On flexible hydropower and security of supply: Spain beyond 2020

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 A note on flexible hydropower and security of supply: Spain beyond 2020 Luis Mª Abadie a, José M. Chamorro b*, Sébastien Huclin a, Dirk-Jan van de Ven a a Basque Centre for Climate Change (BC3), Sede Building 1, 1st floor, Scientific Campus, University of the Basque Country UPV/EHU, 48940 Leioa, Spain. E-mails: [email protected], [email protected], [email protected] b University of the Basque Country UPV/EHU, Dpt. Financial Economics II, and Institute of Public Economics, Av. Lehendakari Aguirre 83, 48015 Bilbao, Spain. E-mail: [email protected] *Corresponding author. October 2nd 2019 ABSTRACT Generation adequacy is a key ingredient to security of electricity supply (SoS). Some national plans envisage a future decrease in the number of coal-fired stations and an increase in renewable installed capacity. This forecast, along with the future reduction of nuclear capacity, will lead to a combination of less baseload plants and sizeable intermittent generation. Hence there is a risk that supply will be unable to meet demand and generation adequacy will suffer. We assess how the flexible management of hydro resources can alleviate this risk by adjusting power generation to peak demand. Indeed there is empirical evidence that they are positively correlated. We compute this correlation in the case of Spain (an ‘electric island’). Besides, hydro plants operate in combination with other non-dispatchable technologies within the system. Therefore, we also take their hourly seasonality into account. Next we run a Monte Carlo simulation to derive the risk profile of several adequacy metrics in the coming decades. Our results show that flexible hydro generation certainly mitigates the risk but is insufficient to bring an adecuate level of SoS when the enhanced renewable capacity goes hand in hand with a decreased baseload capacity. The risk further decreases after accounting for seasonal non-dispatchable generation, yet it still looms large. These results can be important for policy makers, system operators, and power companies when analizing investments in renewable energy with a long lifespan. Keywords: security of electricity supply, generation adequacy, hydro stations, uncertainty, Monte Carlo, lost load. 1 INTRODUCTION As the overall demand for electricity is anticipated to increase in the future, security of electricity supply (henceforth SoS) is eliciting ever more attention from all the stakeholders involved. It seems fair to claim that there is hardly a widely accepted definition of SoS. Nonetheless, a common thread arises from the different versions, namely the ability of power supply to meet effective demand on a continuous basis. In a sense this is a ‘narrow’ definition since power demand and supply do not operate in a vacuum. [1] goes beyond it by encompassing also environmental and societal concerns. This makes sense because SoS is affected by a number of factors, among them technology, markets, politics, and the environment. The power supply in particular is a complex chain that is naturally exposed to a number of risks and uncertainties. As a demarcation criterion, the probabilities and/or impacts of the former can be more reliably computed than those of the latter. Sources of uncertainty are typically adressed by means of scenario analysis. Instead, regarding risks, the standard practice is to define and compute a number of risk metrics. This said, supply is only 50 percent of the story. [2] defines system adequacy as the existence within a system of sufficient generation and transmission capacity to meet the load, whether under normal or unusual conditions. It subsequently introduces different approaches to measure adequacy and a list of related metrics. [3] develop a stochastic model that explicitly matches power demand and supply (if possible). From this interplay it is possible to assess generation adequacy by means of several metrics that account for different attributes of potential supply shortfalls. Next they demonstrate the model by example. *Revised Manuscript with No Changes Marked Click here to view linked References This document is the Accepted Manuscript version of a Published Work that appeared in final form in: Abadie L.M., Chamorro J.M., Huclin S., Ven D.-J.V.D. 2020. On flexible hydropower and security of supply: Spain beyond 2020. ENERGY. 203. DOI (10.1016/ j.energy.2020.117869). © 2020 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 3.0 license http://creativecommons.org/licenses/by-nc-nd/3.0/ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2  Specifically, they look at Spain (an ‘electric island’ right now and in the near future at least) beyond the year 2020. Monte Carlo (MC) simulation allows them derive the risk profile of several key variables. Taken together they characterize the risk profile to SoS in great detail. In the end, [3] simulate the performance of the Spanish peninsular generating system under ten different scenarios. Regarding the installed generation capacities from 2020 through 2050, they basically draw on [4]. Importantly, [3] assume that coal-fired and nuclear stations are kept constant from 2017 to 2020 but decrease significantly in 2030 and completely cease to operate from 2040 onwards; natural gas plants, instead, are assumed to remain constant at their 2017 level through 2050. Unlike thermal stations, renewable power technologies grow in all of the scenarios, be it either slower or faster depending on the growth of power demand (either 1.36% or 1.72%). According to their results [3], the system’s adequacy worsens in 2020 and does so dramatically in 2040 and 2050, when coal and nuclear stations are completely replaced by renewable plants. The earlier results in [3] consider all power technologies as feeding their potential output in the system irrespective of demand; this general rule applies to hydro power in particular too. Because of the earth’s gravitational field there is energy stored in the water that flows in rivers from upstream regions toward the sea. So-called diversion or run-of-river hydropower refers to extracting a portion of the energy contained in flowing water itself to produce electricity. Another possibility is to use the potential energy contained by a dam structure for the same purpose; this is frequently called impoundment hydropower; [5]. Importantly, this type of facilities can regulate the flow to be turbined at any precise time. Despite the differences between both types, [3] consider all hydropower plants (HPPs) as a whole. Thus, the results in [3] take monthly seasonality of hydro’s load factor into account, but there is no room for strategic management of hydro plants (i.e. no aim at maximizing profits by producing more electricity at demand peaks within the month).1 By no means this is exclusive of [3]; indeed it seems to be the usual practice. For example, [2] presents the findings from an empirical analysis on adequacy metrics and standards adopted in Europe. From the research conducted via public sources, one of the general conclusions drawn reads as follows: “In no case was it mentioned how the operation of hydropower plants with reservoirs is considered. In countries with medium or high participation of hydropower in the generation mix, this factor is crucial for system security. In fact, in some of these countries, a dry year may be the most stressful situation in relation to generation adequacy. The use of historical series of generation data would ignore the possibility of operating reservoirs in a conservative manner, in order to increase generation adequacy (or equivalently, to reduce the risk of load shedding)”. In view of this, the EC urges to consider at least the probabilistic characterization of a number of factors, among them: “Hydroelectric energy availability depends on the reservoir operation strategies established by the owners of plants”. Hydropower plants with reservoirs can in principle serve several purposes, for example irrigation needs or flooding control. HPPs can be managed as SoS devices also. They are normally designed for generation during peak hours.2 Further, some HPPs are equipped with reversible turbines or separate generating and pumping equipment (so-called pumped storage hydropower).3 They enable the system to pump water (using electricity) from a lower reservoir up to a higher one when power demand (and presumably price) is low; when demand (price) increases, the flow is reversed. This ‘load leveling’ is a widespread type of load management; [7]. ‘Ramping and load following’ are other types of load  1 Note that deciding when it will be more profitable to produce electricity is no easy task. At one level, suppliers draw on limited hydro energy resources available. On the other hand, future inflows are uncertain and there is a risk of spillage. According to [6], generators try to hedge against risk and are usually conservative. For example, they generally opt for deploying limited water resources when prices are moderately high, instead of waiting for a possible (uncertain) scarcity of generating resources (when the peak price would be very high) in the future. 2 The flexibility of hydro reservoirs is often seen as the perfect complement to a system dominated by intermittent renewable sources; [7], [8]. [9] and [10] even claim that a system based on only wind, water and solar power could serve 100% of energy purposes by 2050 in a reliable and affordable way. However, this claim has received various critiques, e.g. that these authors are too optimistic about the balancing role of hydropower [11]. 3 Pumped hydro storage is the major energy storage technology. It accounts for 96% of the world storage capacity [9]; compressed air, batteries, thermal and flywheel energy storage play very minor roles. [7] and [12] highlight some of its applications (along with some barriers to its development), such as offsetting the intermittence of renewable sources and providing ancillary services to the power system (e.g. voltage regulation). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3  management, in which energy storage is used to assist generation to follow the load changes. In this regard, [13] point out that the business case for price arbitrage has vanished partly owing to the injection of subsidized renewable electricity during peak demand periods. To avoid becoming uneconomic, pumped storage stations have to find additional sources of revenue. [14] consider the Austrian-German spot power market and the Austrian balancing energy market through the years 2012-2015. They find that earnings from the latter may exceed those from the former many times over. The empirical evidence shows that hydro operation does follow demand to some extent. Specifically, these stations generate relatively more power during peak hours and less in non-peak ones. On the other hand, these plants operate alongside other (non-dispatchable) technologies in a system. For example, wind energy blows during the night, when power demand is relatively lower; pump stations can avoid wasting this energy by storing it. Consequently, a detailed analysis of the contribution of hydropower to SoS calls for taking due consideration of non-dispatchable sources.4 This note is an extension of [3] on at least three accounts. First, it aims to account for that positive correlation between maximum hourly demand and hydropower generation to check the potential of flexible management to reinforce SoS. Second, we disaggregate hydro stations between run-of-river (RoR) stations and the remainder (non-RoR) stations.; this way we want to account for the different degree of freedom between the two types when it comes to flexible management. Third, we also consider the hourly seasonality in generation from non-dispatchable technologies during peak hours. In addition, for these three reasons, now the numerical application (via MC simulation) gets more complex than in [3]. Thus, relative to [3], this paper contributes in scope, method, and policy implications. To our knowledge, no other paper on applied SoS adequacy metrics addresses the role of hydro-based generation in mitigating power supply shortfalls or the potential of seasonal non-dispatchable generation in meeting peak demands (let alone in the way we do). In 2017 hydro stations (including pumped storage) represented about 20% of the total capacity installed in the Spanish mainland system (20,331 MW out of 99,311 MW); in terms of power generation, they provided around 8.3% of the total. Would the flexibility of hydropower alleviate estimates of supply shortages in [3]? How effective is it in enhancing SoS in mainland Spain? In the same vein, does consideration of seasonal non-dispatchable generation contribute to quell SoS concerns? If so, to what extent? According to our results, the positive correlation between hourly peak demand and flexible hydropower’s generation significantly tempers the severity of the negative impacts of demand surges. The situation further improves when hourly seasonality of non-dispatchable generation is considered. Nonetheless, the expected energy not served (EENS) jumps above historical levels in 2030 and runs into the tens of thousands megawatts-hour thereafter. The issue is of interest not only to Spanish consumers and utilities, but also to other stakeholders involved in the construction of the European internal power market. Further, climate change might exacerbate the high variability that characterizes renewable energy sources in general and hydro power generation in particular; [15]. The remainder of the paper is organized as follows. Section 2 extends the model in [3] to account for the flexible operation of hydropower stations in mainland Spain and also the seasonal pattern of renewable generation. The resulting impact on the adequacy metrics is analyzed in Section 3. Section 4 concludes. 2 ACCOUNTING FOR HYDROPOWER FLEXIBILITY AND SEASONAL NON-DISPATCHABLE GENERATION 2.1. Model extension [3] propose a model for evaluating generation adequacy in the long run from the viewpoint of the facilities installed. Even though power demand can be relatively predictable at this time scale, unexpected peak loads can certainly occur also in the short run; [16]. Given their focus on generation adequacy they naturally pay special attention to peak demand. Typically demand surges are short lived. Publicly available records on power demand stretch back over  4 We thank an anonymous reviewer for bringing this issue to our attention. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 4  many years, even decades. Unfortunately, however, their sample data on peak demand are very limited. They resort to an indirect approach that relies on yearly data; specifically, they relate the hourly peak demand in a future year (, in MWh) to the annual demand in that year (, in MWh): lnln ; (1)  stands for an independent and identically distributed random shock. By assumption, the natural logarithm of maximum hourly demand every year follows a Normal distribution with average αβE󰇟lnQ󰇠 (where E denotes the mathematical expectation operator) and standard deviation equal to the standard error of the regression. This is a stochastic equation: though the average growth rate of q depends on the average growth rate of Q , by its very nature q will grow above it some times, and below it some others. Regarding power supply, they distinguish two groups of generation technologies. The first group comprises thermal technologies: coal () , natural gas (), and nuclear (). Each station has a particular installed capacity (MW) and availability rate (%). Availability is represented by a binary variable (). A particular station  of type ∈󰇝,,󰇞 is in service for a fraction Λ of the year (it can either actually run or remain idle depending on power demand); it is out of service for another fraction 1-Λ (because of failures and maintenance works): 󰇫0,′off󰆒statewithprobability1Λ 1,′on󰆒statewithprobabilityΛ󰇬. (2) The second group of generation technologies includes hydro, wind, solar (both photovoltaic and thermal), cogeneration, and others. The time series of power produced/consumed by these stations subsumes both the usual pattern of failures and their intermittent nature. Consequently, [3] adopt the load factor for describing these intermittent technologies and assume that these show a stochastic behavior with both the monthly average and the volatility changing from one month to another.5 They adopt the Weibull distribution to describe this variable across all of the technologies in this group.6 The probability density function of the load factor () is: 󰇛󰇜󰇫 󰇛 󰇜󰇛 󰇜if0 0if0 󰇬, (3) where ∈󰇛0,∞󰇜 is the scale parameter and ∈󰇛0,∞󰇜 is the shape parameter. The cumulative density function is: 󰇛󰇜1󰇛 󰇜if0 0if0 . (4) The average and the variance are given by: Γ󰇡1 󰇢, (5) 󰇟Γ󰇡1 󰇢󰇡Γ󰇡1 󰇢󰇜󰇤, (6) where  denotes the gamma function. This pattern for the generation technologies in the second group applies to hydropower generation. In this sense, Eqs. (3)-(6) may be a reasonable approach as long as [3] consider hydro generation as a single power source or technology. Nonetheless, unlike [3], here we are going to disaggregate hydro stations between RoR stations and non-RoR stations. The former are relatively more dependent on natural (re)charge and less amenable to strategic management. Consequently, we are going to estimate an independent Weibull distribution for RoR stations according to Eqs. (3)-(4). Hence we can get numerical estimates of the average () and the variance () following Eqs. (5)-(6); the subindex R refers to these particular stations. Non-RoR stations include conventional reservoirs (of seasonal, annual or pluriannual regulation) and pumped storage stations (of daily, weekly or seasonal cycle). In principle they are more amenable to strategic operation and lend themselves more easily to track demand surges. Again, we assume that the load factor of these stations can be characterized by a Weibull distribution, Eqs. (3)-(4), with  5 Multiplying the load factor times the installed capacity allows derive samples of monthly power generation later on. 6 Note that the Weibull distribution does not admit negative values, which is just right when dealing with load factors. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 5  associated average () and () according to Eqs. (5)-(6); we adopt the subindex P for these hydro plants. Unlike RoR, however, the Weibull distribution for non-RoR stations is going to be correlated with peak demand. Now the information available differs from data in [3] in three key respects: (a) we know the maximum hourly demand in each single day of the years 2015, 2016, and 2017, i.e. we have 365+366+365 = 1,096 data; (b) we know hydro-based power generation during the hours of peak demand over those years; (c) we also have hydro-based installed capacity every day (from linear interpolation between monthly values); the combined information of (b) and (c) allows computing this technology’s load factor on a daily basis. Figure 1 displays the time path of hourly peak demand (a) along with non-RoR stations’ load factor in January over the sample period. It suggests that these series are positively correlated. As a matter of fact, the correlation coefficient is 0.256 (the last column in Table 3 below shows the coefficient in the other months). In June it reaches the lowest value, close to zero. The upper bound is almost 45% and applies in March. The main driver behind this comovement is that power utilities manage these plants in an opportunistic or strategic way since peak demands are usually associated with higher prices (indeed hydro is the ‘marginal’ technology on the wholesale power market in many instances). FIGURE 1: Maximum hourly demand and non-RoR stations’ load factor in January 2015-2017. Later on we will run a number of simulations (note that the main adequacy metrics in [3] draw on a probabilistic MC approach). Regarding RoR stations, to this end we will use the average () and the variance () estimated according to Eqs. (5)-(6). However, in the case of non-RoR stations we will need to generate correlated samples. We start by deriving two independent samples  ∗ and  ∗ of non-RoR stations’ load factor and hourly peak demand (note the subindex D). In a second step we normalise each 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6  series by subtracting its average and dividing by its volatility. Thus we obtain two independent, normalised samples  and  of the load factor and peak demand, respectively. In a third step we construct correlated samples,  and , according to the scheme: ;1, (7) where  stands for the correlation coefficient between the two daily series. 2.2. Parameter estimation in addressing correlation Our sample data include daily power generation and installed capacity for the two types of hydro stations. Data on these variables (b) and (c) allow computing separate, specific load factors on a daily basis. Next we arrange all of the daily load factors by month. Thus, there are 31+31+31=93 daily factors in January, 28+29+28=85 factors in February, and so on. With the daily factors in any single month we estimate a Weibull distribution for that particular month, i.e. we estimate the scale () and shape () parameters for every month. 2.2.1. Run-of-river stations The left block in Table 1 shows the monthly estimates of the Weibull parameters for RoR stations along with their 95 percent confidence intervals. For the scale parameter () the intervals are rather narrow. The difference between the upper and lower bounds is minimum in March (4.07%) and maximum in May (10.7%). Instead, the intervals are wider for the shape parameter (). The difference ranges between 33.1% (October) and 40.2% (January). The next step is to substitute the monthly values of  and  in Eqs. (5)-(6) to compute the monthly average and standard deviation of RoR stations’ load factor; see the right block in Table 1. Looking at , the mean is highest in March; henceforth it declines consistently until October and then rises. Similarly, the highest volatility  is reached in April and the lowest one in September. Therefore, through the three sample years, the extreme values of the mean and the volatility are rather contemporaneous. The maximum generation takes place from February to May. In 2017 the installed capacity of RoR stations was 2,104 MW [17]; see Table A1 in the Appendix. Table 1. Run-of-River (RoR) load factor: Parameter estimates (daily data 2015-17). Month Scale () Shape () Average Volatility Value 95% int. Value 95% int.   January 0.520 0.499—0.542 5.163 4.360—6.114 0.479 0.106 February 0.668 0.651—0.684 9.178 7.766—10.846 0.633 0.083 March 0.734 0.717—0.751 9.330 8.019—10.854 0.696 0.089 April 0.715 0.680—0.750 4.424 3.767—5.195 0.652 0.167 May 0.659 0.626—0.693 4.241 3.624—4.961 0.599 0.160 June 0.531 0.507—0.555 4.825 4.153—5.606 0.486 0.115 July 0.412 0.398—0.426 6.364 5.482—7.386 0.384 0.070 August 0.358 0.347—0.370 6.680 5.759—7.747 0.335 0.059 September 0.303 0.293—0.313 6.418 5.500—7.487 0.282 0.051 October 0.270 0.258—0.281 4.962 4.301—5.723 0.248 0.057 November 0.369 0.351—0.387 4.457 3.802—5.224 0.337 0.086 December 0.407 0.390—0.424 5.156 4.454—5.968 0.375 0.083 2.2.2. Non-RoR stations For the rest of hydro (non-RoR) stations, as stated earlier, we assume that the Weibull distribution describing their load factor is correlated with peak demand; see Figure 1. In 2017 the capacity installed amounted to 18,227 MW; see Table A1 in the Appendix. We display the Weibull parameter estimates in Table 2. Again, the confidence intervals are thinner for the scale parameter than for the shape parameter. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 7  Hence we further compute the average and the volatility of the load factor (, ) by means of Eqs. (5)-(6). Table 2. Rest of hydro (non-RoR) load factor: Parameter estimates (daily data 2015-17). Month Scale () Shape () Average Volatility Value 95% int. Value 95% int.   January 0.406 0.385—0.427 4.113 3.513—4.813 0.368 0.101 February 0.447 0.421—0.475 3.692 3.080—4.425 0.404 0.122 March 0.470 0.448—0.492 4.584 3.903—5.383 0.430 0.107 April 0.374 0.343—0.406 2.585 2.198—3.039 0.332 0.138 May 0.355 0.325—0.386 2.492 2.117—2.933 0.315 0.135 June 0.285 0.264—0.306 2.951 2.500—3.483 0.254 0.094 July 0.251 0.230—0.272 2.535 2.153—2.982 0.223 0.094 August 0.225 0.208—0.243 2.837 2.418—3.327 0.201 0.077 September 0.222 0.207—0.237 3.146 2.678—3.694 0.199 0.069 October 0.252 0.232—0.271 2.758 2.336—3.256 0.224 0.088 November 0.262 0.239—0.288 2.343 1.981—2.770 0.233 0.105 December 0.266 0.244—0.289 2.598 2.202—3.065 0.236 0.098 Table 3 shows the descriptive statistics of hourly peak demand and further information about the correlation with power generation form non-RoR stations.7 The latter sheds light on the statistical significance and accuracy of the monthly estimates. We start from the standard (Pearson) formula (thus assuming a linear relationship between both variables). As a safeguard against sampling error we conduct a test. The null hypothesis is 0. The alternative hypothesis is 0 (which requires a two-tail test). The t-test for the correlation observed is: √ , (8) where n stands for the number of observations; this t-test has n-2 degrees of freedom. As for the confidence interval we first turn the observed correlation into Fisher’s transform: 󰆒  . (9) Hence the interval for the z’ transform is computed as: 󰇛󰆒󰇜󰇣󰆒1.96  √;󰆒1.96  √󰇤. (10) And the resulting interval for the correlation observed is calculated as: 󰇛󰇜󰇯󰇧󰇡󰆓. √󰇢󰇨 󰇧󰇡󰆓. √󰇢󰇨;󰇧󰇡󰆓. √󰇢󰇨 󰇧󰇡󰆓. √󰇢󰇨󰇰. (11) The information above allows assess the rosbustness of our numerical estimates. Table 3. Basic statistics of hourly peak demand and correlation with non-RoR’s load factor. Hourly peak demand Correlation Coefficient Month   # Obs.  p-value 95% conf. int. January 35,424 3,207 93 0.256 0.0132 0.055—0.437 February 35,280 2,528 85 0.381 0.0003 0.183—0.550  7 We thank an anonymous referee for raising this point. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 8  March 33,340 2,563 93 0.449 0.0000 0.270—0.598 April 30,715 2,338 90 0.326 0.0017 0.128—0.499 May 30,572 2,251 93 0.101 0.3364 -0.105—0.299 June 33,048 2,953 90 -0.012 0.9115 -0.219—0.196 July 35,290 3,158 93 0.369 0.0003 0.179—0.533 August 33,186 2,954 93 0.215 0.0382 0.012—0.401 September 32,236 2,766 90 0.194 0.0674 -0.014—0.386 October 31,087 2,335 93 0.179 0.0869 -0.026—0.369 N ovember 33,174 2,903 90 0.152 0.1514 -0.057—0.348 December 33,654 2,998 93 0.101 0.3370 -0.105—0.299 We are going to simulate a Weibull distribution 50,000 times each month using the parameter values of  and  and then compute the average load factor and its volatility. Provided the latter closely mirror those derived from our sample data, the numerical estimates of the MC-based adequacy metrics can be considered reliable. Table A2 in the Appendix shows the results from both the sample data and the simulation runs in each month. The (negligible) differences observed can be attributed to the limited number of runs and the very nature of random numbers. Regarding the maximum hourly demand, we resort to Eq.(1). As in [3], we take random samples for the shock term and shift the maximum demand curve in 2017 accordingly. Specifically we use 50,000 simulation runs (i.e. years, each comprising 365 days). We group them by month and compute the monthly average and volatility,  and , respectively; see the left block columns in Table 3. Peak demand surges typically in January (35,424 MWh) and July (35,290); these months are also the most volatile ones (3,207 MWh and 3,158, respectively). The right block in Table 3 proves the importance of extending [3] along the lines drawn in this note. To begin with, at the yearly level (i.e. neglecting differences across months) the correlation between non-RoR stations’ load factor and hourly peak demand is 0.214 (statistically different from zero at the 5% confidence level). The analysis on a monthly basis shows that, for most of the year, there is a mild correlation. It ranges from about 0 to 25% in eight out of twelve months, slightly alleviating power supply shortages (the computation draws on all the daily values of both variables in any single month). Nonetheless, the flexibility advantage of hydropower gets larger in months with a high load factor (January to April), with the correlation coefficient rising up to 45%; this suggests that higher water levels in reservoirs do allow a more flexible and strategic management of those reservoirs; [18], [19]. Just half of the monthly estimates of  are statistically different from zero (again, at the 5% confidence level). Interestingly, they are significant from January to April along with July and August, precisely the months when the coefficient reaches its highest values. This said, we can also observe that the confidence intervals are wide, the upper bound being several times higher than the lower one on many occasions. This confirms the usefulness of accounting for the seasonal behavior of the correlation between non-RoR’s load factor and peak demand, and of using monthly parameters in this analysis. Monthly differences in correlation can be traced back to several issues.8 On the supply side, within non-RoR stations there are HPPs with reservoirs (installed capacity 11,900 MW) and pumped storage stations (6,327 MW). Spain has 20 pumped storage plants.9 They were commissioned through the 20th century mainly to address rainfall variability. So-called Hydrographic Confederations rule the basins; they are legally above hydropower operators since they set limits on the use of water. From this perspective, somehow there is an upper bound on power generation from non-RoR stations which is affected by both  8 We thank an anonymous referee once more for bringing this issue to our attention. 9 They can be further subdivided into two types: pure or closed-loop (where water is first pumped to an upper reservoir and then released to generate power) and mixed or open-loop (when there are water contributions from rivers). Pure pumped storage accounts for 53% of the total (3,337 MW) while mixed pumped storage takes the remaining 47%. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 9  actual rainfall and water needs. The so-called ‘hydropower potential’ measures the maximum amount of electricity that could be theoretically produced from the water contributions during a particular period of time after subtracting the water diverted for irrigation or other uses different from power generation. Table A3 and Figure A1 in the Appendix show that the highest hydropower potentials are available during the first three or four months of the year. They subsequently decline through summer and start rising in autumn. At the same time, power demand also plays a role here; it changes seasonally over time (Table A3 and Figure A1 in the Appendix). The average peak demand in particular is highest in January and July (Table 3) followed by February (which lags close behind, with 35,280 MWh). In general, the first months of the year tend to be also the months when the correlation between peak demand and hydro’s load factor is relatively higher (as shown in Table 3); this also applies to July (maybe in an effort to make ends meet). Anyway, a cautionary note seems in order.Water reserves at the end of 2017 were at their lowest level on record (starting 1990); [20]. Hydro-based generation decreased almost in half with respect to 2016, and reached its lowest value since 2005. Hydro was the third power generation source in 2016 but dropped to the sixth in 2017. The drought in 2017 dragged renewable generation down from 40.3% of total in 2016 to 33.7% in 2017. This episode attests to the high variability of renewable resources, both at yearly and monthly levels (for one, hydro-based generation contributed 26% of total power in May 2016 but 10.1% in May 2017, its lowest level on record). Annual variability certainly complicates drawing conclusions from just three years of observations. Yet a fact speaks for itself: in 2017 the average contribution of pure pumped storage to power generation was just 0.9%; nonetheless, it jumped to 6.7% in the day of peak demand (January 25th); [20]. This fact highlights its role in addressing SoS concerns. 2.3. Parameter estimation in addressing seasonality Our initial model does not account for any hourly seasonality. Note, however, that we do not use the 24 hourly demands in any single day, but only the maximum hourly demand in that day. We proceed as follows. We consider the twelve months of 2017, our base year. Every day in every month has a maximum hourly demand at a particular time. We take each month in isolation and identify the most frequent hour at which the maximum hourly demand takes place. Thus, in the case of January, the typical hour with maximum demand is 21:00; instead, in July it is 14:00. We have hourly power generation by all of the non-dispatchable technologies other than non-RoR (i.e. RoR, wind, solar, cogeneration, and others) from 2015 through 2018, i.e. four years. Now, let’s think of a particular renewable technology, say wind, and a particular month, say January. There are four such months in the sample, each running from day 1 to day 31. We thus have 4×31= 124 January days; we adopt the sub-index k for each one of them, with k =1, 2,…, 124. On the other hand, each day comprises 24 hours, denoted by sub-index i, with i =1, 2,…, 24. Therefore, we have 142 observations for hour 1 in January, another 142 observations for hour 2 in January, 142 observations for hour 3 in January, and so on until hour 24 in January. Initially we compute the hourly average generation in each day (μk) summing up its 24 hourly levels and then dividing by 24. Next, we divide each of these 24 hourly levels in day k by the hourly average that day (μk) just calculated. This way we derive a series of seasonal factors for each hour, with each series comprising 124 terms. We denote each factor by φik (again, with i =1, 2,…, 24 and k =1, 2,…, 124). Drawing on the 124 values for hour i, the i-th seasonal factor for wind in January is just their average:  ∑,   ,1,2,…,24. (12) Thus we get a series of 24 factors (φi, with i=1, 2,…24), one for each hour of the day in Januaries; they can be interpreted as representing hourly seasonality (in generation from wind). Some of them are higher than 1, and some others are lower than 1; they sum to 24: ∑   24. (13) Henceforth, we follow this procedure: we simulate the daily average generation in any single January day from wind (μ). Then we use the above factors φi (based on empirical/historical evidence) to 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 16  References [1] European Commission (2000): "Towards a European strategy for security of energy supply". Green Paper COM (2000) 769 Final, Brussels. [2] European Commission (2016): Identification of Appropriate Generation and System Adequacy Standards for the Internal Electricity Market. Brussels. [3] Abadie L.Mª, Chamorro J.M. (2019): “Physical adequacy of a power generation system: The case of Spain in the long term”. Energy 166, 637-652. [4] Bailera M., Lisbona P. (2018): “Energy storage in Spain: Forecasting electricity excess and assessment of power-to-gas potential up to 2050”. Energy 143, 900-910. [5] Tester J.W., Drake E.M., Driscoll M.J., Golay M.W., Peters W.A. (2005): Sustainable Energy: Choosing Among Options. 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(2018): “Deploying storage assets to facilitate variable renewable energy integration: The impacts of grid flexibility, renewable penetration, and market structure”. Energy 145, 856-870. [24] Red Eléctrica de España (2014): Importancia del Equipo Generador Hidroeléctrico en la Operación del Sistema Eléctrico. Madrid. [25] Vieira F., Ramos H.M. (2008): “Hybrid solution and pump-storage optimization in water supply system efficiency: A case study”. Energy Policy 36, 4142–4148. [26] Spanish Government (2019): Plan Nacional Integrado de Energía y Clima, 2019. Available at: https://www.miteco.gob.es/es/cambio-climatico/participacion-publica/marco-estrategico-energiay-clima.aspx(accessed 04/30/2019). [27] McPherson M., Karney B. (2017): “A scenario based approach to designing electricity grids with high variable renewable energy penetrations in Ontario, Canada: Development and application of the SILVER model”. Energy 138, 185-196. [28] Schlachtberger D.P., Brown T., Schramm S., Greiner M. (2017): “The benefits of cooperation in a highly renewable European electricity network”. Energy 134, 469-481. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 18  Appendix Table A1 displays the total installed capacities (in MW) of power technologies in mainland Spain and the peninsular total annual demand (in GWh). Source: [3]. Table A.1. Peninsular Spanish power system.  (demand growth: +1.36%)  (demand growth: +1.73%) 2017 2020 2030 2040 2050 2020 2030 2040 2050 Nuclear 7,117 7,117 3,040 0 0 7,117 3,040 0 0 Coal 9,536 9,536 6,642 0 0 9,536 6,642 0 0 Natural Gas 24,948 24,948 24,948 24,948 24,948 24,948 24,948 24,948 24,948 Hydro: 20,331 20,331 21,900 24,700 25,600 20,331 23,300 25,900 28,600 RoR 2,104 2,104 2,104 2,104 2,104 2,104 2,104 2,104 2,104 Non-RoR 18,227 18,227 19,796 22,596 23,496 18,227 21,196 23,796 26,496 Wind 22,863 26,000 28,700 32,100 35,800 24,500 32,600 39,800 44,400 Solar 6,730 16,000 20,500 24,600 29,400 15,100 20,300 27,300 39,300 Cogen. 6,373 8,100 9,900 10,800 11,600 8,100 10,800 13,200 16,100 Others 1,413 1,200 2,800 3,800 5,300 1,200 2,000 3,500 6,200 Total(MW) 99,311 113,232 118,430 120,948 132,648 110,832 123,630 134,648 159,548 Demand (GWh) 253,082 263,621 302,026 346,026 396,436 266,564 316,909 376,762 447,920 Table A2 displays the basic statistics derived from our sample data of non-RoR stations (left block) and those resulting from 50,000 simulation runs (on the right). They are almost identical, which renders our MC-based adequacy metrics relatively reliable. In other words, this table basically serves as a cross-check of our non-RoR paremeters in the simulations above. For pumped-storage stations we use an availability rate of 60.66% of their installed capacity; this is the 95th percentile of the 2015-2017 daily series. Table A2. Non-RoR: Estimated Weibull parameters and those from Monte Carlo simulation. Estimated Simulated Month Mean  Volatil.   Mean  Volatil.   January 0.368 0.101 0.256 0.368 0.101 0.256 February 0.404 0.122 0.381 0.404 0.122 0.382 March 0.430 0.107 0.449 0.430 0.107 0.451 April 0.332 0.138 0.326 0.332 0.138 0.326 May 0.315 0.135 0.101 0.315 0.135 0.100 June 0.254 0.094 -0.012 0.254 0.094 -0.013 July 0.223 0.094 0.369 0.223 0.094 0.368 August 0.201 0.077 0.215 0.201 0.077 0.216 September 0.199 0.069 0.194 0.199 0.069 0.193 October 0.224 0.088 0.179 0.224 0.088 0.180 November 0.233 0.105 0.152 0.232 0.105 0.153 December 0.236 0.098 0.101 0.235 0.098 0.100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 19  Table A3 shows the maximum generation potential from hydro stations (in Spanish, ‘producible hidráulico’) and power demand as an approach to explaining the factor(s) behind the monthly changing correlation between the former’s load factor and the latter. Table A3. Behind the correlation between demand and hydro’s load factor. Month Hydropower potential (GWh) Power demand (GWh) 2015 2016 2017 2015 2016 2017 January 2,612 6,024 1,124 22,694 21,470 23,109 February 4,204 4,889 3,802 21,013 20,848 19,912 March 4,133 4,603 2,667 21,184 21,477 21,128 April 2,913 6,105 1,546 18,851 19,931 18,833 May 2,576 5,483 1,990 19,832 19,732 20,242 June 1,535 2,112 1,074 20,377 20,247 21,709 July 578 915 557 23,470 22,235 22,401 August 647 367 253 20,880 21,464 21,809 September 877 470 287 19,591 20,845 20,215 October 1,503 729 411 19,728 19,852 20,252 November 1,980 1,592 528 19,880 20,663 20,950 December 1,314 1,378 1,734 20,897 21,336 22,181 Source: Red Eléctrica de España (REE). Figure A1 displays both series from Jan 2015 to Dec 2017. Hydro potential is measured along the left vertical axis; demand goes along the right one. In both cases, monthly values represent percentages, i.e. the abosulte levels are divided by the yearly totals. For instance, demand in Jan 2015 accounted for 9.14% of total demand in 2015; hydro potential in the same month represented 11.31% of total potential in that year. A clear seasonal pattern arises, particularly in hydro potential, which is at its highest in winter and lowest in summer; instead, demand peaks in January and July. Overall the two (whole) series seem pretty much uncorrelated (the coefficient is -0.14); different seasonal patterns can explain this to some extent. There are wide gaps and trend mismatches in summer, but the two series comove a number of months. FIGURE A1: Hydropower potential and power demand in mainland Spain 2015-2017. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 20  Figure A2 below displays the actual operation profile of pure pumped storage (PHES) plants in Spain. We have collected their hourly generation over the period 2014-2018, i.e. 43,824 observations. Each bar shows the number of hours when their net generation level falls between the bounds shown on the horizontal axis. Even though their aggregate installed capacity amounts to 3,337 MW, their usual net output is quite far from operation at full capacity. FIGURE A2: Hours with positive net generation from PHES stations, 2014-2018. Source: Own elaboration on REE data.