Maximum power point tracking

IV curve

Photovoltaic cells have a 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 V _oc and Short-Circuit Current I _sc . In this paper, it is often used to estimate the maximum power of an optimal load under given conditions, P = FF * V _oc * I _sc . For most purposes, FF, V _oc , and I _sc are required to provide a relevant approximate model of the electrical behavior of a photovoltaic cell under typical conditions.

For any given set of operational conditions, 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 inverse inverse exponential relationship between current and voltage. From basic system theory, the Power Delivered from gold to a device is optimized Where the derivative (Graphically, the slope) dI / dV of the IV curve is equal and opposite the I / V ratio (Where d P / 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 greater than this value, the power drawn would be less than the maximum available, and thus the cell would not be used as it could be. Maximum power point trackers utilize different types of control circuit or logic to achieve this point and thus to allow the converter circuit to extract the maximum power available from a cell.

MPPT 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 derives from 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 used 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 (or duty ratio) the operating point will be at the peak power transfer point. The IV curve of the panel can vary with variation in atmospheric conditions such as radiance and temperature. Therefore,

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 of the array and measures power; if the power increases, further adjustments in that direction. This is called the most common method in the field of 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, and the fall above that point. ^[15] Perturb and observe is the most commonly used MPPT method. ^[13]This method is suitable for a predictive and adaptive hill climbing strategy. ^[16] [17]

Incremental conductance

In the incremental conductance method, the controller measures incremental changes in the current array and voltage to predict the effect of a voltage change. This method requires more computation in the controller, but can change and observe method (P & O). Like the P & O algorithm, it can produce oscillations in power output. ^[18] This method utilizes the incremental conductance (dI / dV) of the photovoltaic array to compute the signal of change in power with respect to voltage (dP / dV). ^[19]

The incremental conductance method computes the maximum power point by comparison of the incremental conductance (I _Δ / V _Δ ) to the array conductance (I / V). When these two are the same (I / V = ​​I _Δ / V _Δ ), the output voltage is the MPP voltage. The controller maintains this voltage until the irradiation changes and the process is repeated. ^[13]

The incremental conductance method is based on the observation that the maximum power point dP / dV = 0, and that P = IV. The current from the array can be expressed as a function of the voltage: P = I (V) V. Therefore, dP / dV = VdI / dV + I (V). Setting this equal to zero yields: dI / dV = -I (V) / V. Therefore, the maximum power factor is achieved when the incremental conductance is equal to the negative of the instantaneous conductance.

Current sweep

The current sweep method uses a PV array which is such that the characteristic of the PV array is obtained 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 is used to describe the voltage in the field of constant voltage. measured open circuit voltage (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 maximize power point, so it does not have a maximum power point tracking technique in a strict sense, although it does have some advantages in cases when the MPP tracking tend to fail, and thus it is sometimes used to supplement an MPPT method in those cases.

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 is measured. The controller then resumes operation with the voltage controlled at a fixed ratio, such as 0.76, of the open-circuit voltage V _OC . ^[23] This is usually a value that has been determined for the maximum power point, or empirically based on modeling, for expected operating conditions. ^[18] [19] The operating points of the PV array is THUS kept near the MPP by regulating the voltage array and matching it to the fixed reference voltage V _ref = kV _OC . The value of V _refmay be chosen to give optimal performance to other factors as well as the MPP, but the central idea in this technique is that V _ref is determined as a ratio to V _OC .

One of the inherent approximations to the “constant voltage” ratio is that the ratio of the MPP voltage to V _OC is only approximately constant, so it leaves room for further possible optimization.

Comparison of methods

Both perturbations and observations, and incremental conductance, are examples of “hill climbing” methods that allow maximum power point analysis. ^{[6] [15] [18]}

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

The incremental conductance method has the advantage over the disturbance and observation (P & O) method that it can determine the maximum power point without oscillating around this value. ^[13] It is possible to perform a better performance under the conditions of higher incidence of irradiation. ^[13] However, the incremental conductance method can produce oscillations (unintentionally) and can perform erratically under rapidly changing atmospheric conditions. The sampling frequency is decreased to the higher complexity of the algorithm compared to the P & O method. ^[19]

In the constant voltage ratio (or “open voltage”), the current of the photovoltaic array must be set to zero, and the rate of change is generally high, usually around 76%. ^[19] Energy can be wasted during the time is set to zero. ^[19]The approximation of 76% as the MPP / V _OC ratio is not necessarily accurate. ^[19] Although simple and low-cost to implement, the interruptions reduce array efficiency and maximize the power point. However, efficiencies of some systems may reach above 95%. ^[23]

MPPT placement

Traditional solar inverters perform MPPT for the whole 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 MPPs (due to manufacturing tolerance, partial shading, ^{[24] and} so on) result in different MPPs, resulting in lower efficiency. ^[25]

Some companies (see power optimizer ) are in the process of being able to operate on individual modules, allowing them to operate at peak efficiency, even after shading, soiling or electrical mismatch.

Data suggests having one inverter with one MPPT for a project that has east and west-facing modules presents no disadvantages when compared to having two inverters or one inverter. ^[26]

Operation with batteries

At night, an off grid PV system can use batteries to supply loads. Although the battery pack 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. The maximum power point voltage panel can be determined at this point, and an MPPT can resolve this mismatch.

When the batteries in an off-grid system are fully charged and the production of local power is higher than that, it can not be used to the maximum power. The MPPT must then shift to the point of production. (An alternative approach commonly used in spacecraft is to divert surplus power to a resistive load.

In a grid connected photovoltaic system, it will be delivered to the grid. Therefore, the MPPT in a grid connected PV system will always be able to exploit the PV modules at its maximum power point.

References