# What is the quasi-maximum power point tracking method?

The quasi-maximum power point tracking method includes mathematical formulas or tables obtained from empirical data, such as curve fitting method and pre-stored data comparison look-up table method, as well as sampling and control based on a single output parameter of the photovoltaic array, for example, using open circuit voltage method, short circuit method, etc. Current method to track the maximum power point. The quasi-maximum power point tracking method cannot be applied to all loads, and it may not be able to accurately track the maximum power point under any weather conditions.

① Curve fitting method
Take the DC/DC converter in Figure 1 as a classic BUCK circuit (in fact, BOOST circuit and BUCK BOOST circuit have the same properties) as an example to illustrate a curve fitting method. Assuming that C is a constant, and 0<C<1, the sampling period is Ts. When the duty cycle D changes uniformly in steps from close to 0 to close to 1, it can be seen from Figure 2 that the curve of the expression (C-D) (-dVpv/dt) is basically consistent with the change trend of the photovoltaic array output power. Therefore, tracking the maximum power point of the photovoltaic array is equivalent to tracking the maximum point of the expression (C-D) (-dVpv/dt). The expression (C-D) (-dVpv/dt) becomes (C-D) (-OVpv/Ts) after discretization, and the duty cycle D is represented by the formula (1), (2) and (3). In the formula, △Vpv=Vpv (n) -Vpv (n-1), Vpv (n-1) and Vpv (n) are the output voltage of the photovoltaic array during the n-1 and nth sampling period, D (n-1) and D(n) are the n-1 and nth duty cycles of the DC/DC converter, respectively, and ΔD is a constant duty cycle step. It can be seen from Figure 2 that when the expression (C-D) (-dVpv/dt) =0, the size of the constant C can be obtained. It is obvious from Figure 2 that the constant C can be used as the upper limit of the duty cycle D, and the sampling period T. It is always greater than zero, so the expression (C-D) (-△Vpv/Ts) can be simplified to a judgment on the sign of △Vpv.

When (C- D(n-1)( APpv/T)>0, D(n)= D(n-1)+△D————(1)
When (C- D(n- ))(OVpv/T)<0, D(n)=D(n-1)﹣△D————(2)
When (C- D(n-1))(SVpv/T)=0, D(n)=D(n-1)————(3)

Corresponding experiments were carried out with the photovoltaic array simulator E4351B produced by Agilent in the United States instead of the real photovoltaic cell array. Among them, the relationship between the optimal voltage and the open circuit voltage is Vmpp=0.85Voe, and the relationship between the optimal current and the short-circuit current is Impp=0.81sc. The DC/DC converter adopts the BOOST circuit, and the load is an old 20V battery, which is equivalent in series. Resistance 9.7Ω and capacitance 360F, switching frequency 10kHz, sampling frequency 1kHz, constant C=0.75, △D=0.001.

Figure 2 is the waveform of each variable when D changes from 0.05 to 1.0, which verifies that the expression (C-D) (-△Vpv/Ts) is basically consistent with the change trend of the output power of the photovoltaic array simulator, and has a unimodal nature. Figure 3 shows the waveform under the condition that the same open-circuit voltage is used to simulate the temperature basically unchanged, and the different short-circuit currents are used to simulate the change of light intensity. Among them, Voc=21.7V, Isc changes from condition 1 (1.4A), condition 2 (2.5A) to condition 3 (3.2A) respectively. Fig. 5 is the waveform under the condition that the same short-circuit current is used to simulate the light intensity basically unchanged, and the different open-circuit voltage is simulated under the condition of temperature change. Among them, Isc=2.5A, Voc changes from condition 4 (21.7V), condition 5 (14.5V) to condition 6 (11.5V) respectively. It can be seen from Figure 3 and Figure 4 that regardless of the short-circuit current change or the open circuit voltage change, the output voltage and current of the photovoltaic array simulator are basically equal to the optimal voltage and optimal current set, so the correctness of the curve fitting method is proved .

The advantage of this method is that it is simple to implement, but the disadvantage is that the size of the duty cycle step △D and the sampling accuracy of the voltage Vpv have a great influence on the accurate tracking of this method.

②Look-up table method
The look-up table method is to store the voltage and current data corresponding to the maximum power point of the photovoltaic array under various weather conditions in advance, and then compare the measured output voltage and/or current of the photovoltaic array to continuously correct the power converter Working status. The disadvantage of this algorithm is that it can only target specific photovoltaic cell arrays. It requires both large-capacity memory to store data and constant adjustment of sample data. At the same time, it is difficult to accurately record and store data under various conditions.

③Constant voltage (CVT) method
As shown in Figure 5, when the light intensity is high, the maximum power points under different light intensity conditions are almost distributed on both sides of a vertical voltage line, which shows that the maximum power output point of the photovoltaic array roughly corresponds to a certain constant voltage. Therefore, it is only necessary to obtain the maximum power point output voltage Vmpp data from the manufacturer (Vmpp is usually approximately equal to 0.71 to 0.8 times the open circuit voltage Voc), and the output voltage of the photovoltaic array is always equal to the Vmpp value. In fact, the CVT method simplifies the MPPT control to PI closed-loop voltage stabilization control, so it is very simple to implement, as shown in Figure 6.

Although this method is simple to control, easy to implement, and the system has good stability, this method is only suitable for strong light intensity conditions where the light is basically unchanged, and it is not suitable for areas where the temperature difference between morning and evening and the four seasons changes drastically. In many cases, photovoltaic arrays can only work near the maximum power point. Therefore, the CVT method must be used in combination with other methods in order to achieve a better tracking effect.

④Open circuit voltage proportional coefficient method
Even under varying light intensity and ambient temperature, there is an approximate proportional relationship between the open circuit voltage Voc of the photovoltaic array and the maximum power output voltage Vmpp, as shown in equation (4). In the formula, Kv is constant under a certain range of light intensity and ambient temperature.
Vmpp =KvVoc————(4)
Since Kv is related to the characteristics of the photovoltaic array used, before each use, test the characteristics of the photovoltaic cell module under different light intensity and temperature, and calculate the proportional coefficient under different open circuit voltages. According to literature reports, the scale factor is generally 0.71 to 0.80. Once the scale factor of the photovoltaic cell module is determined, the open circuit voltage can be measured by periodically cutting off the battery module and the circuit connected behind it, and then Vmpp can be calculated according to the scale factor. . In fact, the BUCK converter is particularly suitable for this method, because when the power switch is turned off, it can be approximately considered that the photovoltaic cell module is in an open state.
Although this method is simple and economical, part of the power is lost due to continuous testing of the open circuit voltage, and when the photovoltaic cell module is used for a long time, its physical characteristics will change to a certain extent, so the original measured scale factor will no longer be used. Accurate, the true maximum power point tracking function is not realized at this time. In addition, different photovoltaic cell modules have different Kv， and need to be tested again.

⑤ Short-circuit current proportional coefficient method
Similar to the open circuit voltage proportional coefficient method in the previous section, there is a certain proportional relationship between the short-circuit current of the photovoltaic array and the output current at the maximum power point, as shown in equation (5).
Impp = KiIsc————(5)
The proportional coefficient Ki mainly depends on the manufacturing process, fill factor and environmental factors of the photovoltaic cell module. For polysilicon, the scale factor value is generally close to 0.85.
Before the photovoltaic power generation system operates, it is also necessary to obtain the short-circuit current proportional coefficient Ki under different light intensities and temperatures. Then, during the operation, the photovoltaic array is periodically short-circuited to obtain the short-circuit current, and the corresponding Ki is obtained. The maximum power point refers to the current Impp. In fact, the BOOST converter is particularly suitable for this method, because when the power switch tube is turned on, it can be approximately considered that the photovoltaic cell module is in a short-circuit state.
This method is simple in principle and easy to control, but it is not suitable for all environmental conditions like the open circuit voltage proportional coefficient method, and when the photovoltaic cell module ages, the calculated proportional coefficient is no longer accurate.

⑥ Finite cycle current perturbation method
The working principle of maximum power point tracking based on finite period current disturbance is shown in Fig. 8. Among them, Tiu and Tid respectively correspond to the rise time constant and fall time constant of the reference output current of the DC/DC converter, and Tiu is much larger than Tid. τpi is the equivalent time constant of the current PI regulator, which satisfies the condition of Tidpi<Tiu.

When the circuit starts to work, the one-of-two switch MUX is connected to 1/Tiu. Under the action of the integrator, the reference output current signal Iref of the DC/DC converter accumulates and rises in an approximate ramp manner, and it is subtracted from the feedback current Ifk to produce an error current. The signal Ierr, under the action of the current PI regulator, Ierr will gradually decrease.
When Iref rises to a certain level, the output power of the photovoltaic array just matches the maximum power required by the load, that is, the maximum power point is reached. At this time, Iref will continue to accumulate, which will inevitably cause the actual current of the DC/DC converter to no longer follow the reference current Iref, so the absolute value of the difference between the two currents Ierr will increase if it exceeds the preset current error constant △Ilimit, the comparator is inverted, and the MUX switch is connected to -1/Tid. Therefore, the reference current Iref will drop rapidly according to the slope to ensure that when the reference current Iref has not had time to drop too much, the absolute value of the error current signal Ierr will quickly exceed △Ilimit, so the two-choice switch MUX is reconnected to 1/Tiu, After that, Iref begins to slowly rise again in the working process of the cycle above, as shown in Figure 8. It can be seen that this working process will produce a so-called non-linear oscillation “limit cycle” that occurs near the maximum power point, thus realizing the quasi-maximum power point tracking control.

Using PSIM simulation software, the circuit simulation was carried out on the basis of BOOST converter and resistive load. The simulation parameters: photovoltaic cell peak power 150w, short-circuit current Isc=5.4A, corresponding optimal current Impp=4.3A, load resistance 26Ω.
It can be seen from Figure 9 that the feedback current of the BOOST converter always follows the reference current, and at the same time it oscillates around the maximum power point. The actual output current of the photovoltaic cell also oscillates around the optimal current with the same limit cycle.

The advantage of this method is that the maximum power point tracking can be achieved only by relying on the information of the output current, without the need for a voltage sensor to detect the input or output voltage information. Therefore, this method can reduce the system cost, but its shortcomings are also obvious. The output power of the photovoltaic cell always oscillates at the maximum power point, and the tracking power loss is large. At the same time, it is necessary to select the appropriate time constant Tid, τpi and Tiu.