*3.5. Fast Frequency Response of Hybrid Plant in IEEE 9-Bus System*

The above tests verified the secondary control capability of the hybrid plant and its controls. The subsequent tests were performed to verify the primary controls. The hybrid plant was integrated to the IEEE 9-bus system [29], as indicated in Figure 13, and a load was applied suddenly at bus 5 at *t* = 60 s. As a result, the frequency of the system declined. The frequency profile for this test is shown in Figure 14a,c,e, where the TPSH is in generation mode, pump mode with HSC active, and pure pump mode. The real power contributions from the hybrid and TPSH plant are compared in Figure 14b,d,f. In all cases, the hybrid plant outperformed the TPSH plant in that it improved the frequency nadir and damped frequency oscillations. This was mainly attributed to the joint response of the PV and TPSH plant. The PV plant utilized its reserves for inertia control and droop control, to support frequency.

**Figure 13.** IEEE 9-bus system with proposed PV plant and controls at bus 3.

**Figure 14.** FFR results of frequency and real power output: (**a**,**b**) generation mode, (**c**,**d**) pump mode with HSC, and (**e**,**f**) pure pump mode.

#### **4. Conclusions**

To cope with high flexibility and resilience requirements of future low inertia power systems, this paper proposes a novel PV + TPSH hybrid plant and designs its controls using a neural network-based structure. The TPSH was chosen because of its pump mode flexibility. The aim was to exploit the flexibility of the TPSH and leverage the controller-induced flexibility of the PV system to make the hybrid plant be-have as a conventional plant. The advantages of the proposed hybrid configuration include (a) the addition of generation capacity, (d) the formation of a self-sufficient source, and (d) reduced transmission loss in pump mode. If a floating PV system is used, the additional advantages of that can be realized as well.

The designed controls can be decomposed into three parts: (a) hybrid plant control, (b) PV plant control, and (c) TPSH plant control. The hybrid plant control distributes the set-point among the TPSH and PV systems, while the array controls make sure that the hybrid plant control commands are followed accurately, and that the primary control is

provided. The TPSH control is a nominal hydro-governor enhanced with mode change capability. To control the PV arrays, a neural network-based reference governor framework was used, with a mixture of CFNN and FFNN. Here, two separate neural networks are used to accurately regress the required DC link voltage and the maximum power as a function of irradiance and temperature.

Through detailed simulation case studies, it was shown that, using the designed controls within operational constraints, the hybrid plant behaved like a conventional plant. In addition to configuration advantages mentioned above, it is concluded that the controls can (a) enable the PV plant to track set-points, (b) coordinate the response and coordination of shaded and unshaded PV arrays, (c) enhance the response of the TPSH plant for set-point tracking in generation and pump mode with HSC, (d) enable pure pump mode set-point tracking (f) can firm the PV plant with array control, systematic curtailment and TPSH response, and (g) enhance fast frequency response through combined response of PV and TPSH.

**Author Contributions:** Conceptualization, S.N., and K.Y.L.; methodology, S.N., and K.Y.L.; validation, S.N., and K.Y.L.; investigation, S.N.; writing—original draft preparation, S.N.; writing—review and editing, K.Y.L.; supervision, K.Y.L.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

The parameter values used for TPSH governor turbine, excitation, and synchronous machine can be found in the tables below.

**Table A1.** Synchronous machine parameters [28].


**Table A2.** Exciter parameters [29].


**Table A3.** Governor turbine system parameters referring to Figure A1.


**Figure A1.** Governor and turbine model for the TPSH.

### **Appendix B**

The pseudo code for the automatic mode change algorithm is described below. Here, the modes 1, 2, and 3 correspond to generation, pump, and pump with hydraulic shortcircuit modes; MC indicates the required mode change where, for example, 23 indicates pump to pump with hydraulic short-circuit; *ρ<sup>p</sup>* and *ρ<sup>t</sup>* are binary variables that indicate on/off status for the pump and turbine gates as in Figure A1.

