The maximum power point tracking of solar cells is an indispensable part of photovoltaic power generation systems. The purpose of maximum power tracking is to make solar cells work at the maximum power point all the time. By tracking and searching the maximum power point of the solar cell, the grid-connected current is maximized and the grid-connected power is maximized. The methods commonly used in photovoltaic systems to track the maximum power point include: hysteresis comparison method, conductance increment method, optimal gradient method, disturbance observation method, etc. The common point of these methods is to search for the corresponding voltage according to the maximum power point on the characteristic curve of the solar cell. Each of these methods has its own merits, and appropriate control methods should be selected as appropriate for different needs.

**1. Constant voltage method**Constant voltage tracking (CVT) is the simplest method of maximum power point tracking of photovoltaic modules, and its theoretical basis is the output characteristics of photovoltaic modules. From the P-V output characteristic curve of the photovoltaic module, it can be known that under the condition of a certain temperature, the approximate distribution of the maximum power point of the photovoltaic module under different light intensities. That is to say, ignoring the effect of temperature on the maximum power point, the output voltage corresponding to the maximum power point of the photovoltaic module under different light intensities does not change much, and can be approximated as a constant Vw. Therefore, through a certain impedance transformation between the photovoltaic module and the load, the system can realize the function of a voltage regulator, so that the operating point of the module is always stable at a constant Vw, which is equal to the voltage corresponding to the maximum power point under a certain sunshine intensity, The maximum power output of photovoltaic modules can be roughly guaranteed at this temperature, and the maximum power point tracking can be simplified to constant voltage tracking.

The advantage of the constant voltage method is that the control structure is simple, the reliability is high, the stability is good, the intervention of the digital processor is not required, and the cost is low. However, the disadvantage of this method is relatively obvious. Since the constant voltage method ignores the influence of temperature on photovoltaic modules, the control accuracy of this method is low. For areas with large temperature difference, this method cannot completely track the maximum power of the module, resulting in energy of waste.

**2. Interpolation calculation method**In the open-loop control strategy, the method of numerical analysis can also be used for control, especially when the external conditions change greatly, the method of interpolation of the sampling point data can be used to approximate the maximum power point.

In the photovoltaic grid-connected power generation system, the operating point of the solar cell is adjusted by controlling the on-duty ratio of the power device, so the maximum power can be controlled by establishing a mathematical model of the characteristics.

The idea of interpolation is to use multiple sampled working points to perform Lagrangian interpolation, fit a curve, and compare the fitted curve with the actual power. When the two powers meet certain conditions, the This operating point is output as the maximum power point.

To obtain the Lagrangian interpolation function, d

_{min}, d

_{int}, and d

_{max }represent the on-duty ratios of the three sampling points, respectively, satisfying d

_{min}<d

_{int}<d

_{max}, and the corresponding output powers are P

_{min}, P

_{int}, and P

_{max}, then

Among them: L_{0}, L_{1}, L_{2} are the basis functions of Lagrangian difference respectively.

Therefore, the Lagrangian difference function is obtained as:

By fitting the output power curve with the above formula, the duty d_{max} corresponding to the maximum output power can be calculated:

Interpolation MPPT algorithm flow:

When the difference between ▔ P_{max} and ▔ P’_{max} is small enough, the actual measured power value can be considered as the maximum power value. When this requirement cannot be met, the minimum power point is discarded, and a new power point is selected for difference calculation until this condition is met.

**3. Hysteresis comparison method**The hysteresis comparison method (HCM) is proposed to overcome oscillation and misjudgment. Oscillation is determined by the characteristics of the algorithm itself (differential way instead of differential), and misjudgment is caused by the continuous change of light intensity. Misjudgment is actually an oscillation generated when the external environment changes dynamically. Phenomenon.

The basic idea of the hysteresis comparison method: when the power fluctuates within the set loop width, the output voltage of the solar cell remains unchanged, and only when the power fluctuation exceeds the set loop width, the voltage at the operating point is changed to change power. As shown in Figure 1.

The principle of the hysteresis comparison method: starting from the current working point A, according to the judgment, perturb to point B, and then reversely perturb two steps to point C. The powers P_{A}, P_{B}, and P_{C} in turn are compared to the power of the three points. Power judgment. This leads to the nine cases in Figure 2:

In Figure 3, when P_{C}>P_{A} is marked as “+”, when P_{B}>P_{A} is marked as “+”, the rest are marked as “one”. If the comparison is “+”, the voltage is perturbed in the original direction; if the comparison is “one”, the voltage is perturbed in the opposite direction. The hysteresis comparison method is actually to improve reliability through bidirectional disturbance to avoid misjudgment, and its flow chart is shown in Figure 3.

Although the hysteresis comparison method can avoid oscillation and misjudgment to a large extent, if the step size is too long, it will still be far from the maximum power point. If the step size is too small, the search speed will be slowed down, which makes it necessary to take into account the speed and precision requirements are still very difficult.

**4. Conductance incremental method**Incremental conductance (INC) is a method to complete maximum power point tracking by comparing the instantaneous conductance of photovoltaic modules with the change in conductance. It can be known from the output characteristics of photovoltaic modules that the characteristic curve is a first-order continuous derivable single-peak curve. At the maximum power point, the derivative of power to voltage is zero. The power expression of the photovoltaic module is:

Taking the derivative of V at both ends of the above formula, and taking I as a function of V, we can get:

which is:

Equation (7) is the condition that needs to be met to reach the maximum power point of the photovoltaic module. The conductance increment method determines the direction of the reference voltage change by comparing the instantaneous conductance of the photovoltaic module and the change in conductance, which can be divided into The following three situations:

(1) When the operating point of the photovoltaic module is on the left side of the maximum power point, that is, dP/dV>0, dl/dv>-I/V, it means that the reference voltage should change in the direction of increase.

(2) When the operating point of the photovoltaic module is located on the right side of the maximum power point, that is, dP/dV<0, dl/dV<-I/V. It means that the reference voltage should change in a decreasing direction.

(3) When the operating point of the photovoltaic module is at the maximum power point, that is, dP/dV=0, the reference voltage will remain unchanged at this time, and the photovoltaic module will work stably at the maximum operating point.

In the conductance increment method, the change direction of the reference voltage at the next moment depends entirely on the relationship between the instantaneous immittance and the change in the immittance at the moment, and has nothing to do with the voltage and power of the operating point at the previous moment, so there will be no disturbance. Therefore, it can adapt to the rapid change of light intensity and has high control accuracy, but because the magnitudes of dl and dv are small, the accuracy of the sensor is required to be high, and the implementation cost is relatively high.

**5. Optimal gradient method**The optimal gradient method (gradient mehtod, GM) is a calculation method for unconstrained optimization problems based on the steepest descent method. value, defined as follows:

Assuming that the objective function f(x) is continuous and can be first-order differentiable near the x

_{k}point, let g

_{k}=▽f(x

_{k})≠0. Taylor expansion of f(x), we can get:

Let x-x_{k}=a_{k}d_{k}, then the above formula can be converted into:

In the formula: a_{k} is the incremental coefficient, which is a non-negative constant. It can be seen from the above formula that if dk satisfies g_{k}^{T}d_{k}<0, then f(x_{k}+a_{k}d_{k})<f(x_{k}) At this time, the iteration direction is the descending direction. Under the condition of constant a_{k} , the larger g_{k}^{T}d_{k} is, the faster f(x) falls at the position of x_{k}. According to the Cauchy-Schwartz inequality:

If and only when d_{k}=-g_{k}^{T}, -g_{k}^{T}d_{k} reaches the minimum, -g_{k} is the optimal gradient direction, and the method with -g_{k} as the optimal gradient direction is called the optimal gradient method. The iterative algorithm is:

The P-V output characteristic curve of photovoltaic modules is a nonlinear function, and the problem of maximum power point tracking can be regarded as solving the maximum value of the P-V curve. Therefore, the optimal gradient method can be applied to the maximum power point tracking of photovoltaic modules. By changing the negative gradient direction to the positive gradient direction, the maximum value of the P-V curve can be gradually approached through n iterations. Corresponding to the positive gradient direction, the iterative algorithm is modified accordingly:

Replace the independent variable x with the output voltage V of the photovoltaic module, there are:

In the formula: a_{k} is the incremental coefficient, and the value is constant to ensure that the iteration direction is the same as the gradient direction. The expression of gradient g_{k} is:

In the formula: V is the output voltage of the photovoltaic module, P(V) is the output power function of the photovoltaic module with V as the only variable, which is a nonlinear function, and is a continuous first-order differential function. The current equation of the photovoltaic module can be P(V) is expressed as:

The optimal gradient method determines the search direction by calculating the gradient g_{k}. If g_{k}>0, it means that the search direction is close to the maximum power point along the positive direction of the V axis; if g_{k}<0, it means that the search direction is along the V axis at this time. The negative direction of the axis approaches the point of maximum power. The optimal gradient method and the maximum power point tracking method can effectively prevent the misjudgment caused by the sudden change of light intensity and temperature, and ensure the stability and reliability of the system.

**6. Disturbance observation method**Perturbation and observation (P&.O) is a commonly used maximum power point tracking method. Its working principle is to increase or decrease the output voltage of photovoltaic modules at regular intervals, disturb its operating point, and observe the disturbance after The change of output power is used to judge the disturbance direction of the next working point until the component works at the maximum power point.

The maximum power point in the P-V characteristic curve of a solar cell is a single-peak extreme value function, which also provides the basis for finding the maximum power point for the perturbation observation method. The perturbation observation method adopts a step-by-step search method, as shown in Figure 4.

(1) When the output voltage V changes in the direction of voltage increase, that is, when V_{1}=V+ΔV, if P_{1}>P, it means that the current operating point is on the left side of the maximum power, and the output voltage continues to increase to the voltage perturb the direction.

(2) When the output voltage V changes in the direction of voltage increase, that is, when V_{1}=V+ΔV, if P_{1}＜P, it means that the current operating point is on the right side of the maximum power, and the output voltage continues to decrease. perturb in a small direction.

(3) When the output voltage V changes in the direction of voltage reduction, that is, when V_{1}=V-ΔV, if P_{1}>P, it means that the current operating point is on the right side of the maximum power, and the output voltage continues to decrease. perturb in a small direction.

(4) When the output voltage V changes in the direction of voltage reduction, that is, when V_{1}=V-ΔV, if P_{1}<P, it means that the current operating point is on the left side of the maximum power, and the output voltage continues to decrease. The perturbation is performed in the opposite direction of the small direction.

For the fixed-step perturbation observation method, the operating point may cross the maximum power. Therefore, the fixed-step perturbation observation method needs to be improved, so that the system can track the maximum power point faster and more accurately. According to the solar cell curve, the following characteristics can be obtained:

According to this feature, the voltage disturbance expression can be constructed:

In the formula: V_{ref }is the reference voltage of the operating point, and a is the correction factor, that is, the step change factor.

According to formula (17), when the operating point of the solar cell is far from the maximum power point, the tracking step size will increase, and when the operating point is close to the maximum power point, the tracking step size will become smaller until dP/ dV=0. However, there are oscillations and misjudgments in both the fixed-step and variable-step perturbation methods. It can be seen from the above steps that the perturbation step size directly determines the efficiency of the method. A larger perturbation step size will shorten the perturbation time, but At the same time, the accuracy of the perturbation will be reduced. In addition, since this method constantly disturbs the operating point, the operating point of the photovoltaic module will always oscillate near the maximum power point, and cannot be stabilized at the maximum power point, resulting in power loss. At the same time, when the light intensity changes rapidly, it will cause the wrong judgment of the power difference in two cycles, which will lead to the wrong judgment of the direction of the voltage disturbance at the operating point, and increase the time of the maximum power point tracking.

The advantage of the disturbance observation method is that the control method is simple, the control loops have been modularized, and the accuracy requirements of the hardware are not high.

However, this method oscillates near the maximum power point of the module, which cannot make the module work stably at the maximum power point, resulting in a certain power loss. The choice of the disturbance step size cannot take into account the tracking accuracy and response speed, and in special cases, errors may occur. judgment, prolong the tracking time, and even cause the tracking to fail.