Maximum Power Point Tracking

Photomodules have a complex relationship between environmental conditions and maximum power output . The fill factor (KZap) is a parameter that determines the nonlinear electrical behavior of the photocell. The duty cycle is defined as the ratio of the maximum power of the photomodule to the product of the open circuit voltage U _ХХ and short circuit current I _КЗ . In reference data, it is often used to determine the maximum power that a photocell can provide with optimal load under given conditions: P = KZap · U _XX · I _KZ . For most purposes, knowledge of short-circuit protection, U- _XX and I- _{short circuit is} enough to give a useful approximate model of the electrical behavior of a solar cell in typical conditions.

For any given operating conditions, the solar cells have one operating point at which the instantaneous values ​​of the current ( I ) and voltage ( U ) of the solar cell determine the instantaneous power at the operating point. According to Ohm's law , these values ​​correspond to a specific load resistance , which is equivalent to U / I. The power P is determined by the formula P = U · I. In a useful section of the current – ​​voltage characteristic, the photocell acts as a constant current source ^[2] . In the region of maximum I – V characteristic power, the photocell has an inverse exponential relationship between current and voltage. From the theoretical foundations of electrical engineering, the power from or to the device is optimized in the place where the derivative of the function (graphically the slope) dI / dU of the I – V characteristic is equal to and opposite to the I / U ratio (where dP / dV = 0) ^[3] . This place on the current-voltage characteristic is called the maximum power point (TMM) and corresponds to the curve bend.

The reciprocal of the load with resistance R = V / I determines the maximum power from the device. This resistance is sometimes called the characteristic resistance of the photocell. The characteristic resistance is a dynamic value depending on the level of insolation , temperature, age of the solar cell and other factors. If the resistance is greater or less than this value, then the output power will be less than the maximum available power and, therefore, the photocell will not be used with all available efficiency. Maximum power point tracking devices use various types of control circuits to search for this point in such a way as to obtain the maximum available power from the photocell.

The output current-voltage characteristic of electric alternators with excitation from permanent magnets (magdino, bicycle dynamos, wind generators) and a rectifier has a shape similar to the shape of the I-V characteristic of photomodules: the current in the short circuit mode is limited by the reaction of the armature and the inductive resistance of the windings, and the voltage in the mode idling - emf induction, depending on the engine speed. Therefore, to select the maximum power from such generators, the same algorithms apply as for photomodules, with the only difference being that it takes less reaction time of the system, since the number of revolutions of the engine rotating the generator can change at a significantly higher speed compared to the conditions insolation of photomodules.

Controllers typically use one of three algorithms to optimize the output power of photomodules. In some devices for tracking the maximum power point, several algorithms are implemented, and switching between the algorithms is based on the operating conditions of the array ^[4] .

Resentment and Observation

In this method, the OTMM device changes the input resistance by a small amount, as a result of which the voltage of the solar installation changes and measures the power, if the power increases, the controller continues to change the voltage in the same direction until the power stops increasing. This method is the most common, despite the fact that it leads to power fluctuations ^{[5] [6]} . This method is also referred to as the ascent method, because it depends on the curve P = f ( U ), which increases to the point of maximum power and decreases after this point ^[7] . The prevalence of this method is due to the simplicity of its implementation ^[5] . The perturbation and observation method will be highly effective if an accurate predictive and adaptive ascent algorithm is provided ^[8] .

Increasing Conductivity Method

In this method, the controller measures the increase in current and voltage of the solar installation to predict the effect of voltage changes. The method of increasing conductivity requires more calculations in the controller, but it can track changes in conditions faster than the perturbation and observation (ViN) method. Like the ViN method, it leads to power fluctuations ^[9] . This method uses the increasing conductivity ( dI / dU ) of the array of photomodules to calculate the sign of the change in power with respect to voltage ( dP / dU ) ^[10] .

The method of increasing conductivity calculates the point of maximum power by comparing the increasing conductivity (Δ I / Δ U ) with the conductivity of the array of photomodules ( I / U ). When these values ​​are the same ( I / V = Δ I / Δ V ), the output voltage is the maximum power voltage. The controller maintains this voltage until the insolation changes; after the change, the process is repeated ^[11] .

Current Scan Method

This method uses a sweep signal for the current of the array of photomodules to update the current-voltage characteristic at fixed intervals. The maximum power voltage is calculated according to the characteristic with the same frequency ^{[12] [13]} .

DC Voltage Method

The term “constant voltage method” in tracking the maximum power point is used to describe different techniques by different authors. This term refers to a method in which the output voltage is controlled by a constant value, regardless of the conditions, or a method in which the value is determined by the ratio of the current output voltage to the open circuit voltage ( V _OC ). Some authors call the latter method “open circuit voltage” ^[14] . When the output voltage of the array does not change, the controller does not try to track the maximum power point, that is, strictly speaking, the operating point is not the maximum power point. But this method in complex cases when other methods are mistaken continues to work, therefore it is sometimes used together with other methods.

The controller working according to this method momentarily disconnects the array from the load and measures the open circuit voltage, after which the controller continues to operate with a voltage controlled by a constant coefficient, for example, 0.76 from the open circuit voltage U _XX ^[15] . As a rule, this value was determined as the point of maximum power either empirically or based on modeling for the expected operating conditions ^{[9] [10]} . Thus, the operating point of the array of the photomodule is set next to the point of maximum power by adjusting the voltage of the array and comparing it with a fixed reference voltage V _ref = kV _OC . The value of V _ref can be adjusted in order to obtain optimal performance with respect to other factors, including the point of maximum power, but the main idea of ​​this technique is that V _ref is defined as a ratio to V _OC .

One of the inherent approximations of this method is that the ratio of the maximum power voltage to V _OC is an approximate constant and leaves room for further possible optimization.

Method Comparison

Perturbation and observation and the method of increasing conductivity are examples of "climbing" methods that can find the local maximum power for the operating state of the array and thus provide a true point of maximum power ^{[7] [9]} .

The perturbation and observation method can create fluctuations in the output power of the array of photomodules even with constant insolation.

The method of increasing conductivity has several advantages compared to the method of perturbation and observation - it can determine the point of maximum power without power fluctuations and, in rapidly changing conditions, more accurately tracks the point of maximum power ^[5] . But this method under rapidly changing atmospheric conditions can work randomly and create power fluctuations. Also, in comparison with the ViN method, the computation time is increased due to the complexity of the algorithm, which leads to a decrease in the sampling frequency ^[10] .

In the method of constant voltage (open circuit voltage), the current of the array of photomodules should be set to zero to measure the open circuit voltage and reduce the operating voltage by a predetermined part of the measured voltage, as a rule, about 76% ^[10] . For the time while the current is set to zero, the generated energy is lost ^[10] . The given value of the ratio V _MM / V _OC , equal to 76%, is not always accurate ^[10] . The constant voltage method, despite the ease of implementation, is inefficient and inaccurate due to interruptions in the work necessary to determine the open circuit voltage. Nevertheless, the efficiency of some systems can reach 95% ^[15] .

Network inverters track the maximum power point for the entire array of photomodules; in such systems, the inverter sets the current that flows through all the photomodules. With this arrangement of the system, energy losses occur due to the fact that different photomodules have different I – V characteristics and maximum power points (due to manufacturing tolerances, partial shading ^[16] , etc.) and therefore do not work at maximum power ^[1] .

Some companies (see the power optimizer ) produce maximum power point converters for individual panels, the use of which allows each photomodule to operate at maximum power regardless of shading, pollution and electrical imbalances.

The data show that using an inverter with one device to track the maximum power point in a project with photomodules installed west and east has no drawbacks compared to two inverters or one inverter with two devices for tracking the maximum power point ^[17] .

In network photovoltaic stations, all the power generated by the photomodules is transferred to the network.

An autonomous photoelectric system in the dark uses the energy stored in batteries to power consumers. In this system, the voltage of fully charged batteries may be close to the voltage of the maximum power of the photomodules, but in the morning the batteries are discharged and their voltage is much lower than the voltage of the maximum power. The battery charge begins with a voltage that is much less than the voltage of the maximum power point; to eliminate this discrepancy, maximum power point tracking devices are used.

When the batteries in the autonomous system are fully charged and there is no load for the consumption of photomodule generation, the maximum power point tracking device transfers the operating point, reducing the power until it matches the consumption. (An alternative approach is widely used in the construction of spacecraft, when the excess power of photomodules is used to power a resistive load, and thanks to this, the array always works at maximum power.)

• MPPT tracker by Daniel F. Butay ( Microchip PIC based)