*2.2. Hybrid Pant Control*

The plant control, as shown in Figure 3, performs the secondary control which involves set-point distribution among the resources of the hybrid plant.

$$P\_{ref\\_TPSH} = Plant\_{ref} - \sum\_{i=1}^{N} P\_{PV\_{i\prime}} \tag{1a}$$

$$P\_{ref\\_TPSK} \stackrel{\*}{}{} = \begin{cases} \begin{array}{c} \frac{\text{PG\\_TPSK}}{\text{P\\_TPSK}}, & \text{P\\_sch} > 0, \quad \text{Pref\\_TPSK} < \frac{\text{PG\\_TPSK}}{\text{P\\_TPSK}}\\ \hline \overline{\text{PG\\_TPSK}}, & \text{Psch} > 0, \quad \text{Pref\\_TPSK} > \overline{\text{PG\\_TPSK}}\\ \begin{array}{c} \overline{\text{PP\\_TPSK}}, & \text{P\\_sch} < 0, \quad \text{Pref\\_TPSK} < \frac{\text{PP\\_TPSK}}{\text{P\\_TPSK}}\\ \overline{\text{PP\\_TPSK}}, & \text{P\\_sch} < 0, \quad \text{Pref\\_TPSK} > \overline{\text{PP\\_TPSK}} \end{array} \end{cases} \tag{1b}$$

where *Pref* \_*TPSH*, *Pref* \_*TPSH*∗, *Plantref* , and *Psch* stand for the real power reference for TPSH, constrained real power reference for TPSH, reference to the entire plant, and scheduled power for the TPSH; *PGTPSH*, *PGTPSH*, *PPTPSH*, and *PPTPSH* stand for the minimum and maximum possible generation from TPSH, and minimum and maximum possible pump power consumption of TPSH.

**Figure 3.** Schematic of the hybrid PV + TPSH plant control.

The plant control estimates the PV generation using NN\_P and the array's curtailment gain *Kcn*, where NN\_P is a neural network emulating the maximum output power of each array (as the output of the NN\_P) given the solar irradiance, G, and temperature, T, as inputs. As shown in Figure 3, the plant control utilizes the PV plant reserve and control capability for (a) compensating for sudden changes in insolation through Δ*PPV\_comp*, (b) compensating for hydro plant nonlinear behavior through Δ*PPSH\_comp* and, (c) curtailing the PV plant through Δ*Pcurt*. The TPSH is used mainly for (a) firming slow disturbances in PV output, and (b) generation shifting. Both PV and TPSH system participate in voltage control. Some of the design features of the plant control are as follows:


$$\rho\_m = \begin{cases} 1, & V\_{\text{min}} < V < V\_{\text{max}} \text{ and } f\_{\text{min}} < f < f\_{\text{max}}\\ 0, & \text{otherwise} \end{cases} \tag{2}$$

$$
\Delta P\_{PSH\\_comp} = \begin{cases} \ 0 \ \ \rho\_m = 0 \\ \ \ P\_{\mathcal{E}\prime} \ \ \rho\_m = 1 \end{cases} \tag{3}
$$

where, *Vmin*, *Vmax*, *fmin*, and *fmax* refer to the minimum and maximum limits of terminal voltage *V* and frequency *f* , respectively.


$$
\Delta P\_{curt} = \begin{cases}
\begin{array}{c}
\operatorname{del}\\_PV\_{\prime} \quad \operatorname{del\\_PV} > 0 \\
0, \quad \operatorname{del\\_PV} < 0
\end{array}
\end{cases}
\tag{4}
$$

where *del*\_*PV* stands for deviation of total generation of the hybrid plant from the plant's reference.

• The PV plant compensates for the difference between desired and actual plant behavior using the Δ*PPSH\_comp* channel through *Pc*.

To enable the implementation of the described control, Equations (1)–(4) were used in the software defined controller, as shown in Figure 3.
