# Research on MPPT Algorithm with Stability and Fastness

On the basis of the basic analytical expression (Formula), two approximations will be adopted, namely:

① Ignore the (U+IRs)/Rsh term, because this term is much smaller than the photocurrent under normal circumstances;
②Set Iph-Isc, this is because RS is much smaller than the forward conduction resistance of the diode under normal circumstances, and is defined in:
a. In the open state, I=0.U=Uoc;
b. Maximum power point, U=Um, I=Im
Establish a solar cell engineering model under the conditions.

At the maximum power point, I=Im, U=Um, we can get

Under normal temperature conditions, exp[Um/(λ2Uoc)]》1, you can ignore the -1 term in formula 2, simplify and organize

In the open state, I=0, U=Uoc, substituting formula 3 into formula 1, get

Since exp(1/λ2)》1, one of the items in the above formula can be ignored, simplifying and finishing

This model only needs to input the usual technical parameters of solar cells Isc, Uoc, Im, Um, and then λ1 and λ2 can be obtained according to formula 2 and formula 5. Then the Isc and Uoc under different illuminations are measured experimentally, and finally the volt-ampere characteristics of the solar cell under different illuminations can be determined by formula 1.

The following is the calculation of the maximum power point:
Transform the formula 1 into:

Since exp[U/(λ2Uoc)]》1, one item in the above formula can be ignored, and it can be simplified and sorted out;

Finished up:

Then the output power of the solar cell is

P is derived from I,

When I=Im, dP/dI=0, that is

Finished up:

When U=Um, substituting into the formula 8, we get

Substituting into the formula (12), we get

Finished up:

Um and Im can be calculated by formula (12) and formula (15), and the maximum power point Pm can be obtained by calculation.

For us, it is how to ask for Isc and Uoc well.

Generally, the solar radiation intensity S on the ground varies from 0-1000W/m², and the temperature of solar cells varies greatly, ranging from 10 to 70°C.

According to the standard, take Sref=1000W/m², Tref=25℃ as the reference solar radiation intensity and reference battery temperature. When the insolation intensity and battery temperature S (W/m²), T (℃) are not the reference insolation intensity and the reference battery temperature, the influence of ambient temperature conditions on the characteristics of the solar cell must be considered, and it is set at any insolation intensity S and any environment The solar cell temperature at temperature Tair, after fitting according to a large amount of experimental data, the following formula is proved to have sufficient accuracy in the engineering sense

In the formula, K can be determined by experimentally measuring the slope of the T(S) line. For common solar array brackets, it is advisable

When the battery temperature T is measured, the sunlight intensity S can be obtained according to formula (16).

According to the reference sunshine intensity and the Isc and Uoc at the reference battery temperature, the new sunshine intensity and the I’sc and U’oc at the new battery temperature are calculated,

In the calculation process, it is assumed that the basic shape of the 1/U characteristic curve remains unchanged, and the typical values ​​of the coefficients a, b, and c are

The new I’sc and U’oc after the change of battery temperature T and sunlight intensity S can be calculated by formulas 18, and then substituted into formulas 12 and 15 , Um and Im can be calculated, so that the maximum power point Pm under the current battery temperature and light can be approximated.

The perturbation observation method (also known as the hill climbing method) is to continuously disturb the working voltage of the photovoltaic array when the photovoltaic array is working normally. When the voltage changes, the detection power also changes. The decision is made according to the direction of the power change. The direction of the voltage change in the next step.

The working process of the stable and fast MPPT algorithm is: first calculate λ1 and λ2 according to the usual technical parameters of solar cells Ise., Uoc, Im, Um, and then measure the current battery temperature T, according to the formula 16 Calculate the current sunshine intensity s, calculate the current battery temperature T and sunshine intensity S through formula 16 and formula 18 to calculate the new I and U., and then substitute into formula 12 and formula 15 Um and Im can be obtained by calculation. When the maximum power point P is calculated, disturbance observation is introduced. The MPPT converter first disturbs the input voltage value (Um+ΔU), compares the measured power value P with the power value P stored in the system at the previous moment, and determines the adjustment direction of the reference voltage according to the comparison result. The specific adjustment scheme is: Let ΔP-P, -P be the difference between the current output power and the previous power. If: ①ΔP>0, that is, the power has increased from the previous time, indicating that the adjustment direction of the reference voltage is correct, continue to adjust in the original direction; ②ΔP<0, that is, the output power is smaller than the previous time, indicating that the adjustment direction of the reference voltage is wrong , The original adjustment direction needs to be changed. The corrected maximum power point Pm can be further obtained, the current Im and voltage Um of the solar cell at this time can be detected, combined with I’sc and U’oc into equations 3 and 4 to re-correct the parameters: And 22, and then recalculate Um and Im according to formula 12 and formula 15 to obtain the maximum power point Pm. At this time, the system works on an IU curve under the current battery temperature T and light S, which corresponds to a set of parameters λ1 and λ2. When the temperature and light change, it works on a new I/U curve, corresponding to a new set of I/U curves. The revised parameters λ1 and λ2 are used to calculate the new maximum power point Pm.

Predecessors conducted a detailed study on the relationship between the temperature change of a crystalline Si solar panel and the open circuit voltage and short-circuit current. The light intensity was fixed under artificial simulation of the sun, and the temperature of the solar panel was measured with a temperature probe, and the output short-circuit current of the solar panel was recorded at the same time. , Using the same method to record the open circuit voltage, get the following two empirical relations:

That is, for every 1°C increase in battery temperature, the open circuit voltage decreases by 2.3mV, and the short-circuit current increases by 0.107mA.

We stipulate that when the maximum power point Pm is reached, the disturbance will not continue. The algorithm also sets a threshold ε within the allowable error range. When the maximum power changes within the threshold ε, Pm is considered unchanged, and the threshold ε corresponds to the battery temperature T. An allowable error range ΔT, in which we consider the maximum power point Pm unchanged.

Calculation of threshold ε: When we find the maximum power point Pm, the battery junction temperature at this time is T, and the allowable error range ΔT is 2℃. The battery can be calculated by formula (3-46) and formula 18 The new I’sc and U’oc after the temperature T and the sunshine intensity S change, and then substituting into the formula 12 and formula 15 to calculate Um and Im, so that the current battery temperature and The allowable error range of the maximum power point Pm under illumination, that is, the threshold ε, changes in this range, we consider the maximum power point Pm unchanged.

Such continuous calculation of Pm and correction of λ1 and λ2 can make the maximum power point P under different battery temperatures and illumination more accurate.

The analysis of the stability and rapidity of the maximum power point is as follows.

Comparative analysis with the disturbance observation method: the disturbance observation method is to continuously disturb the working voltage of the photovoltaic array when the photovoltaic array is working normally. At the same time as the voltage changes, the detection power also changes. According to the direction of the power change, Decide the direction of the voltage change in the next step.

The advantage of the disturbance observation method is that it is relatively simple, reliable, and easy to implement. One of its disadvantages is that the system must introduce disturbances, and the final result of the optimization is that the system oscillates back and forth in a small range near the maximum power point, which will cause energy loss. Especially when the atmospheric environment changes slowly, the energy loss is more serious. This is the biggest shortcoming of the disturbance observation method.

The MPPT algorithm based on the solar cell model (combined with disturbance observation) can accurately and quickly track Pm, which is determined by the algorithm itself. It avoids power loss caused by disturbances near the maximum power point. Once the system reaches Pm, it will not do any voltage adjustment through the CPU command, and keep the system working at this point for a long time until the external environment changes. This is not only fundamentally different from the hill climbing method that still oscillates near the maximum power point, it avoids unnecessary power loss.

Another shortcoming of the disturbance observation method is that when a cloud passes by, the sunlight intensity changes rapidly, and the reference voltage adjustment direction may be wrong and cause the system to misjudge.

The MPPT algorithm based on the solar cell model (combined with perturbation observation) does not blindly move the working point when the light intensity changes suddenly, and then track it after the amount of sunlight stabilizes. This situation (that is, the sky is blocked by clouds) is included in the system and has reached the maximum In the case of the power point, the two do the same processing; blindly adjust the operating voltage without following the rapid change of the amount of sight. This avoids the system from excessively fast oscillation. This processing will cause a small amount of power loss, but it is relative to the entire system. It is worthwhile for stable operation. Assuming that the original system is at the maximum working voltage Um1, the corresponding current detected is I m1, the maximum working voltage that should be reached after a sudden change in sunlight is U m2, and the corresponding current is I m2, then the system does not move and work The power loss caused by the point is P=P m2-P m1-U m2 I m2-U m1 I m1. As the sun quickly returns to the original amount of sunshine, the unmodified U m1 becomes the maximum operating voltage again, and the system returns to its original stability. State, this process keeps changing, avoiding the misjudgment of P m by the mountain climbing method and the phenomenon of back-and-forth oscillation.

The MPPT algorithm based on the solar cell model (combined with disturbance observation) is more complicated. In order to adapt to the sudden change of sunlight, when judging the maximum power point, the detection of parameters such as voltage and current and the A/D conversion speed are relatively high, which is especially important for the system hardware. The control of the processor puts forward high requirements and increases the investment cost. However, due to the use of software control, the MPPT algorithm based on the solar cell model reduces the misjudgment phenomenon in the program operation, and the voltage is only small even when the light changes sharply Shake to achieve stable tracking. The MPPT algorithm based on the solar cell model is better than the hill climbing method in terms of tracking stability. It is suitable for occasions with large changes in light intensity, such as photovoltaic systems installed in areas with changeable climates.