Optimal operation scheduling of a pump hydro storage system coupled with a wind farm

The variability in non-dispatchable power generation makes essential the improvement of production management. This study focuses on the development of an optimisation model for a renewable power unit, composed of a wind farm and a hydro-pump storage power plant, to maximise its revenue. The combination of the two technologies allows the mitigation of risks associated with wind production and electricity price variability. The problem is formulated using linear programming and encompasses the selling of electricity in the Iberian day-ahead market and through a bilateral contract. The model is tested and scrutinised with sets of real historical generation and price data. In the day-ahead market scenario, the proposed methodology leads to an average yearly increase of net revenue ranging between 5 % and 20 % . In the bilateral contract scenario, the coupling of the wind farm and hydropower plant can reduce the imbalances costs substantially. Furthermore, the work identiﬁes a positive correlation between reservoir dimension, turbine capacity and revenue value. The study also detects a revenue reduction tendency related to the decrease in the volatility of electricity prices.


INTRODUCTION
Due to the currently rapid expanding 100% renewable movement, renewable energy power plants capacity is growing worldwide [1]. Nevertheless, the use of renewable energy sources has very different characteristics from conventional energy resources, which might create an unbalance between electricity demand and supply, mainly due to the variability and uncertainty of renewable resources [2]. The unbalance between demand and supply could provoke a disruption in the electrical grid frequency resulting in severe problems for consumers [3][4][5]. One of the solutions taken to address the variability of generation from renewable sources is to cut off production, which may imply a larger share of non-renewable sources in the electricity consumption, the waste of endogenous resources, and a smaller revenue for the producers [6]. Other of the options to mitigate the problem of variable renewable electricity (VRE) is the commissioning of energy storage options [7] or the introduction of other grid flexibility options.
In the field of energy storage, there is a variety of technologies with different advantages, and distinct features, from which it is pointed out electric batteries, hydrogen, flywheels, compressed air energy storage, electric mobility and hydroelectric pump-storage [8]. Among these, the most employed technology to avoid the wind energy cut off is the hydroelectric pumpstorage, due to its large storage capacity, high efficiency and low carbon footprint [9][10][11]. Furthermore, wind speed and rainwater have average annual variations with a high degree of correlation [12][13][14], which turns hydro storage as one of the best answers to adjust consumption to wind electricity production. Another of the compelling points of hydro pump storage is that it may not involve the building of new power plants, but only the retrofitting of existing hydro reservoirs, which increases the available balancing capacity. By using previously constructed reservoirs, hydropower becomes more economically attractive to electricity producers [16,17]. Additionally, when weighing pump-storage with the second most relevant energy storage solution, electrical battery storage, several advantages of pumpstorage are highlighted. According to the literature [9], pumpstorage has lower installation, operation and maintenance costs, and longer equipment lifetime. Notwithstanding, electrical battery storage is more suitable for small energy grids and regions with a scarcity of hydro resources.
As a result of the advantages above of pump-storage, this storage solution became one of the central technologies of the European Commission in the Projects of Common Interest [18], and several countries, such as Portugal, supported in the recent past the construction of new pump-storage hydropower plants [19]. During the operation of these power plants in the European electricity market, it will be necessary to plan the buying and selling of electric power to pump water or produce electricity. This demand and supply management of renewable electricity in today's liberalised market can be posed in the framework of an optimisation problem [20]. In this regard, this study focuses on the development of an optimisation model to support decision-making in the operation of pump-storage hydropower plants. The model takes into account the variability of electricity production of wind farms and the energy price volatility in a regional European electricity market, the Iberian electricity market.
A brief literature review on the topic allows understanding that the study of electricity storage via pump-storage hydropower plants started decades ago [21,22]. With the increase of wind power capacity worldwide, and due to the correlations between wind speed and rainfall [23], the use of pump-storage power plants to incorporate wind electricity generation, promote the deployment of other variable renewable energy sources and improve grid stability, became more predominant [24]. In this sense, numerous optimisation processes were developed to make the most of the integration of renewable electricity in the grid using wind-hydro projects, but also to maximise the monetary profit of the coordinated operation of such projects. Mathematical programming and, more specifically, stochastic programming have been used to solve the problem of planning the wind-hydro combined generation in day-ahead markets [25,26]. Linear programming and, mainly mixed-integer linear programming [27], is the standard approach to model hydro scheduling. However, in recent years an increase in the use of non-linear approaches has been observed, which consider a broader set of parameters and meteorological datasets [28,29].
Regarding the study of the optimal participation in the wholesale electricity market of a wind producer using pump-storage, it is worthwhile mentioning the study of Ding et al. [30]. The work in Ding et al. [30] proposes one of the simplest models about the participation of a wind power producer in the Dutch electricity pool, and it accounts only for the economic impact of imbalances. Another similar approach is found in Cobos et al. [31]. The study of Cobos et al. [31] determines the day-ahead energy and reserve scheduling with predicted wind power and uses bulk storage to address the real-time error between actual wind power and the predicted one. Nonetheless, both study [30], and [31], use a small set of scenarios and are only focused on the day-ahead market. The work of Karhinen et al. [32] performs a comprehensive analysis of the wholesale market, studying day-ahead, intraday, and balancing markets, and concludes that predicting the electricity prices for day-ahead should be one of the preconditions for a successful operation scheduling. Another relevant study is the work of Akbari-Dibavar et al. [33]. In [33], the researchers assume the hydropower plant can arbitrate in the market, which increases the economic gains of the wind-hydro system substantially. In the literature, it is also found that coupling other electricity generation technologies with pump-storage [34][35][36], can be an efficient strategy to enhance quantitative market results, and minimise the power output fluctuation.
Regarding the specific study of the VRE integration using pump storage in the Iberian Wholesale Electricity Daily Market (MIBEL), several approaches of wind-hydro bidding strategies to deal with the power uncertainty are found. In de la Nieta et al. [27] besides the day-ahead option, bilateral contracts are also modelled, which allow selling energy forward to the grid. Due to the joint operation of a pump-storage hydropower plant and a wind farm, contract penalties, resulting from the resource variability and difficulty in prediction are significantly reduced. In Eliseu et al. [37], the joint operation of the wind-hydro system delivers 25% of the total capacity of the wind farm as a constant power, which contributes to diminishing the variability of supply. In Crespo-Vazquez et al. [25], a scheduling framework under uncertainty for wind and pump-storage system participating in day-ahead and reserve markets is developed. The stochastic model conceived in [25] can provide a theoretical market gain of 67%. In Section 10 (Appendices), a taxonomy table with a summary of recent hydro pump storage systems coupled with renewable energy technologies' studies is presented.
From the above literature, it is observed that the majority of studies are carried out for reduced periods, which may impair their conclusions. Moreover, the literature review allows identifying that the effect of the size of the reservoir in the revenue increase of the wind-hydro system is generally not addressed. Therefore, in this research, an efficient bidding framework to help the wind power producer decision-making in wholesale markets, through a bilateral contract and in the day-ahead market, is developed and analysed for extended periods (2014-2019). Besides, the methodology offers a thoughtful analysis of the long term effect of pump-storage in the revenue increase of a renewable system and studies the outcome of increasing/decreasing the storage capacity of the reservoir in the windhydro systems. Despite the study focus on the MIBEL, the conclusions and developed methodology are applicable and meaningful to other wholesale electricity markets.

Objectives
A joint operation between a wind farm and a pump-storage hydropower plant in a wholesale electricity market is proposed. The main objective is to develop an optimisation of scheduling power model for the day-ahead market, and for ensuring bilateral contracts' agreements, which maximises the system revenue. In this sense, the electricity power producer has to fix for each hour, the amount of electricity stored in the hydropower plant and the amount destined to the day-ahead market/bilateral contract. Technical constraints associated with reservoir (storage) capacity are also considered. The methodology uses linear programming and is tested for several years. The proposed scheduling optimisation methodology is benchmarked with an ideal case, and with the wind farm standalone scenario. The main contributions of this work are summarised as follows: i. A novel algorithm to simulate the hourly wind-hydro joint operation in the day-ahead market and subjected to bilateral contracts. In order to achieve the maximum economic efficiency.
ii. An analysis of the maximum theoretical wind generation revenue increase energy storage could provide, iii. The study of several electricity generation scenarios of a wind-hydro power producer operating in a day-ahead market, iv. An analysis of the effect of the reservoir capacity and hydropower capacity in the improvement of the profitability of the wind farm, and v. A methodology that could help power producers examine the economic viability on the refurbishment of regular hydropower plants to pump-storage hydropower plants.
The paper is organised as follows. Section 2 describes the wind-hydro facility and the main idea of the paper. Section 3 outlines the proposed method, including the objective function and constraints. Section 3 also includes variants of the problem. In Section 4, the heuristic methodology and the algorithm results evaluation methods are explained. Section 5 introduces the case study and the parameters used in the problem. The results are shown and discussed in Section 6. Finally, the main conclusions are presented in Section 7.

DESCRIPTION OF THE WIND-HYDRO SYSTEM
A wind power producer (the same can be applied to other variable renewable sources producers, such as solar or ocean energy) have to manage their assets efficiently with the goal of revenue maximisation, facing increased uncertainty, due to both the resource uncertainty and the variability of the electricity price.
In general, in the Iberian electricity sector, wind resource has a higher availability during the night and early afternoon [38]. However, during that period, the price of electricity is also lower [39], as can be seen in Figure 1, mainly due to the renewable feed-in effect in market price [40,41]. Figure 1 illustrates the negative correlation between a generic wind farm power generation and the electricity price in the Iberian day-ahead market, for the first week of 2012, and the hourly wholesale electricity price for the same period. The grey vertical lines in the figure To prevent having the return of the wind farm investment constrained by the wide variation of electricity price in the market, two options may be taken by the producer: • To negotiate bilateral forward contracts with electricity traders or large electricity consumer units, in which both supplier and buyer agree on an energy trading scheme and electricity price a priori. The bilateral contracts allow both the electricity buyer and seller to have price stability and certainty necessary to perform long-term planning of investments. • To have a storage system connected to the wind farm. A pump-storage hydropower plant or large battery storage can store the electricity produced by the wind farm and sell it to the grid, in such a way that its profitability is not subject to wind resource variation or the electricity price volatility.
An efficient management of this system is to store electricity, especially in periods when its price is low, and transmitting it back to the grid when electricity prices are higher. In this sense, the wind-hydro system under study comprises a wind farm with a capacity of 10 MW connected to both the Portuguese electricity grid and to a pump-storage hydropower plant (see Figure 2). The hydropower plant also has a capacity of 10 MW and is also connected to the grid. The wind-hydro power producer is operating in the MIBEL. In one approach the system operator sells the electricity in the day-ahead market. In other approach, the system operator sells the electricity generation through a bilateral contract. Consequently, it has to schedule 24 h ahead,when the wind electricity is to be sold directly to the grid (or delivered to satisfy the contract), when it will be stored via the pumpstorage, and when the hydropower plant will generate electricity using the previously stored energy. It is assumed that the hydropower plant cannot store and generate electricity at the same time. It is also defined that, over the period under study, the reservoirs adjacent to the hydropower plant do not receive water from groundwater, rain or other sources, and that the evaporation does not change the volume of water in the reservoirs. That is, the total amount of water present in the system does not vary over time. The electrical losses of energy transmission between the wind farm and hydropower plant are in the order of 2% of total electricity generated [42]. This paper presents a new methodology to optimise wind generation revenue combining it with a hydropower plant. The time frame to evaluate the problem is 6 years, between 2014 and 2019, using real electricity price values from the MIBEL. The problem was studied for several parameters of the hydropower plant.

THE OPTIMISATION PROCEDURE
The operation schedule of the wind-hydro system has at its core finding an energy offering strategy that maximises the revenue. The linear programming model includes variables, objective function and constraints introduced in this section. Sections 3.1-3.4 are focused on the day-ahead approach. The bilateral contract approach is described in Section 3.5.

Variables
The variables are divided into two groups: decision or auxiliary. The decision variables are unknown values determined by the solution of the problem and influence the performance of the renewable system management. Thus, the definition of decision variables constitutes one of the most crucial parts of the problem formulation. Since wind-hydro system management comprises decisions about which periods of pumping, electricity generation in the hydropower plant or direct sale of electricity from the wind farm to the grid occur, as well as the power values involved in each of these three tasks, binary variables are proposed for each hour of the day corresponding to the respective decision. In this sense, binary variables T 1 t,d are considered which assume the value 1, for each period t on day d, when pumping occurs, binary variables T 2 t,d are considered which assume the value 1 when the hydropower plant is generating electricity, and finally, binary variables T 3 t,d which assume the value 1 when the wind farm is selling electricity directly to the network. Auxiliary variables are calculated with the values of the decision variables. The total value of water released by the upper reservoir at each hour is shown in the following equation: where Q G represents the water flow in m 3 , released by the hydropower plant per second, given by the following equation: In (2) P rh corresponds to the installed capacity of the pumpstorage hydro power plant, ΔH represents the drop of elevation, or head, of the river between the upstream and downstream of the water turbine, ΔH G corresponds to head losses, g represents the gravity and T the efficiency of the hydro power plant while generating electricity.
The volume of water stored in the upper reservoir at hour t of day d is: where Q P represents the water flow stored by the reservoir per second, defined as follows: In (4) W t,d represents the power produced by the wind farm in period t and day d, ΔH P corresponds to pressure losses and P the efficiency of the hydro power plant while pumping water. With a larger water flow in (4) more energy is available to be stored in the reservoir.
Moreover, the auxiliary variables also include the corresponding energy stored in the upper reservoir in MWh, translated mathematically in (5) and (6). Equation (5) represents the accumulated energy stored in the reservoir, in (5) electricity from the wind farm W t,d is being stored in the upper reservoir by means of potential energy of water, (see (5)).
where SW 0,1 represents the initial volume of water present in the reservoir.
In (6) the accumulated energy stored in the reservoir is defined by the total value of the energy previously stored SW t −1,d subtracted to the electricity being generated P rh , (see (6)).

Objective function
The objective function maximises the gross revenue of selling electricity in the Day-Ahead Iberian Market. The revenue of the MIBEL's share corresponds to the sum of the revenue of the electricity generated in the hydropower plant and the revenue from the electricity generated in the wind turbine W t,d that is sold directly to the grid. This function decides the optimal offer of a wind farm and a hydro unit, per period t and day d, depending on the daily electricity market prices, wind production and water reserves, it is defined as (7):

Constraints
The constraints are classified into two types: hydro reservoir constraints and operational constraints. The constraints are presented in the following subsections.

Hydro reservoir constraints
The maximum volume (V maximum ) of the upper reservoir is limited by the height of the dam. The minimum volume (V minimum ) is a result of both environmental and technical impositions [43]. In this sense, the volume used to store water, and consequently, the electricity generated by the wind farm is given by (see (8)).
The second hydro reservoir restriction implemented in the model, Equation (9), enforces that the water volume at the reservoir at the beginning of the each hour is obtained by the sum of the previous stored volume of water (V t,d ) plus the pumped volume (V Pump t,d ), subtracted by the volume that is displaced hourly for electricity generation (V Prod t,d ), (see (9)).

Operation constraints
One of the operational constraints emerges from the inability of simultaneously use the turbine to pump water and to produce electricity. Thus, it is essential to establish that at every hour the binary variables associated with those operations cannot take both the value 1, which can be translated to the following equation: Another constraint arises from the initial conditions of the system, since it was established that the electricity generated by the wind farm every hour is sold and transmitted to the grid,or is used to pump water to the hydropower station. Therefore, the two situations cannot occur at the same time which implies that T 3 t,d and T 1 t,d also cannot be both equal. This is represented in the following equation:

Variants of the day-ahead bidding problem
Two variants of the problem were developed to analyse better the day-ahead bidding algorithm, denominated isolated wind farm and wind-hydro-grid system. This section is devoted to the formulation of the problem for the two variants of the windhydro system, clarifying the changes made in parameters and the objective function.

Isolated wind farm
To define the baseline of the problem, that is, the minimum value to which the optimisation results have to be compared, a variant of the problem that assumes the wind farm operates alone (there is no storage system connected to the generators) is considered. In this scenario, all the generated power is directly sold in the MIBEL. Accordingly, there is no need to optimise the production of the system and make hourly decisions about its management, in contrast to the wind-hydro system. In this variant, there are no decision variables or constraints on the problem. As a result of the simplicity of this variant, the gross financial revenue of the wind farm is given by the following expression:

Wind-hydro-grid system
The variant wind-hydro-grid system always operates at the maximum power capacity (parameter P rh ) both in pump and generation mode, in order to increase the gross financial return of the optimised management of electricity selling. This implies redefining the pump flow parameter, which becomes constant and independent of the wind farm electricity generation. In this context, Equation (4) is modified to the following: The objective function of the problem should also be redefined for this variant. For the turbine to work at maximum power, when pumping, electricity from the grid must be used whenever the wind farm generation is lower than P rh . This means adding a cost, represented mathematically by (14), to carry out water pumping, associated with the share of electricity bought to the electricity grid.
Thus, the objective function for the wind-hydro-grid system takes into account the aforementioned cost and is translated mathematically by the following expression (see (15)).

Bilateral contract problem
An additional approach for the bidding of the electricity generation was developed. The new approach assumes the wind-hydro system operator trades its production mainly via a physical bilateral contract. Using the pump-storage power plant, the operator can store the wind generation, when it exceeds the physical bilateral contract value. In situations that the current wind generation is below the physical bilateral contract value, the previously stored generation in the hydropower plant's reservoir can supply the energy difference. If the bilateral agreement is not satisfied, the operator is penalised. This section is devoted to the formulation of the problem for the bilateral contract approach.

Bilateral contract variables
In the bilateral contract approach, binary variable T 5 t,d is set to decide if the electricity generated by the wind farm is used or not to fulfil the agreement. The variable T 4 t,d is set to decide whether the electricity previously stored in the hydro unit is sold to satisfy the agreement. This situation only occurs if the current wind generation is less than the physical bilateral contract value BC t,d . The binary variable T 6 t,d translates the situation in which that due to water volume constraints in the reservoir, wind generation surplus has to be sold in the electricity mar-ket. The variable T 7 t,d is set to define the penalty costs associated with the violation of the bilateral contract, that occurs when the current wind-hydro system generation is lower than BC t,d . Finally, binary variable T 8 t,d is set to decide whether the electricity surplus from the wind farm is stored or not by the pump-storage unit.
In the current approach, the auxiliary variables consist on the total volume of water released and stored per hour at the reservoir. The value of water released by the upper reservoir at each hour is shown in (16): where Q G represents the water flow in m 3 , and is given by (17): The volume of water stored in the upper reservoir at hour t of day d is: where Q P represents the water flow stored by the reservoir per second, defined as follows:

Bilateral contract objective function
In the bilateral contract problem, the objective function is equal to the sum of the revenue of the electricity sold via the agreement, and the revenue from the electricity generated in the wind turbine W t,d that is sold in the day-ahead market, subtracted by the imbalance costs Ic t,d due to the violation of the bilateral contract.
The revenue of the electricity sold via the agreement will be represented as (20): The revenue from the electricity surplus that is sold in the day-ahead market is shown in (21): In the case, the sum between the present wind electricity generation and the present hydropower plant generation cannot satisfy the physical bilateral contract, the operator has to pay a penalty for imbalances Ic t,d . The total imbalance costs from the violation of the contract agreement will be represented as (22): The sum of the previous equations gives the objective function of the bilateral contract, per period t and day d, (see (23)).

Bilateral contract constraints
The operation constraints of the renewable system, establish that penalties for imbalances, cannot occur if the current generation is higher than BC t,d , which is represented in Equation (24): The other operation constraint sets that imbalances penalties cannot occur if the at the present moment the hydropower plant is using previously stored electricity to ensure that the physical value of the bilateral contract BC t,d is achieved. This constraint is represented in Equation (25): Furthermore, in this approach the water volume constraints (8), and (9) continue to be valid. If at period t and day d, the water volume constraints are at the risk of being infringed, the wind generation surplus will be sold at the day-ahead market as shown in (21).

HEURISTIC METHODOLOGY TO GENERATE SOLUTIONS-DAY-AHEAD APPROACH
In the previous sections, it was verified a negative correlation between the price of electricity in wholesale markets and the electricity generated by wind farms. As a consequence, scheduling the operation of the wind-hydro system for the day-ahead approach should be made according to the variation of electricity prices. Given that only past prices are known for the man-ager of the power plant, scheduling the wind-hydro system has to take that information as the primary input.
Nevertheless, using an extensive historical record of electricity market past prices, to define the operation of the wind-hydro system, may not be useful, since it would not detect a more recent price trend. On the other side, scheduling the operation of the wind-hydro system with a recent price trend could lead to irregular operation decisions that may not increase the monetary revenue of the system. Taking this into consideration and after some trials, it was decided to choose a past weekly price average to define the operation of the power plant. More specifically, it was decided to compare the price at each hour with the average weekly price observed in the previous week, in this perspective: i. When the price is significantly lower than the previous week average price, the wind farm generation will not be sold to the grid but transmitted to the hydropower plant to pump water; ii. When the electricity price is higher than the previous week average price, the previously stored water will be used to generate electricity.
In this sense, parameter M i , i ∈ {1, … , N weeks } will be used to represent the weekly average of the electricity prices in week i of the year under analysis. It should be highlighted that instead of the weekly average several other more precise methods could have been used as input to forecast electricity price. The average was employed to reduce computational power since the goal of this study is studying the wind-hydro joint system management and not develop an electricity prediction model. To give elasticity to the electricity prices and the past weekly average of the electricity prices parameters K 1 and K 2 are used during the operation scheduling decision. In more detail: i. When at day d-2, the price of energy at hour t, Pr t,d −2 , is less than the average price of the previous week, M i , multiplied by K 1 and the volume of the reservoir satisfies condition (8), the decision is to pump water in the next hour and the decision variable T 1 t,d is equaled to 1.
ii. If Pr t,d exceeds the average electricity price of the previous week multiplied by K 2 and the variable V t,d satisfies condition (8), the stored water is used to generate electricity and the decision variable T 2 t,d is equaled to 1. When the water is being used to generate electricity in the hydropower plant, and since the power plant cannot store and generate energy at the same time, the wind farm power generation is also being sold directly and transmitted to the electricity grid network. In this circumstance, the variable T 3 t,d is also equal to 1.
iii. In the intermediate situation, that is, when the value of Pr t,d −2 is between M i multiplied by K 1 and M i multiplied by K 2 , the wind farm power generation is sold directly to the grid, without the occurrence of hydropower generation or storage. When volume constraints (8) are at risk of being exceeded, that is, hydro generation or water pumping water at the current time may imply violation of the restriction (8), only the direct sale of the electricity generated in the wind farm to the grid will occur.
In summary, water pumping will occur when constraints (8) and (26) are satisfied, (see (26)). On the other hand, electricity generation via both hydropower plant and wind farm will  (8) and (27) are satisfied, (see (27)). Whenever volume of energy stored or electricity generation in the hydropower plant does not satisfy (8) or when condition (28) is observed, the electricity generated in the wind farm should be sold directly to the grid, (see (28)). Figure 3 illustrates the methodology used to schedule the wind-hydro system operation. In Figure 3, the electricity price at time 3 of day 9, Pr 3,9 , is compared with the average electricity price of the week preceding the current week, M 1 . In this example, the current price satisfies condition (26), which leads to assigning the value 1 to the decision variable which represents pumping water, T 1 3,11 = 1. Thus, the decision to be taken by the power producer is to pump water in the hydropower plant using the electricity generated at the wind farm at the third hour of day 11.

Criteria to define the parameters K 1 and K 2
The parameters K 1 and K 2 can be changed for each season of the year. This adjustment increases the sensitivity of decisionmaking according to changes in electricity prices. The use of these sensitivity parameters generally translates into an improvement of the solution. The reason for selecting different values for the parameters is due to the large variety of electricity prices seasonally. As example, in the first semester of 2019 the Portuguese electricity wholesale market had an average price of €52.2/MWh, while in the second semester the market average was €43.6/MWh [44]. Usually, in winter the electricity price is lower in the wholesale market due to the effect of renewable feed-in [39][40][41]. In winter the mean rainfall and wind speed in Iberian Peninsula are substantially higher than the rest of the year [45,46], leading to an increase in the capacity of the wind and hydropower electricity generation, which decreases the wholesale electricity price. Thus, the objective function is calculated five times, according to the season of the year, to take into account the seasonal price variability. The periods were defined between Day 1 and 78 (winter), between 79 and 172 (Spring), 173 and 266 (summer), 267 and 356 (autumn) and between 357 and 365/366 (winter), the annual return is the sum of the best solution per season.

Evaluation of the heuristic methodology results-Maximum value
The heuristic approach to solving the problem of electricity management gives successive hourly indications of decisionmaking. At the end of a year, there is an aggregated result of these decisions, which indicates the gross monetary return achieved with the optimisation. The quality of the outcome achieved by this process should be assessed to determine whether the methodology used is valid in the context of the problem and whether reliable results are produced. The maximum theoretical monetary revenue of the system should be calculated to assess the quality of the methodology. Consequently, a model is considered with the same mathematical formulation presented in Chapter 3, in which at the beginning of the year all parameters are known, in particular, the prices of electricity in the spot market and the electricity generation profile of the wind farm. The solution of the perfect knowledge model is compared with the result of the heuristic approach and, due to the relative revenue difference between the two solutions, it is possible to evaluate the quality of the initial heuristic model.

Input data
The model is initially tested for a wind farm with a 10 MW capacity, connected to a hydro pump storage facility. MIBEL's day-ahead real values are used to test the day-ahead bidding approach. For the bilateral contract approach, it was defined a bilateral contract price equal to 120% of average day-ahead market following the analysis of [27]. The wind farm generation profile was obtained using the dimensionless generation profile of the overall Portuguese wind sector [47]. The hydro pump storage facility can accumulate energy in the form of potential energy with an efficiency of 85%, and generate electricity with 95% efficiency [10,48]. The hydro pump facility is composed of upper and lower reservoirs, turbine/pump, pipelines connecting these elements, and the control system. The initial volumes of the reservoirs are V initial = 0.2 hm 3 , for the upper reservoir, and 0 hm 3 , for the lower reservoir. The case study is tested for 1 year (8760 hours) and it is assumed the total available capacity in both reservoirs is the same during the study. The operation and maintenance costs for the wind farm, parameter C W , is €17/MWh [27], for charging the reservoir, parameter C P , is €1.5/MWh, and to discharge the reservoir, parameter C H , is €1/MWh [37]. The global parameters, that stay constant in all the variants of the problem, are presented in Table 4 (see in Appendices). For the variant of the problem wind-hydro-grid system, described in Section 3.4.2, in which the hydropower plant pumps water always at maximum power, parameter ΔH P is equal to 15 m, since an increase of the water inflow leads to a rise of the head loss value [49].

Scenarios
This section details the studied cases used to investigate the coordinate bidding strategy. A generic wind farm connected to a pump-storage hydropower plant located in Mainland Portugal was used to show the results of the model. The scenarios are combined forming a tree. The tree is formed by: six scenarios of wind generation and market prices, corresponding to years from 2014 to 2019. The six scenarios of day-ahead market prices, consist of real prices between 2014 and 2019 and have been obtained in the online transparency platform of the European Network of Transmission System Operators for Electricity (ENTSOE) [44]. Since there is a correlation between the electricity price, the load demand and the variable renewable electricity generation [13], it was decided to use the wind generation profile and the day-ahead market price of the same year. The scenarios for the yearly day-ahead market prices average are shown in Figure 4, which shows that the lower market prices occur between 2 h and 5 h and the highest prices occur between 19 h and 22 h. Table 1 presents the average annual prices in the day-ahead market and the standard deviation for every year under study. The correlation between hourly wind generation and load demand are also shown in Table 1. The annual standard dayahead market deviation was calculated using (29):  In expression (29), the average value of the day-ahead market price in €/MWh is represented by . In Table 1, a decreasing trend in the volatility of the market price is recognised, which is associated with a reduction of the standard deviation. The same decreasing trend is observed in the Iberian market by Aleasoft [50], and in other European electricity markets, in the work of A.Sapio [51].
Since the market prices are influenced by several factors, such as the electricity consumption in the Iberian market, it becomes relevant to study the evolution of demand. Figure 5 shows the demand of electricity between 2014 and 2019 for the Portuguese and Spanish Mainland systems. In that figure, it is noticeable that the electricity demand grew in both countries, however faster in Spain, which may account for the increase of day-ahead market price [52] verified between 2014 and 2018. Figure 6 depicts the wind farm daily generation average between 2014 and 2019. That figure shows that, on average, the production is lower between 10 h and 15 h and is at its highest during the night period.
The correlation between wind generation, load demand, and MIBEL prices is presented in Table 2. The scenario tree structure of the analysed cases is presented in Figure 7. In addition to the scenarios of wind generation, three scenarios of hydropower capacity, namely 5 MW, 10 MW and 15 MW, and three scenarios of reservoir capacity, 0.8 hm 3 , 1 hm 3 and 1.2 hm 3 , will be used to assess the two different bidding approaches, bilateral contracts and day-ahead market. In the day-ahead market, for the wind-hydro approach, it was also considered a situation in which the transmission grid suffers an unforeseen congestion, ranging between 10 and 30% of the total installed power of the wind farm. Due to study of several reservoir and pump-turbine capacities, it is possible to assess the effect of the size of the pump-storage equipment on the revenue increase provided to a specific wind farm. The total number of scenarios is 6×3×3×4 = 216 as shown in Figure 7.
In Figure 7, BC 20 % symbolises the bilateral contract approach (Section 3.5), in which the wind-hydro system has to supply continuously to the grid 20 % of the total installed power of the wind farm, due to a physical bilateral contract. In the BC 20% the physical bilateral contract agreement stipulates the electricity is contracted by the a price 20% higher than the average yearly value of the day-ahead market price. The value of the bilateral contract should increase according to an increase in the constant load needed to be supplied as defined by [27]. The scenario WHG, does not put restrictions or requirements to the operation of the wind-hydro-grid system (Section 3.4.2), in the day-ahead approach. The scenario WH, represents the wind-hydro day-ahead approach, Sections 3.1-3.4, and does not put restrictions to the operation of the system.
The main input and output data needed to test the developed method is displayed in Figure 8.

RESULTS AND DISCUSSION
This section introduces the main results obtained by the simulation procedures used to evaluate the model proposed in Sections 3-5. The presented model has been implemented in XPRESS-IVE, using the MILP solver integrated in the software, the total number of variables and constrains of the model is 43,796, and 61,315, respectively. The initial case study uses the data shown in Figures 4 and 6. The results are obtained using the Equations (7), (15), and (23).

Operation and economic results
This section presents the operation results (hydro storage and generation patterns), for the initial optimisation problem, windhydro system, the variant of the problem, wind-hydro-grid system, the scenarios with transmission restrictions, and the bilateral agreement approach. Furthermore, it also displays the revenue increase due to the coupling of the wind farm and the pump-storage hydro. Optimal hourly scheduling of the pump hydro storage system, heuristic methodology

Wind-hydro system-Day-ahead
The average of results for the optimal operation scheduling of pump hydro storage system, for the 54 WH scenarios, using the heuristic methodology, are shown in Figure 9. In that figure, positive bars represent the electricity pumping/storage, negative bars symbolise the electricity generation from the hydropower plant (energy released), and the blue line represent the dayahead market prices in MIBEL. Figure 9 shows that the energy charging/discharging profile follows closely the market price pattern and the most common hours of the water pumping (energy storage) occur in hours of likely low electricity market prices, which are more pronounced during the night period (from 0 h to 7 h). The most common values of the hydropower electricity generation occur in periods of high prices, mainly in the morning period (between 7 h and 12 h) and in peak hours (around 20 h). Additionally, the computational model generated several water storage profiles, translating the the optimal hourly scheduling of the system. One example of these profiles is illustrated in Figure 10, for the year of 2014, for the scenario in which the maximum water volume is 0.8 hm 3 and the turbines' maximum power capacity is 10 MW. In 2014, the maximum volume of accumulated water has three maximums close to 800,000 m 3 , all in the first half of the year (winter and spring period). In that same period the largest consecutive number of hours of pumping/generation occurs. In the second half of the year the storage regime remains more stable and there are some periods between 5000 and 6200 h where barely exists pumping or generation. Figure 10 also shows that the minimum volume of water in the reservoir corresponds to 0.2 hm 3 .
Concerning the expected revenue of the analysed renewable system, Figure 11 shows the results for the average of each scenario per year. In Figure 11, lower bars (light orange) represent the expected profits if the wind farm did not have a storage system. That represents the baseline of the problem. Green bars gives an idea about the increase in the monetary revenue of the wind farm due to the use of pump storage, using the heuristic methodology developed. Finally, purple bars denote the maximum theoretical net revenue, a value that is only used to analyse the quality of the heuristic method. As can be seen, the use of pump storage increases the wind farm return in every scenario. After studying all different 54 WH scenarios, the conclusion is that the maximum yearly increase of net revenue for the heuristic method was found in 2014, corresponding to a 16% increase (€84,480). By its turn, the lowest revenue increase was found in 2019, corresponding to an average increase of 1.3%. The capability of the storage to increase the profit is reduced over the years, hinting that the price volatility may be the most determining parameter in the optimisation.
The average value of revenue for each configuration is presented in Table 3. The table highlights that the coordination of the operation of the wind farm and the hydropower plant represents a yearly net revenue increase, using the heuristic model, (theoretical max.)

FIGURE 12
Average expected revenue per year-High uncertainty situation of 4%. Furthermore, it was identified a maximum theoretical increase in revenue of the wind-hydro system of 15%, when compared to the baseline solution. These values demonstrate the potential of energy storage to improve the revenue of a VRE power plant.

Wind-hydro system-Day-ahead approach with transmission congestion
In the situations with high levels of congestion in the transmission grid, it is verified a decrease in the average revenue values for all the years in the wind standalone scenario ( Figure 12). Nevertheless, using the wind-hydro system it is verified the developed methodology was able to increase the revenue of electricity trading.
Under the high uncertainty scenario, it is still verified the potential of the hydropower plant to increase the expected yearly revenue. The situation with transmission congestion the revenue of the wind-hydro system was 7% higher than the standalone wind farm.

6.1.3
Wind-hydro-grid system Figure 13 shows the average optimal hourly energy charge/ discharge of the hydropower plant, for all scenarios between

FIGURE 13
Optimal hourly scheduling of the wind-hydro-grid system, heuristic methodology 2014 and 2019, for the wind-hydro-grid system. In this variant of the original problem the hydropower plant is not only used to optimise the electricity generation from the wind farm but also allowed to buy electricity from MIBEL. When buying electricity from the market, the hydropower plant will not only act as a wind farm revenue booster but also as an electricity trader, exploiting the variability of the day-ahead prices to enhance its profits. When comparing the shape in Figure 13 with the results from the wind-hydro system, it is possible to verify a similar pattern. The pattern is similar due to the fact that the day-ahead prices of MIBEL used in the study are the same for both systems, which may hint that the prices act as the main parameter affecting the operation of the system. Figure 11 also shows that, similarly to the wind-hydro system, the most common values of the bid for the wind-hydro-grid configuration occur in consumption peak hours. In the wind-hydro-grid system, the average values of the energy stored/released are substantial higher than the original configuration, described in Section 7.1.1. An example of the volume of water profile in the upper reservoir, for the wind-hydro-grid configuration, is illustrated in Figure 14, for the year 2015, for the scenario in which the maximum water volume is 1.2 hm 3 and the turbines' maximum power capacity is 10 MW. In 2015, the maximum volume of accumulated water has only one maximum around 1,200,000 m 3 , which occurs in the first quarter of the year. It is also observed that in the first quarter of the year there is a more active generation/pumping operation, while in the second and third quarter of the year the volume is kept almost constant. This fact highlights that in the latter period of the year the hourly electricity price difference did not justified the storage of energy The net revenue of the wind-hydro-grid system can be observed in Figure 15. In that figure, lower bars represent the net revenue of the wind farm standalone version and green bars represent the rise in the revenue as a result of the addiction Average expected revenue per year, wind-hydro-grid system of energy storage, using the heuristic methodology developed. The top bar (purple bars) represents the maximum theoretical net revenue increase, if a price a prior knowledge methodology was applied. In this variant of the original problem, an average revenue increase of 13% is attained, which means that the wind farm could increase its revenue yearly by €137,783 as a consequence of the addition of the storage component. The year 2014 is the one with a higher revenue increase (59%), around €314,000, when compared to the baseline value. It is also noticeable that, in 2014, the difference between the developed methodology and the perfect solution is very reduced (only €39,000).
The average value of revenue for each configuration is presented in Table 5. Besides the 13% increase in profit as a result of the storage system, it is observed that a more precise mathematical model could have reached an average revenue increase of  about 26%, and could have generated an yearly profit of around €190,770.

Bilateral contract approach
In the bilateral contract approach it is seen than the coupling of the wind and hydropower plants can greatly increase the revenue costs, as shown in Figure 16, due to the decreasing of the electricity imbalance payments. The highest increase of revenue occurs in 2015, when the wind-hydro system was able to increase the revenue of the bilateral contract near €1.2 million in relation to the wind standalone approach.
In average the use of pump storage to manage shortages/excess of wind generation translated into an yearly gain of €713,972 ( Table 6).
The pattern of energy stored/discharged is presented in Figure 17. It is verified the pattern is substantially more irregular than the day-ahead option.

Influence of the pump-storage size and hydropower plant capacity
Additionally, it was also studied the effect of the pump-storage size on the increase of profit provided to a specific wind farm. For this, the expected revenues were calculated for a set of Optimal hourly scheduling of the wind-hydro system, bilateral contract approach different pump-storage sizes (0.8, 1 and 1.2 hm 3 ). The study considers different pumping and turbine capacities, 5, 10 and 15 MW. The turbine and reservoir capacities are also modified so that the same proportion rate with the pumping power is maintained. The study was conducted to the two aforementioned configurations of the system, the wind-hydro system, and the wind-hydro-grid system. The results of the wind-hydrogrid system are illustrated in Figure 18, which shows that, in the conditions previous defined for the problem, a relative increase in the reservoir is translated to a higher revenue, with a correlation of 64%, in the heuristic methodology approach. When analysing the effect of the turbine/pump capacity and the revenue increase in the heuristic methodology, no correlation was found. In the perfect knowledge approach no correlation between the size of the reservoir, capacity of the turbines and revenue was found.

CONCLUSION
The main motivation of this study is to provide an efficient methodology that improves the monetary revenue of a wind farm coupled with a pump-storage hydropower plant, in a wholesale electricity market. In this work, several operation configurations, and trading scenarios were developed. Three approaches assumed the wind-hydro system traded its generation in the day-ahead market, and one approach assumed the system traded the electricity generation long-term via a bilateral contract. The revenue of the system was formulated as a linear function, subjected to constraints related to the operation of the wind and hydropower plants. The case studies were analysed and compared with scenarios in which no optimisation methodology was employed to manage the wind electricity generation, and with the maximum theoretical revenue. By using the developed mathematical model, the wind farm registered a yearly average increase of revenue of 4%, consisting of €28,508, for the unconstrained day-ahead market approach. In the scenarios with grid congestion the system increased its revenue in 7%. In the second the hydropower plant can arbitrate in the market, the yearly average increase in revenue was substantially higher, around 13% or €95,683.
In the bilateral contract approach, the mean revenue increased attained the value of 326% or €713,942. Both alternatives illustrated the potential of pump-storage to enhance the gains of the wind power producer. The analysis of results also showed that higher volatility in prices might be the most significant parameter affecting the decision of charging and discharging the energy storage, and consequently, the expected revenue of the system in the day-ahead scenarios. Additionally, the outcome of the reservoir size and the turbine/pump capacity on the increase of the wind farm profit was also studied. The results obtained showed a correlation between the growth of revenue and the increase of reservoir available volume in the heuristic methodology. The optimisation methodology results showed that this model could provide investors with a cost-effective operation scheme planning of their wind farms/hydropower plants, and a decent revenue increase. The proposed method can be promptly adopted to study the operation and optimal operation of other VRE technologies, such as solar PV, and under diverse electricity markets. The developed model could also be useful for assisting in investment decisions about new pumpstorage facilities, or requalification of existing hydropower plants.
For future studies, the following directions are critical. First, the proposed method should be extended to analyse the economic and technical comparison between the use of pumpstorage hydropower to store the wind farm generation, and other energy storage solutions, such as an electrical batteries. Second, it would be essential to analyse the benefits resulting from pump-storage hydropower auxiliary services, such as power reserve. In addition, a more comprehensive methodology that integrates more clean energy sources needs to be developed. P Efficiency of the pump-storage hydropower plant for water pumping, P ∈ {0, 1}. ΔH Head drop of the river between the upstream and downstream of the water turbine, m. ΔHP Head losses due to friction and viscosity effects inside pipe walls during water pumping, m. ΔHG Head losses due to friction and viscosity effects inside pipe walls during electricity generation, m. V maximum Maximum volume of water in the upper reservoir, m 3 .
V minimum Minimum volume of water in the upper reservoir, m 3 . V initial Initial volume of water in the upper reservoir, m 3 . K 1 Vector used to give elasticity to the algorithm, K 1 ∈ {0.05, 1}. K 2 Vector used to give elasticity to the algorithm, K 2 ∈ {1, 2.8}. Q G Water discharge for electricity production, m 3 ∕s. Q P Water flow pumped by the pump-storage hydropower plant for storage, m 3 ∕s. g Earth's acceleration of gravity, m∕s 2 C W Cost of generating electricity in the wind farm, €/MWh.