# Maximum power point tracking

(Redirected from Incremental conductance method)
Maximum power point tracking of the solar PV array

Maximum power point tracking (MPPT)[1][2] or sometimes just power point tracking (PPT)[3][4]) is a technique used commonly with wind turbines and photovoltaic (PV) solar systems to maximize power extraction under all conditions.

Although it primarily applies to solar power, the principle applies generally to sources with variable power: for example, optical power transmission and thermophotovoltaics.

PV solar systems exist in many different configurations with regard to their relationship to inverter systems, external grids, battery banks, or other electrical loads.[5] Regardless of the ultimate destination of the solar power, though, the central problem addressed by MPPT is that the efficiency of power transfer from the solar cell depends on both the amount of sunlight falling on the solar panels, the temperature of the solar panel and the electrical characteristics of the load. As the amount of sunlight and temperature of the solar panel vary, the load characteristic that gives the highest power transfer efficiency changes, so that the efficiency of the system is optimized when the load characteristic changes to keep the power transfer at highest efficiency. This load characteristic is called the maximum power point (MPP) and MPPT is the process of finding this point and keeping the load characteristic there. Electrical circuits can be designed to present arbitrary loads to the photovoltaic cells and then convert the voltage, current, or frequency to suit other devices or systems, and MPPT solves the problem of choosing the best load to be presented to the cells in order to get the most usable power out.

Solar cells have a complex relationship between temperature and total resistance that produces a non-linear output efficiency which can be analyzed based on the I-V curve.[6][7] It is the purpose of the MPPT system to sample the output of the PV cells and apply the proper resistance (load) to obtain maximum power for any given environmental conditions.[8] MPPT devices are typically integrated into an electric power converter system that provides voltage or current conversion, filtering, and regulation for driving various loads, including power grids, batteries, or motors.

• Solar inverters convert the DC power to AC power and may incorporate MPPT: such inverters sample the output power (I-V curve) from the solar modules and apply the proper resistance (load) so as to obtain maximum power.
• The power at the MPP (Pmpp) is the product of the MPP voltage (Vmpp) and MPP current (Impp).

## Background

Photovoltaic solar cell I-V curves where a line intersects the knee of the curves where the maximum power transfer point is located.

Photovoltaic cells have a complex relationship between their operating environment and the maximum power they can produce. The fill factor, abbreviated FF, is a parameter which characterizes the non-linear electrical behavior of the solar cell. Fill factor is defined as the ratio of the maximum power from the solar cell to the product of open circuit voltage Voc and short-circuit current Isc. In tabulated data it is often used to estimate the maximum power that a cell can provide with an optimal load under given conditions, P=FF*Voc*Isc. For most purposes, FF, Voc, and Isc are enough information to give a useful approximate model of the electrical behavior of a photovoltaic cell under typical conditions.

For any given set of operational conditions, cells have a single operating point where the values of the current (I) and voltage (V) of the cell result in a maximum power output.[9] These values correspond to a particular load resistance, which is equal to V / I as specified by Ohm's Law. The power P is given by P=V*I. A photovoltaic cell, for the majority of its useful curve, acts as a constant current source.[10] However, at a photovoltaic cell's MPP region, its curve has an approximately inverse exponential relationship between current and voltage. From basic circuit theory, the power delivered from or to a device is optimized where the derivative (graphically, the slope) dI/dV of the I-V curve is equal and opposite the I/V ratio (where dP/dV=0).[11] This is known as the maximum power point (MPP) and corresponds to the "knee" of the curve.

A load with resistance R=V/I equal to the reciprocal of this value draws the maximum power from the device. This is sometimes called the 'characteristic resistance' of the cell. This is a dynamic quantity which changes depending on the level of illumination, as well as other factors such as temperature and the age of the cell. If the resistance is lower or higher than this value, the power drawn will be less than the maximum available, and thus the cell will not be used as efficiently as it could be. Maximum power point trackers utilize different types of control circuit or logic to search for this point and thus to allow the converter circuit to extract the maximum power available from a cell.

power-voltage (P -V) curve

If a full Power-voltage (P -V)curve is available then the maximum power point can be obtained using a bisection method.

## Implementation

When a load is directly connected to the solar panel, the operating point of the panel will rarely be at peak power. The impedance seen by the panel determines the operating point of the solar panel. Thus by varying the impedance seen by the panel, the operating point can be moved towards peak power point. Since panels are DC devices, DC-DC converters must be utilized to transform the impedance of one circuit (source) to the other circuit (load). Changing the duty ratio of the DC-DC converter results in an impedance change as seen by the panel. At a particular impedance (i.e. duty ratio) the operating point will be at the peak power transfer point. The I-V curve of the panel can vary considerably with variation in atmospheric conditions such as radiance and temperature. Therefore, it is not feasible to fix the duty ratio with such dynamically changing operating conditions.

MPPT implementations utilize algorithms that frequently sample panel voltages and currents, then adjust the duty ratio as needed. Microcontrollers are employed to implement the algorithms. Modern implementations often utilize larger computers for analytics and load forecasting.

## Classification

Controllers can follow several strategies to optimize the power output of an array. Maximum power point trackers may implement different algorithms and switch between them based on the operating conditions of the array.[12]

### Perturb and observe

In this method the controller adjusts the voltage by a small amount from the array and measures power; if the power increases, further adjustments in that direction are tried until power no longer increases. This is called the perturb and observe method and is most common, although this method can result in oscillations of power output.[13][14] It is referred to as a hill climbing method, because it depends on the rise of the curve of power against voltage below the maximum power point, and the fall above that point.[15] Perturb and observe is the most commonly used MPPT method due to its ease of implementation.[13] Perturb and observe method may result in top-level efficiency, provided that a proper predictive and adaptive hill climbing strategy is adopted.[16][17]

### Incremental conductance

In the incremental conductance method, the controller measures incremental changes in PV array current and voltage to predict the effect of a voltage change. This method requires more computation in the controller, but can track changing conditions more rapidly than the perturb and observe method (P&O). Like the P&O algorithm, it can produce oscillations in power output.[18] This method utilizes the incremental conductance (${\displaystyle dI/dV}$) of the photovoltaic array to compute the sign of the change in power with respect to voltage (${\displaystyle dP/dV}$).[19] The incremental conductance method computes the maximum power point by comparison of the incremental conductance (${\displaystyle I_{\Delta }/V_{\Delta }}$) to the array conductance (${\displaystyle I/V}$). When these two are the same (${\displaystyle I/V=I_{\Delta }/V_{\Delta }}$), the output voltage is the MPP voltage. The controller maintains this voltage until the irradiation changes and the process is repeated.

The incremental conductance method is based on the observation that at the maximum power point ${\displaystyle dP/dV=0}$, and that ${\displaystyle P=IV}$. The current from the array can be expressed as a function of the voltage: ${\displaystyle P=I(V)V}$. Therefore, ${\displaystyle dP/dV=VdI/dV+I(V)}$. Setting this equal to zero yields: ${\displaystyle dI/dV=-I(V)/V}$. Therefore, the maximum power point is achieved when the incremental conductance is equal to the negative of the instantaneous conductance. The characteristic of the power-voltage curve also shows that: when the voltage is smaller than the maximum power point, ${\displaystyle dP/dV>0}$, so ${\displaystyle dI/dV>-I/V}$; when the voltage is bigger than the maximum power point, ${\displaystyle dP/dV<0}$ or ${\displaystyle dI/dV<-I/V}$. Thus, the MPP tracker can know where it is on the power-voltage curve by calculating the relation of the change of current/voltage and the current voltage themselves.

### Current sweep

The current sweep method uses a sweep waveform for the PV array current such that the I-V characteristic of the PV array is obtained and updated at fixed time intervals. The maximum power point voltage can then be computed from the characteristic curve at the same intervals.[20][21]

### Constant voltage

The term "constant voltage" in MPP tracking is used to describe different techniques by different authors, one in which the output voltage is regulated to a constant value under all conditions and one in which the output voltage is regulated based on a constant ratio to the measured open circuit voltage (${\displaystyle V_{OC}}$). The latter technique is referred to in contrast as the "open voltage" method by some authors.[22] If the output voltage is held constant, there is no attempt to track the maximum power point, so it is not a maximum power point tracking technique in a strict sense, though it does have some advantages in cases when the MPP tracking tends to fail, and thus it is sometimes used to supplement an MPPT method. In the "constant voltage" MPPT method (also known as the "open voltage method"), the power delivered to the load is momentarily interrupted and the open-circuit voltage with zero current is measured. The controller then resumes operation with the voltage controlled at a fixed ratio, such as 0.76, of the open-circuit voltage ${\displaystyle V_{OC}}$.[23] This is usually a value which has been determined to be the maximum power point, either empirically or based on modelling, for expected operating conditions.[24][19] The operating point of the PV array is thus kept near the MPP by regulating the array voltage and matching it to the fixed reference voltage ${\displaystyle V_{ref}=kV_{OC}}$. The value of ${\displaystyle V_{ref}}$ may be also chosen to give optimal performance relative to other factors as well as the MPP, but the central idea in this technique is that ${\displaystyle V_{ref}}$ is determined as a ratio to ${\displaystyle V_{OC}}$. One of the inherent approximations in the "constant voltage" ratio method is that the ratio of the MPP voltage to ${\displaystyle V_{OC}}$ is only approximately constant, so it leaves room for further possible optimization.

### Temperature Method

This method of MPPT estimates the MPP voltage (${\displaystyle V_{mpp}}$) by measuring the temperature of the solar module and comparing it against a reference.[25] Since changes in irradiation levels have a negligible effect on the maximum power point voltage, its influences may be ignored - the voltage is assumed to vary linearly with the temperature changes.

This algorithm calculates the following equation:

${\displaystyle V_{mpp}(T)=V_{mpp}(T_{ref})+u_{V_{mpp}}(T-T_{ref})}$

Where:

${\displaystyle V_{mpp}}$ is the voltage at the maximum power point for a given temperature;

${\displaystyle T_{ref}}$ is a reference temperature;

${\displaystyle T}$ is the measured temperature;

${\displaystyle u_{V_{mpp}}}$ is the temperature coefficient of ${\displaystyle V_{mpp}}$ (available in the datasheet).

• Simplicity: This algorithm solves one linear equation. Therefore, it does not consume much computational power.
• Can be implemented as analog or digital circuits.
• Since temperature varies slowly with time, there are no steady-state oscillation and instability.
• Low cost: temperature sensors are usually very cheap.
• Robust against noise.

• Estimation error might not be negligible for low irradiation levels (e.g. below 200 W/m²).

### Comparison of methods

Both perturb and observe, and incremental conductance, are examples of "hill climbing" methods that can find the local maximum of the power curve for the operating condition of the PV array, and so provide a true maximum power point.[6][15][24]

The perturb and observe method requires oscillating power output around the maximum power point even under steady state irradiance.

The incremental conductance method has the advantage over the perturb and observe (P&O) method that it can determine the maximum power point without oscillating around this value.[13] It can perform maximum power point tracking under rapidly varying irradiation conditions with higher accuracy than the perturb and observe method.[13] However, the incremental conductance method can produce oscillations (unintentionally) and can perform erratically under rapidly changing atmospheric conditions. The sampling frequency is decreased due to the higher complexity of the algorithm compared to the P&O method.[19]

In the constant voltage ratio (or "open voltage") method, the current from the photovoltaic array must be set to zero momentarily to measure the open circuit voltage and then afterwards set to a predetermined percentage of the measured voltage, usually around 76%.[19] Energy may be wasted during the time the current is set to zero.[19] The approximation of 76% as the ${\displaystyle V_{MPP}/V_{OC}}$ ratio is not necessarily accurate.[19] Although simple and low-cost to implement, the interruptions reduce array efficiency and do not ensure finding the actual maximum power point. However, efficiencies of some systems may reach above 95%.[23]

## MPPT placement

Traditional solar inverters perform MPPT for the entire PV array (module association) as a whole. In such systems the same current, dictated by the inverter, flows through all modules in the string (series). Because different modules have different I-V curves and different MPPs (due to manufacturing tolerance, partial shading,[26] etc.) this architecture means some modules will be performing below their MPP, resulting in lower efficiency.[27]

Some companies (see power optimizer) are now placing a maximum power point tracker into individual modules, allowing each to operate at peak efficiency despite uneven shading, soiling or electrical mismatch.

Data suggests having one inverter with one MPPT for a project that has identical number of east and west-facing modules presents no disadvantages when compared to having two inverters or one inverter with more than one MPPT.[28]

## Operation with batteries

At night, an off-grid PV system may use batteries to supply loads. Although the fully charged battery pack voltage may be close to the PV panel's maximum power point voltage, this is unlikely to be true at sunrise when the battery has been partially discharged. Charging may begin at a voltage considerably below the PV panel maximum power point voltage, and an MPPT can resolve this mismatch.

When the batteries in an off-grid system are fully charged and PV production exceeds local loads, an MPPT can no longer operate the panel at its maximum power point as the excess power has no load to absorb it. The MPPT must then shift the PV panel operating point away from the peak power point until production exactly matches demand. (An alternative approach commonly used in spacecraft is to divert surplus PV power into a resistive load, allowing the panel to operate continuously at its peak power point in order to keep the panel cooler as much as possible.[29])

In a grid-connected photovoltaic system, all delivered power from solar modules will be sent to the grid. Therefore, the MPPT in a grid connected PV system will always attempt to operate the PV modules at its maximum power point.

## References

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