Economic Feasibility of Semi-Underground Pumped Storage Hydro Power Plants in Open Pit Mines

This work aims at the economic evaluation of a semi-underground pumped hydro storage power plant erected in an abandoned open pit mine. For the exploratory model-based analysis, we develop and apply both a simple deterministic and a stochastic net present value (NPV) approach, the latter of which uses Monte Carlo simulation to account for revenue uncertainty from electricity price fluctuations. The analytical framework developed is applied to two promising sites in the Rheinland region in Germany, Hambach and Inden, making reasonable parameter value assumptions and considering and ignoring the lenthy duration of lower reservoir flooding. The investor's value-at-risk is computed for alternative performance indicators (the NPV, net cash recovery, profit-toinvestment ratio, and specific production costs) to compare the different outcomes in terms of the project's financial risk distribution. Calculations show that a semi-underground pumped hydro storage power plant in an abandoned open pit mine can be constructed at reasonably low investment costs and operated at low specific production costs. However, because the investment has to be made long before the pit lake is (naturally) flooded a process that for realistic flow rates may take up to 20 years the project is highly uneconomical and would require substantial subsidies, as compared to a situation where flooding happens immediately.


Introduction
Germany is shifting its power production away from fossil fuels and nuclear power towards renewable energies [1]. With increasing wind and solar photovoltaic power supply fluctuations, security of supply and long-term sustainability need to be managed [2]. One solution to this problem is the expansion of electricity storage capacities. The pumped hydro storage (PHS) technology is suitable for efficient electricity storage with low specific production costs [3]. To create high capacities, large areas and large height differences are required. Typically, PHS are placed in mountainous areas (e.g. in Austria, Switzerland, and Norway), often creating controversies due to their substantial socio-economic-ecological impacts. Potential locations for PHS are thus rare in Germany, but several lignite open pit mines will cease operation in the years to come (due to the planned 100% phaseout of coal-fired power generation until 2035/2038), resulting in some areas being recultivated with large pit lakes. Due to soil extraction, height differences have been developed in the form of mine dumps. The aim of our investigation is to show whether such locations can be used profitably for the installation of what we call semi-underground PHS (semi-UPHS) power plants, in order to contrast them with UPHS built in underground coal mines (cf. [4], and references therein). Reasonable parameter values, based on future pit lakes in Germany (Hambach; Inden), are used for the empirical analysis and boundaries for maximum head and storage volume are set. The model-based economic investigation is performed by applying the net present value (NPV) method and a sensitivity analysis, as well as a Monte Carlo simulation to account for electricity price uncertainties and a Value-at-Risk analysis for decision-making under uncertainty.
Literature on PHS in abandoned open pit mines is still very scarce. Menéndez et al. [5,6,7] study the geological potential of an area with closed open pit coal mines in northwestern Spain.
Pujades et al. [8,9] investigate the influence of groundwater exchange with reservoirs built in abandoned open pit mines on the efficiency of UPHS. Madlener and Specht [4] analyze the economic viability of UPHS in deep abandoned coal mines in the Rheinland area in Germany.
To the best of our knowledge, our study seems to be the first to analyze the economic feasibility of semi-UPHS in open pit mines. On the very complex and manifold interactions of the mining industry with water resources more generally, an excellent reference is Northey et al. [10], and on mine closure and pit lakes as terminal sinks see McCullough et al. [11]. To the best of our knowledge, the present study is the first detailed economic analysis on the use of abandoned coal mines for (semi-subsurface) PHS power plants.
The remainder of this article is structured as follows. In Section 2, we present and investigate the UPHS concept used in the study. Part of the concept is a cost analysis, the time flow of the pit lake flooding, revenue considerations, and relevant fees and regulations. In Section 3, the methodology is presented and relevant parameters are introduced. Section 4 presents the results of the analysis. Section 5 offers some conclusions and an outlook for further research.

Principles of PHS and situation in Germany
Pumped hydro storage is utilized by storing water in an elevated basin in times of power surplus, and releasing it through turbines down to a lower basin in times of power demand. Capacities of 50 GWh at a discharge time of 1000 h can be achieved. PHS is a sophisticated but wellestablished and mature technology, which is used all over the world. It reaches high efficiencies of up to 80% and a high flexibility due to its black-start ability [12]. PHS can participate in all three reserve markets (primary, secondary, and tertiary) and has the lowest specific production 4 costs of 7.73 €-ct/kWh compared to other storage technologies [13]. With 1060 MW of power and a capacity of 8.5 GWh, Goldisthal is the largest PHS power plant in Germany [14]. The disadvantage in Germany is that potential natural locations with existing water reservoirs and effective head are rare and are largely under use already. Furthermore, social acceptance must be considered. Planned projects, such as the one in Simmerath (Eifel region, Germany, 640 MW, 3.8 GWh), have encountered resistance from the local citizens because of its adverse environmental, recreational and tourism impacts and was turned down in 2013.

Markets for large-scale storage operation
Electricity storage technologies draw profit by peak shaving on the spot market and with grid services, such as offering balancing energy [15]. One assignment of the German transmission system operators (TSOs) is to maintain equilibrium between electricity fed into and withdrawn from the grid. There are four TSOs in Germany: Amprion, Transnet BW, Tennet, and 50 Hertz [16].

Energy storage and conversion
PHS stores energy in the form of potential energy, which is dependent on the flow rate, the gravitational constant, the head, the density of the medium, and the efficiency of the pumping process. It is calculated with the following equation [23]: where # denotes the number of machine units, the power of loading process [kW], the volumetric flow rate of the loading process [m 3 /s], the gravitational constant (9.81 m/s 2 ), η the efficiency of the loading process [%], h the head [m], and ρ the density of water (~1000 kg/m 3 ). The conversion of the potential energy into kinetic and electric energy is calculated as: where represents the power of the discharging process [kW], the volumetric flow rate of discharging [m 3 /s], and η the efficiency of the discharging process [%]. The correlated capacity is also dependent on the storage volume and the flow rate and is the product of the maximum power and the duration of complete discharge of the storage volume: where is the discharge time [h], the capacity discharge [kWh], and the utilizable volume [m 3 ]. The overall efficiency of PHS power plants is calculated by the product of the loading efficiency in the pumping mode ( ) and the discharging efficiency ( ) in the turbine mode.
An exemplary overview of the energy losses and the resulting efficiency of PHS is provided in Figure 1.

Technical concept
The future pit lake functions as the lower reservoir, whereas the mine dump of the abandoned pit mine functions as the bed of the upper reservoir. The two reservoirs are connected by underground pressure pipes and the powerhouse excavation with turbines, transformer, and connection to the electricity line (cf. Figure 2). In times of power surplus, water from the pit lake is pumped into the upper reservoir, where the electricity is stored as potential energy. In times of power demand, water runs down the pipes, and the potential energy is transformed into kinetic energy, running the turbine, and finally turning into electrical energy via the generator.  The upper reservoir is constructed with a kind of circular embankment. The width of the dam crest amounts to 15 m with an inclination of 32° at a height of 10 m and freeboard of 2 m (Popp, 2015 [25]; on the dimensioning and economic analysis of ringwall storage power plants see [26]. In our study, the maximum water level is limited to 8 m in order to minimize possible subsidence of the mine dump. This value has to be individually adapted depending on the project. Another project-specific parameter is the available area on the mine dump for building the upper reservoir determining its volume. The inside of the reservoir has to be sealed with an

Capital expenditures (Capex)
The specific investment costs of PHS can vary significantly (600-3000 €/kW) depending on the site-specific conditions [28,29]. The capital costs for the mechanical facilities of an open pit mine PHS are comparable to the investment of other PHS power plants. The largest share is the powerhouse with 37%, followed by the upper reservoir with 19%, owner's costs at 17% (these include paid-up royalties, preproduction costs, inventory capital, and land costs, cf. [30]), and engineering-, procurement-and construction-management services at another 17% [30]. It Summing up, the specific capital costs amounted to 1726 €/kW. The specific capital costs in a related study by [13] amount to 750 €/kW, which makes a difference of nearly 1000 €/kW. In order to obtain a reference value, the specific capital costs of a series of planned PHS projects (see Table 2) has been plotted with specific capital costs and power in Figure 3. The average of projects with only one existing reservoir is about approx. 1100 €/kW. The specific capital costs for powerhouse, powerhouse excavation, tunnels and engineering, procurement, and construction management services are taken over proportionally by the values from [30] and are adapted to 1100 €/kW, which leads to power-related specific capital costs of 704 €/kW. The 8 costs for the upper reservoir, owner's costs, and other arising costs are assessed in this study and offer cost reduction potential. It is also reasonable to look at these two groups separately, because the volume of the upper reservoir does not influence the power in kW but it does influence the capacity in kWh, and thus should be excluded for the power-related specific capital costs.  Source: [28] The costs of the upper reservoir are composed of owner's costs, embankment construction and material as well, as sealing costs [25]. As an illustration, at a diameter of 1000 m and a height of 10 m, costs of approx. €16 million arise, which is comparatively low due to the synergies Note that we deliberately restrict the costs to some embankment construction and sealing costs, and ignore those for recultivation. The reason is that we assume that these costs would occur anyhow, and are thus no additional costs arising as a consequence of building the (semi-)underground PSPH plant. Neither cost data nor clear plans and legislation seem to be available for reconverting the open pit coal mines in Germany back to some acceptable state, let alone any documentation for UPSPH as an alterative recultivation scenario or risk management strategies and liabilities taking the polluter pays principle into account. Hence it seems fair to say that as of today it is far from clear what the overall societal costs of the coal phase-out will be. Internationally, the situation does not seem to be any better, as the discussion, e.g. on the best available practice for mine closure and long-term management of pit lakes in arid regions discussed in McCullough et al. [11], indicates.  5 10 20

Embankment construction & material costs [€/m 3 ]:
Summing up, the specific investment costs per kW and kWh depicted in Figure 5 were calculated as a function of storage volume for a construction with an installed power of 700 MW and embankment construction and material costs of 5 €/m 3 (see Figure 4). The costs per installed power rise slightly with the storage volume, whereas the costs per installed capacity fall rapidly. Compared to the Capex of other PHS projects reported in Table 2, the costs of an open pit mine PHS are in the lower range.

Operational expenditures (Opex)
The operational expenditures are split into fixed and variable expenditures. The fixed annual costs for operation and maintenance are estimated at 10,000 €/MW [13]. According to [13], the variable costs are composed of (1) costs per start load of 2 €/MW_start; (2) costs per start discharge of 2 €/MW_start; (3) other costs of 1 €/MWh; and (4) average power procurement costs at 24 €/MWh (power procurement costs are adapted for specific scenarios).

Flooding of pit lake
Flooding is an important impact for the technical scenarios. The PHS power plant cannot start operation until the pit lake has been filled and groundwater inflow has been prepared. The investment in and construction of the power plant will take place when the pit mine operation is over and the slope construction for the pit lake begins. The flooding is assumed to be achieved by water extraction from surrounding flowing waters, and is either cost-free for hydropower plants (see also Table A.2) or paid for by the pit mine operator as part of the recultivation process (note again that we assume that no additional recultivation costs arise due the construction of a semi-underground PSH power plant). Water losses through evaporation,

Specific power costs
Specific capacity costs seepage, discharge or physical entrainment in the tailings materials is ignored for simplicity reasons (for a review of the manifold and complex issues related to the quantification of the water footprint of mining operations, and scarcity and site-specificity of mine site water data, we refer to [10]). Groundwater inflow will not take place until the pit lake has been filled, in order to reduce acid mine drainage (AMD). The duration of flooding is dependent on the surrounding flowing waters. Every river has a maximum extraction volume depending on its flow rate. A filling rate of 40 x 10 6 m 3 /a is assessed for the pit lake in Inden (Scen. 2) by water extraction from the Rur river [22]; 270 x 10 6 m 3 /a from the Rhine is assessed for the flooding in Hambach (Scen. 1) (Hemm et al., 2000;RWE, 2011) [27,32]. More than 20 years will elapse until a pumped-storage hydro power plant goes into operation after an investment of several hundred million Euros. During these years, obviously, such a power plant will not generate any revenues. The maintenance costs for this time are assumed to be 10% of the maintenance and operation costs during operation.

Fees and regulations
In the following, an overview regarding the assumptions made on relevant fees and regulations for PHS is given.

Grid-use fees
Consumers of grid electricity are legally bound to pay fees to the TSO. PHS electricity in Germany is also regarded as an end customer of the grid and must therefore pay network charges in the form of grid-use fees in accordance with Art. 3(25) EnWG (German Energy Industry Act) [33]. While they usually have to pay fees for the procurement of electricity, this does not apply to the grid feed-in (see also section 2.8.2). Also, new electricity storage facilities that go into operation between August 4, 2011 andAugust 3, 2026 are excluded from grid-use fees for the first 20 years. In our calculations, such fees are not taken into account in the economic evaluation, assuming that PHS plants will continue to be exempted also in the future. This is also in line with Steffen [31], who considers grid fees not to be a barrier for new PSPH plants and ignores them in his calculations as well, and mentions that at the time of his analysis the federal government had just doubled the exemption period from all grid-use fees from 10 to 20 years.

EEG levy
In accordance with Art. 60 EEG (German Renewable Energy Sources Act) [34], electricity suppliers have to pay an EEG levy to the TSOs for every kWh delivered to end consumers. This is necessary to cover the difference between revenues and expenditures for the priority feed-in of renewable energy pursuant to the EEG (netztransparenz.de, 2020) [35]. Although the operator of a PHS system is regarded as an end consumer, he/she is exempted due to special regulations that the EEG stipulates for PHS [36].

Water extraction fees
The European water framework directive 2000 requires adequate pricing of water usage, but allows for exceptions due to environmental, social or economic reasons, defined by the member states (European Commission 2000, Art. 9) [37].
While in this study we assess the possibility of a PHS plant in the state of North Rhine-  (1) stipulates explicitly that climate protection requirements have to be considered when granting permits, whereas section (2) foresees exemptions from recultivating waterbodies that were used for hydro power due to their social welfare benefits (as stipulated in WHG Art. 6(2)).

Economic model and input description
The results of the economic evaluation are presented in terms of net present value (NPV) and net cash recovery (NCR). Further, the robustness of the model results is scrutinized deterministically by means of a sensitivity analysis and, probabilistically, also by using Monte Carlo simulation. Figure 6 displays the setup of the economic model. In the following, the parameters are specified in tabular form.
13 Figure 6. Overview of the economic model Table 3 shows the PHS system-related parameters using Hambach as an example. The values are chosen and calculated in accordance with the underlying conditions described in Section 2.    Economic parameters and values assumed are listed in Table 6. The interest rate and the related discounting factor are essential for the NPV analysis, and thus detailed sensitivity analyses are undertaken in the empirical part. The former denotes the minimum return over the operational lifetime of the project. Table 7 shows the variables involved in the economic analysis presented in Section 4.1, which are discussed next.

Economic evaluation
Calculations The annual cash flow is divided by the interest factor to reflect the time value of money in dependence on selected rates: Thus, the interest factor makes the different cash flows in time comparable [40]. In the case of an investment project with a lifetime of up to 70 years, aside from the interest rate, it is important to also account for the inflation rate , which counteracts the former: .
The NPV method without consideration of the inflation rate is called the nominal NPV (eq. (9); including the inflation rate it is referred to as the NPV in real terms (eq. (10) (cf. [41]): The latter can be used to calculate the dynamic amortization (or payback time) as follows: A related, simplified economic measure is the net cash recovery (NCR). Since it does not take either of the rates into account, it simply reflects the net cash flows without any time value, i.e.
The annuity factor , is derived from the as follows: With the annuity factor , the annuity can be calculated, which gives the constant payment over periods required to provide a complete redemption of both the investment, 0 , and the running costs, [41]: Dividing the annuity by the expected amount of electricity generated within a year gives the maximum specific costs in €/kWh permissive to avoid any losses: Still another often used indicator is the profit -o-investment ratio (PIR): which is the quotient of and 0 . For obvious reasons, if PIR > 1 (< 1), the project should be accepted (rejected).

Integration of cash flow
The cash flow consists of expenditures and revenues. The expenditures can be separated into investment costs and annual expenditures. The former comprise the power-related capex as well as the Capex for the upper reservoir: The annual expenditures consist of variable and fixed costs. The fixed operation and maintenance (O&M) costs are dependent on the installed power. The variable costs are dependent on installed power, number of starts per turbine, and power procurement costs, i.e.: Revenues comprise the sold electricity within a year as well as any service provision revenues from the secondary reserve market:

Monte Carlo simulation
The

Statistical testing
To simulate adequate spot prices, historical data are tested on different probability distributions.
Three different goodness-of-fit tests are applied to a set of probability distributions: (1) (3) Anderson-Darling test.
The distributions and the results for the peak prices 2014 are given in

Empirical analysis of historical spot prices
For the illustrative analysis, data from 2009 to 2014 have been used. The data are provided in an hourly resolution. The annual means and standard deviations for base-load and peak-load times are given in Table 9. Average spot market prices vary from 30 €/MWh to 55 €/MWh. Standard deviations around the mean value amount to about 8 €/MWh to 15 €/MWh and provide some evidence regarding the price volatility. While the variation of average prices is relatively high in the annual comparison, the price spreads have a more constant level with a negative trend. Supply and demand have to be in balance at any time and any place. Furthermore, electricity is needed in daily processes of the economy and households and cannot easily be substituted by other factors. That is why electricity prices show seasonality, cyclicality, and mean-reverting [43]. On a winter day, the peak is typically at around 6 p.m. in the evening hours, while it shifts in summer days to around 12 a.m. The cyclicality and seasonality of the daily structure of spot prices are applicable to the weekly structure, where the daily cycle is relatively constant for summer and winter days on the five weekdays, and decreases on weekends and public holidays.
For simplicity, holidays have been neglected in the analysis. On an annual scale, the fluctuations and the volatility of spot prices are noticeable in the total grid load.
Although the power price development is exposed to short-term fluctuations and to volatility, it reverts to its mean value after a specific amount of time, instead of drifting in a random direction [43]. This shows that the cycle of load and the coherent spot prices are predictable and can be simulated with stochastic functions.
The future development of the spot prices has a large impact on the feasibility of electricity storage facilities. To generate high revenues, a wide price spread of base-and peak-load hours is necessary. One theoretical aspect is that the extension of PV capacity can be expected to lead to a smoothed peak-price curve, because of the high feed-in of PV at noon, another one that due to high wind feed-in, the volatility of spot prices will expectedly increase and generate higher price peaks.

Simulation of spot prices
To simulate adequate spot prices, an hourly price forward curve (HPFC) is created. The HPFC is a popular tool for assessing the feasibility of power plant investments. To create the characteristic cyclicality and seasonality of spot prices, the spot price curve of 2014 is used. For simplicity, holidays are again neglected. Each peak-hour price is divided by the annual average peak price, and each base-hour price is divided by the annual average base price. These relations can be multiplied by an expected PHELIX base price and PHELIX peak price in order to create an HPFC that allows to simulate the expected spot market prices on an hourly resolution. Figure   7 shows the daily average spot price for peak and base hours with a yearly average base of 25 €/MWh and yearly average peak of 45 €/MWh, resulting in a daily average price spread of 20 €/MWh.
A possible operation of a PHS plant on a daily scale is presented in Figure 8. It is aspired to drive a whole cycle in one day in order to achieve a maximum of full-load hours per year. At an installed power of 700 MW the exemplary day would create expected revenues of €185,400.  Tables 11 and 12 show the secondary reserve capacity market data for 2014 from the German tendering platform regelleistung.net (https://www.regelleistung.net/ext/data/), which are used in the economic model. Table 10 (upper part) gives an overview of the positive secondary reserve capacity used when demand exceeds the forecast. Table 10 (lower part) presents the data for negative secondary reserve capacity, which becomes necessary in times when demand is lower than the forecasted value. The data comprise offered capacity, demand rate, and energy rate for base and peak times with mean, standard deviation, minimum, and maximum.

Retrieval of secondary reserve capacity
Additionally, the mean energy rate and demand rate for 2014 are shown in Figure 9. The high standard deviations and spreads between maximum and minimum of the demand rates are remarkable. The reason for this is the probability of successful tendering. A low demand rate bid will be successful with a high probability, whereas a high demand rate has a low probability but generates high revenues. For the economic evaluation, we assume that the PHS plant will participate in every weekly tendering and will be successful in the bidding, i.e. we assume the most optimistic outcome.

Sensitivity analysis
The sensitivity analysis shows the impact of key parameter variation on the NPV, varying the key parameter values by ± 50% in 10% steps. The sensitivity analysis allows to check for the robustness of the results, the but also to check for the relative impact of the system parameters, which can also help to make improvements to the model.

Results
The economic results are presented in the following.

Economic evaluation
The economic evaluation is carried out twice. First, the flooding time is excluded, assuming the PHS plant could start operation right after the investment, in order to show whether the power plant can be operated profitably at all under the parameter values and limitations assumed. In a second step, the flooding time is explicitly taken into account -as a situation of several years of fixed O&M costs but no revenues. The economic outcomes are reported in terms of NPV, NCR, specific production costs, and PIR, each before and after tax (BT, AT; we assume a corporate tax rate of 25%, which is representative for both Germany and the Rhineland region).
Additionally, the NPV BT is displayed as a function of the interest rate and price spread, respectively, in order to show the impact of the two parameters, and to see at which values the project would become economically viable.

Excluding flooding time
The economic evaluation is presented in Table 12. First, the scenario parameters are listed, followed by the cash flow items and the economic outcomes before and after tax. The temporal developments of NPV and NCR (BT and AT) are reported in the Appendix.
Scenario 1 shows a positive NCR before tax and a PIR > 1. The SPC are, at 0.08 €/kWh, an order of magnitude lower than the value in [13] (0.77 €/kWh). According to [13], specific production costs < 0.1 €/kWh are necessary to break even. The NPV turns out to be negative even before taxation. After tax, the NCR remains positive, but the PIR is < 1, and the SPC are only slightly below 0.1 €/kWh.
For Scenario 2, in contrast, we find a positive NCR as well as a positive NPV before tax.
The PIR of 2.05 suggests a profitable scenario, and the specific production costs of 0.07 €/kWh are again low, and retain the value of 0.07 €/kWh after tax. The NCR remains positive after tax, and the PIR is slightly greater than 1. The NPV after tax is even lower than in Scenario 1. None of the two scenarios would amortize during the technical lifetime, as the dynamic amortization calculation with a moderate interest rate of 6% shows. Figure 10 displays the impact of the interest rate on the NPV BT for both scenarios. The interest rate has a particularly high influence because of the long lifetime of a PHS power plant.
Again, due to the lifetime, the net cash recoveries are high because they are unaffected by the interest rate. The graph shows a higher influence for Scen. 2, because of the higher cash flowsthat can be realized due to the higher power and capacity of the system. Scen. 1 creates a 23 positive NPV BT at interest rates < 5%, whereas for Scen. 2 this is already the case at an interest rate of < 6.5%.   Figure 11 shows which price spreads need to be expected in order to generate revenues that allow for a profitable project. Today, the average price spread is around 10 €/MWh. Scenario 1 needs price spreads of over 14.5 €/MWh to allow a profitable scenario before tax. The gradient of Scen. 2 is higher because of higher power and capacity, and cutting the x-axis at 9.5 €/MWh. The gradient shows the high impact of the price spread; a higher price spread of 1 €/MWh increases the NPV by approx. €40 million. Due to the prolonged lifetime of the project, the discounting factor has a greater impact.
Combined with additional costs for maintenance and market risks, the investment case is subject to uncertainty. Table 14 shows the results in terms of NCR, NPV, and PIR calculations before and after tax and for both scenarios. The temporal development of NPV and NCR (BT and AT) can again be found in the Appendix.
It is still possible for each scenario to create a positive NCR before and after tax. The increased discounting factor has no influence on the NCR and, therefore, has no influence on the PIR, because it is derived from the NCR. Except for Scen. 1 and AT, all PIRs exceed unity.
However, none of the two projects is expected to yield a positive NPV, neither before nor after tax. Also, at an interest rate of 6%, none of the scenarios is found to pay back within the technical lifetime when using the dynamic amortization method.
Taking flooding time into account, the impact of the interest rate and the resulting discounting factor is obviously higher, as Figure 12 shows. NPV BT for Scen. 1 approaches 0 at an interest rate of about 4%. For Scen. 2, the NPV BT becomes positive at an interest rate of approx. 4.5%.  Figure 13 illustrates what price spreads would be necessary in order to achieve a positive NPV before tax. If the flooding time is explicitly taken into account, an NPV BT is not reached under an average daily price spread of 22 €/MWh, which is very high compared to today's spread of 10 €/MWh, and therefore an unlikely case.

Sensitivity analysis
The sensitivity analysis is applied to Scen. 2 only, and excluding flooding time, because it is more likely to become an economically feasible project. The analysis is displayed in a spider diagram depicted in Figure 14. The robustness of the results with regard to different key system parameters, such as cash flow elements and the interest rate, are tested for variations of +/-50%.
The lowest sensitivity is given by the O&M expenditures and the revenues from the balancing market. The O&M expenditures for pumped hydro storage are very low, hence alteration does not have a high impact. The revenues of the balancing market are low compared to the revenues that are generated on the spot market. This is why parameter variations only have a very little impact on the project's economic viability.

Value-at-risk
The value-at-risk (VaR) calculates the probability distributions of the economic outcomes, considering price uncertainties on the spot and balancing markets. The data of the spot and balancing markets are reported in Section 3.4. The Monte Carlo simulation is applied with 5000 runs. The resulting histograms are reported in the Appendix. The fitted distributions with mean, standard deviation, and confidence interval, e.g. an NPV > 0, are listed in Table 14. The valueat-risk is applied to NPV, NCR, PIR, and SPC -before and after tax -and for both scenarios, excluding and including flooding time.

Excluding flooding time
The results for Scen. 1 are given in Table 14. Under the given price uncertainties, Scen. 1 will create a positive NPV AT with a probability of 18.8%. The probability of NCR AT > 0 is 66.07%. The price uncertainties induce standard deviations for NPV and NCR of up to €346.01 million, which again reflects the high sensitivity of revenues gained on the spot market. Despite the high NCR AT, the mean value of PIR AT is still < 1. The SPC have a low standard deviation, but are only < 0.1 €/kWh, with a confidence level of 39.53%. However, regarding the sensitivity analysis it is questionable whether this criterion set by [13] really holds. An increase in storage volume would easily outweigh an increase in specific production costs (cf. Figure 14, upper part). The values for Scen. 2 are also reported in Table 14 (lower part). The SPC (BT and AT) are low and, with a probability of almost 100%, smaller than 0.1 €/kWh. But the high standard deviation, a negative mean value for the NPV AT, and a probability of only ~35% of becoming positive are not a secure investment even when flooding time is ignored.

Including flooding time
If flooding time is included, Scen. 1 yields many negative values (see Table 15, upper part).
There is little chance whatsoever of the NPV (BT or AT) becoming positive. Even for the NCR, the probability of success is very low. At negative NCR, the PIR cannot turn out to be favorable either. The SPC are lower when excluding flooding, because the annuity is dispersed over 20 more years. The situation for Scen. 2 is slightly better, but still poor (Table 15, lower part).
Although the NCR is positive and creates a PIR > 1 (BT and AT), the mean NPV turns out to be negative, with a very slim probability of becoming positive. The low SPC are again explained by the lower annuity.

Conclusion
This study shows that a pumped storage hydro power plant in an open pit can be constructed at relatively low investment costs, and could be operated profitably and with low specific production costs, if it were not for the long flooding time.
The sensitivity analysis carried out shows that the probability of a feasible scenario increases mainly with the storage volume, output and price spread which is also reflected by the

Appendix B: Statistical testing
The most common chi-square test is the Pearson test [45] where a data set is divided into cells.
The tested hypothesis is whether values occur in each cell with equal frequency, as they do in the tested distribution. The lower the chi-square value, the better the tested distribution fits to the data. The probability function of chi-square has the following density [46]: The Kolmogorow-Smirnoff test is used in the case of smaller sample sizes. The test measures the distance of two distribution functions, in this case the sample distribution (d) and the tested probability distributions (d1). The lower the measured distance, the better the goodness of fit.
The greatest vertical distance is calculated with [46]: f is the cumulative distribution function of the specified distribution and the ordered data.