A strategy for the photovoltaic-powered pumped storage hydroelectricity

Abstract

Pumped storage hydroelectricity is the most natural and almost the only bulk energy storage technology available today. Due to the variability of energy demand, and recently also of the supply side of the energy market, there is a need to compensate these differences. In market reality this is usually done on the so-called balancing market where energy prices are significantly higher than on the power exchange market. In this paper we introduce a mathematical model for simulating the operation of photovoltaic-powered pumped storage hydroelectricity along with an optimization model and a procedure for operation on the balancing market. A simulation was performed based on data covering the year 2015 with an hourly time step. The results from the proposed approach were juxtaposed with an optimal solution generated from the optimization model.

Keywords

Energy market photovoltaics pumped storage hydroelectricity variable renewable energy

Introduction

In recent years the world has observed a remarkable growth in terms of installed capacity and energy derived from so-called renewable energy sources (RES).¹ This trend is driven mainly by a significantly decreasing levelized cost of electricity coming from RES² but also due to the increasing awareness of the man-made causes of global warming and climate change,³ which has led to the sustainable energy sector being perceived as one of the possible ways to avoid far-reaching changes in the environment. One may remain skeptical of whether industrial, agricultural, or other human activities have such power to impose a real impact on the Earth’s fragile climate, but the increasing role of RES in the national power systems (NPS) is a reality. It is a reality in which despite decreasing energy cost per kW h of energy generated from photovoltaics (PVs)⁴ and wind turbines⁵ (the two major players on the RES market⁶), their integration to the NPS comes with additional costs⁷ and often unintended consequences.⁸ Regardless of the economic aspects of PV and wind energy, their intermittent, nondispatchable nature and, as properly noted by Li et al.,⁹ their dependence on momentary weather conditions such as wind speed and irradiation values, are the most important hindrances to their larger market penetration (Figure 1).

Figure 1.

The hourly irradiation values variability over seven consecutive days observed in Kłodzko and Legnica (southern Poland) from 1 to 7 July 2014. Source: own elaboration based on http://www.soda-pro.com/.

The problem of RES integration to the NPS has recently been addressed by several authors including Jones⁷ and Delucchi and Jacobson.^10,11 The former work suggests several ways which may ease and enable the process of covering the world energy demand from RES. Those concepts have been thoroughly investigated and pertain to renewable resources’ spatial and temporal complementarity^12–14; energy storage^15–17; demand-side management (DSM)^18,19; hybrid power sources^20–22; forecasting energy yield from PV^23,24 and wind turbines^25,26; forecasting energy flow between hybrid energy sources and the NPS,²⁷ etc.

This research builds upon the concepts of wind- and solar-powered pumped storage hydroelectricity (PSH) hybrid power sources which have already been thoroughly investigated in the literature.^28–33 To the best of the authors’ knowledge, the concept of purely PV-powered PSH has been investigated only twice by Ma et al.^34,35 where they investigated the perspectives of covering of the whole energy demand of a remote island by means of a PV-PSH energy source. The perspectives of using PV-PSH presented in Ma et al.^34,35 concentrated on small isolated systems where the main objective of such hybrid energy source war to ensure the energy autarky or to decrease the dependence of finite fossil fuels. Hybrids like PV-PSH or WT-PSH or even PV-WT-PSH are rarely considered as a part of the larger NPS. However, with an advent of energy systems with high share of variable RESs such coupling may also become a part of the mainland power systems. The prospects of integrating nondispatchable wind energy by means of the PSH have been investigated in numerous papers from various perspectives.^36–41 Authors proposed different scheduling approaches and concluded that by combining wind energy with storage while providing appropriate scheduling algorithm may increase such sources dispatchability. Here, we introduce a novel mathematical model for simulating the operation of the PV-powered PSH on the balancing market (BM). In our approach we are neglecting the limited predictability of the energy yield from the PV and also the energy demand variability on the BM. The proposed strategy of the PV-PSH operation on the BM is determined by the upper reservoir state of filling (available energy) and the statistical behavior of the BM.

Here it is important to elaborate on the definition and the role of the BM in the current and future energy systems. The world is heading toward an RES-dominated energy sector. The prospect of independence from finite energy sources is foreseeable, but there is still much to do to maintain current trends. RES should not be permanently supported by various subsidies, so the scientific and business world is constantly searching for market niches where unsupported RES will be superior to conventional power sources. To some extent one may claim that it is easy to manage and control the energy system based on dispatchable power units which power output can ramp up and down. Naturally, each type of power plant has a limited range of possible power output variability but the diversity of technologies, energy storage, international transmission lines, or the so-called DSM make it possible to balance the operation of the whole system. In the extreme case, for example power unit failure, there is always a backup in the form of reserve power plants. With the advent of variable renewable energy sources (VRES) especially in the form of PVs and WTs there is not only need to adjust the power output of the conventional power plants to the changing demand but also to accommodate the fluctuating energy availability from the renewable generation. One of the possible options is to couple those energy sources with the energy storage and use them on the BM. The BM is the part of an energy market where the discrepancies between forecasted and actual energy supply—demand balances—are leveled out. Usually the prices of energy sold or bought are significantly higher and may make the energy generation from RES more profitable. However, the variability of wind and solar energy sources would make the participation in such a market a very risky business for an owner of a PV or wind park. But coupling the nondispatchable energy source with an energy storage device makes it more or less dispatchable. In consequence, the owner can easily determine the volume of the energy which can be sold on the BM in the upcoming hours. This paper introduces the concept of a PV-powered PSH operating on a BM.

The authors would like to make it clear to all potential readers that we perceive this research as a first step toward our much more highly elaborated analysis of the operation and prospects of RES-powered PSH hybrids being an integral part of NPSs. Therefore, this first paper focuses on introducing a discrete mathematical model for simulation and optimization of PV-PSH operation, presenting two various approaches to PV-PSH operation strategy on a BM, and analyzing the basic characteristics of the proposed hybrid energy source. Further research directions are briefly introduced in the last section.

Materials and methods

For the purpose of this study the existence of a hypothetical solar-powered PSH station has been assumed to be operating under the conditions of the Polish BM and with irradiation values generally observed in Poland. The time series describing the BM was obtained from PSE S.A.,⁴² while irradiation values are from SoDa.⁴³ The PV-PSH simulation and operation strategies have been represented by means of a mixed-integer mathematical model, introduced in “Simulation model” subsection. The scheme of the proposed PV-PSH operating on the BM is presented in Figure 2, whereas Table 1 presents variables and parameters, etc. used in the simulation models. Accordingly to the diagram shown in Figure 2 the variable energy yield from PV is used to power the PSH’s turbines to pump the water from the lower to the upper reservoir. Therefore, the electricity is being stored in the form of the potential energy of water. The bigger the height difference between both reservoirs the lower is need for their volume and less water is needed to store the same amount of electricity. When the energy demand on the BM occurs the PV-PSH operator may make a decision to discharge some amount of the previously stored water in the upper reservoir and generate electricity by means of the PSH turbines. In case of the PSH projects, the most relevant losses occur mainly due to the not perfect efficiency of pumps and turbines sets as well as due to the water evaporation from the upper reservoir. However, the last one seems to be negligible since they can be balanced by precipitation.

Figure 2.

Conceptual design of the PV-powered PSH operating on the balancing market. PSH: pumped storage hydroelectricity; PV: photovoltaic.

Table 1.

Parameters, variables, and model outputs used in simulation and optimization models.

Indices	Denotes	Range
l	Years	l=1 … 5, where 1 denotes the year 2010
k	Months	k=1 … 12, where 1 denotes January
i	Day	Depending on month length
j	Hours	j=1 … 24
Parameter	Symbol	Unit	Value
Upper reservoir capacity	V^UPPER	MW h	10
Lower reservoir capacity	V^LOWER	MW h	No smaller than V^UPPER
Pumping efficiency	η^PSH,P	%	90^{28,29,34–39}
Generating efficiency	η^PSH,G	%	90^{28,29,34–39}
Overall PV system performance ratio	η^PV	%	80⁴⁴
Energy demand on the BM during day i hour j—valid for the year 2015	$d_{ij}$	MW h	Given as a time series
Energy demand on the BM during year l, month k, day i, hour j—used to determine $p_{k, j} (d)$ —valid for the period 2010–2014	$d_{lkij}$	MW h	Given as a time series
Energy price on the BM during day i hour j	$c_{ij}$	PLN/MW h	Given as a time series
Irradiation during day i hour j	$H_{ij}$	MW h/m²	Given as a time series
Standard testing conditions (STC) irradiance	$H^{STC}$	MW/m²	0.001
Percentage energy demand during hour j within given month k with relation to the total daily demand	$p_{kj} (d)$	%	Given as a time series
Variable	Symbol	Unit
Energy supplied from PSH to the BM during day i hour j	$s_{ij}$	MW h
Maximal generating and pumping throughput of PSH turbines	$E^{P_{Max}} E^{G_{Max}}$	MW h
Nominal power of the PV system	P^PV	MW
Auxiliary variable	Symbol	Unit
Binary variable	$x_{ij}$	Dimensionless—binary [0,1]
Binary variable	$y_{ij}$	Dimensionless—binary [0,1]
Model output	Symbol	Unit
Monetary value of the energy sold on the BM during day i hour j	$Z_{ij}$	PLN
Energy yield from PV during day i hour j	$E_{ij}^{PV}$	MW h
Energy rejected/surplus from PV	$E_{ij}^{PV_Rej}$	MW h
Energy stored in the upper reservoir	$E_{ij}^{V_upper}$	MW h
Auxiliary energy parameter during day i hour j	$E_{ij}^{Aux}$	MW h

BM: balancing market; PSH: pumped storage hydroelectricity; PV: photovoltaic.

Simulation model

Energy generation from the PV installation ( $E_{ij}^{PV})$ has been calculated based on equation (1), which has been successfully applied by, inter alia⁴⁴

E_{ij}^{PV} = \frac{H_{ij} P^{PV} η^{PV}}{H^{STC}}

(1)

where

H_{ij}

is the irradiation during day i and hour j (MW h/m²),

P^{PV}

is the PV installation nominal power (MW),

η^{PV}

is the PV installation overall performance ratio (%), and

H^{STC}

is the irradiance in standard testing conditions (MW/m²).

In order to determine the energy stored in the upper reservoir, an additional parameter must be calculated based on equation (2). This equation calculates the theoretical inflow and outflow of energy from the upper reservoir. The first part of the equation, $min (E_{ij}^{PV} η^{PV}; E^{P_Max})$ , ensures that the volume of the energy stored will not be greater than the maximal throughput of pumps. The second part is used to determine the volume of energy discharged from the upper reservoir and sold on the BM. This, similarly to the case above, cannot be greater than the maximal energy generation capacity of the PSH turbines. The whole formula also incorporates the value of energy stored in the upper reservoir from the previous hour

E_{ij}^{Aux} = min (E_{ij}^{PV} η^{PV}; E^{P_Max}) + V_{ij - 1} - min \times (s_{ij} (\frac{1}{η^{PSH, G}}); E^{G_{Max}})

(2)

where

E_{ij}^{Aux}

is the additional parameter (MW h);

E^{P_Max}, E^{G_{Max}}

is the maximal throughput of PSH turbines in, respectively, pumping and generating mode (MW h);

s_{ij}

is the energy from the PSH sold on the BM (MW h); and

η^{PSH, G}

is the PSH energy generating efficiency (%).

The value of $E_{ij}^{Aux}$ is then used to determine whether the binary variable $x_{ij}$ will be 0 or 1

x_{ij} = {1, if E_{ij}^{Aux} \geq V^{UPPER} 0, otherwise

(3)

After estimating the value of $x_{ij}$ one can easily calculate the volume of energy stored in the upper reservoir, based on equation (4)

V_{ij} = x_{ij} V^{UPPER} + (1 - x_{ij}) E_{ij}^{Aux}

(4)

The monetary value of the energy sold on the BM can be expressed as a product of the energy sold volume ( $s_{ij})$ and its current price ( $c_{ij})$ , as shown in equation (5)

Z_{ij} = s_{ij} c_{ij}

(5)

Due to the intermittent nature of solar radiation, limited storage potential of the upper reservoir, and the random occurrence of demand on the BM, a situation may occur, in which some part of the energy derived from the PV installation will be rejected—in other words, lost.^a Equation (6) enables calculation of the volume of the rejected energy from PV

E_{ij}^{PV_Rej} = max [E_{ij}^{PV} - (V^{UPPER} - V_{ij - 1}) \frac{1}{η^{PSH, P}} - s_{ij} \frac{1}{η^{PSH, G}}; 0]

(6)

Optimization model and the operation strategy

The aim of PV-PSH operation on the BM is to maximize revenue. The BM appears to be a promising place where available energy can be sold, due to its relatively higher energy prices. However, the operation on the BM comes with uncertainty about the future behavior of the market. The decision maker not only does not know when the energy demand will occur, but also is unsure about the prospective price of that energy. In the case of the PV-PSH, he/she is certain only about the volume of the energy stored in the upper reservoir over the hour j, but changes which will occur due to the variable nature of PV generation are beyond his/her knowledge. The decision maker is forced to make an energy offer without the knowledge about the behavior of the PV installation (or one limited to the accuracy of the yield forecasts), expected energy prices on the BM, and the possible delay in selling the energy and continuing to store it in the upper reservoir. What is more, one has to decide whether it would be more beneficial (less risky) to sell the energy in smaller portions over an extended period of time or immediately and, as much as possible, only when the demand occurs.

Considering only one year, the decision made each hour effects those which will be made over the remaining hours and so underpins the monetary side of the PV-PSH operation. The optimal solution to such a problem can be found by means of a determinist simulation model such as that given in equations (1) to (6) and an interrelated optimization model with all its constraints given in the following equations (7) to (10). The objective function is to maximize the profit of the PV-PSH operation on the BM by changing the volume of energy sold $s_{ij}$

max Z = \sum_{i} \sum_{j} s_{ij} c_{ij}

(7)

Certainly the objective function is subject to several constraints. First of all the volume of energy sold ( $s_{ij})$ on the BM cannot be greater than the actual demand ( $d_{ij})$ , as shown in equation (8)

s_{ij} \leq d_{ij}

(8)

Second, the offered quantity of energy to be sold on the BM should not lead to a situation in which the theoretical volume of energy stored in the upper reservoir will be negative; this is ensured by a constraint represented by equation (9)

V_{ij} \geq 0

(9)

Additionally, as has been previously mentioned, no energy rejection from the PV system is allowed; therefore a constraint (equation (10)) has been introduced

E_{ij}^{PV_Rej} = 0

(10)

The optimization model is executed on the assumption that the values of irradiation, energy demand, and prices are known a priori for the whole period (in this case year 2015, a total of 8760 h).

Because events which make a BM necessary are random in nature, a subject (supplier of energy on demand) on this market operates in the face of a constantly unknown and nonpredictable future. However, over the course of each day it is possible to distinguish certain hours during which energy demand will occur with the highest probability. It has been assumed that the energy which can potentially be stored during hour j due to its generation from a PV system cannot be considered as energy available on the BM within hour j. Therefore, the volume of energy which can be delivered during hour j to the BM has been calculated based on energy stored in the upper reservoir in the period j−1.

The calculation procedure of energy sold on the BM is presented in Figure 3, and its mathematical form is given in equations (11) to (13). The procedure in Figure 3 is defined as follows: if energy demand ( $d_{ij})$ on the BM is greater than 0, then one must determine whether the volume of energy stored in the upper reservoir ( $V_{ij - 1})$ is also greater than 0. If so, it is possible to sell some portion of this energy on the BM according to equation (13). The formulation of the mathematical model imposes the introduction of an additional binary variable ( $y_{ij})$ which will determine whether the aforementioned conditions ( $d_{ij} > 0 Λ V_{ij - 1} > 0)$ are met and can be calculated based on equation (11)

y_{ij} = {1, if d_{ij} > 0 Λ V_{ij - 1} > 0 0, otherwise

(11)

Figure 3.

PSH operation scheme on the BM. BM: balancing market; PSH: pumped storage hydroelectricity.

Typical patterns of energy demand on the BM have been calculated based on the available data covering the period 2010–2014. Equation (12) provided twelve 24 h long time series depicting the average demand on energy during the statistically averaged day in each month over the year. The resulting time series are presented in Figure 4—please note their resemblance to the typical energy demand patterns, as shown, for example, in^45,46

p_{kj} (d) = \frac{\sum_{l = 1}^{5} \sum_{i = 1}^{m} d_{lkij}}{\sum_{l = 1}^{5} \sum_{i = 1}^{m} \sum_{j = 1}^{24} d_{lkij}} for all k, j

(12)

Figure 4.

Probability with which the energy demand on the BM will occur—2010–2014. BM: balancing market.

The volume of energy which will be sold based on the proposed approach can be calculated based on equation (13). The interpretation is as follows: over the theoretical hour j day i in the month k, the volume of energy sold will be equal to the lowest of the three possible values. Namely, either: the probability of demand occurrence multiplied by the volume of the energy stored in the previous hours multiplied by the PSH generating efficiency; the observed demand augmented by the losses on the PSH efficiency; or the maximal energy generation capacity of the PSH. The two last values are there in order to prevent the model from selling more energy than is demanded and exceeding the PSH generation potential. The models described above have been implemented in MS Excel software and solved by means of a freeware OpenSolver add-in⁴⁷

s_{ij} = min [p_{kj} (d) V_{ij - 1} η^{PSH, G}; (\frac{1}{η^{PSH, G}}) d_{ij}; E^{G_{Max}}] y_{ij} for all i, j

(13)

Scenarios

Since every energy system is characterized by a multitude of various parameters for the sake of the clarity of the conducted research, the following assumptions have been made. First, that the optimal (deterministic) strategy for the operation of the PV-PSH on the BM will be generated for a nameplate capacity of PVs equal to 100 kW. Second, that the maximal capacity of the PSH pumps will be equal to the maximal energy generation potential of the PV, hence $E^{P_{Max}} = E^{PV_Max}$ . Naturally, such situation when PVs will be generating electricity with the output close to their maximal potential will occur rarely—mainly during cold and sunny days. And third, that while the generating throughput of the PSH turbines will be a part of the sensitivity analysis, its initial value for a benchmark (optimal strategy) scenario—Scenario 3—will be 100 kW. In this study the impact of precipitation and evaporation on the volume of water stored in the upper reservoir of the PSH has been neglected. The remaining parameters will remain the same as given in Table 1. Considering the characteristics described above, the following scenarios have been proposed:

Scenario 1—the PV-PSH operation on the BM is determined by the probabilities of the demand’s occurrence calculated by equation (12);

Scenario 2—similar to Scenario 1, but the demand probability $p_{kj} (d)$ was subjected to the optimization procedure. A simple optimization procedure was applied in which $p_{kj} (d)$ values were variables and were also subject to the constraints given in equations (8) to (10). The objective function was to maximize profit (equation (7)). The optimization of $p_{kj} (d)$ was conducted based on the available data covering the period 2010–2014.

Scenario 3—was created as a benchmark for the other scenarios. The optimal decisions which could have been made over the year 2015 were established based on the optimization model described in “Optimization model and the operation strategy” subsection.

In addition to the sensitivity analysis, another optimization has been suggested in which the objective function and constraints remain the same as in equations (7) to (10), while the nameplate capacity of PVs was a variable. The goal of this optimization was to determine what the maximal nominal power of PVs is which can be considered for the strategies presented in Scenarios 1 and 2 for a V^UPPER= 10 MWh and $E^{P_{Max}}, E^{G_{Max}} = P^{PV}$ .

Results and discussion

As has been mentioned, three various scenarios have been considered. In each case the energy generation from the PVs, the capacity of the upper reservoir, and the maximal energy throughput of PSH turbines have been the same. The behavior of the PV-PSH hybrid has been simulated over the year 2015 and Table 2 summarizes the characteristics of its operation, whereas Figure 5 presents the modified probabilities of the energy demand occurrence. The energy generated from the 100 kW PV installation in the case of the considered theoretical location was equal to 100.9 MW h and this yields a capacity factor equal to 11.5%. Both operation strategies based on the probability of the demand occurrence (Scenarios 1 and 2) as well as the benchmark/optimal strategy presented in Scenario 3 resulted in a similar volume of energy sold on the BM, which was, respectively, 82, 85, and 88% of the total energy available from the PVs. From the perspective of the objective function (equation (7)) the optimal solution for the investigated problem (Scenario 3) would bring revenue amounting to 19.5 thousand PLN, whereas those in Scenario 1 and 2 would be, respectively, smaller by 13 and 8%. At this point it is important to note that a growth in volume of energy sold from 82.7 MWh in Scenario 1 to 89.1 MWh in Scenario 3 (an increase of 9%) leads to an increase in revenue of 13%. This results from the fact that the same energy was sold on the BM when the price was more beneficial. It is worth underlining that the simple strategy based on the probabilistic approach to selling the energy on the BM gives relatively similar results to the optimal solution calculated based on a deterministic model.

Table 2.

Basic characteristics of the PV-PSH operation on the BM over the year 2015.

Scenario	PV energy yield (MW h)	Energy sold on the BM (MW h)	Mean hourly volume of energy sold (kW h)	Mean volume of energy stored in the upper reservoir (MW h)	Highest single revenue (PLN)
Scenario 1	100.9	82.7	25.7	695.1	61.8
Scenario 2		85.7	29.7	1924.0	133.6
Scenario 3		89.1	48.1	2059.3	133.9

BM: balancing market; PSH: pumped storage hydroelectricity; PV: photovoltaic.

Figure 5.

Modified probability values enabling maximization of profit over the years 2010–2014.

The significant differences between those strategies can be observed when one compares the mean hourly volume of energy sold on the BM within individual hours (0 values were not considered while calculating the average). In the case of Scenario 1 the mean amounts to 25.7 kWh, which is slightly over 25% of the considered maximal throughput of the PSH turbines. However, this does not mean that the full capacity of turbines has not been utilized. In the case of Scenario 1, 3% of 3216 transactions made on the BM were equal to the maximal generating capacity of the PSH. The number of transactions in Scenario 2 and 3 was, respectively, 2883 and 1852 whereas those for which the volume of energy sold was equal to 100 kW h amounted to 428 and 760 (respectively, 15 and 41%). Therefore, the mean value of the energy sold on the BM in the optimal scenario was almost 90% greater than in Scenario 1. Such differences in the operation of the PSH turbines may have an impact on their durability and on their maintenance and operation costs; this does not fall into the scope of this research, but appears to be an interesting direction for future works.

Similar differences can be observed in the volume of energy stored in the upper reservoir. The mean hourly values have been presented in Table 2 and depicted in Figure 6. Please note the black line representing Scenario 1 which clearly indicates that the strategy adopted there discharged energy at much higher frequency and did not tend to store it for a prolonged period of time. What is more the values observed in Scenario 1 are 276 and 292% smaller than in Scenario 2 and the optimal strategy—Scenario 3. This indicates the underutilization of the PSH storage potential in Scenario 1 and the possibility of adding some additional kW to PVs. But an issue arises in the case of Scenarios 2 and 3 where energy (water) is stored in the upper reservoir over an extended period of time and is prone to evaporation and precipitation. The question for further research is then: would precipitation and evaporation balance out and have no impact on PV-PSH operation? As can be seen in Figure 6 the maximal capacity of the PSH upper reservoir has been reached only once—in Scenario 3. The volume of energy stored in the upper reservoir in Scenario 1 remains below 30% of the maximal capacity—this results from the fact that the energy is being sold every time that demand occurs simultaneously with some energy being available in the upper reservoir. This was opposite to the improved strategy in Scenario 2 and the optimal solution from Scenario 3 which both suggested that the energy should be stored in larger quantities for an extended period of time and then sold. To observe this phenomena please note in Figure 7 the changing volume of energy stored in the upper reservoir. The marked there mean monthly values of the upper reservoir occupancy do not only correlate with the energy availability from PV but also the energy demand on the BM. In the winter–spring (December–March) period, the energy sold on the BM tends to follow the same pattern in each scenario. Significant differences start to occur when the energy generation from the PVs increases (April–August). In Scenarios 2 and 3 the energy is being stored and, when the high PV-yield period is over, the process of selling on the BM starts, and soon the upper reservoir is using less than 10% of its capacity. The maximal mean volume of energy stored in the upper reservoir in Scenarios 2 and 3 occurs in August (Figure 7).

Figure 6.

Hourly values of energy stored in the upper reservoir over the year 2015.

Figure 7.

Mean monthly values of energy stored in the upper reservoir.

The changes in energy stored in the upper reservoir are a direct consequence of the selling transactions performed on the BM. The volume of those transaction results from the varying demand, prices, and also the changing energy generation from the PVs. The bar chart presented in Figure 8 shows the total sum of energy sold on the BM within individual months in each scenario. Significant differences between them start to occur from April to September when the energy generation from PV is at its highest. As already mentioned, in Figures 6 and 7 the possibility of storing the energy from PV allows it to be sold much later. This situation has been presented in Figure 9, where the ratio of the volume of energy sold to the volume of energy generated from PVs within individual months has been calculated. In Scenario 1 this ratio ranges from 0.63 to 0.95, whereas in Scenarios 2 and 3 it is 0.5–1.29 and 0.56–1.6, respectively. In the optimal solution in September, 160% of the energy generated in this month should be sold on the BM, which means that this extra 60% will come from the PSH upper reservoir and has been stored there in the previous months. Those varying ratios result from the changing prices on the BM. The modified strategy (Scenario 2), which enabled slightly greater revenue than Scenario 1, does exhibit lesser variations in the ratio of energy sold to energy generated than Scenario 3. An interesting situation occurs in July when over half of the energy generated is being stored in the PSH upper reservoir and the intensified selling process starts in August and September. As can be seen in the figure (hourly stored), this selling (red line) happened in two parts, where the first was followed by a period of storing energy.

Figure 8.

Energy sold on the BM in case of each scenario over the year 2015. BM: balancing market.

Figure 9.

Ratio of energy sold on the BM to energy generated from PV over each month. BM: balancing market; PV: photovoltaic.

The additional optimization which was conducted in order to estimate the maximal capacity installed in the PV revealed that in Scenario 1 it is possible to increase it from 100 to 344 kW. In consequence, revenue increased from 17 thousand PLN to almost 61.2 thousand PLN (an increase of 360%). The mean hourly volume of energy sold on the BM increased almost fourfold from 25.7 to 92.4 kWh. A similar situation was observed in the case of the upper reservoir, where the mean value of the energy stored growth from 695 to 2396 kWh. In the modified Scenario 1, the limit of the PSH storage capacity was reached only once. The difference between Scenario 1 and its modified version (with increased nameplate capacity of PV) in terms of the changes in the energy stored in the upper reservoir has been presented in Figure 10. Also, the ratio of energy sold to energy generated from the PV has changed and, in comparison to the basic Scenario 1, the minimal ratio amounted to 0.63 and maximal to 1.05. This indicated that, due to the adopted operation strategy, the increased yield from the PV could not always be sold within the month when it was generated and had to be used during the next period.

Figure 10.

Energy stored in the upper reservoir for two versions of Scenario 1.

The sensitivity analysis has been performed for the Scenarios 1 and 2 and the impact of the generating capacity on the revenue has been investigated. For the purpose of this analysis, generating capacities ranging from 50 to 500 kW h with a step equal to 50 kW h were used. No other parameters were changed. The results of the analysis are presented in Figure 11. In the case of the operation strategy used in Scenario 1, the lower energy generating capacity enabled an increase in total revenue of 4%. This results from the fact that in this scenario a decrease in generating capacities means basically that the energy on the BM will be sold more often and, in consequence, the probability increases that it will be sold for a higher price. Lower generating capacity leads to a situation in which there is often more energy stored in the upper reservoir which could be potentially sold but, in consequence, a greater upper reservoir is needed. In Scenario 1, when the generating capacity was changed to 50 kW h from 100 kW h, the maximal volume of the energy stored in the upper reservoir increased from 3 to 7 MWh. For the five times greater generating capacities (500 kW h), this impact was negative and the maximal volume of the energy stored decreased to 2.5 MWh. Interestingly, an increase in generating capacity led to a decrease in revenue, but this relation stopped when the generating capacity exceeded 200 kW h.

Figure 11.

The impact of storage capacity on revenue.

In Scenario 2 a different situation was observed. Initially the increasing generating capacity led to a simultaneous increase in revenue, but this reached its peak value at 150 kW h. Then a slight decrease started and, after exceeding the 350 kW h generating capacity, the revenue plateaued. From the conducted observations, the following conclusion can be drawn. In Scenario 1, a decrease in generating capacity would have a positive impact on revenue, whereas in Scenario 2 the generating capacity should be increased to 150 kW h in order to observe a growth in revenue of 0.1%.

Conclusions

The proposed mixed-integer mathematical model enabled the simulation and optimization of the investigated PV-powered PSH operating on a BM. The suggested operation strategies, which were based on the probability of the occurrence of energy demand on the BM does not significantly diverge from the optimal solution obtained for the testing year 2015. The suggested operation strategy in Scenario 2 yields slightly better results in terms of total revenue but also requires a greater storage capacity.

With the advent of modern energy systems which satisfy a significant part of the energy demand by means of a variable and nondispatchable energy sources, the structure of the energy market underwent major changes. To those one must account the fact that the power system operator not only has to properly schedule the operation of the conventional power plants but also prepare the whole system for a ramping power output from wind and solar generation. The current trends in the energy sector clearly indicate that the transition from fossil fuels-based energy generation to one utilizing RESs is keeping up its pace and seems to be unavoidable. However, in the author’s opinion not all policy makers (especially in Poland) perceive this as an opportunity for improving the energy independence and securing the quality of the environment for the future generations.

It is important to underlie that almost from its beginning the polish energy system is based on hard and brown coal extracted in several mining areas lying within Poland borders. Therefore, all the changes in the energy system which have potential to reduce the need to burn native coal are perceived as a threat and are bargaining card during major elections. In general, the polish energy policy is “fluctuating with each passing season” (ruling party). The lack of common strategy (one accepted by all parties) is visible since the last century. Poland once aimed at diversifying its energy portfolio by building a nuclear power plant in Żarnowiec (near Baltic Sea) coupled with the PSH. However, the works were withheld and only the PSH has been completed. Now, after almost 30 years Polish government is once again considering an investment in a nuclear power plant.

The attitude of Polish government toward the RESs development is also very challenging for potential investors. Despite constantly changing regulations (like the minimal distance from wind turbine to the residential buildings or the feed-in tariffs), a significant increase in the installed capacity in wind turbines, PV, and biogas plants was observed.

Considering the above briefly described status of the Polish energy system it is clear that it needs stabilization and precise goals. As a member of the European Union, Poland has to increase the share of RES in covering the electricity demand to 20% by the end of 2020. In our opinion, VRESs like solar and wind energy can be introduced to the Polish energy system by coupling them with various forms of energy storage. Especially, in situation when Poland has a significant potential for the development of new PSH projects (e.g. there is an uncompleted project of a 750 MW PSH project Młoty since the1970s). The strategy for the PV (or any other variable energy source) powered PSH proposed in this paper can be employed to simultaneously ease the process of RES integration to the power system, increase the share of RES in covering energy demand, reduce the need for ramping up and down the power output of the coal-fired power plants, decrease the need for gas power stations which are commonly used during peak demand hours, improve the environment quality by curtailing the exploitation of depletable natural resource. Additionally, by implementing this approach Poland would not only act in line with the actions aiming at reducing the greenhouse gasses emissions but also increase its energy security by reducing the need for gas power stations which could be replaced by the PV-PSH or WT-PSH hybrids which do not require purchasing fuel from abroad.

This research has answered several questions but has also asked a great deal of new ones and opened interesting directions for future research. The main question which has not been answered and is of great importance is the economic cost-effectiveness of the proposed solution.

What would be the levelized cost of the energy derived from such a hybrid?

Could such a hybrid power source be competitive on the BM?

The authors would like to concentrate on these questions and present answers in future publications.

Footnotes

Acknowledgements

The authors are grateful to two anonymous reviewers and editors for reading the manuscript very carefully and providing constructive comments which helped us to improve the quality of our paper. This paper was realized as a part of a research grant number: 11/11.200.322.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This paper was realized as a part of a research grant number: 11/11.200.322.

Note

In reality this energy may be directly fed to the power grid; however, this will only lead to greater variability on the energy market.⁴⁵ Therefore, in optimization model it has been assumed that energy rejection from the proposed PV-PSH hybrid is not permissible.

Jakub Jurasz was born in 1990 in Bielsko-Biała (Poland) and graduated from the Faculty of Management of the AGH University in 2016. He holds a PhD in Industrial Engineering and his primary research interests are in area of renewable energy sources integration to the national energy system and water management from the perspective of energy generation and retention. Currently, he works as a research assistant at the Department of Engineering Management at the AGH University.

Jerzy Mikulik graduated from the Faculty of Electrical Engineering, Automatics, Computer Science and Electronics of the AGH University of Science and Technology. Currently, he works at the Department Engineering Managment of the same University as Processes Automation Laboratory manager. He has been researching the theory and practice of security systems in intelligent buildings for many years. He is an author of many articles and books on the management of the security and comfort of intelligent buildings. Since 2000, he has been the leading organizer of the International Congress on Intelligent Building Systems InBuS, devoted to control systems in intelligent buildings.

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