Solar–hydro hybrid power station as a way to smooth power output and increase water retention

Solar Energy 173 (2018) 675–690

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Solar–hydro hybrid power station as a way to smooth power output and increase water retention

T

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Jakub Jurasz , Bartłomiej Ciapała AGH University, Kraków, Poland

A R T I C LE I N FO

A B S T R A C T

Keywords: Energy source variability Non-dispatchable Power system Hybrid energy source Integration

There is environmental, societal and also economic pressure to increase the share of renewable energy sources in covering energy demand. However, the stochastic and non-dispatchable nature of the two main such sources (photovoltaics and wind generation) complicates their integration into the power system. The operation mode of the run-of-river power plant with pondage that is considered here has potential to smooth electricity generation from photovoltaics, whilst also maintaining the hydropower capacity factor and increasing water retention – an important aspect when a decision-maker has to make a trade-off between power generation and, for example, irrigation. This paper presents the theoretical background to our research, introduces a discrete mathematical simulation and optimization model and provides a detailed analysis of the obtained results and the operation of the entire system. We also highlight the impact on the capacity factor of hydropower as well as addressing the potential need to install more than one water turbine to ensure greater flexibility of hydropower and efficient utilization of water resources. The optimization results of the analyzed case study show that for an observed average flow rate of 1.3 m3/s and annual irradiation of 1050 kWh/m2 a 176-kW water turbine and pondage capacity of 1.36 MWh is sufficient to smooth the power generation of a 687-kW PV installation while also satisfying constraints imposed on reliability and performance.

1. Introduction Over recent years, significant attention has been devoted to the problem of integrating variable renewable energy sources (VRES) (especially photovoltaics and wind generation) into power systems (Jones, 2014) – systems which in most cases are dominated by large scale coal/gas/oil or nuclear power plants. Several approaches and solutions which might be used to facilitate and smooth VRES integration were summarized by Delucchi and Jacobson (2011) and consider: interconnecting dispersed generators; using complementary and nonvariable energy sources to cover demand; applying demand-response and flexible loads; storing electricity at its place of origin; oversizing VRES to meet demand and generate hydrogen; storing electricity where it is consumed and in electric vehicles; and using forecasts (e.g. of weather) to predict the energy output of PVs or WTs. Although hybrid wind–solar–water systems have been widely elaborated, the possibility of balancing unstable PV power generation by using hydro sources in order to improve system reliability has recently drawn significant attention. Thoroughly worked-through solutions are well-described by different authors (Aihara and Yokoyama, 2016; Aihara et al., 2011; Ogueke et al., 2016), including net energy return on

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energy invested by Kittner et al. (2016). Feasibility studies and simulations by Kusakana et al. (2009), Margetaa and Glasnovic (2010), Zhou et al. (2013) (and efforts at optimization on a variety of scales) have been made in very recent years by others (Kenfack et al., 2009; Kougias et al., 2016; Jurasz and Ciapała, 2017). The main factor supporting claims of hydropower’s potential to integrate variable photovoltaics is their temporal complementarity and especially the flexibility of hydropower due to its storage potential, which has been presented and analyzed in several studies. Beluco et al. (2008) proposed a dimensionless index for assessing the complementarity between hydraulic and solar energies and in their followup study (Beluco et al., 2012) presented a method for scrutinizing the impact of solar–hydro complementarity on the operation of hybrid plants. Palfi and Zambon (2013) and De Jong et al. (2013) assessed the complementarity of solar, wind and hydropower in Brazil, showing that solar energy can be used to reduce the need for hydropower generation in the hot months, when water is needed for irrigation purposes. Three other studies, (An et al., 2015; Ming et al., 2017; Relva et al., 2015), introduced a method for PV–hydro hybrid operation which exploited their temporal complementarity. Meanwhile, Kougias et al. (2016) went further and proposed an approach for optimizing (increasing)

Corresponding author. E-mail address: [email protected] (J. Jurasz).

https://doi.org/10.1016/j.solener.2018.07.087 Received 24 April 2018; Received in revised form 20 July 2018; Accepted 28 July 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.

Solar Energy 173 (2018) 675–690

J. Jurasz, B. Ciapała

EHP EPV EPV_CS EPV_N g H hROR hI hII HSTC PH PPV RR RRO RRS Q RRQ QDis QMax T t TSTC V α β γ δ ε ηPV ηTur ρ μ

Nomenclature Abbreviations BES CF CS CSP ESS LOLP PV RoR SOC STC VRES WAI WT

battery energy storage capacity factor clear sky concentrated solar power energy storage system loss of load probability photovoltaics run-of-river state of charge standard testing conditions variable renewable energy source water abstraction index wind turbine

Indices t

time (t = 1, … , N) [hours]

Parameters, Variables & Constants a EB EB_N EH EH_B EH_PV EH’ EHD

pondage width and length [m] contracted electricity generation from RoR [kWh] not covered contracted electricity yield from RoR [kWh] electricity yield from RoR [kWh] RoR potential which can be used to cover contracted energy demand [kWh] RoR generation used to smooth PVs yield [kWh] electricity generation from unconstrained RoR operation [kWh] demand on hydropower [kWh]

RoR electricity generation potential [kWh] electricity yield from PVs [kWh] electricity yield from PVs under CS conditions [kWh] not smoothed PVs generation [kWh] gravitational acceleration [m/s2] irradiation [kWh/m2] RoR head [m] basic RoR head [m] RoR head resulting from pondage [m] irradiation in STC [kWh/m2] installed capacity in RoR [kW] installed capacity in PVs [kW] ramp rate [kW/h] ramp rate observed [kW/h] ramp rate sum [kW/h] flow rate [m3/s] ramp rate quantified [kW/h] water discharged from RoR [m3/s] water turbine maximal throughput [m3/s] temperature [°C] time [hour] temperature in STC [°C] pondage capacity [m3] minimal allowed ramp rate [%] maximal allowed ramp rate [%] not realized contracted RoR yield [%] PVs not smoothed to CS conditions [%] allowed CF reduction [%] overall PVs efficiency [%] water turbine efficiency [%] water density [1000 kg/m3] PV cell temperature reduction factor [%/°C]

which is to some extent a dispatchable power source (within the capacity of pondage and turbine output), can be successfully used to smooth the energy exchange with the grid. What is more, the results have shown that an RoR with pondage can be used to accommodate significant capacity from PVs without unexpected energy deficits and surpluses, which in turn translates into smaller ramp-ups and rampdowns for conventional power plants. Considering the results presented in (Jurasz and Ciapała, 2017), and encouraged by a recently published paper by François et al. (2017) which presented a method for estimating the complementarity between hydro–solar energy sources (where the hydro part uses small, ungauged rivers, which constitute the majority of rivers) and by the hydropower–PV hybrids mentioned above, we believe there is a still-untapped potential for hydropower to facilitate the integration of VRES into the power system. In our previous work (Jurasz and Ciapała, 2017), the role of the RoR–PV hybrid was to provide as much energy as needed (which resulted from the observed energy demand in a given part of the electric grid), with an acceptably small margin of RoR. Additionally, taking into account the various capacities of the RoR’s pondage, the objective function of the optimization was to maximize the installed capacity in PVs by adjusting the grid’s coverage of the baseload. In the present work, the baseload was estimated for two periods only – daylight and night time. Those periods were determined based on clear-sky (CS) models, which identify the times when energy can theoretically be generated by PVs. Here we want to depart from the problem of covering energy demand using RoR–PV and focus instead on exploiting the temporal variability and complementarity of the two energy sources, as well as

hydro–solar complementarity. Francois et al. (2016) investigated solar–hydro complementarity in northern Italy and showed how such sources behave in energy systems entirely supplied from run-of-river power plants and photovoltaics. Another two papers by Jurasz and Piasecki (2016), Jurasz et al. (2016) have analyzed the temporal complementarity of solar and hydropower in Poland. In terms of the complementarity of energy resources, an exhaustive review study by Engeland et al. (2017) was recently published which can be used for further reference. Considering the above, it can be said that solar and water resources exhibit significant potential for being coupled in a single hybrid energy source. This possibility of solar–hydro generators has already been presented in several papers. An interesting approach is presented in work by Kougias et al. (2016), which proposed the possibility of exploiting the energetic potential of the downstream faces of dams by equipping them with PV installations. Some advantages of using concentrated solar power (CSP) instead of PV for solar energy in a hydropowerdominated national grid system are defined in a study by Tomaschek et al. (2016). Particularly worthy of attention is a solution described by Guan et al. (2015) which successfully simulates the parallel operation of hydropower and a PV–battery scheme. On the large scale, on-grid topology for a similar set-up has also been designed by Zhou et al. (2013). The promising possibility of cooperation between PV and hydropower is addressed in paper by Chankhamrian et al. (2014), where PV is intended to provide DC voltage for a dynamic voltage restorer, which improves power quality. This paper is a follow-up on our recent work (Jurasz and Ciapała, 2017) on using an RoR power plant with pondage to integrate PVs into a local (low-voltage) grid. Those results indicated that hydropower, 676

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model is introduced in Section 2; the input data is presented in Section 3; Section 4 describes the obtained results; and the main conclusions and future prospects are briefly summarized in Section 5.

the storage potential of RoR’s pondage, which will be varied during the analysis to explore its impact on system performance. On the one hand we are aiming at managing the variable electricity yield from PVs by using hydropower to ensure that their power output will be exactly equal to that observed in CS conditions. Such an objective will ensure the greater predictability of PV operation and improve the power system operation by reducing uncertainty. On the other, we want to avoid the situation in which RoR’s potential to generate electricity is wasted simply because its primary objective is to smooth PV electricity yield. This second objective is realized by assuming that, depending on month and time of day (daylight/night), the hydropower is set to provide a fixed amount of energy to the grid (in other words the hydropower covers fixed loads depending on month and time of the day).

2. Problem description & optimization 2.1. RoR and PV hybrid design and objectives For the purpose of this paper we built upon the model presented in (Jurasz and Ciapała, 2017) but decided to simplify the pondage modelling by assuming it has cuboidal dimensions. For clarity of reasoning, we introduce the whole model of the hybrid operation presented in Fig. 1 in Appendix A.

Result seen from the power system operator point of view Energy

Variable irradiation

Variable flowrate Pondage

hII V

hI

Intake

Dead/inactive storage or part of RoR structure

RoR used not only for PV’s integration

Smoothed and reliable PV energy generation

Sunrise Sunset Legend: - contracted RoR energy generation: daylight and - nighttime. - energy from PV. ….- RoR smoothing PV’s yield to that under CS conditions.

Dam

Power house

QMax

Fig. 1. Conceptual design and schematic presentation of the general idea behind RoR–PV hybrid operation.

The considered system consists of a dam and photovoltaic power plant (single, or an ensemble of dispersed household installations), all operating within a given small part of the electricity grid. Within that system, the PV installations aim to produce as much energy as possible, although this is often substantially lower than expected, and is limited by variable irradiation. Extreme drops in capacity, of as much as 63% of rated power per minute, are known to occur, but in one-second resolution 50% drops in irradiation (on the horizontal plane) are also observed, as shown by Alam et al. (2014), while variations of up to 90% per minute have been recorded elsewhere by Marcos et al. (2011). Such rapid fluctuations are described in terms of ramp-ups and ramp-downs and may cause non-negligible difficulties in maintaining proper quality of supplied power. So, while the extent of these fluctuations can be predicted, their exact timings cannot, as shown by Kleissl (2013) and they are thus practically impossible to accommodate through scheduling of industrial-sized power plants, because drops and rises in PV output are very rapid. Multiple solutions are proposed in the related literature, namely: battery energy storage (BES), superconducting magnetic energy storage, fuel cells and electric capacitors. The use of BES is being widely considered, despite problems with system durability. BES allows changes to be limited in both the ramp-down and the ramp-up. Usually, a moving average model is proposed, but, due to the memory effect of this method, other improved approaches are also considered. There are known formulas for estimating the power (Marcos et al., 2014) (introduced by Macros et al.) and energy (De la Parra et al., 2015) (introduced by de la Para et al.) which needs to be provided by energy storage systems (ESS). Generally, the solutions tend to lower local electricity production peaks and to store surplus energy for later use during ramp-down episodes. Such an approach provides a significantly

Unlike other studies in this paper we considered the possibility of using hydropower to smooth PV output to the electricity yield curve observed under clear-sky conditions – in former works hydropower was only used to balance the variability of solar power, but in the context of observed load. Considering the above, the assumptions with regard to the hydropower operation priority are: 1. hydropower buffers the difference between theoretical electricity yield from PVs under clear-sky conditions and those observed in reality; 2. hydropower generates energy to cover some defined demand. The defined energy demand has to be fixed at a level which will not disrupt the buffering operation. In our research this is based on a deterministic model and a monthly interval, but in reality will be created based on inflow forecasts and can be performed on an hourly basis. Taking the above into account, we summarize the three main objectives of this contribution as follows: (a) to develop an adequate simulation and optimization model (based on hourly data) for the problem of using hydropower both to smooth solar generation, and to deliver scheduled energy to the grid, with a context and assumption which are both novel; (b) to investigate the impact of the proposed operation mode on the small water retention/the pondage state of charge; (c) to develop an index for quantifying and assessing the ramp rates of such a hybrid operating under given constraints. The paper is organized as follows: the simulation and optimization 677

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P H = ηTur ghRORρQ

smoother electricity production curve, which is more easily accommodated by the power grid. The literature provides various power output fluctuation limits that can be accepted by the power grid, from 1 to 5%/min (in Mexico), typically 10%/min, and up to 30% in deeply penetrated grid networks on islands. As shown by Elsinga and Sark (2015), Cole et al. (2016) spatial distribution of PVs may to some extent reduce observed ramp rates. Regarding ramp rates it is also worth noting that the modular nature of PV systems enables their various configuration and orientations (azimuth and inclination angle) that are suboptimal in terms of electricity generation, but that may increase the match between power supply and demand as shown by for example Chattopadhyay et al. (2017). As indicated by Kies et al. (2016), there is also some potential to accommodate sudden ramp-rates using “demand side management”, which involves adjusting the power demand of certain appliances to forecasted changes in the power generation of variable sources. In the proposed model, a small hydropower with pondage discharges previously cumulated water at varying rates to match variations in energy shortfalls. However, it immediately becomes obvious that the proposed system cannot compensate for power shortages lasting for less than the turbine’s reaction time (reaction time caused by turbine and water inertia). In the case of an already-spinning turbine (which is typical in the considered scenario), reaction time varies depending on the turbine’s size and type, from minutes to seconds (or less than a second in micro-hydropower installations) (Márquez et al., 2009). However, the system is fully capable of smoothing the power curve of longer-lasting power drops. It is also noteworthy that short power deficits are usually related to small clouds or other objects that shade a comparatively small area of the earth’s surface, and spatial distribution therefore allows a comparatively smooth electricity production curve to be attained, as noted by other authors (Marcos et al., 2012; Wiemken et al., 2001; Lave et al., 2012; Murata and Otani, 1997). It is also worth noting that although small hydropower does not allow the ESS to be completely removed, it has significant potential to limit stored energy requirements, making the entire system less susceptible to battery degradation over the years. As shown by Solomon et al. (2016), the existence of strong temporal complementarity between individual energy sources can significantly reduce the need for energy storage. Unlike when smoothing by means of the ESS, the proposed solution does not face the problem of a charging/discharging strategy in rampup situations, nor of the trade-off between keeping the battery charged and discharged (level of battery charge). Still, there is the problem of water retention and the strategy for preventing shortages, although this problem is not so great, as it is well described and independent of PV power production. Hence, the objective function is clearly stated – the amount of stored water should be maximal.

where: – hydropower head [m] The energy EH [kWh] which can be obtained from a water turbine is expressed in the following equation:

EH = QhRORηTur gtρ

where: Q – flow rate [m /s], – head [m], – water turbine efficiency [%], g – gravitational acceleration [m/s2], t – time [3600 s], ρ – water density [1000 kg/m3]. For the formulation of the mathematical model for hybrid operation simulation as well as calculation of ramp rates, please see the appendix section. The optimization problem is defined as in the following section.

hROR

ηTur

2.3. Optimization The optimization problem is defined as follows: By changing the installed capacity in PVs (PPV) as well as the 24 fixed amounts of energy which should be delivered by the RoR to the grid (EBt ), find the maximal value of the objective function given in Eq. (4) whilst satisfying the constraints imposed in Eq. (5)–(7). n

maxZ =

∑ EtPV t=1

m ∑t = 1 EtB _N m ∑t = 1 EtB

(4)

≤γ (5)

n

∑t = 1 EtPV _N n ∑t = 1

m

EtPV _CS

≤δ

i=1

(6)

m

∑ EtH ≥ ε ∑ EtH ' i=1

(7)

The goal of the optimization problem is to deliver the maximal possible amount of energy from photovoltaics to the grid, whilst ensuring that:

• RoR electricity generation not used to cover the fixed values of • •

energy (not-realized contracted RoR yield) should be delivered to the grid, while not exceeding γ , here taken as 5% (Eq. (5)); the percentage difference between electricity yield from combined generation of PVs and hydropower on the one hand, and PVs under CS conditions on the other, should not be greater than δ , here taken as 5% (Eq. (6)); the capacity factor of the RoR operating under the mode introduced in this paper (smoothing PV electricity yield and delivering constant amounts of energy to the grid) should not be smaller than ε (here ε = 50%) of the unconstrained RoR’s CF (Eq. (7)).

The term “contracted electricity generation” refers to the amount of energy that the hydropower station should deliver to the power grid during particular hours of the day. In this model we use 24 such values – a daylight and a night-time value for each month of the year. However, this can easily be modified and such “contracted electricity generation” values can be defined for every hour of every day individually, depending on the forecasted irradiation and flow rate, as well as the assumed objective function, such as, for example, profit maximization.

The electricity yield EPV [kWh] from a photovoltaic generator P PV [kW] over period t [h] depends on the global horizontal irradiation H [kWh/m2] and irradiaton in standard testing conditions HSTC [kWh/ m2], ambient air temperature T [°C] (Hanif et al., 2012), temperaturedependent efficiency reduction factor µ [%/°C], cell temperature in standard testing conditions T STC (Duffie and Beckman, 2013) and performance ratio η PV of all remaining system components (inverter efficiency, wire losses, shading, etc.).

H [1−μ (T −T STC )] P PV η PV t H STC

(3) 3

2.2. RoR and PV generation

EPV =

(2)

hROR

3. Input data (1) For the purpose of our analysis we have used a three-year-long hourly flow rate and irradiation time series representative of a small river and observed solar conditions in Southern Poland. Fig. 2 visualizes

The nominal capacity of RoR can be calculated based on the following formula:

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12

20 18

Flow rate [m3/s]

14

8

12 10

6

8 4

6 4

Irradiation [kWh/m2]

10

16

2

2 0

0 Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Month +/- 2 Standard Deviations of Irradiation

Flow rate

Mean irradiation

Fig. 2. Daily mean sum of irradiation and its variability within +/- two standard deviations and box plot for observed hourly flow rate – calculated based on the hourly time series covering the period 2006-2008.

various pondage capacities and water turbine throughputs were considered. The results of the solved optimization problem in terms of installed capacity in PVs and amount of energy which should be delivered by hydropower (fixed load not used hydropower to smooth PV yield) during daylight and night periods of individual months (EB) are given in Table 2. Naturally, due to the annual variability of irradiation, as well as the observed difference between irradiation under clear-sky and real conditions, the need to use RoR to smooth PV yield varies. For example, in January an exemplar 1-kW PV installation will deliver only about 21 kWh of electricity, whereas under clear-sky conditions this should be over 43 kWh. Meanwhile, during summer (June) the electricity yield of such an installation will be 153 kWh, and close to 200 kWh under clearsky conditions. This means that over months where higher irradiation values are usually observed it will be necessary at the same time to use more hydropower to compensate for the varying output of PVs. Such a conclusion is supported by the results presented in Table 2, where one can observe that during the daylight period the RoR is basically used only to smooth PVs (0.0 values – which indicate that the hydropower is not used to cover some fixed loads but only to buffer PV generation). In scenarios which considered a fixed water turbine throughput

those two phenomena. Flow rate data was obtained from (http://www. imgw.pl/) and irradiation data from (http://www.soda-pro.com/). The remaining parameters used in the simulation and optimization part of this paper are summarized in Table 1. Considering the fact that the investigated RoR–PV hybrid is located in Southern Poland (warmsummer humid continental climate zone), we have neglected the impact of temperature on evaporation from pondage. This aspect may be of greater importance in regions where observed temperatures are significantly higher. Fig. 2 shows that mean monthly flow rate is fairly stable throughout the entire year, generally not exceeding 2 m3/s, with only a few extremes or variations. Extreme flows occur during spring and autumn in particular, mainly due to melting snow cover and the first heavy showers. The variability of the flow and its low values, especially during summer, when high irradiation values are also observed, will be the main reasons for using hydroelectricity for smoothing PVs power output only during this period. To address the problem of hydropower variability we have considered various pondage dimensions (which translate into their storage capacity) and water turbine throughputs (which translates into its capacity expressed in kW). We did not change the basic RoR head as it impacts both turbine capacity and pondage capacity.

Table 1 Parameters used in simulation and optimization; for a and QMax we have analyzed various values from considered ranges, assuming increments of 25 m and 0.25 m3/ s, respectively. Parameter Pondage width/length Basic RoR head Pondage head Turbine efficiency PV performance ratio Min Ramp Rate Max Ramp Rate PV + RoR yield ≠ CS, see Eq. (6)

Symbol a hI hII ηT ηPV α β δ

Value

Parameter

25–275 [m] 10 [m] 5 [m] 80 [%] 80 [%] 0.9; 0.95; 1 1; 1.05; 1.1 5 [%]

Irradiation STC Temperature STC PV reduction factor Turbine throughput G-force Water density CF of RoR reduction, see Eq. (7) Not realized RoR base, see Eq. (5)

Symbol STC

H TSTC μ QMax g ρ ε γ

Value 1000 [Wh/m2] 25 [°] 0.5 [%/°C] 0.25–2.75 [m3/s] 9.81 [m/s2] 1000 [kg/m3] 50 [%] 5 [%]

(Q = 1.5 m3/s for 174 kW of power generation), values of EB greater than 0 occurred in only a few months. Meanwhile, in scenarios which investigated various turbine throughputs with a constant pondage capacity (a = 150 m for 0.54 MWh of energy) RoR delivered more contracted energy during daylight hours. This is due to the fact that variable water turbine throughput results in different capacity factors of RoR operating in benchmark mode (where hydropower is not used to smooth PVs output). In consequence, considering the mean flow rate

4. Results and discussion 4.1. Optimization results The presented mathematical model was implemented in MS Excel 2013 and the optimization problems were solved using the in-built Solver using an Evolutionary method with default settings and maximal calculation time set to 7200 CPU seconds. In total, 22 scenarios of 679

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Table 2 Optimization results: PPV – installed capacity in photovoltaics, Q – water turbine throughput, each additional 0.25 [m3/s] of throughput translates into 29 [kW] of turbine power, a – pondage length/width, each 25 [m] translates into 0.09 [MWh] of storage capacity, EB – contracted electricity generation from RoR which is not used to smooth variable electricity yield from PVs.

observed in that river, it is easier to meet the imposed constraint of RoR’s CF reduction (see Eq. (7)) whilst maximizing the capacity installed in PVs. As can be noted Table 2, (second quarter), for constant pondage capacity and varying turbine throughputs, the maximal installed capacity in PVs ranges from 84 kW to 884.5 kW. Considering all mentioned parameters in Table 1, as well as the statistical parameters of irradiation and flow rate time series in this region, this means that each 1 kW installed in water turbines will translate into the possibility of accommodating on average 3.6 kW in PVs. The biggest ratio was observed for Q = 0.5 m3/s where 59 kW installed in RoR allowed the electricity yield of 262.6 kW PVs to be smoothed. For scenarios which considered constant throughput and varying pondage capacities, the average ratio of power installed in PV to that in hydropower was around 4.1:1 with the highest observed being as much as 5:1 for pondage capacity of 2.64 MWh (a = 275 m). In Table 2, cells with a “0” value indicate that during a given month the hydropower was only used to buffer PV generation. Table 2 presents results for 22 various scenarios of RoR parameters (pondage and turbine capacity). For better understanding of those results we have selected the mean parameter values (pondage capacity of 1.36 MWh and water turbine power of 176 kW) and visualized how changing one parameter whilst the keeping the second one constant impacts system operation. Such a sensitivity analysis of the impact of installed water turbine capacity (Fig. 3, chart A) and pondage capacity (Fig. 3, chart B) on the maximal power installed in PVs shows that:

•

•

•

• increasing installed capacity in water turbines does not translate

into proportionally greater power in photovoltaics. This is due to the available flow rate being limited, as well as to the imposed

680

constraint that the RoR capacity factor should not be reduced too far. Naturally, smaller CF of RoR will result in a greater cost per unit of generated energy. At the same time, it is impossible under the proposed scheme to schedule more contracted generation from RoR because there is a constant need to smooth the varying output of PVs; for pondage capacity equal to 1.36 MWh, increasing the installed water turbine power from 29 to 118 kW (Fig. 3, chart A) does not significantly reduce the contracted RoR generation. This means that the considered water turbine throughputs are sufficient not only to smooth PVs electricity yield but also to generate some additional energy. It is important to bear in mind that the installation of 118 kW in water turbine results from the considered head and a water turbine throughput of 1 m3/s, which in this case is equal to the mean observed flow rate; since the considered objective function was to maximize the electricity yield in PVs (which translates into greater installed capacity) the use of RoR to smooth PV energy output increased with each kW installed in PVs. As shown on chart B Fig. 3, pondage has a significant impact on the ability to accommodate more power in PVs, but only to a certain level. The first increase in capacity, of 25.6 kWh (an increase in pondage size a of 25 m) from 0.09 kWh to 0.34 kWh, resulted in the ability to add 103 kW in PVs. However, this impact is not very great for the largest pondages, for which an additional increase from 2.36 to 2.64 MWh capacity resulted in only 7.3 kW more installed in PVs; naturally, each additional kW installed in water turbine or greater pondage capacity does not translate into proportionally greater capacity of PVs. Based on the calculated trend equations, this relation has a logarithmic nature;

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16

A 1000

10

600

8 400

6 4

200

2 0

0 29

59

88

118 147 177 206 235 265 Installed water turbine capacity [kW] PV capacity

294

324

Hydro generation

B 1000

25

800

20

600

15

400

10

200

5

Installed capacity in PV [kW]

Mean ROR generation [kWh]

12

Mean ROR generation [kWh]

Installed capacity in PV [kW]

14 800

0

0 0.09

0.34

0.60

0.85 1.11 1.36 1.62 1.87 Pondage capacity [MWh] PV capacity

2.13

2.38

2.64

Hydro generation

Fig. 3. Capacity able to be installed in PVs, and mean daily electricity generation from hydropower not used to smooth variable PV output, for various maximal water turbine powers and upper reservoir capacities. The results in chart A consider constant pondage capacity of 1.36 MWh and results in chart B assume constant water turbine capacity of 176 kW.

observed irradiation values. In the proposed operation mode, the mean hourly contracted energy (EB) was relatively small, at slightly above 8 kWh. However, this enabled the RoR CF to be within the imposed constraint of no less than 50%. In general, 3% of energy which should have been generated was not delivered by the RoR–PV hybrid (meaning that the hybrid system was very reliable and realized 97% of its operation plan). In total, not-realized hydropower generation resulted in 101 MWh (on average 34 MWh/year) of not-smoothed PV generation and 2 MWh of electricity not generated although scheduled.

4.2. Exemplar hybrid operation Fig. 4 shows the structure of energy generated by a hybrid consisting of a 176-kW water turbine, 687 kW in PVs and pondage capable of storing 1.36 MWh of electricity (which is a central value in both the considered turbine and pondage capacities used here as an example). Over the threeyears period, 768 MWh (on average 256 MWh/year) of electricity generated by RoR was used to smooth the electricity yield from PVs, which in turn amounted to close to 2 GWh (on average 667 MWh/year) under the

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2. 0

226.7 768.25

101.3 99. 3 1986.65

PV: Normal conditions

ROR: Base generation

Hydro used for PV smoothing

ROR: Base generation not realized

PV: Not smoothed to CS within allowed margin Fig. 4. Electricity production over the years 2006/08, considering the allowed deficits – all values in MWh. Results for Q = 1.5 [m3/s] (PT = 176 [kW]) and a = 150 [m] (V = 1.36 [MWh]) and 687 [kW] of installed capacity in PVs.

Despite this, over the whole year the proposed operation mode for RoR–PV was still capable of ensuring that the non-smoothed electricity generation from PVs will not exceed 5% of total electricity yield from PVs under CS conditions. From the perspective of three years the ordered electricity generation chart for the scenario which assumed both the largest pondage and the smallest water turbine throughput is presented in Fig. 6. The electricity yields presented there for the mode of

Those changes in electricity generation from individual sources can be observed in detail in Fig. 5, where three consecutive days in April 2006 are presented. The contracted electricity generation from RoR concentrates during night-time (almost 50 kWh), whereas, during daylight, hydropower is used mainly to smooth the PV electricity yield. Over the 72 h considered here, on 9 occasions the installed capacity in water turbine was not sufficient to cover the PV electricity yield. 450 400

Energy [kWh]

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Fig. 5. RoR – PV hybrid operation over three consecutive days in April; results for same scenario as Fig. 4.

0 Hydro_Not_Used_For_Buffering_PVs

Fig. 6. Ordered electricity generation for scenario Q = 0.25 m /s and pondage capacity V = 2.64 MWh, installed capacity in PPV = 83.97 (kW). 682

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amounts of energy depending on solar variability. These results are valid in terms of water usage but do not consider the expected capital investment difference between a single unit and multiple turbines (even if cumulative capacity is the same). The economic aspects of the proposed operation strategy can be assessed to some extent based on the constraint given in Eq. (7), which ensures that the capacity factor of the hydropower station is not reduced by more than a given value. Considering this, and knowing the current price of electricity generated by a given existing hydropower facility, is it possible to estimate the cost of the new operation mode.

PV–RoR operation introduced in this paper are significantly higher than for a single PV installation. This will impact the possibility to connect such a hybrid power station to the local transmission network. 4.3. Operation mode impact on turbine work The new operation scheme for the RoR–PV hybrid proposed in this paper is not without impact on the observed turbine operation in terms of water flowing through its shoulder blades. Fig. 7 visualizes the change in observed flow. This figure consists of a scatter plot and two histograms that compare the hydropower operation. If the dots are aligned along the theoretical line y = x then the new operation mode had no impact on the hydropower operation in comparison to independent operation (run-of-river mode). The histograms summarize turbine operation. Clearly the new operation mode (smoothing PV yield) changes the water turbine operation regimes. As shown in Fig. 7 the turbine tends to often operate under low flows.

4.4. Ramp rates analysis Owing to the fact that the calculations presented in this paper were performed on an hourly time series, it was impossible to grasp any of the sudden (minute-by-minute or second-by-second) variations in PVs electricity yield which result from changing cloud cover. Nevertheless, based on Eqs. (1)–(14) (Appendix A) we have conducted a preliminary analysis of the mean ramp rate observed in all 22 scenarios. This analysis also considered three levels of acceptable deviation from the ramp rates observed for PVs operating under CS conditions. These acceptable changes can be adjusted by the power system operator according to system flexibility or legal requirements. The changes in mean ramp rates dependent on the installed capacity of the water turbine, pondage energetic capacity and PVs power are presented in Fig. 8. This analysis considered only ramp rates which were different than those observed under CS conditions (parameters α and β in Eq. (12)). As can be observed in Fig. 8, coupling PVs with RoR (PV + RoR) significantly reduces the observed mean ramp rates which will inevitably occur if PVs operate alone (PV). Specifically, in all considered scenarios, mean ramp rates were less than 8 kW/h and no significant difference was observed for various α and β parameters. Conversely, on average the ramp rates for PV solo operation were four times higher than those observed for PVs supported by RoR. The proposed operation strategy works sucessfuly for various parameters of the hybrid system (capacity of pondage, PV and water turbine). Even for the investigated PV capacity, which ranged from 84 to 884 kW, the observed mean ramp rates were not higher than 8 kW/h. This proves that the proposed operation scheme significantly reduces the unpredictable (or, in other words ‘needing-to-be-forecasted’) variability of PVs. However, there is a pressing need to investigate those ramp rates on a more detailed time scale (minutes and seconds) while taking into account water turbine inertia. The charts in Fig. 8 also show to some extent the limit of the river hydropower potential to smooth the electricity generation curve from PV. As can be seen in both charts, improving the hydropower parameters (pondage capacity – upper chart and turbine installed power – lower chart) does not correspond to a proportional increase in PV capacity. Installing more capacity in PVs is not only impossible according to the constraints imposed in the model but also according to the theoretical potential of the river considered in this study.

Fig. 7. Comparison between water discharge for RoR being operated as a single power station (horizontal axis) and being used to smooth the PVs output while also providing some power to the grid (vertical axis). The parameters of the considered system are: Q = 1.5 (m3/s) and V = 2.64 (MWh), installed capacity in PPV = 687 (kW).

In our analysis we have assumed a constant efficiency of water turbine but this is only true if the flow is within a certain range. Flows lower than 20% (depending on turbine type and efficiency curve) of designed throughput lead to significantly lower efficiency. Therefore, we claim that if the hydropower were to be used to smooth PVs variable generation then at least two or more turbines should be installed to maximize the efficiency of water usage. The effectiveness of water usage will be achieved by ensuring that the turbine operates in the high efficiency zone. A hydropower station equipped with a set of turbines with different throughputs will be able to efficiently provide various

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Parameters of RoR–PV hybrid. Top: installed capacity in PVs [kW]; middle: pondage capacity [MWh]; water turbine installed capacity [kW]

Relative mean ramp rate [kW/h]

PV+RoR (0.9;1.1)

PV+RoR (0.95;1.05)

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Parameters of RoR–PV hybrid. Top: installed capacity in PVs [kW]; middle: pondage capacity [MWh]; water turbine installed capacity [kW] PV+RoR (0.9;1.1)

PV+RoR (0.95;1.05)

PV+RoR (1)

PV (0.9;1.1)

PV (0.95;1.05)

PV (1)

Fig. 8. Mean ramp rates for PVs operating under real conditions and PVs supported by RoR smoothing their power output. Values in brackets represent α and β parameters.

consecutive days and their hourly values. As can be seen, the smoothing operation increases the pondage’s state of charge and simultaneously changes the energy output patterns. In the case of charts a, b and c the electricity yield from PVs has been significantly smoothed (to that observed under clear-sky conditions) whereas for the three days presented in chart d the hydropower failed to do so. This results from the relatively low availability of hydropower resources. Nevertheless, the rules of the proposed operation strategy do increase pondage SOC during the night, thus providing some potential for daytime smoothing of PV generation.

4.5. Operation mode impact on water retention One of the potential benefits of coupling hydropower with PVs under the operation mode introduced in this paper is a beneficial increase in water retention. For that purpose, in Figs. B1 and B2 (Appendix B) we have compared the mean pondage state of charge with electricity generation from RoR and PV under various scenarios. Detailed changes in the pondage state of filling and hydropower operation are presented in Fig. 9. The central chart depicts monthly averages and the remaining ones show three arbitrarily-selected

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Fig. 9. Hydropower operation in two modes (only RoR – maximizing electricity yield and RoR + PV – smoothing PV generation) for the following system parameters: Q = 1.5 (m3/s) and V = 2.64 (MWh), installed capacity in PPV = 687 (kW). SOC – state of charge. Left y-axis – pondage state of charge, right y-axis – electricity generation.

defined as a water–energy nexus, which, due to the increasing variability of water availability and energy fluctuations resulting from varying supply from VRES, has drawn significant attention over recent years. For further details and exemplar analysis we refer readers to the paper by Gaudard et al. (2017).

As mentioned above, in the presented approach, pondage should always be able to discharge water for energetic purposes, and need not necessarily be ready to accept a further portion of water flowing down the river. Thus, as can be observed in the above charts, the mean amount of stored water is significantly higher than what one would potentially obtain if the main objective were hydropower generation. This result is especially important in countries which are developing small water retention, i.e. various forms of preventing water run-off, e.g. small pondages (Ryszkowski and Kedziora, 1996) counteracting deforestation and urban surface transformation. Under such schemes, storing small amounts of water in multiple reservoirs (not only pondages) provides more even water flow in rivers, inhibits flooding and droughts, and improves water environment quality thanks to the permanent abundance of water in rivers. All these benefits are in accordance with major environmental directives in the EU, e.g. 2000/60/ WE Directive. The proposed method of small pondage operation is a kind of trade-off between hydropower generation and exclusive water storage, and this fact may make such an investment more attractive from the economical and utilitarian point of view. The issue of water retention is especially important in Poland, where the Water Abstraction Index (WAI), defined as the relation between the mean annual water consumption and long-term freshwater availability, is disadvantageous (Hotloś, 2008). The problem presented above can be

4.6. Solution applicability, benefits, smoothed PV energy, energy cost The presented approach may be useful for power system operators, which are contracted to provide a certain amount of energy generated from renewables. An RoR–PV hybrid operating in such a mode gives them an opportunity to contract power with higher reliability. The described idea for scheduling water turbine power production may also be used in planning major hydropower schedules and will in consequence make it easier to integrate non-dispatchable renewable energy sources into the grid. Their integration based on the proposed operation scheme will be facilitated by the reduced need for backup power plants and energy storage. In the case of off-grid systems, the PV–RoR hybrid has huge potential for low loss of load probability (LOLP), which defines system reliability. What is more, the operators of large PV power plants can couple them with existing RoR with pondage in order to minimize the risk of making excessively large offers on the day-ahead energy market based only on irradiation forecasts. Such systems are 685

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already in use; for example, the Longyangxia hydro–PV plant in China which combines 850 MW in PV generation and 1280 MW in hydro generation. In the proposed scheme, forecast errors RoRs can be overcome by the operational dispatchability of RoR with pondage. There is also a possibility of assessing the power of PV generators that can cooperate with small hydropower to provide smooth and easily predicted power output. Such a model may also be used to estimate the required pondage and water turbine parameters to smooth the output of existing PV generators. As pointed in the earlier research on RoR-PV hybrid (Jurasz and Ciapała, 2017), this solution may be not only applied to existing RoRs with pondage but also developed from scratch, in the case of the still large, untapped potential for hydropower development in various parts of the world (Kosnik, 2010; Kucukali and Baris, 2009; Dudhani et al., 2006). What is more, small-scale hydropower is perceived as a viable solution on a regional and local scale (Balkhair and Rahman, 2017). The hybrid and proposed operation mode considered here suffer from not having taking into account some overflow discharge as a possible source of electricity; this has been neglected due to its intermittent nature. The concept presented in this paper may also rise questions with regard to the actual smoothed PV energy and the operation mode impact on the energy cost. We briefly address those two questions. First of all, the “PV smoothed energy” is strongly dependent on the context (the power system) and it fits very well into the broad problem of integrating variable renewable energy sources into the power system. The “PV smoothed energy” is a concept which ensures that photovoltaics can be considered as a reliable energy source in terms of ensuring that over a given time horizon a certain amount of energy will be generated. In consequence, it will be easier to optimally schedule the operation of the whole power system when one does not have to take into account the variability of solar generation. In the case of insular systems this concept is of lesser importance, as hydropower will usually be used as a dispatchable power source and will be operating in the load following mode (residual load – PV generation). In our approach we aimed at smoothing PV generation to the generation curve observed under clear-sky conditions because generation under CS conditions is well described and can be accurately modelled. The second issue (energy cost), which was not directly addressed in our paper can be connected to the hydropower change in capacity factor. It is commonly accepted that economic analysis is a very complex problem which is subject to multitude varying and uncertain factors. One is not only dealing with the problem of considering an existing dam or transforming a non-powered one but also the resources availability (hence the results of the economic analysis are very strongly location dependent). Nevertheless, to some extent we are able to answer this question by elaborating on the constraint presented in Eq. (7) (Section 2.3). As you can see in the optimization model we have imposed a constraint which ensures that the capacity factor of the hydropower, as a consequence of the new operation mode, is no smaller than the ε of the capacity factor observed in the run-of-river operation mode. In simulations we have assumed that the capacity factor of the hydropower under the new operation mode should not be less than 50% of that observed in the run-of-river operation mode. For all considered scenarios this constraint was satisfied. Therefore, in general it can be said that in the new operation mode the energy cost from hydropower (expressed as levelized cost of electricity) should be twice as high as the run-of-river operation mode. The question then emerges as to whether this is a significant increase or not? Of course, our model enables a different assumption with regard to the capacity factor reduction. For example, one can assume that it should not be reduced by more than 10%. Here we are using hydropower to compensate for the variable generation from photovoltaics. Usually for such purposes power plants (gas fuelled) are swiftly ramped up and down, or energy storage is

employed. Currently the market shows that hydropower is the cheapest dispatchable energy source and batteries are on their way to reaching market maturity. Considering this, it can be said that the economic operation of the ROR–PV hybrid has to be adjusted depending on the market situation. Therefore, using capacity factor reduction as a constraint makes this quite straightforward. 5. Conclusions Based on the performed analysis the following conclusions can be drawn:

• the complementarity between hydropower and PV lies in the for-

•

• • •

mer’s flexibility (due to the available storage) as it can effectively support solar generation by quickly adjusting its power output. The sizing of such a hybrid system is determined by the short- and longterm variability and availability of hydropower; therefore, in the proposed operation mode (smoothing PV yield) the capacity of PVs will be constrained by hydropower potential; hydropower is a perfect example of the complex relations between electricity generation and water usage. The results of our analysis show that coupling RoR with a PV installation can on the one hand facilitate the process of variable generation integration to the power system and on the another can increase the retention by keeping the reservoir at a higher state of charge over the whole year (especially the dry period); the proposed mode of operation was found to be an effective tool in smoothing the variable generation of PV, which translates into decreasing the uncertainty in the power system’s operation which results from increasing the role of variable generation; operating hydropower in this mode to smooth PVs to CS will require two or more water turbines with different capacities to be installed, to ensure that the water is efficiently utilized. This operation mode requires the water turbine to provide power with significant flexibility; aiming at using hydropower to achieve a PV electricity yield equivalent to that of clear-sky conditions makes their combined yield more reliable; however, it increases the observed maximal electricity yield and will impact connecting such a hybrid power station to the local transmission network.

This research points to several important and interesting aspects of PV–RoR hybrid operation which should be addressed in follow up studies. These include:

• the simulation model should use input data characterized by shorter • • •

686

time steps (ideally minutes) and consider the water turbine inertia. Additionally, the decision process (hydro unit commitment) should be tested on a probabilistic model; since hydropower is basically used here as a backup energy source, an economic analysis of such a solution should be conducted. The economics of RoR should be compared to those of other commonly used backup energy sources, such as gas turbines, diesel generators or fuel cells (generators); the untapped potential of water flow resulting from pondage overflows should be investigated either from the perspective of generating electricity (which will lead to the emergence of yet another variable energy source) or by coupling RoR–PV with some sort of ESS; since this paper focused on small rivers which usually have only one reservoir, future works should also consider the possibility of coupling PVs with a cascade of hydropower stations located on a larger river or a whole catchment.

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Appendix A A.1. Operation simulation In this subsection we present the idea (in the form of mathematical expressions) behind the concept of the ROR–PV hybrid. Firstly, the hydropower potential EtHP [kWh] in a given moment, considering the maximal water turbine throughput Q Max [m3/s], pondage state of filling VtI− 1 [m3], and current head hI + hII [m] can be estimated based on the formula below:

VI EtHP = min ⎛⎜ t − 1 ; Q Max ⎞⎟ g (hI + hII ) ηTur ρ ⎝ t ⎠

(1)

The basic head hI used in Eq. (1) remains constant throughout the study, whereas hII , being a consequence of the pondage’s variable state of filling, is calculated by Eq. (2). This ensures that the whole model considers both the constant and the changing hydropower head.

hII =

VtI− 1 a2

(2)

The hydropower potential results from the changing volume of water stored in pondage. Which is derived in turn from the balance of water inflow (QtIn ) and discharge (QtDis ) . Naturally, Eq. (3) ensures that the volume of water in pondage will not exceed its maximal capacity (V Max ) , which in turn is defined as V Max = a2hII , where a is both the width and the length of the pondage [m] and hII is its height [m].

VtI = min [VtI + t (QtIn−QtDis );V Max ]

(3)

The inflow is a natural process resulting from the river regime and climate, whereas the volume of discharged water the demand on energy which should be generated by the water turbine (EtH ) :

QtDis =

tg (hI

(QtDis )

EtH + hII ) ηTur ρ

directly results from

(4) (EtHD )

(EtH )

is determined based on observed demand and hydropower potential. Naturally, as shown The energy generated by the water turbine in Eq. (5), the energy generated by hydropower cannot exceed either the current potential of RoR or the observed demand:

EtH = min (EtHP ; EtHD )

(5)

The demand on hydropower generation considered in Eq. (8) results from the difference between electricity yield from the PVs operating under clear-sky (EtPV _CS ) and real conditions (EtPV ), as well as on the fixed value of energy which should be delivered to the grid by the RoR power plant (EtB ). The EtB is the net load which should be covered by hydropower after buffering PV electricity yield to that observed under clear-sky conditions. Therefore, the demand on hydropower generation (EtHD ) is a sum of not realized PV generation and the contracted hydropower which should be delivered to the grid:

EtHD = EtPV _CS−EtPV + EtB

(6)

The fixed amount of energy (EtB ) (i.e. the energy generated by RoR independently of its operation for smoothing the electricity yield from PVs) is a variable in the optimization model. It is determined for each of the twelve months separately, for both the daylight and the night period, giving a total of 24 values. This ensures that the RoR power plant with pondage is not only used to smooth PV electricity yield, but also simultaneously maintains the capacity factor (CF) as requested. The status of a given hour t, whether it belongs to the daylight or night period, is determined based on the clear-sky model (Bird and Hulstrom, 1981). Hydropower potential which can be used to cover the fixed amount of energy (EtH _B ) to be delivered to the grid can be calculated by Eq. (7). Please note that, according to this equation, priority is given to RoR usage for smoothing the non-dispatchable operation of the PVs.

(

(

(

EtH _B = min EtB ; max 0; EtHP− EtPVCS−EtPV

)))

(7)

The energy generated by a water turbine used to smooth PV generation is calculated based on the following formula:

EtH _PV = min(EtH ; max(EtPV _CS−EtPV ; 0))

(8)

Naturally, the proposed hybrid energy source will not always be able to generate enough electricity to smooth the PVs generation and/or deliver a fixed amount energy to the grid. The missing energy for smoothing PVs (EtPV _N ) and ROR contracted operation (EtB _N ) is calculated based on Eq. (9) and Eq. (10), respectively.

EtPV _N = EtPV _CS−EtH _PV

(9)

EtB _N = EtB−EtH _B

(10)

The proposed operation/role of the RoR with pondage is not without impact on its electricity yield and capacity factor (CF). As a benchmark we use an operation mode which focuses on the hydropower plant generating the maximal amount of energy with no consideration of either its dispatchability or smoothness. In order to do so we introduce a simple modification to the model presented above, where the EtH in Eq. (5) is replaced by EtHP , previously calculated in Eq. (1). This enables us to calculate the energy potential of a given RoR power plant with pondage. Such RoR operation is not constrained by the variable yield of PVs or the contracted values of energy which should be delivered to the grid, despite still being limited by the maximal throughput of the water turbine. In the case of unconstrained operation of the RoR power plant, the energy generated(EtH' ) is equal toEtHP . This means that we are able to easily calculate and compare the CF of such a hydropower plant with that observed when it operates under the constraints presented in the simulation model, as shown in Section 2.3.

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A.2. Ramp rate The ramp rate (RRtX ) of phenomena X is defined as follows:

RRtX = |EtX− 1−EtX |

(11)

where: EtX – an observed value of the considered time series over hour t. In this study we investigated the ramp rates of three hour-by-hour time series, namely: electricity yield from PVs under clear-sky conditions (used as a benchmark) and under real conditions, and the combined electricity yield from PVs under real conditions and hydropower. Since the ramp rates of PV generation under clear-sky conditions are used as a benchmark, the assumption has been made that any ramp rate either from PVs operating under real conditions or combined PV–hydro yield whose value is within an acceptable range will be neglected (as in Eq. (12)). In other words, if the observed ramp rate is different than that observed under clear-sky conditions (+/- assumed deviation) then it will be considered as meaningful from the perspective of power system operation. This is based on the assumption that the power system can easily use supercapacitors, spinning reserve and other methods to accommodate small changes in power supply. Here, we have arbitrarily assumed that three subsets of alpha and beta parameters will be considered: namely: (0.9; 1.1), (0.95; 1.05) and (1; 1), where the last requires the observed ramp rates (RROtX ) to be exactly equal to those observed for PV under CS conditions. If the observed ramp rates are exactly as under clear-sky conditions, then PV power generation does not have to be predicted and can be considered as a stable/reliable power source. It is important to underline that the ramp rates for PVs operating under CS conditions are almost entirely predictable. Even considering the variable impact of temperature on PV performance. What is more, such an impact can easily be integrated into the simulation models based on weather forecasts.

RROtX =

forRRtX ∈ [αRRtPVCS ; βRRtPVCS ] ⎧ 0 ⎨ RRtX otherwise ⎩

(12)

Based on Eq. (12), only ramp rates which are meaningful from the perspective of the power system operator will be considered. Knowing that, we can now calculate the share of ramp rates in the energy generated in a given energy source by means of Eq. (13) and Eq. (14) for PVs under real operating conditions (RRSPV ) and PVs supported by the hydropower (RRSH _PV ) , respectively. Please note that the ramp rates for the PVs cooperating with hydropower are calculated for the sum of solar generation and the share of hydropower used to smooth them, not the total hydropower production. n

RRSPV =

∑t = 1 RRQtPV n

∑t = 1 EtPV

RRSH _PV =

(13)

n ∑t = 1 RRQtH _PV n ∑t = 1 (EtH _PV + EtPV )

(14)

Appendix B B.1. Water retention – Pondage state of filling See Figs. B1 and B2.

1. Water retention – pondage state of filling

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Fig. B1. Pondage stage of charge in conventional operation mode and when hydropower is used to smooth PVs. Chart based on results presented in Table 1, and corresponding parameters of Q = 1.5 m3/s and a = 25,…,275 m. 688

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RoR normal opeartion mode [MWh]

Fig. B2. Pondage stage of charge in conventional operation mode and when hydropower is used to smooth PVs. Chart based on results presented in Table 1, and corresponding parameters of Q = 0.25,…,2.75 m3/s and a = 150 m.

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