58 Chapter-4 Fixed and Variable Step-Size Perturb Voltage MPPT Control for Photovoltaic System 4.1 Introduction Owing to the global development toward the design and analysis development of PV systems as alternative energy sources, this effort will explore the potential of using solar energy systems in the domestic and industrial application. One of the disadvantages of PV systems is their low efficiencies compared to their cost. In order to overcome these drawbacks, maximum power should be extracted from the PV systems. Maximum power point tracking is a concurrent control scheme applied to the PV systems, to extract the maximum power from the PV module. The power delivered from the source to the load is maximized when the input resistance is matched with the source resistance. For further improvement of tracking efficiency, the fixed step-size perturb voltage (FSPV) maximum power point algorithm and Variable step-size perturb voltage (VSPV) maximum power point algorithms are proposed and explained in this chapter. These both MPPT methods are capable of attaining maximum power equal to the maximum load power. Therefore, the tracking efficiency is improved. 4.2 FSPV MPPT Method The tracking efficiency can be further improved by employing a hill-climbing MPPT technique such as the FSPV control algorithm. This simple control algorithm does not require previous knowledge of the PV system characteristics or the measurement of solar irradiance and cell temperature, and is easy to implement with analogue and digital circuits. In addition, this method operates by periodically changing the duty ratio of the boost converter and evaluating the corresponding output
59 power. When the maximum of the product, I max * V max is found, the maximum power point (MPP) has been located. 4.3 Model of FSPV MPPT Method By investigating the performance of system configuration, the maximum power operating point can always be tracked by keeping derivative of power and voltage (dp/dv) equal to zero with changing of solar irradiance and cell temperature. The power slope dp/dv can be calculated digitally by sampling the PV array voltage and current at successive time intervals (k-1) and (k) as follows. dp P( k) P( k 1) ( k) dv V ( k) V ( k 1) (4.1) V ( k) Vref V (4.2) Where V Perturb voltage P( k) V ( k). I( k) The algorithm of FSPV, the operating point of the PV array by increasing or decreasing a control parameter by a fixed amount (fixed size) and measures the PV array output power before and after the perturbation. When the power increases, the algorithm continues to perturb the system in the same direction; otherwise, the system is perturbed in the opposite direction. In this fashion, the peak power tracker continuously seeks the maximum power operating point with significance. Fig. 4.1 shows a block diagram for photovoltaic system with proposed FSPV method, in which the PV array output voltage reference is used as the
60 control parameter in conjunction with a controller to adjust the duty ratio of the MPPT power converter. Fig.4.1 Block diagram of proposed FSPV MPPT with PV System 4.4 FSPV MPPT Algorithms The principle of FSPV is to perturbation by acting decrease or increase on the duty cycle of the boost converter by using reference voltage (V ref ) and then observing the direction of change of PV output power. If at any instant k the output PV power P(k) & voltage V(k) is greater than the previous computed power P(k 1) & V(k-1), then the direction of perturbation is maintained otherwise it is reversed. The algorithm steps are as follows. Step 1 : Start Step 2 : Initialize the value of Duty cycle between 0 and 1. Step 3 : Measure the values of PV array current and voltage. Then, calculate and predict of power at k th and k th -1 instants.
61 Step 4 : Calculate the change in power (dp) and change in voltage (dv). Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 : If dp <0 & dv >0 then decrease the duty cycle. : If dp <0 & dv <0 then increase the duty cycle. : If dp >0 & dv >0 then increase the duty cycle. : If dp >0 & dv <0 then decrease the duty cycle. : Go to Step 3 and repeat the above steps until it reaches the Maximum power Point. : Stop. Fig 4.2 FSPV control action In fixed step-size perturb voltage MPPT algorithm first, it initializes the range of the duty ratio is normally between 0 and 1. Next, it measures the output voltage and current of photovoltaic array, then calculate the output power at the present instant by using measured values. By comparing with the present and previous output power and voltage, based on the difference fixed step-size perturbs value either it can be increased or decreased. Let us consider at case 1 here dp<0 and dv<0, so that perturb is increased to reach MPP and at case 2 dp<0 and dv>0 so that perturb is decreased to reach MPP. Similarly, at case 3 dp>0 and dv<0, perturb is decreased to reach MPP
62 and at case 4 dp>0 and dv>0, perturb is increased to reach MPP. This process is continued until it reach as the maximum power point (MPPs). 4.5 Flowchart of FSPV MPPT Algorithm Fig.4.3 Flowchart of FSPV Algorithm
63 Apparently, the flowchart of FSPV consists of two loops. Firstly, the MPPT control algorithm based on the calculation of the PV out coming power and power change, which is identified by resulting the present and previous values of PV voltage levels. The secondly, regulates the array voltage according to the set reference voltage. The flowchart of FSPV is shown in Figure 4.3. 4.6 Results of Proposed FSPV MPPT Control FSPV MPPT algorithm based PV system was simulated using MATLAB/Simulink. The PV system was simulated with the same operating conditions as in earlier cases. That is irradiance between 200W/m 2-1000W/m 2 and the range of temperature is 25 0 C-55 0 C. 4.6.1 Variation of Irradiance The simulation results of proposed FSPV control method has been presented in this section. From Fig 4.4, it is observed that the steady state performance of the array output voltage is significantly less (15.2V), when solar irradiance operated at 1000W/m 2 and the corresponding cell temperature is 25 o C. Fig 4.4 FSPV MPPT: Simulated waveforms of the output Voltage of PV system.
64 Fig 4.5 FSPV MPPT: Simulated waveform of the output current of PV system. Fig 4.6 FSPV MPPT: Simulated waveform of the output power of PV system. Fig.4.5 shows the output current of the PV array is achieved at steady state value of 5.292A. Likewise, Fig.4.6 shows the corresponding output power of photovoltaic array as 80.4 Watts (tracking power) out of 100 Watts (available power). Therfore, the maximum tracking effeicincy of PV system with proposed FSPV method is 80.4%.
65 (a) (b) (c) Fig 4.6 (b) FSPV MPPT: Simulated waveform of the output voltage, current and power of PV system at 200W/m2 with 25C.
66 From Fig 4.6(b), it is observed that the steady state performance of the array output voltage is significantly less (14.5V), when solar irradiance operated at 200W/m 2 and the corresponding cell temperature is 25 o C. Fig.4.7 FSPV MPPT: Simulation results of PV array current, voltage and power at sudden change of a irradiance, Fig. 4.8 FSPV MPPT: Analytical evaluation of PV array voltage at different irradiance
67 Fig. 4.9 FSPV MPPT: Analytical evaluation of PV array current at different irradiance Fig. 4.10 FSPV MPPT: Analytical evaluation of PV array power at different irradiance
68 Fig. 4.7 shows the simulation results of current, voltage, and power of the PV array for the proposed FSPV MPPT algorithms for a sudden increase in the irradiance from 400W/m 2 to 1000W/m 2. Fig 4.8 shows the analytic repersentation of output voltage with different value of solar irradiance, It is observed, when the irradiance is increased from 400W/m 2 (low) to 1000 W/m 2 (high) the coressponding output voltage of PV array is slightly incerased from 10.71V to 15.2V respectively. Similarly, when the irradiance is increased the coressponding output current and power is also incresed,and its analytic repersentation is shown in Fig 4.9 and 4.10. Fig. 4.11 shows the performance evaluation of output power with various proposed MPPT control algorithms (FVF, FCF and FSPV.) From the figure, it is clear that, the FSPV method gives more tracking power than FVF and FCF. Fig. 4.11 FSPV MPPT: Analytical evaluation of output power vs irradiance with various proposed MPPT method
69 Table 4.1 FSPV MPPT: Analytical evaluation of PV output Voltage, Current and power at different Temperature Temperature ( c) 25 Irradiance (w/m2) FSPV MPPT Technique V mp (V) I mp (I) P mp (W) 15.2 5.292 80.4 35 14.51 5.301 76.92 1000 45 13.83 5.305 73.40 55 13.15 5.311 69.89 Table 4.2 FSPV MPPT: Analytical evaluation of PV output Voltage, Current and power at different Irradiance Irradiance (w/m 2 ) Temperature ( o C) FSPV MPPT Technique V mp (V) I mp (A) P mp (W) 1000 15.2 5.292 80.4 800 15.08 4.233 63.89 600 25 14.89 3.177 47.32 400 14.07 2.115 29.75 200 10.71 1.139 12.2
70 From the tabulated results, it is observed that, the numerical evaluation of output voltage, current and power with proposed MPPT control algorithm can be obtained when the temperature is increased from 25 o C to 55 o C with a fixed irradiance at 1000W/m 2. From table 4.1, it is obvious that the maximum tracking power is 80.4 watts (extracting power) from 100 watts (available power) at temperature 25 o C and irradiance is 1000 W/m 2 (standard condition). From Table 4.2, it is observed that when the irradiance increases with fixed temperature, the photovoltaic voltage increases and the current also increases proportionality. Similarly, the photovoltaic power is increased when the irradiance is increased. 4.6.2 Investigation of Various Fixed Step-size Voltage Perturbation Fig. 4.12 shows the analytic repersentation of tracking efficiency with various fixed step-size voltage perturbations ( V) has been achieved at standard test conditions (STC). From table 4.3, it is clearly observed that when voltage perturb ( V) is increased, the oscillation around the MPPs is also increased, i.e ΔV is 5% and Corresponding-tracking efficiency is 78.28%. Fig. 4.12 FSPV MPPT: Tracking Efficiency vs voltage perturb ( V)
71 Table 4.3 FSPV MPPT: Analytical evaluation of PV array voltage, current, power and tracking efficiency with different voltage Perturbation 4.6.3 Variation of Load Fig. 4.13 FSPV MPPT: Tracking Efficiency Vs Load
72 The resulting array tracking efficiency is shown in Fig. 4.13. The estimated power follows the maximum power under very fast varying load with a very good precision. The tracking power is shown in Table 4.4. Table 4.4 FSPV MPPT: Analytical evaluation of PV array voltage, current, power and tracking efficiency at different load The main issue of FSPV method is that the I-V and P-V response is slow in case of rapidly changing atmosphere conditions (temperature and irradiance) and there are more oscillations around the MPPs can be found. To overcome this drawback, the variable step-size perturb voltage MPPT algorithm is proposed which is presented in section 4.7.
73 4.7 Variable Step-size Perturb Voltage (VSPV) MPPT Method The restriction of the FSPV algorithm of tracking under rapidly changing irradiance is attained. The proposed VSPV MPPT algorithm retains the benefit of the FSPV MPPT algorithm having fast response to track the maximum power point quickly. 4.8 Model of VSPV MPPT Method The Fig.4.14 shows that this method involves additional measurement of power. The expression of VSPV tuning method is given (4.5). Fig.4.14 Block diagram of proposed VSPV MPPT with PV System
74 The original expressions perturb and observe MPPT is dp ( k) P( k) P( k 1) (4.3) dp k) dp ( k) dp ( ) (4.4) ( 1 2 k where, dp1 ( k) Pc ( k) P( k) And dp2 ( k) P( k 1) Pc ( k) Therefore, dp( k) P ( k) P( k) P( k 1) P ( k) c c dp( k) 2Pc ( k) P( k) P( k 1) (4.5) 4.9 Variable Step-size Perturb Voltage MPPT Algorithm It is very clear to analyze the proposed MPPT algorithm, the watts-volts curve is shown in Fig.4.15. The algorithm steps are, Step 1: Start Step 2: Initialize the value of duty ratio between 0 to 1. Step 3: Measure the value of array voltage, current and power at K th, C th and (K-1) th instants.
75 Step 4: Calculate the change in power dp and change in voltage dv Step 5: If dp <0 & dv >0 then decrease the duty cycle. Step 6: If dp <0 & dv <0 then increase the duty cycle. Step 7: If dp >0 & dv >0 then increase the duty cycle. Step 8: If dp >0 & dv <0 then decrease the duty cycle. Step 9: Go to Step 3 and repeat the above steps until it reaches the Maximum power Point. Step 10: Stop. Fig.4.15 VSPV control action 4.10 Flowchart of VSPV MPPT Algorithm Fig.4.16 shows the flowchart of VSPV MPPT algorithm. A further irradiance control loop has been proposed in this improved version. If there is a sudden change in photovoltaic array output current, this is due to a sudden change in irradiance, which has caused by fast moving atmospheric condition like clouds. The
76 array current change dd necessities to be define as a system parameter. With this extra irradiance control loop, fast tracking can be achieved. However, it loses stability if operated at a high perturbation rate and voltage feedback signal. Fig.4.16 Flowchart of VSPV Algorithm
77 4.11 Results of Proposed VSPV Control Algorithm 4.11.1 Variation of Irradiance To show the usefulness of improved perturb and observe MPPT control of PV system, mathematical simulation has been carried out by using MATLAB/Simulink. (a) (b) (c) Fig 4.17. VSPV MPPT: Simulated waveforms of PV Output (a) Voltage (b) Current (c) Power at standard test conditions.
78 The model parameters and specifications of the PV module and DC-DC converter used in this thesis is given in Appendix. From Fig.4.17 it is realized that the performance of the PV output voltage (16.40V), current (5.076A) and power (83.25W) at standard test condition. (a) (b) (c) Fig 4.18. VSPV MPPT: Simulated Waveforms of PV Output (a) Voltage (b) Current (c) Power at Irradiance is 200 W/m 2 and Temperature is 25 o C.
79 Similarly, from the Fig.4.18 it is observed that the performance of output voltage, current and power of the PV system the oscillations are significantly more due to low irradiance 200W/m 2 respectively. (a) (b) (c) Fig.4.19. VSPV MPPT: Simulated Waveforms of PV Output (a) Voltage (b) Current (c) Power at Irradiance 1000 W/m 2 and Temperature at 55 o C.
80 The Fig.4.19 shows the response of PV output voltage, current and power with irradiance at 1000 W/m 2 at cell temperature of 55 o C. It is clear that, the output power of the PV system is reduced as compared to cell temperature of 25 o C. Fig.4.20 VSPV MPPT: Simulation results in array current, voltage and power at Fixed irradiance. Table 4.5 VSPV MPPT: Evaluation of PV Output Voltage, Current and Power with different Temperatures at Constant Irradiance condition
81 Fig. 4.20 shows the simulation results of current, voltage, and power of the PV array for the proposed VSPV MPPT control algorithms for a fixed irradiance is 1000W/m2. And it is observed that, power gives 83.25 Watts (tracking power) out of 100 Watts (available power). Therfore, the maximum tracking effeicincy of PV system with proposed VSPV method gives 83.25%. It can be found from Table 4.3, that the maximum output power of the PV system is 83.25 W can be obtained when the solar irradiance is 1000 W/m 2 at cell temperature of 25 o C and 71.20W at cell temperature of 55 o C. Table 4.6 VSPV MPPT: Evaluation of PV Output Voltage, Current and Power with different Irradiance at Constant Temperature condition It is clear from the Table 5.4, that the minimum output power of the PV system of 12.40 W can be obtained from the solar irradiance is 200 W/m 2 at cell temperature of 25 o C and maximum tracking power (83.25 W) can be achieved at standard test conditions.
82 Fig 4.21 shows the analytic repersentation of tracking efficiency with different solar irradiances, It is observed, when the irradiance is increased from 200W/m 2 (low) to 1000 W/m 2 (high) the coressponding extracted power of PV array is slightly incereased from 12.40 W to 83.25W respectively. Similarlly, Fig.4.22. gives the analytical evalution of output power vs irradiance with various proposed methods. From the analytical evalution, VSPV control algorithm gives significant improvement among with various MPPT control alogrithms. Fig. 4.21 With VSPV control algorithm: Tracking Efficiency Vs Irradiance From table 4.8, it is observe that the output power response of the PV system in terms of settling time it is observed that for high/low irradiance (1000/200) W/m 2 for FSVP it takes to reach steady state 0.08/0.06 sec, for VSPV MPPT control technique, convergence search due to additional loop is large. Therefore, time taken to reach steady state is significantly more, i.e. 0.15/0.25 sec respectively. From the tabulated results, it is observed that,there is siginificant improvement in output power of the PV system of proposed VSPV method is analized.
83 Fig. 4.22 With VSPV control algorithm: Analytical evaluation of output power vs irradiance with various proposed methods Table 4.7 Comparative analysis of FCF, FSPV and VSPV MPPT algorithms at different irradiance.
84 Table 4.8 Analysis of Time Response Response Irradiance (W/m 2 ) MPPT Control Methods FCF FSPV VSPV Settling Time (in sec) 1000 (High) 0.08 0.08 0.15 200 (Low) 0.1 0.06 0.25 4.11.2 Variation of Voltage perturbation ( V) Fig 4.23 shows the analytic repersentation of tracking efficiency versus perturb voltage ( V), As the pertrub voltage increases, the oscillation boundary around the MPPs is increcease and the tracking efficiency is reduced. The coresponding numerical respentation is shown in table 4.9. Fig. 4.23 With VSPV control algorithm: Analytical evaluation of Tracking efficiency (%) vs V.
85 Table 4.9 VSPV MPPT: Comparison of PV Output Voltage, Current and Power with different V. 4.11.3 Variation of Load Fig. 4.24 With VSPV control algorithm: Analytical evaluation of Tracking efficiency (%) vs Load Resistance (Ohms).
86 Table 4.10 VSPV MPPT: Comparison of PV Output Voltage, Current and Power with different Load Resistance. Fig 4.24 shows the analytic repersentation of tracking efficiency versus load resistance. From the tabulated results it is clearly observed that, the PV array gives the maximum power at about 83.25Watts which is observed in Table 4.10. 4.12 Conculsions This chapter proposes a simulation based FSPV Maximum Power Point Tracking technique designed for photovoltaic systems which experience voltage and current (power based) conditions. The strength of the proposed algorithm is demonstrated by means of Lyapunov s arithmetical approach. This method has several advantages like simplicity, ease of implementation and good performance. However, it experiences several demerits due to fixed perturb values, while the steady state oscillations are relative to the perturb value. Large perturb values cause more oscillations, smaller perturb values result in slower response. Therefore, the problem between faster response and steady-state oscillations is intrinsic. To improve the module performance further, an variable step-size perturb voltage method has been proposed in the same chapter. In this technique, the additional irradiance loop is involved in VSPV algorithm, with varying perturbation; the system has a quicker
87 response to irradiance and temperature transients. However, the problems in choosing the voltage incremental and decrement step dv and current change threshold remain unsolved. To overcome this problem, an advanced MPPT algorithm is presented in the next chapter.