A Novel Method to Integrate Hydropower Plants into Resource Adequacy Assessment Studies

Abstract

This paper presents a novel methodology for modeling hydropower plants (HPPs) with and without pumping capability in resource adequacy assessment studies. The proposed method is based on the premise that HPPs should maximize their contribution to system adequacy within their technical constraints by using the energy reserves in their upper reservoirs without significantly deviating from their market schedule. The approach of this paper differs from the conventional operating policies for incorporating HPPs into resource adequacy assessment studies, which either adhere to a fixed market schedule or perform peak shaving, and are inelastic to real-time events or do not resort to realistic temporal correlations between natural water inflows on upper reservoirs and the water discharge needs to cover demand peaks, respectively. The modeling approach focuses on large-reservoir HPPs with natural inflows and is generic enough to deal with both stations incorporating pumping capabilities and those without. It utilizes the state-of-the-art Monte Carlo simulation technique to form the availability of system assets and determine the loss of load incidents. The market schedule and level of reservoir fulfillment for the HPPs are retrieved from a cost-optimal power system simulation algorithm executed offline before the application of the resource adequacy assessment. The effectiveness of the proposed methodology is demonstrated through its implementation in a case study of a power system experiencing different levels of adequacy, comparing the obtained results with various traditional HPP modeling methods from the literature.

1. Introduction

The ongoing energy transition towards CO₂ emissions’ elimination calls for a fundamental transformation of existing power systems, including the gradual decommissioning of thermal power plants in favor of increasing the penetration of renewable energy sources (RES) in the energy mix [1,2,3]. In such an RES-dominated landscape, flexible assets such as hydropower and battery systems will be required to complement intermittent renewable generation and mitigate any loss of load events, thus allowing the system to maintain acceptable levels of resource adequacy [4,5,6]. In this regard, HPPs, comprising mature low-carbon generation technologies in existing power systems, are expected to perform a key role as dispatchable power sources, provided that their full potential is exploited and their contribution to system adequacy is properly assessed [7].

The contribution of an asset to the adequacy of a system is assessed based on its impact on the Loss of Load Expectation (LOLE) and Expectation of Energy not Supplied (EENS) reliability indices as a result of its presence in the power system or by using the capacity value metric. Conceptually, the capacity value aims to establish a common basis for comparing the abilities of different generation and storage resources to improve the system’s reliability. It is measured using several metrics, such as the equivalent firm capacity (EFC), the equivalent conventional capacity (ECC), and the effective load carrying capability (ELCC) [8,9,10,11,12].

Interestingly, HPPs’ capacity values vary significantly across various resource adequacy assessment studies, reflecting the different operating policies applied in each case. Higher capacity values usually indicate that HPPs are simulated according to reliability-driven operating policies, having as their sole objective the contribution of the hydro plants to system adequacy and the reduction in loss of load events. An extensively used reliability-based method is peak shaving, in which the scheduling of the HPP operating profile is adjusted to supply energy to the system exclusively during peak load periods. This is based on the assumption that these periods represent the most crucial time spans for potential energy shortfall occurrences. Although this HPP simulation technique overlooks critical operating constraints, such as the plant’s reservoir capacity and the temporal correlation between the peak shaving needs and the availability of natural inflows, which are eventually considered to all be known and available for use at the beginning of every time interval, several recent adequacy studies are still adopting this technique, with variations regarding the application period (e.g., week, month, and year) and the number of hydrological scenarios examined [13,14,15,16]. Another major drawback of reliability-based simulation methods, as noted in [17], is their lack of consideration of economic aspects during system operation, leading to unrealistic modeling of HPPs and, thus, to an overoptimistic assessment of their ability to contribute to system adequacy.

In this context, some adequacy studies, such as those of ENTSO-e [18], Pentalateral Energy Forum [19], National Grid ESO [20,21], and IESO [22], take into consideration the economic aspects of power system operation, extracting the HPPs’ operating profiles by applying market-oriented unit commitment and economic dispatch models, which can feasibly determine the hourly dispatch of the plants while adhering to their fundamental technical and operational constraints. Apparently, the level of detail of each model leads to a more accurate HPP dispatch plan. For instance, the analysis of ENTSO-e in [18] includes modeling the mandatory water discharge of the plants to shape their final operating profiles. Although these market-based operating policies appear to better reflect the actual operating profiles of HPPs, aspects related to HPPs’ realistic operation during the loss of load events for evaluating system adequacy levels are not fully addressed, as, in the respective studies, the market schedule of HPPs remains fixed and inelastic to adjustments to any capacity shortfall incidents.

All adequacy studies in the literature [13,14,15,16,18,19,20,21,22] use probabilistic techniques to measure system reliability, as they can capture the inherent uncertainty of stochastic variables, such as unexpected generation outages and variations in RES generation [23]. However, none of them account for unplanned generation outages of HPPs, leading to an overestimation of their ability to contribute to power supply.

A further issue not fully addressed in the literature and the studies carried out by competent institutions is the incorporation and management of real-time outages in adequacy studies. More specifically, available resource adequacy assessment (RAA) studies do not account for the impacts of unplanned outages of system-generating assets on HPP operation. Hence, in RAA, hydro plants adhere to a fixed and unyielding operating profile built upon the maximum system asset availability hypothesis obtained by market-based simulation modeling. This profile persists unchanged, even in the event of unforeseen capacity shortages, restricting the ability of the HPP to contribute to adequacy from a study-level perspective and limiting its capacity value. In reviewing the present methodologies for evaluating system adequacy and potential future improvements that can be implemented by stakeholders, the authors of [17] highlight the need to include real-time outages in resource adequacy assessments and accordingly adjust the operating profiles of the available generation assets. In [24], a real-time redispatch methodology was developed concerning energy storage systems (ESSs), pointing towards real-time operational adjustments of dispatchable generation components and serving as a basis for the proposed HPP redispatch methodology.

Apart from resource adequacy studies carried out by system operators and relevant organizations, the assessment of HPPs’ contribution to system adequacy has received limited attention in the relevant literature. The authors of [25] performed a sensitivity analysis regarding HPPs’ different storage capacity levels and their impacts on system adequacy employing a probabilistic approach, while in [26], the contribution of HPPs and intermittent RES portfolios was investigated using historical operating data and employing a peak shaving technique. An interesting analysis by Karki R., Hu P., and Billinton R. [27] addressed the coordination of HPPs and wind farms, where HPPs were used either as balancing units for wind power fluctuations or as peaking units to satisfy the system’s demand. Reliability indices reached their optimal values when one-third of the available hydro generation was used to regulate wind power fluctuations, while the rest were assigned as peaking units.

Despite hydroelectric plants constituting the principal large-scale energy storage technology in existing power systems, as they fall into the extended storage class due to their substantial reservoir capacity that enables daily and seasonal energy arbitrage [28], there have been no significant improvements in the modeling of their operation and the evaluation of their capacity value in recent RAA studies. Evidently, most of the relevant literature depicts the operation of HPPs in a rather one-dimensional and simplistic manner, applying either a market-driven or a reliability-driven policy, thus failing to capture a balanced real-world operating profile. Key technical and operational aspects, such as their capacity limitations and obligation for mandatory water discharges, are omitted or partially addressed, while the likelihood of unplanned generation outages is completely ignored.

Identifying the aforementioned gaps in the literature, this paper proposes a novel methodology for modeling hydroelectric plants in the context of RAA studies. The underlying principle of the proposed methodology is that HPPs should contribute to mitigating loss of load events in real time to the maximum possible extent while adhering to their technical constraints and avoiding severe deviations from their market schedule to maintain the system’s economic operation, as identified by the cost minimization dispatch model that is applied offline prior to the execution of the RAA. To this end, a redispatch algorithm is developed to enforce modifications to HPPs’ scheduled operations in real time according to the actual system capacity needs in order to enhance the system adequacy. At the end of a disturbance event, the algorithm ensures the continuity of the market-based scheduled operations of HPPs by applying corrective redispatch orders to restore the reservoir levels to their scheduled values. Thus, HPPs’ contribution to system adequacy is captured by maintaining a reasonable operating profile that is capable of satisfying both market-and reliability-driven objectives. This approach provides a more comprehensive perspective than the prevailing simulation approaches, which show a more one-dimensional operating profile. The proposed methodology incorporates the unscheduled outages of hydropower units that occur during real-time operation and implicitly considers the operation of the hydropower fleet for purposes beyond electrification as part of the initial market dispatch plan, including mandatory outflows to cover irrigation and water supply needs.

Overall, a realistic simulation of HPPs’ operation is achieved, taking into account their full potential to contribute to adequacy while respecting their inherent constraints. In addition to securing an operational profile that closely resembles the actual operation of HPPs, the adequacy metrics derived from the proposed methodology consistently exhibit a higher level of reliability compared to those obtained from alternative operating policies. This outcome demonstrates the crucial role of the proposed methodology, which involves a real-time assessment of system adequacy and the adjustment of HPPs’ dispatch from their market schedule, when required and to the greatest extent technically possible, to ensure the mitigation of inadequacy events without severely compromising market decisions and negatively impacting system operating costs.

The stochastic assessment of system adequacy is performed using the state-of-the art sequential Monte Carlo simulation (SMCS) approach, yielding the LOLE and EENS adequacy indices, as well as the capacity value of the HPP assets, calculated using the EFC metric. The market schedule and scheduled level of reservoir fulfillment of the HPPs are retrieved from a cost-optimal power system simulation algorithm performed before applying the resource adequacy assessment method. The present study examines two HPP types—HPP reservoirs without pumping capabilities and open-loop pumped hydro stations (PHSs). The redispatch methodology is adapted to the operational characteristics of each technology and applied both separately to each HPP type, as well as in aggregate by examining the joint contribution of the two HPP technologies to system adequacy.

The rest of this paper is organized as follows. Section 2 describes, in detail, the principles of the real-time redispatch methodology. Section 3 provides a brief overview of the case study system and the principal outcomes of the proposed methodology. Section 4 outlines a widely used reliability-driven simulation technique that serves as a comparative approach. Section 5 presents a sensitivity analysis regarding HPPs’ nameplate capacity and output power. The key findings are summarized in Section 6.

2. Methodology

2.1. Resource Adequacy Assessment Framework

The RAA study of this paper uses the SMCS technique, as this is the most appropriate for dealing with stochastic uncertainties [29]. Multiple states of the modeled system are generated by sampling a sequence of random outages of conventional power plants to determine the available power output of the generation system. A two-state model is assumed to express the annual availability profile of each power plant [30,31]. This profile consists of the two following time intervals: the time period during which a unit is fully available until its next outage event (Time to Failure—TTF) and the time period required to repair the failure and become available again (Time to Repair—TTR). TTF and TTR variables have randomly generated values following exponential distributions with mean values of λ = 1/MTTF and μ = 1/MTTR, respectively, where MTTF is the mean TTF and MTTR is the mean TTR. TTF and TTR are calculated as shown in Equations (1) and (2), where U and U’ are sequences of uniformly generated numbers in [0,1].

$$\mathrm{TTF}=-\mathrm{MTTF} · \mathrm{lnU}$$

(1)

$$\mathrm{TTR}=- \mathrm{MTTR} · {\mathrm{lnU}}^{\prime }$$

(2)

The MTTR and MTTF values are used to define the Forced Outage Rate (FOR) of each plant, a key parameter that expresses the probability of the plant being out of service.

$$\mathrm{FOR} [\%]={\displaystyle \frac{\mathrm{MTTR}}{ \mathrm{MTTR}+\mathrm{MTTF}}}·100\%$$

(3)

For every SMCS sample year s, the annual availability profile of each thermal and hydropower unit is produced and then aggregated to calculate the total available conventional capacity (${\mathrm{ACC}}_{(\mathrm{t},\mathrm{s})}$) of the system, (4). ${\mathrm{ACC}}_{(\mathrm{t},\mathrm{s})}$ is subsequently compared to the residual load of the system (${\mathrm{P}}_{{\mathrm{L}}_{\left(\mathrm{t}\right)}}$), defined as the demand load (${\mathrm{P}}_{{\mathrm{R}}_{\left(\mathrm{t}\right)}}$) plus the ESS charging power (${\mathrm{P}}_{{\mathrm{ESS-c}}_{\left(\mathrm{t}\right)}}$) minus the RES production (${\mathrm{P}}_{{\mathrm{RES}}_{\left(\mathrm{t}\right)}}$) and the ESS discharging power (${\mathrm{P}}_{{\mathrm{ESS-d}}_{\left(\mathrm{t}\right)}}$), as shown in (5). Comparisons are carried out hourly and indicate whether the available generation is sufficient to meet the system’s needs or whether there is a capacity deficit. In the case of the latter, inadequacy events are quantified using the Loss of Load Duration (${\mathrm{LLD}}_{\left(\mathrm{s}\right)}$) and Energy Not Supplied (${\mathrm{ENS}}_{\left(\mathrm{s}\right)}$) metrics, which represent the total number of hours per year that load curtailments must be applied and the cumulative amount of energy not supplied, respectively, for every sample year s of the SMCS process, as calculated by (6) and (7).

$${\mathrm{ACC}}_{\left(\mathrm{t}, \mathrm{s}\right)}={\mathrm{ATC}}_{\left(\mathrm{t}, \mathrm{s}\right)}^{\mathrm{RT}}+{\mathrm{P}}_{{\mathrm{HPP}}_{(\mathrm{t}, \mathrm{s})}}^{\mathrm{RT}}$$

(4)

$${\mathrm{P}}_{{\mathrm{L}}_{\left(\mathrm{t}\right)}}{=\mathrm{P}}_{{\mathrm{R}}_{\left(\mathrm{t}\right)}}{+\mathrm{P}}_{{\mathrm{ESS-c}}_{\left(\mathrm{t}\right)}}-{ \mathrm{P}}_{{\mathrm{RES}}_{\left(\mathrm{t}\right)}}-{ \mathrm{P}}_{{\mathrm{ESS}\mathrm{-d}}_{\left(\mathrm{t}\right)}}$$

(5)

$${\mathrm{LLD}}_{\left(\mathrm{s}\right)}={\displaystyle \sum }_{\mathrm{t}=1}^{8760}{(\mathrm{ACC}}_{\left(\mathrm{t}, \mathrm{s}\right)}{ < \mathrm{P}}_{{\mathrm{L}}_{\left(\mathrm{t}\right)}})$$

(6)

$${\mathrm{ENS}}_{\left(\mathrm{s}\right)}={\displaystyle \sum }_{\mathrm{t}=1}^{8760}\max {(0, (\mathrm{P}}_{{\mathrm{L}}_{\left(\mathrm{t}\right)}}-{ \mathrm{ACC}}_{(\mathrm{t},\mathrm{s})}))$$

(7)

The final reliability indices reflecting the system’s adequacy level as a result of the implementation of the SMCS technique, namely, LOLE (8) and EENS (9), correspond to the mean values of LLD and ENS, respectively, over N SMCS sample years and are calculated as follows.

$$\mathrm{LOLE}= {\displaystyle \frac{{{\displaystyle \sum }}_{\mathrm{s}=1}^{\mathrm{N}}{\mathrm{LLD}}_{\left(\mathrm{s}\right)}}{\mathrm{N}}}$$

(8)

$$\mathrm{EENS}={\displaystyle \frac{{{\displaystyle \sum }}_{\mathrm{s}=1}^{\mathrm{N}}{\mathrm{ENS}}_{\left(\mathrm{s}\right)}}{\mathrm{N}}}$$

(9)

The target reliability indices converge to their final value as the number of sample years in the SMCS process rises. In this study, the convergence condition adopted to terminate the SMCS model is set at 1% and is applied to the EENS metric, defined by (10) and (11), as it has a lower convergence rate compared to the LOLE index. The termination criterion is stated by the accuracy metric, calculated using the standard deviation of the EENS after N SMCS sample years.

$$\mathsf{\alpha }={\displaystyle \frac{\mathsf{\sigma }}{\mathrm{EENS}}}$$

(10)

$${\mathsf{\sigma }}^2={\displaystyle \frac{1}{\mathsf{{\rm N}}·(\mathsf{{\rm N}}-1)}}·{\displaystyle \sum }_{\mathrm{s}=1}^{\mathrm{N}}{{(\mathrm{ENS}}_{\left(\mathrm{s}\right)}-\mathrm{EENS})}^2$$

(11)

2.2. HPP Real-Time Redispatch Modeling

As previously stated, the HPP operation is scheduled in accordance with a cost-driven operating policy and developed outside of the SMCS process. More specifically, the operating profiles of ESS and HPPs are derived from applying a market-based generation and storage dispatch algorithm with a cost minimization objective. The generation scheduling algorithm is built upon the linear programming mathematical optimization technique, as in [28]. Optimization has an annual look-ahead horizon to capture the seasonal operations of HPPs and their hourly granularity, while assuming the maximum availability for system assets.

The proposed method takes into account the market schedules of HPPs and real-time capacity outages to determine the final position of the system’s HPP fleet. The main feature of the described methodology is that the market schedule of the HPPs, as defined by the market-based cost minimization algorithm of [28], must always be followed to minimize system costs unless a loss of load incident occurs. In such cases, the power output of hydro plants is adjusted (real-time redispatch) to mitigate inadequacy incidents as much as technically feasible, deviating from the dispatch orders imposed by the market scheduling processes. Once the HPPs’ corrective action fully or partially resolves the loss of load event, HPPs undergo another stage of power output adjustment to restore the stored energy in their upper reservoirs to the levels denoted by their initial market schedule. This is a crucial part of the proposed methodology, as it ensures that the upper reservoir of the hydro plants will always be filled with an adequate amount of water to meet the stations’ market obligations, as well as other needs beyond power supply, such as irrigation and water supply, which are explicitly considered in market dispatch processes. Note that the mandatory water discharge of HPPs cannot be compromised to enhance the system adequacy, as this water usage is considered to cover the needs of a higher order of merit.

In brief, the following three stages can be identified regarding the modeling of hydropower plants in resource adequacy assessment study:

• Normal operating stage: When the power system is not experiencing any adequacy risk, HPPs operate according to their market schedule.
• Urgent redispatch stage: In the occurrence of a shortfall event, HPPs are redispatched from their scheduled operation to contribute to system adequacy, to the greatest extent technically and operationally feasible.
• Restoration redispatch stage: Upon the resolution of the shortfall event, HPPs’ operating profile isrestored according to their scheduled reservoir levels.

These guidelines apply to the redispatch algorithm developed for each type of hydropower technology, namely HPP reservoirs and open-loop PHSs. Appropriate adjustments are made to ensure that the specific characteristics of each HPP type are properly accounted for in the modeling.

The methodology architecture considers three cases to accurately and comprehensively represent the redispatch of different types of HPPs in the resource adequacy assessment study. These cases address the contribution to adequacy of the following:

(a)

HPP reservoirs with natural inflows and without pumping capabilities,

(b)

HPP reservoirs with natural inflows and with pumping capabilities (open-loop PHSs), and

(c)

the coordinated operation of the above assets in the presence of generation outages to ensure mutual contributions to system adequacy.

The two first cases, (a) and (b), perform redispatch actions only to the HPP examined, while the remaining technology is incorporated into the RAA study with its scheduled operating profile. The third case, (c), addresses the cooperation of the two HPP technologies in mitigating any loss of load events and securing the system adequacy.

A representative redispatch example referring to open-loop PHS operation is shown in Figure 1, together with a corresponding flowchart regarding the individual redispatch algorithm of each HPP technology (cases (a) and (b) above). The four graphs in Figure 1b depict the system operation (Figure 1(b1)), the amount of energy not supplied (Figure 1(b2)), the open-loop PHS’s real-time operation (Figure 1(b3)), and the deviation from its scheduled operating profile (Figure 1(b4)). The blue color in the upper graphs corresponds to the total available conventional capacity, comprising the available thermal production and HPPs’ generation, according to their initial market schedule (${\mathrm{ATC}}_{\left(\mathrm{t}, \mathrm{s}\right)}^{\mathrm{RT}}+{\mathrm{P}}_{{\mathrm{HPP}}_{(\mathrm{t}, \mathrm{s})}}^{\mathrm{SCH}}$). The dark red line indicates the residual load curve (P_L), including RES and ESS operation. The dashed light blue line represents the total available generation after the HPP is redispatched (${\mathrm{ATC}}_{\left(\mathrm{t}, \mathrm{s}\right)}^{\mathrm{RT}}+{\mathrm{P}}_{{\mathrm{HPP}}_{(\mathrm{t}, \mathrm{s})}}^{\mathrm{RT}}$).

Figure 1b illustrates the resolution of a shortage event due to an open-loop PHS redispatch that commenced in the second hour of the day, when the demand load requirements exceeded the available output power of the system. This loss of load incident persisted until the sixth hour of the day, prompting the redispatch of the plant to enhance its output and contribute to system adequacy. The open-loop PHS was scheduled to idle during the period of the incident (hours 2 to 6). However, it was eventually switched to production mode to mitigate the loss of load event, operating under the urgent redispatch stage. As described in the corresponding flowchart in Figure 1a, the amount of additional energy supplied by the HPP in each hour from 2 to 6 was equal to the amount of energy not supplied, with a limit up to the hourly maximum available output of the HPP. During the 7th hour of the day, since there was no risk of inadequacy in the system, the hydroelectric plants switched to pumping mode, operating under the restoration redispatch stage, to restore their scheduled reservoir levels (here referred to as the State of Charge—SoC), as indicated by the first step of the redispatch flowchart, which aims to achieve compliance with the scheduled SoC. It is worth noting that, during the first two hours of the restoration (7th–8th), the amount of pumping was being limited by the residual load curve to avoid the occurrence of a further loss of load event. In the 10th hour of the day, the necessity to restore the reduced reservoir level exceeded the scheduled output of the HPP (purple bar in the open-loop PHS operation graph). However, the amount of mandatory water discharge (yellow bar in the open-loop PHS operation graph) was provided to the system as a fundamental function regulating the operating profile of the HPPs, as indicated in the first step of the redispatch flowchart. The 12th hour indicated the conclusion of the HPP’s redispatch period. At this point, the ${\mathrm{ATC}}_{\left(\mathrm{t}, \mathrm{s}\right)}^{\mathrm{RT}}+{\mathrm{P}}_{{\mathrm{HPP}}_{(\mathrm{t}, \mathrm{s})}}^{\mathrm{RT}}$ curve aligned with the ${\mathrm{ATC}}_{\left(\mathrm{t}, \mathrm{s}\right)}^{\mathrm{RT}}+{\mathrm{P}}_{{\mathrm{HPP}}_{(\mathrm{t}, \mathrm{s})}}^{\mathrm{SCH}}$ line, and the HPP SoC returned to its market schedule, allowing the HPPs to operate under the normal operating stage. The example provided pertains to a fully resolved loss of load event resulting from the open-loop PHS being redispatched while respecting its technical and operational restrictions.

The HPP redispatch flowchart, illustrated in Figure 1a, applies to each HPP technology type being redispatched separately. The main difference between the two HPP technologies concerns the open-loop PHS’s pumping mode. In the event of an inadequacy, when hydro plants are forced to operate in the urgent redispatch stage, the reduction in energy that is scheduled for pumping by the open-loop PHS is the first measure to be applied. Conversely, pumping increases in the open-loop PHS when the restoration redispatch stage is applied, to assist the plants in rapidly restoring their lost energy and returning to the normal operating stage as soon as possible. In the case of the HPP reservoir, compliance with the scheduled operation is achieved through idling, which enables the replenishment of the upper reservoir with natural inflows without discharging as scheduled after the clearance of the inadequacy incident.

It is worth noting that the two steps in the flowchart represent the real-time redispatch algorithm that operates on an hourly basis for each sample year s within the SMCS process. The first step ensures compliance with the scheduled operating profile by ensuring the supply of mandatory water discharge and adjusting the HPP’s operations to comply with the planned reservoir levels. This step determines the extent to which the HPP’s production should be limited after a shortage event, during the restoration redispatch stage. The second step assesses whether the available hourly generation satisfies the system demand load and involves the redispatch actions that are performed in the case of a loss of load event within the power system. The hourly real-time output power of the plant is determined in the last step of the flowchart.

The third case of the proposed methodology entails the redispatch of both HPP technologies and their co-ordination, with the objective of eliminating loss of load events. Thus, it constitutes the most comprehensive framework for simulating the operation and evaluating the contribution of HPPs to resource adequacy assessment. Figure 2a depicts the combined HPP redispatch flowchart, which is conceptually similar to Figure 1a. It outlines the initial step of the algorithm in a concise manner and notes that SoC compliance is implemented independently for each HPP technology. It then proceeds to discuss the sequence of steps to be taken in the event of an inadequacy occurrence, referring to the urgent redispatch stage, which are as follows:

• Pumping Reduction: This is the initial action to be applied and refers to the hours where the loss of load event is synchronized with the pumping mode of an open-loop PHS. The pumping reduction is equal to the desired energy amount to be supplied or to the maximum energy that has been pumped in this hour. The ${\mathrm{P}}_{{\mathrm{L}}_{\left(\mathrm{t}\right)}}$ curve is modified, and the energy balance is tested again.
• Proportional Production Increase: This action pertains to both HPP types and signifies that each HPP type increases its output power in accordance with its installed capacity, contingent upon its energy capacity and the maximum available output power for the given hour. The ${\mathrm{ATC}}_{\left(\mathrm{t}, \mathrm{s}\right)}^{\mathrm{RT}}+{\mathrm{P}}_{{\mathrm{HPP}}_{(\mathrm{t}, \mathrm{s})}}^{\mathrm{RT}}$ is altered, and the adequacy status is checked again.
• Extra Production Increase: The final step is initiated if, during the second step, one of the HPP aggregated units is unable to deliver the requested power amount due to an energy deficiency or output power limitation. In such an instance, the remaining one continues to produce either until the depletion of its capacity or until the inadequacy event is entirely alleviated, circumventing the proportionality of a production increase in favor of improving the system adequacy levels.

Figure 2b shows a partially resolved shortfall event arising from the combined contribution of the two HPP technologies to system adequacy. The redispatch performed by the two HPP units decreases the amount of unsupplied energy, as shown in Figure 2(b2). However, the demand cannot be fully covered, as both HPP typologies have reached their maximum output power (hours 4–6). During the remaining two hours of the inadequacy event (hours 7–8), the HPP reservoir (Figure 2(b3)) raises its power output to its hourly maximum, while the production of the open-loop PHS (Figure 2(b4)) drops as its stored energy levels in the upper reservoir deplete (Figure 2(b6)). This aligns with the Extra Production Increase step of the common redispatch algorithm, whereby HPPs without pumping capabilities contribute further to system adequacy due to the energy deficit of the open-loop PHS.

2.3. Capacity Value Estimation

The contribution of the HPPs to system adequacy is assessed by applying the capacity value metric, which reflects the additional reliability provided to the power system by integrating the examined production asset [32]. In the present study, the capacity values of HPPs are quantified using the EFC metric, which refers to a perfectly reliable generating unit that would deliver the same system adequacy outcome as the unit under consideration [33,34]. Τhe EFC is calculated through the iterative process shown in Figure 3. The principle is to gradually increase the generation capacity until the target reliability index is reached. At each step, the adequacy metrics obtained by adding firm capacity are recalculated. The smaller the iteration step, the more accurate the output. The final EFC value is equal to the firm capacity that provides the same level of adequacy to the power system as the unit under consideration. It can be expressed either in MW or as a fraction of the installed capacity of the HPP.

3. Case Study and Main Results

3.1. Case Study

The proposed methodology is applied to the Greek power system in its stage of expansion in 2030 [35], with some variations in the composition of the thermal fleet to serve the purpose of the analysis. The annual load of the system is approximately 62 TWh, with an hourly peak of 11.6 GW. The system includes 8.3 GW of combined cycle gas turbines (CCGTs), 3.1 GW of hydropower plants (HPPs), 13 GW of photovoltaic (PV) systems, 9 GW of wind farms (both onshore and offshore), and 0.4 GW of small run-of-river hydro. In addition, ~3 GW of energy storage (including both battery systems and closed-loop PHSs) completes the generation mix. As mentioned above, the HPPs are divided into 2.4 GW of aggregated HPP reservoirs without pumping capacity and 0.7 GW of aggregated open-loop PHSs. Their reservoir capacities are 3600 GWh and 4.5 GWh, respectively, which implies tighter constraints for open-loop PHSs in terms of deviation from their scheduled operation due to their limited reservoirs. The operating profile of the RES, ESS, and HPPs, together with the demand load time series, are derived from the CEP model outside the SMCS process.

The reliability indices applied to the conventional units are obtained from the latest ENTSO-e resource adequacy studies [36]. The FOR is 5% for newer and 8% for older thermal units, while the MTTR is 24 h for all conventional power plants. The aforementioned assets refer to the base case power system. The subsequent sensitivity analysis presents modifications to the thermal capacity and nameplate characteristics of the HPPs. The RAA model, the redispatch algorithm, and the power system simulations are conducted in MATLAB [37].

3.2. Main Findings for the Base Case Power System

The proposed real-time redispatch methodology is implemented for 35 different climate years (CYs) for each of the three modeling cases (HPP reservoirs, open-loop PHSs, and their joint redispatch modeling). The objective of this study is to investigate the impact of various wind and solar data on RES production, the influence of different hydrological conditions on HPPs’ operating profiles (Figure 4), and variations in the demand load curve, as well as the interaction of the aforementioned parameters of the studied power system. This analysis evaluated the adaptability and effectiveness of the developed methodology by applying it to a wide range of hydrological conditions (

Table 1. HPPs’ hydrological data for 35 climate years.

Natural Inflows	Mean Value (TWh)	Standard Deviation (TWh)
HPP Reservoirs	4.2	0.7
Open-loop PHSs	0.6	0.15

) and operational states for the given generation system. The required climate data are procured from the Paneuropean Climate Database and are those employed by the ENTSO-e in their most recent resource adequacy assessments [36]. Figure 4 presents the annual aggregated reservoir levels of HPP reservoirs, as indicated by the operating profile derived from the cost minimization algorithm.

The 35 CYs are investigated for both the scheduled market-driven operation policy for HPPs and the redispatch methodology for all three modeling cases. Figure 5 presents a comparison of the retrieved reliability indices and capacity values for the two operational policies. Figure 5(a1–a3) concern the HPP reservoir redispatch, Figure 5(b1–b3) the open-loop PHS redispatch, and Figure 5(c1–c3) their joint redispatch methodology. The CYs refer to the years 1982 to 2016 and are presented in chronological order on the x-axis (i.e., 1 = 1982, 2 = 1983, etc.).

As illustrated in all diagrams of Figure 5, the LOLE and EENS indices resulting from the developed method are consistently lower than those observed when the HPPs adhere to their market schedule. In particular, the proposed methodology achieves a more than 98% improvement in the combined redispatch modeling of both HPP technologies compared to their cost-driven operating profiles (Figure 5(c1,c2)). This is evidenced by the elimination of the initial 7.6 h/year LOLE to only 0.1 h/year of load not satisfied.

Each independently redispatched HPP technology demonstrates enhanced adequacy metrics compared to the LOLE and EENS values derived from its market schedule. The HPP reservoirs exhibit superior performances relative to the open-loop PHSs, as evidenced by their smaller total output power (0.7 GW) versus the output power of the HPP reservoirs (2.4 GW). The joint redispatch of both HPP technologies achieves the highest performance among the three modeling cases, allowing for the availability of 3.1 GW of cumulative output power to perform redispatches from their scheduled operation in the event of inadequacy.

In terms of evaluating their capacity value, normalized to the installed capacity of the asset under consideration, the results are significantly higher when the asset is redispatched (87–93%) than when it operates according to its market schedule (15–46%). It is noteworthy that the open-loop PHS redispatch achieves slightly lower capacity values than the other two modeling cases, due to its comparatively smaller storage capacity (4.5 GWh). This storage volume corresponds to approximately seven hours of full charge/discharge modes to achieve the fill-up/empty-out of their tanks. Consequently, the open-loop PHS is not able to perform frequent redispatch for consecutive hours, as required during severe loss of load events, since this would rapidly deplete their reservoirs.

The capacity values retrieved from the cost-optimal operating policy in all three modeling cases are comparatively low, which is consistent with the findings in the relevant literature. This is due to the initial objective of the applied market schedule, which is to minimize system costs rather than to ensure a high level of system reliability.

4. Comparison with a Reliability-Driven Operation Policy

In order to achieve a comprehensive evaluation of the proposed real-time redispatch methodology and its obtained results, a reliability-driven operating policy is chosen as a further comparison method. The most commonly used reliability-oriented approach for HPP modeling is the peak shaving technique, which is briefly explained and subsequently applied to the same base case power system of the 35 CYs analysis to perform a direct comparison between the two HPP modeling approaches.

4.1. Peak Shaving Principles

The fundamental concept of peak shaving is the scheduling of HPPs to operate during peak demand periods [38]. This operation policy considers peaks as the most critical hours for the occurrence of a shortfall event and, therefore, allocates the natural inflows of HPPs to the hours with the highest load values. In this way, the operation of HPPs is integrated into the residual load curve, resulting in a smoothed load curve where the demand peaks have been shaved off. The present modeling approach assumes that the amount of natural inflows is known and fully available to be allocated on demand for the selected time interval where peak shaving is performed. The most common time periods for implementing peak shaving in resource adequacy studies are weekly, monthly, or yearly.

The flowchart diagram of the peak shaving technique is shown in Figure 6a. First, the implementation interval is determined, and then the natural inflows are allocated via an iterative, stepwise process. This process considers the maximum available output power of the given HPP plant and the remaining amount of inflows to be dispatched. Once the iterative calculation is complete, a threshold is established that defines the peak load hours during which the HPP inflows are allocated and the remaining load hours during which the HPPs are not scheduled to operate. Subsequently, the shaved load curve is extracted (Figure 6b).

4.2. Adequacy Results

The peak shaving technique is applied to the 35 CYs of the base case study for the most commonly used implementation time intervals (week, month, and year) in all three HPP modeling cases. The results of the joint HPP modeling are shown in Figure 7. For comparison purposes, the corresponding reliability results achieved by the proposed methodology are also shown.

It can be observed that a shorter application interval is associated with a deterioration in the LOLE (Figure 7a) and EENS (Figure 7b) indices, as well as the capacity value metric (Figure 7c). This is due to the fact that peak shaving dispatches smaller amounts of inflows in shorter implementation periods. In addition, the algorithm only has access to a limited sample of the load curve, while being forced to allocate all available inflows in that particular time frame. As the application period increases, the available inflows can be dispatched in a more optimal manner, as peak load hours can be addressed more effectively.

A further point of interest illustrated in Figure 7 is that the annual peak shaving provides slightly superior reliability results compared to the joint redispatch modeling. This can be attributed to the main assumptions of the peak shaving technique, one of which is neglecting the reservoir capacity of the plant. In this regard, the total amount of inflows is deemed to be known and available at the beginning of each implementation interval and dispatched on demand, without factoring in the reservoir capacity of the plant. In particular, the peak shaving method allows for each plant to be scheduled to either provide energy that is not contained in its tank, resulting in negative reservoir level values, or to store large amounts of energy without having the capacity to support it, exceeding 100% of the reservoir level. Peak shaving’s particular drawback arises from its failure to account for the timing of natural inflows, which is partially addressed by shortening the implementation period. However, this is particularly noticeable when applied to plants with a relatively limited capacity, such as open-loop PHSs in the given power system.

Figure 8 depicts the duration curves and operating curves of the reservoir level for each HPP technology, as determined by the scheduled market-driven operating policy (purple line) and annual peak shaving modeling (grey line). As demonstrated in the preceding analysis, the curve of the latter approach in the open-loop PHS modeling (Figure 8(b2)) exceeds the accepted storage range almost throughout the year, indicating a completely infeasible operating profile.

In the case of HPP reservoirs, peak shaving also results in a deviation from their planned operating curves (Figure 8(a2)), albeit modest and within the designed boundaries of their reservoir levels. This is due to the vast aggregated reservoir capacity of the HPP reservoir within the existing power system. This feature allows for redispatch whenever necessary, with the sole constraint being the maximum available output power. Consequently, in the modeling case where only the HPP reservoir is redispatched, the redispatch reliability indices are never exceeded by the corresponding indices obtained by annual peak shaving. This indicates that the annual peak shaving and the redispatch algorithms yield comparable outcomes in the context of HPP reservoir modeling variations, as neither approach is constrained by the plant reservoir capacity at the given adequacy level of the studied power system.

To gain further insight into the performance of peak shaving, different adequacy levels of the considered power system were examined by gradually removing thermal units, leading to lower levels of system adequacy. It was demonstrated that, as the system became increasingly inadequate, the results demonstrated a decline in the performance of the peak shaving technique. This tendency aligns with the core idea of the peak shaving approach, which is to shave off the load peaks, as these periods are thought to be the most pivotal for loss of load events. However, systems with lower levels of reliability face inadequacy events also during non-peak load periods, which the peak shaving approach is not designed to resolve. Nevertheless, these off-peak inadequacy events are effectively addressed by the proposed methodology in a manner analogous to any other loss of load event. This is due to the real-time adequacy evaluation within the SMCS process, which prompts HPPs to perform redispatch whenever necessary. Thus, the capacity values of the HPPs obtained by the redispatch approach maintain their consistently high values across different reliability levels of the studied power system (Figure 9).

This point of discussion reveals another limitation of the peak shaving technique, namely that, rather than dynamically analyzing the operating state of the system within the HPP simulation process, the technique adheres to a rigid assessment of upcoming adequacy risks within the power system and remains completely unresponsive to real-time generation outages.

The preceding analysis of the peak shaving approach serves to reinforce the view that it fails to account for some of the most important operating parameters of the assets under consideration, resulting in an overestimation of their ability to contribute to system adequacy. In addition, it treats loss of load events as predetermined events, which only applies to significantly adequate power systems where loss of load events tend to be infrequent and minor during peak load hours. The foregoing analysis demonstrated the inability of the peak shaving approach to adequately address shortfall events in power systems with lower levels of adequacy.

5. Sensitivity Analysis

This section performs a sensitivity analysis to investigate the impact of HPP nameplate parameters on system adequacy when operating under the proposed real-time redispatch methodology. This analysis is conducted by gradually increasing both the output power and the storage capacity values of each HPP technology separately and examining their performances at different initial system adequacy levels. A representative CY, namely 2004, is used as a reference case in which the HPP parameters and the time series of the power system exhibit mainly median values.

Figure 10 illustrates the reliability indices and capacity value results for the HPP reservoir and open-loop PHS of the base case power system (8.3 GW CCGΤs), where additional hydro units of each type are added in increments of +175 ΜW. The storage capacity of these additional units is increased in proportion to the output power addition. As extra hydropower units of one technology type are added, the remaining HPP technology remains unaffected. The base case in both configurations (Figure 10(a1–a3,b1–b3)) refers to the initial HPP characteristics described in Section 3, namely 2.4 GW of the HPP reservoir and 0.7 GW of the open-loop PHS. In each of the following steps, the total amount of the hydro generation is identical between the two configurations, with a discrepancy in the hydro generation mix. In particular, the final step of each configuration, where an extra +700 MW of hydropower is added, corresponds to a total of 3.8 GW of hydropower generation and an energy mix of 82% HPP reservoir and 18% open-loop PHS in the case of adding an HPP reservoir. Conversely if open-loop PHS units are added, the mix shifts to 63% and 37%, respectively.

The initial adequacy level of the power system is significantly enhanced by the redispatch of the base case HPP units, with a less than 0.1 h/year LOLE and ~0.025 GWh/year. As anticipated, the introduction of additional hydro units results in a further reduction in the reliability indices, with the final step of generation increase yielding the most favorable adequacy results. It is noted that the incorporation of additional HPP units of both technologies achieves comparable outcomes, with the final increment of +700 MW approaching a value of 0.01 h/year LOLE and ~0.005 GWh/year EENS when either additional HPP reservoir or open-loop PHS units are added. This is explained by the extremely high adequacy level of the studied power system, even in its initial stage (referred to as Base Case in the diagrams of Figure 10), which requires infrequent and undemanding HPP redispatches. Consequently, both technology types can contribute almost equally, in proportion to their installed capacity, since they are not subject to significant operational limitations. The corresponding capacity value results demonstrate minimal variation, remaining stable at approximately 91% to 92%. These values are consistent with the primary objective of the proposed methodology, namely the mitigation of loss of load events.

Figure 11 depicts the same two configurations as in Figure 10, but with a significantly lower level of system adequacy, starting from over 70 h/year LOLE and over 40 GWh/year EENS. Note that, in this case, CCGTs with a total capacity of 3 GW are removed from the system. Once again, the additional hydro units gradually improve the system’s reliability level, although it is apparent that the integration of HPP reservoirs provides better results compared to the addition of the same amount of open-loop PHSs. The discrepancy in the final LOLE index between the two configurations is almost 8 h per year, with the extra HPP reservoir achieving a final LOLE of ~21 h/year, while the open-loop PHS achieves ~29 h/year.

The reason for this outcome can be attributed to the constrained storage capacity, which influences the open-loop PHS redispatch. Even with a storage capacity of +700 MW for the open-loop PHS, which is also doubled to 9 GWh, the redispatch is still constrained by energy limits. In the case of a relatively inadequate power system, as shown in Figure 11, the HPPs’ contribution to system reliability is both extensive and highly demanded. This often leads to the depletion of the open-loop PHS reservoir and, thus, an inability to efficiently contribute to upcoming loss of load events.

To further investigate the performances of the two configurations, intermediate levels of system adequacy are examined between the two “extreme” scenarios of 8.3 GW and 5.3 GW of installed thermal capacity. Figure 12 illustrates the final reliability indices values achieved after the addition of +700 MW of each HPP type for different system adequacy levels. As indicated, lower adequacy levels lead to significant differences in the LOLE and EENS values between the two configurations, however, as the thermal capacity increases, this difference diminishes. This finding lends support to the proposition that there is a robust correlation between the adequacy level of the system and the storage capacity of the unit being redispatched.

It is worth noting that the reason for the varying reliability results between the two configurations lies in the different hydro generation mixes. As the proportion of HPP technology constrained by energy limitations rises, the resulting reliability indices decline, as a greater quantity of generating capacity is unable to fulfil the desired redispatch from its scheduled operation. In both configurations, the dominant HPP technology is the HPP reservoir, which has a high energy capacity due to its large reservoirs and is, therefore, capable of performing the necessary redispatch required by the system’s needs.

Despite representing a relatively minor proportion of the total hydro capacity, with capacity shares ranging from 18% to 37% depending on the increment, open-loop PHSs still impact the resulting reliability indices derived from the joint redispatch modeling of the two HPP technologies due to their energy capacity constraints. This can be observed by examining the reliability level enhancement achieved by incorporating each technology type across varying system adequacy levels, as illustrated in Figure 13. Both graphs in Figure 13 demonstrate the reduction in each adequacy index from the base scenario with no additional HPP units to the final step of the analysis, where an additional 700 MW of hydro capacity is added. The same amount of supplementary hydro capacity produces rather moderate outcomes for both the LOLE and EENS metrics in the case of a relatively inadequate power system, compared to the results achieved at higher adequacy levels of the same power system. This verifies the assertion that, as the level of system adequacy declines and the proportion of energy-constrained HPP units in the total hydro capacity mix increases, the final adequacy indices of the examined power system deteriorate.

6. Conclusions

This paper introduces a novel real-time redispatch algorithm for integrating HPPs with and without pumping capabilities into resource adequacy assessment studies. The proposed modeling approach posits that HPPs are subject to a market-driven operating profile, yet are redispatched in real time to ensure that the adequacy requirements of the power system are satisfied, reflecting realistic operating conditions. A reliability evaluation is performed using the Monte Carlo simulation technique, and the Greek power system in its future development stage serves as a case study. The proposed methodology is compared with a market-driven modeling technique, yielding significantly higher reliability indices and capacity value results in all modeling variations. In particular, the improvement in the LOLE index achieved ranges from 78% to 98% when compared to an HPP operating profile following the market schedule alone and being inelastic to inadequacy incident needs. At the same time, the corresponding HPP capacity values are notably high, attaining values between 78.7% and 94.3%. Furthermore, the proposed method is evaluated against the peak shaving technique, a reliability-driven method, achieving balanced results and demonstrating the inability of the latter to properly account for the inherent technical and operational constraints of HPPs. The adaptability and effectiveness of the developed methodology are proven by investigating different reliability levels of the studied power system, where the capacity value metric exhibits a robust performance, consistently exceeding 91%. A sensitivity analysis is also conducted, considering different HPP nameplate parameters and assessing their impacts on the resulting metrics of the proposed modeling algorithm. The analysis reveals that the reservoir capacity of a hydropower plant has a significant impact on its ability to perform redispatches and, thus, its ability to further contribute to system adequacy. Especially in power systems with lower levels of adequacy, the addition of a 700 MW HPP reservoir provided a 41% improvement in LOLE, while the addition of an open-loop PSH achieved only a 30% enhancement.