*1.3. Motivation and Literature Review*

The modern power system is a hybrid energy system and has the capability to manage multiple energy sources. Thus, the concept of hybridization is not new; however, a collocated PV and TPSH plant is proposed for the first time. No single energy source is optimal for all situations. Hybridization and coordinated control are required to utilize the benefits of each source while overcoming their shortcomings [3]. The designed controls facilitate this using the fast response of PV inverters and the storage capacity of PSH. A TPSH is considered to leverage the pump mode power consumption flexibility of the TPSH to firm the PV system.

To enhance the flexibility of the pumped hydro plant, many configurations have been proposed and implemented, such as the adjustable-speed PSH [4,5] and the TPSH [6,7]. A TPSH is composed of a synchronous machine, turbine, and pump on the same shaft as shown in Figure 1. The pump and turbine are separated with a clutch. Key advantages of the TPSH include (a) rapid mode change without the loss of synchronism, (b) pump mode power consumption flexibility using HSC, and (c) smooth start capability in pump mode [6,7]. In the turbine mode and pure pump mode, its working principles are like hydro turbines and pumps, respectively. When the HSC (or the shared penstock connecting the pump and turbine) is activated in pump mode, a part of (or all of) the water pumped is transferred to the turbine. This in turn causes the turbine to produce torque that is supplied to the shaft. This mechanical torque from the turbine will reduce the current drawn from the grid while still rotating at the synchronous speed. The remaining water is pumped up to the upper reservoir. Another perspective is that, when rotating at the rated speed, the pump still generates the rated head, but the amount of water transferred to the upper reservoir or true work done decreases.

**Figure 1.** Schematic diagram of the TPSH, where P = centrifugal pump, T = Francis turbine, c = clutch, and SM = synchronous machine.

To magnify the benefits of the proposed PV + TPSH hybrid, it can be compared with the quaternary PSH (QPSH) [8]. In QPSH, the pump and turbine have separate shafts and electrical machines, although the HSC still exists. The proposed hybrid provides a better alternative to the QPSH due to several reasons. Firstly, in QPSH, although the converterbased pump adds flexibility, it does not add generation capacity to the existing PSH system. The proposed PV + TPSH system has added generation capacity and added flexibility through the PV system. In fact, the QPSH reduces generation capacity if a retrofitting case is considered, as the space for one unit will have to be spared for the variable speed pump. Secondly, in generation mode the QPSH is similar in performance to any conventional PSH; however, the proposed PV + TPSH takes advantage of the PV inverters to provide rapid response to system disturbances in generation and pump modes. Lastly, the QPSH is a significant investment burden as not only do the pump and turbine have separate shafts but the converter also adds to the cost of the system without adding generation capacity.

The proposed PV + TPSH takes advantage of the existing infrastructure which is unused for PSH plants during the day. In addition, a report from the World bank [9] highlighted that floating PV systems can have several advantages as follows:


The most relevant dynamic modeling and analysis works on a PV + battery + hydro hybrid can be found in Wang and Xu [10], where, to test the stability of the PV hydro system, a dynamic model of a real system was created and simulated with disturbances. The purpose of the collocated PV + battery plant was to supplement the hydrogeneration during the dry season.

The Longyangxia Hydropower plant in Qinghai, China is an example of such a plant with a hybrid hydropower/PV system [11]. On a typical day, the output from the hydro facility is reduced, especially from 11:00 a.m. to 4:00 p.m., while PV generation is high. The saved energy is then requested by the operator for use during early morning and late-night hours. Although the daily generation pattern of the hydropower has changed, the daily reservoir water balance could be maintained at the same level as before to meet the water requirements of other downstream reservoirs.

Gevorgian and O'Neill [12] concluded that, with the fast and precise action of the PV inverters, multiple services such as fast frequency response and power oscillation damping can be provided to the grid, and that the technology required is already available. However, the accurate estimation of available peak power is important for all services, and the extent of these services will depend upon the maximum amount of available PV. When PV penetration is low, there will be other plants in the system that will provide ancillary services; however, when PV penetration increases, it becomes essential that utility-scale PV plants provide these services. The estimation of maximum power available and the DC operating voltage required for a particular power output is of utmost importance.

Hoke, Muljadi, and Maksimovic [13] proposed a second-order polynomial model to estimate the maximum power of a PV module from measured irradiance and temperature, where the coefficients of the model were derived through a linear regression of the PV MPP in different insolation and temperature conditions. Although the model seems accurate when the insolation and temperature is steady, during transient states, the model becomes highly inaccurate. Following the same trend, Hoke et al. [14] stored the P–V curves of the array as a look up table where interpolation is performed with a spline, which requires a considerable amount of memory that introduces error. Pappu, Chowdhury, and Bhatt [15] and Watson and Kimball [16] used pseudo-MPP by controlling the operating voltage to a

value greater than the MPP voltage. Here, the operating point is searched by the Perturb and Observe (P&O) algorithm over the power–voltage (P–V) characteristics, implemented through the DC/DC converter. Neely et al. in [17] used the curtailed PV power to realize the primary frequency control using the fixed-droop characteristics.

This paper is organized as follows: Section 2 describes the modeling and control effort for the PV and TPSH systems while also describing the plant controls. Section 3 describes the simulation results of the control algorithms.
