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20 Oct 2019 
Viktoria 
This technique is based on the verity that the power slope of the PV is null at MPP. The proposed method is verified, and simulated. The simulation showed that the response of the proposed algorithm only needs 22% of the time taken by the conventional incremental conductance algorithm to track the maximum power point (MPP) during solar irradiation variation. In addition, the proposed technique shows a negligent oscillation in the power generated after tracking the maximum power point (MPP).
The rapid depletion of global fossil fuel resources has necessitated urgent research for renewable energy sources. Among the many alternatives, photovoltaic has been considered promising to meet the growing demand for energy. The photovoltaic power source is inexhaustible, the conversion process is pollution-free, and its availability is free [1], [2]. However, the power generated by the PV system is unstable and highly dependent on solar irradiation.
This is why the MPPT controller, which follows the maximum power point, is used to ensure that the PV system always has a high efficiency despite the variation of the solar irradiation [3].
To increase the efficiency of the PV system, several MPPT algorithms have been used. Among them are fractional short-circuit current, fractional open circuit voltage, fuzzy logic, neural network, hill climbing or perturbation and observation (P&O), and incremental conductance [4] – [13]. The most popular one is the incremental conductance algorithm. It is broadly used in the commercial product of PV systems for extracting the MPP because of its simplicity, ease of implementation, and low cost.
The basic flowchart of the incremental conductance algorithm is presented in Fig. 1. In this technique, if the operating power point is on the left side of the MPP, the algorithm must move it to the right to be nearer to the MPP, and vice versa if it is on the opposite side (on the right side).
However, the major problems of the incremental conductance method are the poor tracking of the MPP under fast changing irradiance
This technique proposed a changing the direction of the perturbation of the duty cycle in case of sudden varying atmospheric conditions. An improved INC algorithm has been reported in Ref. 16. This method checks if both voltage and current are increased; in this case, the duty cycle is increased instead of decreased as made by the conventional algorithm. Hence, the INC algorithm is modified to avoid the wrong decision made by the conventional algorithm. A variable step size INC algorithm has been reported in Ref. 17, in this method a variable step size algorithm which is based on the incremental conductance algorithm is proposed to regulate the step size using the slope of power voltage curves of PV system and also to modify step size correspond to sun irradiation levels. Reference 18 suggested a modified incremental conductance MPPT algorithm based on a fuzzy duty cycle change estimator.
To avoid the inefficiency of the conventional IC algorithm, a new IC controller based on a fuzzy duty cycle change estimator with direct control is developed. The new duty cycle is estimated using a fuzzy logic estimator (FLE). FIG. 1. Flowchart of the incremental conductance algorithm. FIG. 2. Proposed PV system with MPPT technique. In this article the proposed algorithm does not require an additional control loop. The proposed system is based on a dc-dc converter that is placed between the PV module and the load. The structure of the proposed system is shown in Fig. 2.
To detect the variation of the level of solar radiation, this algorithm controls the direction of the variation of the current (dI) and voltage (dV). A common decrease the current and the voltage means a decrease in solar radiation. On the other hand, a common increase means an increase in solar radiation. The proposed technique makes it possible to calculate a value of the cyclic ratio of the DC-DC converter very close to that of the new maximum power point (MPP), using the developed equations. A few more steps of conventional incremental conductance algorithm are used to track the new MPP. To minimize the oscillation of the power, a small error is accepted for (dP). The simulation results show the effectiveness of the proposed algorithm in terms of convergence speed or oscillation.
MODELING OF PV SYSTEM
Modeling of a photovoltaic cell The model of photovoltaic cell is shown in Fig. 3, the resistive properties of the cell are presented by a series resistance R_s and leak currents are presented by a parallel resistance R_p [2]. FIG. 3. Model of PV cell The equation which links the current supplied by a module composed of N_s PV cells and the voltage at its terminals is given by equation (1) [3]. Where: I_s is saturation current, q the electron charge, n the diode ideality factor, k the Boltzmann constant, T_c junction temperature. The parallel resistance R_p is normally very large and can be considered as an open circuit. The expression exp((q.(V+I.R_s.N_s))/(n.k.T_c.N_s ))≫1 , so the equation current-voltage of the module can be rewritten as: The reverse saturation current Is is shown as follows: The photo-current Iph is the current value generated where V = 0, I_ph≈I_cc. So (1) can be simplified as follows: Where V_th=n.k.T_c/q
Modeling of DC-DC Converter The DC-DC converter used is a boost Converter. His model is shown in Fig. 4. The MOSFET switch is controlled by a signal of period T and duty cycle D [5]. The relationships of the voltage and current of the dc–dc converter between the input and output sides are shown in (5) and (6). These equations are specifically required for boost Converter which operates in continuous-conduction mode and may be different for other types of converter. FIG. 4. Boost converter. Equation (7) is obtained by dividing (5) by (6): Where V_i the voltage of the photovoltaic generator is, I_i is the current of the photovoltaic generator. R_i is the resistance seen by the PV generator, and R_o is the load resistance.
PROPOSED ALGORITHM
The proposed algorithm adopts the basis of the incremental conductance method: the power slope of PV is null at MPP (dP/dV=0 ). This equality means that (dI/dV=-I_mpp/V_mpp ). With compensation of the formula of current I_pv as a function of voltage V_pv in the derivative ( dI/dV), a relationship between I_mpp and V_mpp is found. From this relation, the value of the resistance seen by the PV module or the input resistance of the converter R_in can be calculated. The calculation of the input resistance of the converter makes it possible to calculate an approximate value of Duty cycle of the converter very close to that of point MPP. This algorithm only needs the current and voltage values to do the calculation that converges quickly to the MPP point.
The power slope of the PV is null at MPP. This rule can be presented by (8) Equation (8) is rearranged to obtain (9) By deriving the equation (4) we obtain the equation (10) Equation ( 4) can be rewritten as follows; The equations (10) and (11) used to obtain Equation (12) At the maximum power point (MPP) The equation(12) can be rewritten as follows: Equation (13) is then simplified to obtain (14) as follows: (14) is multiplied by and simplified to obtain (15), where R_inis the input resistance of the converter or the resistance seen by the PV module. The calculation of parameter of equation (15) : In (7), R_in is substituted by V_pv/I_pv. The load resistance can be calculated as follows: The value of N_s.R_s can be calculated using (4) by substituting the voltage, and current at the maximum power point (MPP). (17) can be rewritten as: The short circuit current is always approximately 〖1.1*I〗_mpp and the approximated open circuit voltage is obtained from 1.25〖*V〗_mpp. The expression of N_s.R_s is substituted into (14) to obtain equation (19) the approximated value of N_s.V_th is calculated as follows:
To ensure the PV module operates near to the new MPP R_in can be calculated as follows: Where: As shown in Fig.5 (a) In case of an increase in solar irradiation, the new short circuit current is approximately as follows: In case of a decrease in solar irradiation as shown in Fig.5 (b), the new short circuit current is approximately as follows: (a) (b) FIG. 5. Load lines on I–V curves for solar irradiation level of 0.5and 1.0 kW/m2 during (a) increase of solar irradiation and (b) decrease of solar irradiation. FIG.6. the different steps of the proposed algorithm.
Accepted the values of R_in who to chek (11), that is to say 0≤ R_in≤R_out The value of R_in is substituted in (11) to calculate the duty cycle D as follows: Figure. 6 shows the different steps of the proposed algorithm. A permitted error of 0.03 as shown in (25), is used in the proposed algorithm to eliminate the steady-state oscillation in the system after the MPP is reached. After any variation of the solar irradiation , (24) is used to calculate the new duty cycle. Until the difference in power (dP) is smaller than 0.03.
SIMULATION RESULTS
To test the effectiveness of the proposed algorithm, it is verified by numerical simulation and compared with other MPPT algorithms. The chosen photovoltaic generator is a module of (PB solar BP sx120) of 120wp. Its current-voltage and power-voltage curves are shown in Figs. 7(a) and 7(b). Table I shows the parameters of the PV module under standard conditions (STC) and the values of the converter elements. The sampling time by the algorithms MPPT, is 1ms. The temperature is taken 25 ° C.
The variation of solar irradiation applied to the MPPT algorithms, is given in Fig. 8. The dynamic responses for the current, voltage and power outputs of the PV generator for the various simulated algorithms are shown in Figs. 9 and 10. (a) (b) FIG.7. Current-voltage (a) and power-voltage (b) characteristics of the PV array for different irradiance levels. TABLE I. Parameters of the PV modules and the boost converter. PV array Values (STC) Open circuit voltage (V_oc) Optimum operating voltage (V_mpp) Short circuit current (I_sc) Optimum operating current (I_mpp) Maximum power (P_mpp) Temperature coefficient of (V_oc) Temperature coefficient of (I_sc) 42.1 V 33.7 V 3.87 A 3.56 A 120 W -0.16 V/°C 0.065 %/°C Boost converter Nominal values Inductance(L) Capacitance (C_in) Capacitance (C_out) Load resistive (R) 7.5 mH 330 μF 200 μF 50 Ω FIG. 8. Solar irradiance profile .
Solar irradiation takes the level of 500w / m2 at the beginning. Then, the algorithms tracked the MPP and the proposed MPPT shows a better performance in terms of power fluctuation with a power oscillation less than at 0.116w(57.06-57.176w).When the modified incremental conductance algorithm[S&M] finds the MPP with power oscillation(54.3 -55.16w). For the conventional incremental conductance the PV power is fluctuating around MPP (56.26 -57.19w). Then solar irradiation increases rapidly from 500w / m2 to 1000w / m2 at t=0.5s, among the simulated techniques, the proposed method presents a better performance in terms of the speed of the achievement of MPP and oscillation, as shown in Figs. 10 (a) and 10(c).
When the proposed algorithm takes only 0.017s to reach the MPP with fluctuation of the steady-state PV power less than 0.36w (119.632-119.987w). Whilst for the modified incremental conductance algorithm [Soon and Mekhilef] it takes 0.045 s (more two times than the proposed MPPT) to follow the MPP with a oscillation power equal to 0.833w(119.097-119.93w). For the conventional incremental conductance algorithm, it takes 0.16 s to follow the MPP with a significant power swing 1.7w(118.378 -119.99w). Finally, a sudden decrease in solar irradiance at t=1s, from 1000 W / m2 to 400 W / m2. Therefore, the proposed method works better than the modified incremental conductance algorithm[S&M] and the conventional incremental conductance algorithm, with neglected steady state PV power oscillation, and the MPP is directly achieved despite the sudden change in the level of irradiance presented in Fig. 10 (b).
The average time to monitor the proposed algorithm during a sudden change in irradiance is 0.0095 s, but with the classical incremental conductance algorithm, it takes 0.245s and the modified incremental conductance requires 0.012 s.
A comparison table presenting the main values obtained in simulation for different MPPT is presented in Table II.
PV voltage and current behaviors during variation in irradiance level. (a) and (b) Conventional incremental conductance, (c) and (d)Modified INC CON,and (e) and (f) proposed algorithm. FIG. 10. PV output power waveforms for different MPPT algorithms. (a) (b) (c) FIG. 11. Zoom of Fig. 10. (a) (b) FIG. 11. Zoom of Fig. 10. TABLE II. Summary of simulation results.
Technique Step change in irradiance 500 1000 W/m2 Step change in irradiance 1000 400 W/m2 Tracking speed time (s) Power oscillation (W) Tracking speed time (s) Power oscillation (W) conventional 0.16 1.612 0.245 0.639 modified IC[S.M] 0.045 0.833 0.012 0.08 Proposed MPPT 0.017 0.354 0.0095 0.08
This paper presents design and simulation of a MPPT control for the PV stand-alone system by using advanced control strategy. The proposed technique has been successfully simulated. Simulation results proved that the proposed algorithm has enhanced the PV system performance compared to the modified incremental conductance algorithm [Soon and Mekhilef] and the incremental conductance algorithm.
The results show that the proposed algorithm detects the fast increase and decrease of irradiation and makes a accurate decision compared to the others techniques. Moreover, by using the proposed technique, steady-state oscillations are almost neglected. As a conclusion, a fast converging and low losses MPPT algorithm is proposed and verified in this paper.