DC-DC Boost Converter Design for Fast and Accurate MPPT Algorithms in Stand-Alone Photovoltaic System

Received May 3, 2018 Revised Jul 12, 2018 Accepted Jul 22, 2018 The main components of a Stand-Alone Photovoltaic (SAPV) system consists of PV array, DC-DC converter, load and the maximum power point tracking (MPPT) control algorithm. MPPT algorithm was used for extracting maximum available power from PV module under a particular environmental condition by controlling the duty ratio of DC-DC converter. Based on maximum power transfer theorem, by changing the duty cycle, the load resistance as seen by the source is varied and matched with the internal resistance of PV module at maximum power point (MPP) so as to transfer the maximum power. Under sudden changes in solar irradiance, the selection of MPPT algorithm’s sampling time (TS_MPPT) is very much depends on two main components of the converter circuit namely; inductor and capacitor. As the value of these components increases, the settling time of the transient response for PV voltage and current will also increase linearly. Consequently, TS_MPPT needs to be increased for accurate MPPT and therefore reduce the tracking speed. This work presents a design considerations of DC-DC Boost Converter used in SAPV system for fast and accurate MPPT algorithm. The conventional Hill Climbing (HC) algorithm has been applied to track the MPP when subjected to sudden changes in solar irradiance. By selecting the optimum value of the converter circuit components, a fast and accurate MPPT especially during sudden changes in irradiance has been realized. Keyword:


INTRODUCTION
In recent years, due to the energy crisis and environment pollution, the direct solar electricity generation using PV system become more significant. The market for solar PV system has grown rapidly over the past decade, as local governments offered various incentives to expand the solar market as well as the declining PV cost. Generally, PV system can be classified into three major categories: Stand-Alone (SA), Grid-Connected (GC) and Hybrid (H) PV system. Stand-Alone PV system are designed to operate independent of the electric utility grid, and are generally designed and sized to supply certain DC and/or AC electrical loads. In the grid-connected PV system, electricity produced from PV array are either used directly, or fed into a large electricity grid. A hybrid PV system is essentially a system that employs at least one more source, other than the PV such as wind turbines or diesel generators, to meet the electrical power demand of the loads [1]. In this work, only Stand-Alone PV system that can be utilized for any heating, cooking and water pumping applications is considered [2,3]. In order to reduce the costs and environmental issues, the battery is not applied in these applications. One major problem with any PV system is that, the amount of electric power generated is constantly changing with weather conditions, especially solar irradiance. If the solar irradiance changes, the operating point of the PV array will shift away from its maximum power point (MPP). To overcome this problem, a Maximum Power Point Tracking (MPPT) algorithms incorporating with DC-DC converter is implemented which has led to the increase in the operation efficiency of the PV array. For SAPV system with fixed load resistance (without battery), maximum power is delivered to the load when input resistance (Rin) of the converter matches with the internal resistance of PV array at (RMPP) based on Maximum Power Transfer Theorem. To do so, MPPT regulates the input voltage of the PV array at MPP by adjusting the duty cycle (D) of the converter.
The most popular MPPT algorithms in practice are perturb and observe (P&O), hill climbing (HC), and the incremental conductance method (INC). These conventional algorithms are widely applied due to their simplicity, ease of implementation and low cost [4]. The other conventional MPPT algorithms used in PV system are presented in [5][6][7][8][9][10][11][12]. In literature [13][14][15][16][17], many new improved performance of MPPT algorithms have been proposed. However, the components sizing of the different topologies of DC-DC converters have not been studied widely although this sizing affects significantly the optimum operation of the MPPT algorithms. For example, the poorly selection of the converter component sizing, especially capacitor and inductor according to the load could make MPPT operate less optimally. Under sudden step changes in irradiance, the selection of the MPPT sampling time (TS_MPPT) must consider the transient response of the MPPT inputs such as PV's voltage and current, in order to avoid the delay and failure in tracking of maximum power. The three most commonly used DC-DC converters in PV system are: buck, boost and buck-boost converters. The circuit parameters and mode of operation of each topology have been discussed in [18,19]. Boost converter has some advantages over the other converters as it is more stable and efficient [20], and hence chosen in this work.
This work focuses on the sizing effect of two DC-DC boost converter components i.e capacitor and inductor, on transient response and speed of the MPPT algorithm. Furthermore, hill climbing (HC) MPPT algorithm has been chosen to track the MPP during suddenly changing solar irradiance. Only DC-DC boost converter used in Stand-Alone PV system with fixed load resistor is considered here.

MPPT FOR STAND-ALONE PV SYSTEM WITH LOAD RESISTANCE
In SAPV system, the battery is crucial for power flow management if the load demands a constant voltage. However, in some applications like heating, cooking and water pumping system where the change in the load voltage will not affect the reliability of the system, the battery is not needed. In those applications, the battery is not applied to reduce cost, frequent maintenance and environmental issues caused by battery usages [2,3]. The main objective of the system is to obtain power from the PV array as much as possible without having to regulate the output voltage and current. As per maximum power transfer theorem, maximum power is transferred to the load when equivalent load resistance referred to the input terminals of the converter (Rin) is match to the internal resistance of PV array at MPP (RMPP). Figure 1 shows such a system.

PV cell modeling
In this work, the simulations model of PV system is based on MATLAB/Simulink simulator developed in [21,22], which utilized a two-diode PV cell model as depicted in Figure 2. It is chosen due to its superior accuracy, particularly at low irradiance level [21]. A number of series-parallel connected PV modules are used to form a PV array for a desired voltage and current level. For a string with N number of modules in series (Ncell), the output current of the cell is given by: where Io1 and Io2 are the reverse saturation currents of diode 1 (D1) and diode 2 (D2), respectively; VT1 and VT2 are the thermal voltages of respective diodes; a1 and a2 represent the diode ideality constants. In this work, 5 PV modules are connected in a single series string and provides about 299.3W as nominal maximum output power under solar irradiance of 1000W/m 2 at standard test condition (STC), as shown in Figure 3. The PV module is simulated using BP MSX-60 model and its specifications at STC are tabulated in Table 1.
In a normal condition, i.e. when the solar irradiance on the entire PV array is uniform, the powervoltage (P-V) and current-voltage (I-V) curves exhibits a single global MPP as depicted in Figure 4. To simulate the fast changing solar irradiance, two different levels of irradiance were selected, 1) highest (Point A, G=1000W/m 2 ) and lowest (Point B, G= 300W/m 2 ). The characteristics variation of P-V, I-V and optimal internal resistance curves of this PV array for these two irradiance levels are shown in Figure 4. It can be  (2) It is not practical to change the load resistance manually at any moment the solar irradiance changes [23]. Therefore, MPPT algorithm has been designed to continuously adjusts the duty cycle of the converter, in order to match the input resistance to the internal resistance of PV array at MPP (Rin=RMPP), and hence extracts maximum available power. At MPP, the duty cycle of the converter is calculated as [3]; By assuming a lossless converter (PPV=Pout), the output voltage (Vout) of the converter at MPP is determined as;

Hill climbing (HC) MPPT algorithm
The goal of employing MPPT is to extract maximum power from PV Array at any varying atmospheric conditions especially solar irradiance changes. To do so, MPPT algorithm perturbs the duty cycle of the DC-DC converter to match the resistance of load as seen by the source (Rin) to the internal optimal resistance of PV Array (RMPP). In this work, the conventional Hill Climbing algorithm as discussed in [4,[24][25][26][27][28] has been applied to track the MPP when subjected to sudden changes in solar irradiance. HC algorithm offers number of advantages: 1) it simplifies the tracking structure, 2) it reduces the computation time, and 3) no tuning effort is needed for the PI gains [28]. Practically, it can replace the expensive MPPT controller with lower cost controller while maintaining similar optimum results.
In HC, at each iteration i, the algorithm starts sensing the voltage, V(i) and current, I(i) of PV array and the corresponding power, P(i)= V(i)×I(i) is then calculated. Next, the duty cycle (D) of the converter is perturbed by an increment of duty cycle step size (Dstep), and the resulting change of power, P = P(i+1) - 1042 P(i) is obtained. If the P is positive, then perturbation is in the right direction, and more perturbation is applied in the same direction to reach the MPP. The perturbation direction is reversed if P is negative, an indication that the tracking is moved away from the MPP. The flowchart of the HC algorithm is shown in Figure 5.
When solar irradiance changes, the tracking speed to reach new MPP using conventional HC algorithm depends mainly on two variables, 1) the duty cycle step size (Dstep), and 2) the MPPT sampling time (TS_MPPT) which is the time given to the MPPT to read all the inputs and solve all the calculations involved in the algorithm at each applied duty cycle (D). Large Dstep will increase the MPP tracking speed but the power losses also increases due to the large oscillation around MPP. Small Dstep will reduce power losses oscillation around MPP but the tracking speed will be low. Hence, the trade-off have to be made to increase the overall MPPT efficiency. In this study, Dstep is set at 10% during exploration process and is set at 0.5% during exploitation process. Meanwhile, large TS_MPPT will reduce the MPP tracking speed and vice versa.
Due to the step change in irradiance, PV voltage and current will undergo a transient response before shortly recovering to its new steady-state condition [17,28,29] . The settling time (TSettling) of voltage and current depends muchly on the circuit components i.e capacitor and inductor, which will be discussed further in the next section. For accurate MPPT, TS_MPPT must be designed to be greater than TSettling and all readings and calculations involved in algorithm must be completed within this specified period. Otherwise, the algorithm might fail to perform in the required manner.

DESIGN OF DC-DC BOOST CONVERTER
For Stand-Alone PV systems [30], a DC-DC boost converter is interfaced between the PV array and the load resistance as shown in Figure 1. The maximum power generated from the PV array at standard test condition (STC) is about 299.3W. The specifications of the PV module (BP-MSX60) are given in Table 1. In DC-DC boost converter, five components needs to be chosen namely, switching device, diode, inductor, capacitor and resistor. In the simulation, a standard power diode and the switching device of Power-MOSFET are chosen since there are widely used for low to medium power applications. The switching frequency is set at 20 kHz after a trade-off between the switching losses and size of inductor. Selection of other components is done as the following.

Selection of the resistor
The relationship between load resistance (RL) of boost converter and optimal internal resistance of PV array at MPP (RMPP) can be expressed as [3]; Where, Dmpp is the converter duty cycle at maximum power point (MPP). In order to track the maximum power, the load resistance of boost converter must be greater than or equal to optimal internal resistance of PV Array at MPP (RL ≥ RMPP), since the range of duty ratio (D) is between 0 to 1. The tracking of maximum power will fails if the above condition is not met [3]. In this work, the value of load resistance is chosen as RL=200Ω, which is greater than the internal resistance of PV array at MPP for lowest irradiance (300W/m 2 ) and temperature of 25°C (STC) as in Table 2. It is a real resistance measurement for 300W rated load bank available at the lab for future hardware execution. This load bank acts as a dumping place for 299.3W power generated from PV array used in this work.

Selection of the inductor
Boost inductor value is selected based on the maximum allowable current ripple which occurs at the MPP under highest solar irradiance (1000W/m 2 ). The higher the inductor value, the lower is the ripple output current and vice versa. To realize a low cost converter, the lower inductor value is preferred, because inductor is the most expensive component compared to the others. In this work, the switching frequency (s) is set at 20 kHz and the permitted amount of ripple current (I) is selected as 40% of the input current [31]. Hence, the minimum value of inductor is determined as [19,29]; Here, a commercially available of 1mH, 5mH and 10mH inductors are chosen for MPPT's transient response study. For example, 1mH boost converter choke (10A, 20 kHz) is available from SMP (www.smp.de).

Selection of the capacitor
In this study, the input and output filter capacitor (Cin & Cout) are chosen to meet the voltage ripple requirement of 0.2%. An approximate expression for the required capacitance is given as [19,29]; To study the effect of the capacitor value on the transient response of MPPT for step change in irradiance, three (3) practical capacitor values available to support the voltage of 250V are selected i.e., 47 μF, 100 μF and 220 μF. Using all the equations above, sets of data used in this work are calculated and tabulated in Table 2. PV array data under highest and lowest solar irradiance at the temperature of 25 0 C (STC) are generated from the MATLAB/Simulink PV simulator model as proposed in [21,22].

SIMULATION RESULTS
The simulation model of the Stand-Alone PV system with MPPT algorithm is carried out in MATLAB/Simulink (2016a) environment as in Figure 6. The PV array model is based on the simulator developed by [21,22] and took place on 2.7GHz, 8GB RAM, Intel Core i7 laptop machine. The electrical parameters at standard test conditions (STC) of PV solar module are taken from BP MSX-60 model as tabulated in Table 1. HC algorithm has been coded in MATLAB's programming language and stored as subroutine (M-file). The simulation is carried out for 3 seconds using the solver of ode23t  (1mH  5mH  10mH). For both cases, sudden decrease in the irradiance is simulated from 1000W/m 2 to 300W/m 2 . Meanwhile, sudden increase is simulated from 300W/m 2 to 1000W/m 2 . Figure 6. Simulation model of SAPV system with MPPT Figure 7 (a) shows the tracking of duty cycle, voltage, current, and power of the PV array using the conventional HC algorithm for a sudden decrease in the irradiance. Initially, the PV array is simulated at irradiance of 1000W/m 2 . Hence, HC algorithm start the exploration process (Dstep=10%) to search the MPP at point A (D=0.64, V=85.7V, I= 3.49A, P= 299.3W). When it enters the zone of MPP A, exploitation process (Dstep=0.5%) is activated to reach the true MPP and oscillates around it as shown at 1s-2s interval in Figure 7 (a). At 2s instant, the irradiance is suddenly decreased from 1000W/m 2 to 300W/m 2 . Therefore, HC starts exploring the new MPP B by reducing the duty cycle from 0.64(MPP A) to 0.54 to 0.44 and to 0.34 (MPP B). As the duty cycle decreases, the PV power will increase from 30W to 46.8W to 66.3W and to 82.3W. Once it enters the zone of MPP B, the exploitation process is used to reach true MPP which is 82.5W. In this case, the MPPT tracking speed is 800ms (TS_MPPT × 4 steps).

Case 1 (L=1mH, C=47F 100F 220F)
The tracking speed can be improved by reducing TS_MPPT but it depends on the transient response of the PV voltage and current. To observe the details of transient response due to the sudden decrease in irradiance, the voltage and current waveforms are zoomed in the interval of 2s-2.2s as shown in Figure 7(b). During this interval, the duty cycle of the converter is still operated at 0.64. As seen, both voltage and current are decreased due to the decrease in irradiance. Voltage drops almost exponentially from 87.5V and after a while it stabilizes at 27.2V. Meanwhile, current undershoot from 3.49A to 0.94A before rising exponentially and stabilizes at 1.11A. By using measurement tools provided in Matlab/Simulink Scope, the settling time (Tsettling) and percentage of undershoot (US)/overshoot (OS) are calculated as tabulated in Table 3. When the capacitor values increase, Tsettling also increases almost linearly from 100ms (47F) to 190ms (100F) and to >200ms (220F). If 47F capacitor is chosen for the converter, the selectable optimum value of TS_MPPT is 100ms and the MPPT tracking speed will be 400ms (TS_MPPT × 4 steps). However, for 220F capacitor the TS_MPPT must be increased to >200ms in order to realize an accurate MPPT and hence decreases the MPPT tracking speed. Otherwise, the MPPT algorithm will measure the wrong values of voltage and current in which will leading to incorrect MPP detection. As for undershoot problem, all three capacitors exhibits the same condition, i.e almost 0% voltage undershoot and 15% of current undershoot. Next, the MPPT transient response under sudden increase in irradiance is investigated as in Figure 8(a-b).
The PV array is simulated at irradiance, G=300W/m 2 at the beginning of the simulation. At steadystate condition, MPPT is oscillates around MPP at point B (D=0.34, V=83.6V, I= 0.99A, P= 82.5W). At 2s instant, the irradiance is suddenly increased to 1000W/m 2 . HC algorithm start searching the new MPP A by increasing the duty cycle from 0.34 to 0.64 with 0.1(10%) increment per step. Time taken to reach the zone of MPP A is 800ms (4 steps including initialise step). Figure 8 (

Case 2 (C=47F, L=1mH  5mH  10mH)
In this case, the capacitor is fixed to its optimum value of 47F. At 2s instant, solar irradiance is suddenly decreased/increased. The transient response of MPPT is observed by increasing the inductance value from 1mH to 5mH and to 10mH. Figure 9 (a-b) shows the MPP tracking results for sudden decreases in irradiance from 1000W/m 2 to 300W/m 2 . As the inductance increase, the settling time of the waveforms will also increase. Tsettling for 1mH inductor is 100ms, while Tsettling for both 5mH and 10mH inductors exceeds the  Figure 10 (a-b) shows the MPP tracking results for sudden increases in irradiance from 300W/m 2 to 1000W/m 2 . Tsettling for 1mH inductor is 5ms, Tsettling for 5mH inductor is 20ms and Tsettling for 10mH inductor is 37ms. Voltage overshoot is between 0 to 2 %. Biggest current overshoot occurs under sudden increase in irradiance, reaching a peak of 195% from its steady state value. The overall results for both Case 1 and Case 2 are tabulated in Table 3

CONCLUSION
The effects of capacitance and inductance of DC-DC boost converter towards MPPT transient response has been demonstrated in this work. The converter is designed for 299.3W Stand-Alone PV systems connected to fixed 200 load resistor. As the value of capacitor and inductor increases, the settling time (Tsettling) of voltage and current waveforms will also increase and vice versa. In order to improve the tracking speed and the accuracy of the MPPT under suddenly (step) changes in irradiance, the value of capacitor and inductor must be selected as low as possible while maintaining the permissible ripple limit. TS_MPPT must be equal to or greater than the maximum Tsettling of the circuit. Otherwise, the wrong MPP might be tracked. In this work, the optimum value of capacitor and inductor are chosen as 47µF and 1mH respectively. The optimum value of TS_MPPT is found to be 100ms. Due to the sudden changes in irradiance, MPPT takes 400ms to reach the new MPP zone. Meanwhile, the biggest current overshoot occurs during suddenly increase in irradiance from 300W/m 2 to 1000W/m 2 i.e 195%. Although, overshoot/undershoot does not directly affects the tracking speed, but it may increase the noise margin and damage the internal FET of the gate IC. By selecting optimum circuit parameter values, a fast and accurate MPPT especially during sudden changes in irradiance is realized.