Photovoltaic system optimization by new maximum power point tracking (MPPT) models based on analog components under harsh condition

PV module

The test will be carried out on the PV module Solbian 52; the main parameters are reported in Table 1.

Real I-V curve

Practically, the real PV parameters always varied, not exactly the same as the manufactured data. Hence, the real PV parameters are simulated by Powersim to show corresponding current-voltage (I-V) and power and voltage (P-V) curves, as Figure 1.

Figure 1:

MPP of PV module.

DC/DC step-up converter

A DC/DC converter is calculated for PV module Solbian 52L like Table 2 to investigate the operation of the MPPT controller.

Digital MPPT

The (P&O) method measures the PV’s terminal voltage and output current, then the actual power can be calculated. The DC-DC converter varies the duty cycle until the MPP is accomplished. The P&O operates the DC-DC converter with the initial set duty cycle and then starts increasing the duty cycle with a specific step width. The power is observed with the addition of each step. When a certain point the power gets less than its previous values, which means that the duty cycle should get one step in the opposite direction.

The SimCoupler Module is an add-on option to the PSIM software. It provides an interface between PSIM and Matlab/Simulink for co-simulation, as shown in Figure 2. With the SimCoupler Module, part of a system can be implemented and simulated in PSIM and the rest of Simulink’s system. One can, therefore, make full use of PSIM’s capability in power simulation and Matlab/Simulink’s capability in control simulation in a complementary way (Powersim 2018).

Figure 2:

Digital MPPT simulation model.

Here, the PV module and DC/DC converter designed by Powersim then sent the voltage and current value to the Matlab Simulink. The P&O code is implemented to the MPPT controller in Matlab function like described in (Femia 2013).

The right value of the Perturbation period of the duty cycle (Tp) will ensure a stable three-point behavior. Tp’s too-small value can confuse the P&O algorithm, and the operating point can become unstable, entering disordered or chaotic behavior. On the contrary, a too high value of Tp penalizes the MPPT speed.

The settling time Tε ensuring that small-signal variations around the steady-state values of power are confined within a band of relative amplitude +/−ε.

To avoid the transient oscillation of the PV system caused by its action

While:

where ζ: the damping factor, ωn: the natural frequency, ε = 0.1 is chosen according to the classical control system theory, R_mpp is the maximum power point resistance (Ω) based on battery resistance, R_cin and R_L are Equivalent series resistance of Cin and L respectively (see Figure 3).

Figure 3:

Duty cycle generation.

The maximum power point (MPP) is tracked around three points of peak curve as shown in Figure 4, depending on duty cycle generation.

Figure 4:

MPPT behavior by traditional P&O.

Analog MPPT

As we mentioned above, an analog method with optimized MPPT efficiency is essential to design for many hard circumstances having an unpredictable variation of irradiation from low to high, especially space. For that reason, the hybrid between the traditional algorithm P&O and the analog structure were researched with the advanced features: high competences, optimized efficiency and still maintains the simplicity. At any instant of time, the goal of MPPT is to trace a voltage level such that maximum power is obtained. The power increases in raising the voltage. Thus the next perturbation would be further increased in voltage level. At point two, the power decreases in reducing the voltage level. Therefore, the next perturbation will be an increment in voltage level. In the case voltage rises up, the power will decrease, so the next perturbation would be reduced in voltage level. At point four, if the voltage drops, the power increases. Thus, the next perturbation would be further reducing voltage till V_MPP is reached. The summary of the algorithm P&O shown as below in Table 3:

This truth table is obtained by considering any increase denoted by a high or ‘1’ and decrement is shown by low or ‘0’. Thus, the truth table is demonstrated as Table 4

From the truth table, we can infer that this MPPT based on the P&O algorithm works on simple XNOR logic. The two inputs are the same, only when the output is high. The power and panel voltage signals are sent to differentiators, which detect the power and panel voltage trend. The signals after differentiators are dP/dt and dVpv/dt. The current and voltage derivatives are fed into hysteretic comparators to get sign (dP/dt) and sign (dVin/dt). The sign signals are the inputs to an XNOR gate to determine if the two signs are in phase or out of phase.

The XNOR gate’s output, as the earlier method, is the input to a Sample and Hold (S&H) block. The S&H with fast acquisition time reduces the length of the sampling interval and the power annulment period. The S&H also has a low drop rate to avoid the deviation of the PV operating point from the MPP during the sampling period (Ishaque and Salam 2014).

An integrator is placed following the output of the S&H block to generate the voltage signal Vref then a capacitor is used to minimize the oscillation of voltage. Finally, Vref is compared to a 200 kHz sawtooth waveform to produce the PWM waveforms for the DC/DC boost converter operation. To distinguish with digital MPPT, the Ipv and Vpv will be noted as Isys and Vsys on the scheme as Figure 5.

Figure 5:

Analog P&O MPPT.

For this analog MPPT, the S&H has the main role in the controller structure which gets the XNOR signal as its input then generates the output signal based on S&H clock. It is clever to observe on Figure 6 that the rising edge of S&H clock activates the sample mode and the falling edge activates the hold mode. Like that, the XNOR signal sampled and held through the S&H function.

Figure 6:

S&H working mode.

After that proceed, S&H output fed into the integrator to generate the reference voltage, compared with the sawtooth signal. As a demonstration of Figure 7:

1. When Vref > Vsawtooth → PWM generates on mode.

2. When Vref > Vsawtooth → PWM generates off mode.

Figure 7:

PWM controller behavior.

With this operating principle, the MPPT controller regulates the switching device to detect the PV maximum power.

Different from the digital P&O method, the analog MPPT directly tracks the optimized point of PV power with only a small variation instead of moving around three points, as demonstrated in Figure 8.

Figure 8:

Tracking mechanism on PV curve.

Design of practical components for MPPT system

1. Design of R-C circuit

S&H Clock: D = 0.5, f_SH = 500 Hz, t_SH = 0.002 s, ton = toff = 0.001 s

1. Discharging time parameters (τ₂):

(5)τ2≫toff

(6)→R2∗C≫0.001

(7)→R2≫10Ω

(8)→R2=500Ω and τ2=5.10−2 s

1. Charging time parameters:

The proposed design is charging time faster than the discharging time five times

(9)5∗τ1=τ2

(10)→5∗R1∗C=R2∗C

(11)→R1=R25=100Ω

1. Differentiator

In this design, a small value capacitor C₂ is connected across the feedback resistor R₂, which avoids the differentiator circuit to run into oscillations (that is, become unstable), and a resistor R₁ is connected in series with the capacitor C₁, which limits the increase in gain to a ratio of R₂/R₁ (see Figure 9).

Figure 9:

Differentiator design.

Since negative feedback is present through the resistor R, we can apply the virtual ground concept, that is, the voltage at the inverting terminal = voltage at the noninverting terminal = 0.

(12)0−Vo1sC2+0−Vo1sC2+0−ViR1+(1sC1)=0

(13)−Vo(1R2+sC2)=ViR1+(1sC1)

(14)VoVi=sR2C1(1+sR1C1)(1+sR2C2)

Call fa as the highest frequency of input signal. Here, we design the differentiator under the operation R₁C₁ = R₂C₂ = R₂C₁ > R₁ = R₂ and C₁ = C₂ there occurs one zero at s = 0 and two poles at:

(15)s=fa=12πR2C1

For such a differentiator circuit, the frequency response would be:

Set fa = 319 kHz, The operating frequency is always smaller than fa as a differentiator otherwise, it works as an integrator (see Figure 10).

(16)R2∗C1=12π∗fa=12π∗319k=5×10−7

Figure 10:

Differentiator characteristics.

Selection: R₁ = R₂ = 500 Ω, C₁ = C₂ = 1 nF

1. Integrator

In this case, Rf is R₆ (feedback resistance) (see Figure 11).

Figure 11:

Integrator design.

The crossover frequency fb, at which the gain is 0 dB, is given by:

(17)fb=12πR4C4

The 3 dB cutoff frequency of the practical circuit is given by

(18)fa=12πR6C4

The gain is relatively constant up to the cutoff frequency and decreases by 20 = dB per decade beyond it. The integration operation occurs for frequencies in the range [fa, fb]:

(19)fa<fb→R4C4<R6C4→R6>R4

Here we select the high crossover frequency to achieve the fast response with transient. fb = 15,9235 Hz.

Selection: R₄ = 10 kΩ, R₆ = 20 kΩ

(20)C4=12πR4fb=0.1 nF

To neglect the effect of the input bias current at the positive terminal of op-amp, it is necessary to set:

R5 = 10 kΩ

Comparision between two MPPT methods by EN 50530 MPPT efficiencies

In this part, the evaluation of MPPT techniques’ performance was carried out by using the European Efficiency Test, EN 50530, which is specifically devised for the dynamic performance of the PV system. The involved test procedure of CENELEC standard EN 50530 is implemented to test and compare the presented algorithms’ dynamic performance. The standard defines a test procedure for the measurement of MPPT efficiency of the PV systems that simulate a PV generator’s output characteristics. It is readily used for DC-DC converters because the main aim is to evaluate the MPPT algorithm’s performance, rather than conversion efficiency itself. The dynamic MPPT algorithm efficiency is determined by two test sequences of different irradiance levels. Sequence ‘A’ covers the interval from 10 to 50% while sequence ‘B’ covers the irradiance from 30 to 100% of standard test conditions (GSTC = 1000 W/m²/s). The sequences of ramp having slopes ranging from 0.5 W/m²/s up to 100 W/m²/s are utilized.

The dynamic efficiency of MPPT (ηMPPT dyn) is calculated as the ratio of extracted energy and available energy of the procedure within the time during each sequence as below:

where Vpv(t) and Ipv(t) represent the instantaneous voltage and current at the output of the PV simulator. The P_MPP(t) represents the available maximum Power of the PV simulator with respect to the instantaneous P_MPP. T represents the time duration of the whole sequence. We used the defined procedure to investigate the dynamic MPP tracking efficiency of the three algorithms.

The test will be carried out by sequence A: Low to medium insolation (100–500 W/m²) and sequence B: Medium to high insolation (300–1000 W/m²) like Figures 12 and 13 respectively. The irradiation’s repeating sequence was designed following the standard EN 50530 to test both digital and analog P&O.

Figure 12:

Low to medium insolation irradiation.

Figure 13:

Medium to high insolation irradiation.

Applying the principle of EN 50530, the MPPT efficiencies have been obtained for both Low to Medium insolation and Medium to High insolation. As we can see Table 5, all of two methods work better at Medium to high insolation. For the P&O digital technique, each test for each slope change, a new calculation for the perturbation amplitude was made with respect to the criteria’s formula. The good MPPT efficiency is achieved. The proposed analog technique shows a highly advanced performance with permanent stability and balanced MPPT efficiency at both of two testing sequences thanks to the fast-tracking and response to irradiation variation in the whole system mechanism.

Series tests for analog MPPT

Steady state

The standard tests of steady state applied to the analog MPPT with the multiplier. The results indicate an outstanding performance of the MPPT controller with minimal oscillation. The tracking power already achieved the maximum available power from PV panels as shown in s 14 and. This point is an advanced aspect over other methods because other ones only can reach very close to the PV maximum power. Still, this manner attains the absolute value of the panel 52.128 W, precisely the actual power data of the Solbian 52L curve.

Since the tracking power has a very small oscillation, so we had to observe on a narrow scale to see its behavior clearly (see Figures 14 and 15)

1. 1000 W/m²

2. 500 W/m²

Figure 14:

The results of MPPT system at 1000 W/m².

Figure 15:

The results of MPPT system at 500 W/m².

At irradiation 500 W/m², like the above test, the sinusoidal behavior proceeded during the tracking process, and the MPPT efficiency guaranteed with a tiny swing on the P-V curve. The tracked Power is approximately half of 1000 W/m² condition that shows the correct operation of the MPPT system.

Irradiation variation

The constant change rate of irradiation

As usual, an irradiation change’s rate of 100 W/m²/s was applied to test the controller’s operation. The rapid evolution of light irradiation requires the fast response of the MPPT controller to the ambient. It is clear to observe in Figure 16 that the tracking trend power moves to correspond to irradiation change. The depreciation of oscillation contributes to the superb efficiency of the whole system.

Figure 16:

The PV power versus the irradiation variation.

Irradiation transient

Based on the impressive result as above simulations, the transient test with wide range of irradiation level: rising stair (400–5000 W/m²) and falling stair (4000–100 W/m²). This test also examines the maximum range where the system is capable of working on.

Firstly, the stair-up transient is tested as Figure 17, which attains a good MPPT controller performance under this circumstance. The MPPT controller perfectly performs its tracking procedures. Until the irradiation 4000 W/m², the tracking power starts to fall away from absolute MPP about 2% and continue to move down from MPP at higher irradiation. Thus, this analog MPPT will be applied for the irradiation level at 4000 W/m² as the maximum limit to accomplish the high efficiency.

Figure 17:

PV power versus stair-up transient.

Considering the irradiation limit of stair-up transient, the stair-down transient only transpired from 4000 to 100 W/m².

Generally, the MPPT controller is well designed for the irradiation variation, as shown in Figure 18. Figure 19 shows the MPPT efficiency at each level of irradiation transient, about 99.99% as average.

Figure 18:

PV power versus stair-down transient.

Figure 19:

MPPT efficiency at irradiation transient.

Space testing conditions for PV

The panel temperature is computed, considering the direct sun radiation, the albedo radiation, the irradiation to deep space, and irradiation between the earth’s surface and the panel itself. The sun illumination is variable during the year and considering only missions around the planet it may range between 1315.0 (summer solstice) and 1426 W/m² (winter solstice).

Due to the elliptical path of the earth around the sun, the variation in the earth-sun distance results in about ±3% in the extraterrestrial solar flux. The formula expresses the extraterrestrial solar radiation intensity G_SC, which is given by (Lotfy et al. 2017).

(22)GSC=GSCO(1+0.033cos360d365)kw/m2

All of the tests will be proceeded according to the ratio of extraterrestrial irradiance at normal incidence to solar constant NASA test criteria in (National Aeronautics and Space Administration 1971).

Variation of solar irradiation

High temperature: 107 °C in dry nitrogen gas, or simulated eclipse conditions. The solar irradiations vary from 1315 W/m² to 1426 W/m² as demonstrated in Figure 20.

Figure 20:

Power at space irradiation variation.

Variation of temperature

Temperature cycling: Five cycles between −55 °C and +125 °C. The minimum solar irradiations on space: 1315 W/m² as Figure 21.

Figure 21:

Power at space temperature variation.

Generally, it was evident that this technology successfully attains the high MPPT efficiency at all necessary tests for space conditions.

At first test, at high temperature and irradiation variation, the MPPT controller adjusts its tracking process according to the trend of the irradiation adequately

At the second test, the rapid change of temperature in space does not affect the controller’s performance. Instead of moving far away from the maximum available power of PV source when the temperature approaches its peak point, the tracking trend continues to cling to the PV energy move.

After two tests based on the space environment, the Analog MPPT offers a superb response to the swift variation of temperature as well as irradiation that shows the high potential capability to place this MPPT controller on the satellites.