the cloud passes the PV array area in 100 seconds, the simulation model of PV array topologies and simulated output characteristics under each shading pattern are shown from Fig.3-9 to Fig.3-24.

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1000 W/m2 600 W/m2 300 W/m2 100 W/m2

(A) (B) (C) (D)

Fig.3-8 Representation of possible patterns of moving shading

3.3.1 Simulation of Simple-Series(SS) topology

The simulation model of a SS topology PV array is presented below. The simulated output characteristics under 4 shading patterns during 100s are shown from Fig.3-10 to Fig.3-13.

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Fig.3-11 Simulated output characteristics of SS topology under shading pattern B

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Fig.3-13 Simulated output characteristics of SS topology under shading pattern D

3.3.2 Simulation of Parallel(P) topology

The simulation model of a parallel connected PV array is presented below. The simulated results under 4 shading patterns during 100s are shown from Fig.3-15 to Fig.3-18.

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Fig.3-16 Simulated output characteristics of P topology under shading pattern B

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Fig.3-18 Simulated output characteristics of P topology under shading pattern D

3.3.3 Simulation of Series-Parallel(SP) topology

The simulation model of a series-parallel topology PV array is presented below. The simulated results under 4 shading patterns during 100s are shown from Fig.3-20 to Fig.3-23.

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Fig.3-20 Simulated output characteristics of SP topology under shading pattern A

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Fig.3-23 Simulated output characteristics of SP topology under shading pattern D

3.3.4 Simulation of Bridge-Link(BL) topology

The simulation model of a BL topology PV array is presented below. The simulated output characteristics under 4 shading patterns during 100s are shown from Fig.3-25 to Fig.3-28.

Fig.3-24 Simulation model of the BL topology

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Fig.3-27 Simulated output characteristics of BL topology under shading pattern C

Fig.3-28 Simulated output characteristics of BL topology under shading pattern D

3.3.5 Simulation of Honey-Comb(HC) topology

The simulation model of a HC topology PV array is presented below. The simulated output characteristics under 4 shading patterns during 100s are shown from Fig.3-30 to Fig.3-33.

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Fig.3-31 Simulated output characteristics of HC topology under shading pattern B

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Fig.3-33 Simulated output characteristics of HC topology under shading pattern D

3.3.6 Simulation of Total-Crossed-Tied(TCT) topology

The simulation model of a TCT topology PV array is presented below. The simulated output characteristics under 4 shading patterns during 100s are shown from Fig.3-35 to Fig.3-38.

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Fig.3-36 Simulated output characteristics of TCT topology under shading pattern B

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Fig.3-38 Simulated output characteristics of TCT topology under shading pattern D

3.3.7 Comparison of the simulated results in typical shading conditions

From the above obtained results, it can be proved that for each topology, when even row shading moving from top to bottom, the short-circuit current and maximum power decrease with the increase of the shading area. No distributed MPP occurs during the whole 100 seconds except the series connection case. The P, SP, BL, HC and TCT configurations present the same performance at each time point i.e. provide the same maximum powers.

When even column shading moving from left to right, for each configuration except the P topology, MPPs occurs with the increase of the shading area, and the number of MPPs is equal to the number of the irradiance level groups in a row. The SS, SP, BL, HC and TCT configurations present the same performance at each time point i.e. provide the same maximum powers.

Under shading pattern C, the variation of the output characteristics of SS, P, SP, BL, HC and TCT configurations are not the same during the whole-time duration, so choose 0s, 10s, 30s, 40s, 50s as example, the simulated results at each time point is in Tab.3-1.

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Topology PM (W) VM (V) IM (A) FF (%) SS 6100.472 766.391 7.960 76.78 P 6099.111 30.627 199.146 76.80 SP 6100.315 154.176 39.567 76.79 BL 6099.529 156.139 39.065 76.80 HC 6100.315 154.176 39.567 76.79 TCT 6100.315 154.176 39.567 76.79

Tab.3-1 Parameter of PV array topologies at 0s(STC) under shading pattern D

Under uniform irradiance condition (1000 W/m2_{), all configurations present the same}

maximum power.

1000 W/m2

600 W/m2

300 W/m2

100 W/m2

Fig.3-39 Representation of the shading condition at 10s under shading pattern D

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SP BL

HC TCT

Fig.3-40 PV output characteristics of PV array topologies at 10s under shading pattern D

Topology PM (W) VM (V) IM (A) ∆PL (%) FF (%) SS 5884.89 744.866 7.901 3.99 74.30 P 5973.54 31.130 191.887 2.55 76.75 SP 5672.86 156.106 36.340 7.01 71.64 BL 5844.92 157.584 37.091 4.17 73.84 HC 5835.71 157.587 37.032 4.34 73.72 TCT 5911.23 155.602 37.989 3.10 74.69

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1000 W/m2

600 W/m2

300 W/m2

100 W/m2

SS P

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HC TCT

Tab.3-3 Parameter of PV array topologies at 20s under shading pattern D

1000 W/m2

600 W/m2

300 W/m2

100 W/m2

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SS P

SP BL

HC TCT

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1000 W/m2

600 W/m2

300 W/m2

100 W/m2

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SP BL

HC TCT

When the corner of the PV array is partial shaded evenly or unevenly, The TCT topology may have more MPPs than the other five configurations (at 40s), but it always presents the best performance i.e. the highest maximum power and hence the lowest relative power losses.

1000 W/m2

600 W/m2

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SS P

SP BL

HC TCT

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When the shading covers the PV array completely and concentrically, the TCT configuration outperforms all the other configurations.

1000 W/m2

600 W/m2

300 W/m2

100 W/m2

Fig.3-49 Representation of the shading condition at 50s under shading pattern B

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SP BL

HC TCT

Fig.3-50 PV output characteristics of PV array topologies at 50s under shading pattern

Tab.3-7 Parameter of PV array topologies at 50s under shading pattern C

When the shading covers the whole PV array completely and randomly, the TCT configuration outperforms all the other configurations.

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3.3.8 Global comparison of the theoretical maximum output power

A global view of the practical maximum power that can be generated by a PV array (5 × 5) arranged in SS, P, SP, BL, HC and TCT topologies under the selected seven typical shading conditions is shown in the figure below.

Fig.3-51 Global comparison on maximum output power of different PV array topologies

Although under all partial shading conditions, the parallel connected PV array shows the highest maximum output power among the all six topologies, it is not suitable for big array condition because its output voltage is too low. It can be found obviously that the TCT topology shows the best performance compared with the other topologies.

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500

Pattern D 0s Pattern D 10s Pattern D 20s Pattern D 30s Pattern D 40s Pattern D 50s Pattern B 50s

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4 Maximum Power Point Tracking (MPPT)

As discussed above, GMPP of a PV curve is given by a unique couple of current and voltage. A different operation point will lead to a lower power supplied by the PV array. In order to exploit the performance of the PV system, a control structure is required to shift the working point to the maximum value, this is the objective of MPPT.

The MPPT is typically implemented by means of a power converter. The control of the power converter varies the duty cycle to obtain and maintain the maximum power. The structure of a typical control loop for a PV array is shown in Fig.4-1.

Fig.4-1 MPPT control loop for a PV array

4.1 MPPT methods

Various methods have been developed to track the maximum power point. They differ from each other on different aspects such as the simplicity level, tracking speed, dynamic response, cost and sensors used. According to the tracking style, the MPPT methods can be classified as Fig.4-2.

P&O

MP&O

EPP

Hill climbing

Forced oscillation

Three point weight

FSCC FOCV Perturbation based RCC Current sweep Load based Temprature based Beta Cell based State space Intelligent methods Hybrid methods Fuzzy logic ANN Firefly PSO Genetic MPPT methods Newton Raphson Secant Stepest decsent Bisection Central point RFM dP/dt dP/dV Numerical methods OCC Power matching Look-up table CV Differential based Curve fitting Conduction based MRFM Parastic capacitance MINC VSINC IVSINC MPPT load based Sliding mode INC PIAINC

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In the following, there will be done a brief overview of some common MPPT techniques in PV systems, highlighting the advantages and disadvantages of their implementation.

4.1.1 Numerical methods

The members of this group operate by solving the equals extracted from equivalent circuit of PV cell via numerical algorithms. These offline methods have a good speed generally. Newton-Raphson, Secant method, linearization and central point method are fast because of their algorithms that converge rapidly. Steepest descent and regula falsi method(RFM) have medium speed but bisection is quite slow. All these methods are high precision thanks to their accurate mathematical theorems and algorithms.

4.1.1.1 Newton-Raphson method

Newton-Raphson is one of the most common iterative approaches. This method approximates the function f(x) by using of tangent to function at a point on f(x), as shown in Fig.4-3, and do this by just one initial guess [34].

Fig.4-3 Newton-Raphson method

In(x) = 𝑓′_(𝑥

𝑛) ∙ (𝑥 − 𝑥𝑛) + 𝑓(𝑥𝑛) (4-1)

x(n + 1) = x(n) − 𝑓(𝑥(𝑛))

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V(n + 1) = V(n) − 𝑓(𝑣(𝑛))

𝑓′_(𝑣(𝑛)) (4-3)

In consideration of f (v) =𝑑𝑃

𝑑𝑉, Eq.4-3 can be rewritten as:

V(n + 1) = V(n) − 𝑑𝑃 𝑑𝑉|𝑣=𝑣(𝑛) 𝑑2𝑃 𝑑𝑉2|𝑣=𝑣(𝑛) (4-4)

This will be repeated until the stop condition |𝑓(𝑥𝑛)| ≤ 𝜀 is met. Where P and V are

output power and voltage of the PV array and 𝜀 is the acceptable tolerance.

The main drawback of Newton-Raphson MPPT method and the other numerical methods is the dependence on initial guess, which causes expensive computation part and increasement of error.

4.1.2 Cell based methods

These methods operate by two important properties of PV cells, open circuit voltage (Voc) and short circuit current (Isc). The main idea of these methods is that in any condition there is just one MPP for each array or cell, so MPP can be tracked by tracking Vmpp or Impp. These methods try to present a relation between Vmpp and Voc (or between Impp and Isc). Two members of cell based methods are Fractional short circuit current (FSCC) method and Fractional open circuit voltage (FOCV) method. These two methods are so similar, they both have medium speed in tracking desired point and it can be because they need to calculate current and voltage factors before changing duty cycle of converter. If current and voltage factors are assumed constant, the speed can become a little high and also the methods will be simpler but the accuracy will decrease.

4.1.2.1 Fractional short circuit current (FSCC)method

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start

Measure Isc, Ipv

Calculate Impp

Impp–Ipv=0?

change duty cycle

No

Yes

Fig.4-4 Flow chart of FSCC method

The relation between Impp and Isc is presented as [36]:

𝐼𝑚𝑚𝑝 = 𝐾𝑖 ∙ 𝐼𝑆𝐶 (4-5)

Where K_𝑖 is current factor and is always less than one, typically between 0.85 and 0.95. K_𝑖 mainly depends on cell specifications, temperature and irradiance, so PV scanning is done for calculating K_𝑖 [37] and Isc periodically. In most time K_𝑖 can be considered as a constant parameter. After calculating Impp by Eq.4-5, current is sampled and compared with Impp to give the signal to converter to change the duty cycle. Measuring Isc during operation has a negative point and it is that during the short circuit, voltage is zero so no power will be supplied in these periods of time. Another problem is the need of additional switch to make short circuit periodically that will result in increment of cost [38].

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4.1.2.2 Fractional open circuit voltage (FOCV) method

start

Measure Voc, Vpv

Calculate Vmpp

Vmpp–Vpv=0?

change duty cycle

No

Yes

Fig.4-5 flow chart of FOCV method

As shown in Fig.4-5, the flow of FOCV method is similar to FSCC method. The relation between Vmpp and Voc is presented as [39] :

𝑉_𝑀𝑃𝑃 = 𝐾_𝑉 ∙ 𝑉_𝑂𝐶 (4-6) Where Kv is voltage factor typically between 0.73 and 0.8 and in some references it is between 0.78 and 0.92 but in general, Kv depends on cell specifications, temperature and irradiance. Kv is calculated by PV scanning and Voc is measured by disconnecting converter, and both should be done periodically. It is possible to assume Kv as a constant parameter for all conditions to make this method simpler. The value of this constant is achieved experimentally by measuring VOC and VMPP under different conditions [40]. It should be noted that assuming Kv as a constant will reduce the accuracy of method. Disconnecting converter for measurement of VOC needs for additional components also causes a big problem and that is power loss.

4.1.3 Perturbation based methods

The perturbation based methods detect MPP by applying perturbation to one or two control parameters and comparing the result with previous point. The perturbation size is so important to speed and accuracy of these methods. Big size means less measurements and calculations and also higher speed but will pull accuracy down,

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while small size means lower speed and higher accuracy. So a tradeoff between speed and accuracy is necessary for these methods. This family of MPPT methods includes perturb and observe (P&O), hill climbing, forced oscillation, estimated-perturb-perturb (E.P.P.) and three point weight methods.

4.1.3.1 Perturb and observe (P&O) method

Start Measure V(k), I(k) P(k)=V(k)*I(k) P(k)>P(k-1)? Vref(k)>Vref(k-1)? No Vref(k)=Vref(k-1)+C No Vref(k)=Vref(k-1)-C Yes Vref(k)>Vref(k-1)? Vref(k)=Vref(k-1)+C Yes Vref(k)=Vref(k-1)-C No Yes Return

Fig.4-6 flowchart of P&O method

P&O method is one of the most common method in papers and commercial systems. Fig.4-6 shows the flowchart of this method. In first stage, voltage and current of PV cell are measured and power is calculated (Pa) then a perturbation with defined size(C) is usually applied to voltage or current and new power is measured (Pb). Now Pa and Pb are compared. If Pb is greater than Pa, it means perturbation was in true direction, so another perturbation will apply in this direction and Pc will be measured and compared with Pb. If Pb is less than Pa, it means perturbation was in wrong direction so another perturbation will apply in reverse and (Pd) will be measured and compared. These steps will be repeated until MPP is achieved [41].

As it was mentioned before, there is a tradeoff between the system dynamics and the steady state oscillations. It is difficult and important to define a suitable size for

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reaching the MPP because the effect of the perturbation could be confused with fluctuations due to measurement errors and to the switching of the converter.

4.1.4 Conduction based methods

These methods are some of the fastest and most accuracy methods for tracking MPP. The fundamental concept of this group is same with differential methods and the group is divided into three main methods: incremental conduction (INC) method, parasitic capacitance method and sliding method. Fundamental concept of INC method is so similar to perturbation methods, but in this method perturbation is not artificial. This causes fast speed for tracking MPP. High accuracy and good efficiency are the other characteristics of this method. Parasitic capacitance method is a comprehensive form of INC method so the specifications of this method are similar to INC. Parasitic capacitance method has very high accuracy and good efficiency in its own list of advantage but taking account of parallel capacitance's effect causes reduction of speed and makes medium speed for this method. Sliding mode uses concept of INC method to control switching of converter. Fast speed, medium accuracy and very good efficiency are properties of this method.

4.1.4.1 incremental conduction (INC) method

INC is one of the most common methods in commercial systems because of high speed and accuracy and also good performance for the rapidly changing atmospheric variables [42].

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According to Fig.4-7, dP/dV is zero at MPP, more than zero on the left of MPP and less than zero on the right of MPP:

{ 𝑑𝑃 𝑑𝑉 < 0 on the right of MPP 𝑑𝑃 𝑑𝑉 = 0 at MPP 𝑑𝑃 𝑑𝑉 > 0 on the left of MPP (4-7)

The slope of the power curve can be written as:

𝑑𝑃 𝑑𝑉 = 𝑑(𝑉𝐼) 𝑑𝑉 = 𝐼 + 𝑉 𝑑𝐼 𝑑𝑉≅ 𝐼 + 𝑉 ∆𝐼 ∆𝑉 (4-8) By replacing 𝑑𝑃

𝑑𝑉 with Eq.4-8 in Eq.4-7, the relation can be concluded as:

{ ∆𝐼 ∆𝑉 < − 𝐼 𝑉 on the right of MPP ∆𝐼 ∆𝑉= − 𝐼 𝑉 at MPP ∆𝐼 ∆𝑉 > − 𝐼 𝑉 on the left of MPP (4-9) Where 𝐼

𝑉 is instantaneous conductance and ∆𝐼 ∆𝑉 is incremental conductance. Start Input V(t), I(t) ΔI=I(t)-I(t-Δt) ΔV=V(t)-V(t-Δt) ΔV=0? ΔI/ΔV>-I/V? No Increment Vref Yes Decrement Vref No ΔI>0? Increment Vref Yes Decrement Vref No Yes ΔI/ΔV=-I/V? No Yes ΔI=0? No Yes I(t)=I(t-Δt) V(t)=V(t-Δt)

Analysis and comparison of PV configurations and MPPT methods to maximize power under partial shading

POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell'Informazione

ANALYSIS AND COMPARISON OF PV

CONFIGURATIONS AND MPPT METHODS TO

MAXIMIZE POWER UNDER PARTIAL SHADING

Supervisor: Prof. Luigi Piegari

Master Thesis by: ZHANG WENLI

Student ID Number: 875060

Contents

Abstract

1 Introduction

2 Photovoltaic System

2.1 Photovoltaic Cell

2.2 Mathematical Modeling of PV Module

2.3 Configurations of Grid-tied Photovoltaic Systems

3 Partial shading

3.1 Bypass diode

3.2 Partial shading effect

3.3 Output characteristic of different topologies under partial

shading conditions

4 Maximum Power Point Tracking (MPPT)

4.1 MPPT methods