**4. Reactive Power Control**

The P-Q curves of a PV generator depends not only on the variation of solar irradiance or temperature but also on the dc voltage applied at the terminals of the PV arrar or the modulation index as part of the internal inverter control. In Figure 14 can be seen the variation of these parameters and how they affect to the P-Q curve.

**Figure 14.** PQ capability curve of a PV generator (**a**) Variable dc voltage (**b**) Variable Modulation index [30] (Reproduced from Solar Energy, Vol 140, Ana Cabrera et al., "Capability curve analysis of photovoltaic generation systems", Copyright (2016), with permission from Elsevier).

These curves obeys to the following expressions:

$$P\_{ref}^2 = \mathcal{S}^2 - \mathcal{Q}\_{ref}^2 \tag{3}$$

$$\left(P\_{ref}^2 + \left(Q\_{ref} + \frac{3V\_{grid}^2}{X}\right)^2 - \left(3.\frac{V\_{grid}V\_{conv}}{X}\right)^2\right. \tag{4}$$

Taking into account this P-Q curve, this section presents a novel control to provide reactive power depending on the grid code requirements. In this case, the reactive power control is set as a priority (Figure 15). This control reads the reference of reactive power given by the plant operator. If the reactive power control is not a priority, the control is developed with a conventional reactive power regulation. But if the reactive power is set as a priority, then the PV generator has to calculate the maximum possible reactive power (*qmpp*) by taking into account the capability curves studied in [30] and the variation of ambient conditions.

**Figure 15.** Control scheme for control of reactive power in PV generators.

The performance of the control will vary depending if it is absorbing or injecting reactive power.

## *4.1. Absorption of Reactive Power*

For the absorption of reactive power, the area of operation is in the fourth quadrant of the PQ capability curve. The maximum limitation of the reactive power varies according to:

$$Q\_{mpp}^2(G, T) = S^2 - P\_{mpp}^2(G, T, \upsilon\_{mpp}),\tag{5}$$

where, the *Pmpp* is the maximum active power that the PV generator can supply at that instant. For a given reference of absorbed reactive power *qref* , the control evaluates if this is higher than the *qmpp* at each instant. If it is higher, then the PV generator has to reduce the injection of active power by the variation of dc voltage. So, the PV generator is not working any longer at MPP instead will be working in other point of operation of active power. The RPPT control should again track the reference of active power calculated due to reactive power reference. Every time the solar irradiance changes, the control has to track the reactive power point by the variation of active power. This control will be called as the reactive power point tracker (QPPT).

This behavior is illustrated in Figure 16, where the first point is for a given solar irradiance (A). At this point, the active power that the PV generator can supply is *Pmpp*. On this instant, a reference of reactive power is given to the generator's control. However, with this power the *Qmpp* is lower than the reference. Thus, a new reference of active power is calculated (*Pref* 1). To achieve this point, the dc voltage has to change from *vmpp* to *vref* so the PV generator starts to work at point B. Then, the generator can supply the value of reactive power equal to the reference (point 3). In the case the solar irradiance changes a new PV curve is generated (blue line), because of the dc voltage value, the new active power is P2 and the PV generator starts to work in point C (PV curve) and 4 (PQ curve). As the RPPT control has to follow the reference of reactive power, then the dc voltage reduces to reach the reference (Point D and point 3).

**Figure 16.** QPPT operation in a variable PQ and ambient conditions: Absorption of reactive power. (1) MPP at one solar irradiance, (2) Variation of active power reference, (3) Reference of reactive power, (4) New active and reactive power

## *4.2. Injection of Reactive Power*

For the injection of reactive power, the area of operation is in the first quadrant of the PQ capability curve. The maximum limitation of the reactive power varies according to:

$$Q\_{mpp} = \frac{3\sqrt{3}}{2\sqrt{2}} \frac{V\_{grid} \cdot \upsilon\_{mpp} \cdot M}{X},\tag{6}$$

where, the modulation index (*M*) varies between 0 and 1. The maximum possible reactive power for a given solar irradiance, temperature and *vmpp* is when *M* is equal to 1. In order to increase this value of reactive power, the modulation index can be higher than 1 but it can cause the increment of harmonics [37].

In the case, the PPC asks a reference higher than *Qmpp*, the control should manage in one hand the dc voltage to reduce the active power and on the other hand the modulation index. This behavior is illustrated in Figure 17, where the first point is for a given solar irradiance (A). At this point, the active power that the PV generator can supply is *Pmpp*. In this instant, a reference of reactive power is given to the generator's control. However, with this power the *Qmpp* is lower than the reference. Thus, a new point of operation is calculated. First, the maximum modulation index varies to a higher value in order to increase the operation area. So, the maximum possible reactive power that the PV generator can inject increases. Then, to reach this point of operation at the specific reference of reactive power, the generated active power is reduced (*Pref* 1). To achieve this point the dc voltage has to change from *vmpp* to *vref* and the PV generator starts to work at point B. The corresponding algorithm that follows the logic illustrated in Figure 18.

**Figure 17.** QPPT operation in a variable PQ and ambient conditions: Injection of reactive power. (1) MPP at one solar irradiance, (2) Variation of active power reference, (3) Reference of reactive power.

**Figure 18.** Logic of control for reactive power in PV generators.

The control of active and reactive power is tested for different scenarios. These tests and the performance of the control are explained in the following section.
