Maximum power point tracking

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]

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.

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]

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.

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 an analog or digital circuit.
• 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).

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]