A Unit Commitment and Economic Dispatch Model of the GB electricity market – Formulation and Application to Hydro Pumped Storage

This paper formulates a fairly simple unit commitment model of an electricity system and applies it to the GB. It demonstrates its use with a case study of the economics of pumped storage (PS). As part of this enterprise, the paper reports, documents and assesses the data sources used for calibrating the model to GB in 2015. The model is subjected to a sensitivity analysis to test its robustness and the data quality, finding that the model and its results are robust against some of the key input and structural assumptions. First, we found that greater volatility of operating reserve requirements (for example as a result of increasing renewables penetration) leads to a higher utilization of PS. Higher wind and solar penetration increase the demand for electric energy storage, but more to provide balancing and ancillary services than as purely price arbitrage. Further, we found that PS and gas-fired stations compete in provision of flexibility services (e.g., spin-up reserve) - when we exclude non-synchronised gas-fired units from providing spinning up reserve, PS utilization increases, underlying the importance of PS in providing balancing and ancillary services. However, excluding non-synchronised gas-fired units from providing spinning up reserve means also very high volatility of system marginal price (SMP) as this puts substantial pressure on synchronized units (coal and gas units that have already been committed and are available) as well as PS to fulfil reserve requirements. In this case, the spin-up reserve market is roughly equally divided between online coal and gas units. But, in all our sensitivity cases, non-synchronized gas-fired capacity covers 99% of all spin-up reserve requirements. Our analysis shows that in response to variations in operating reserve requirements, the variations in the annual output of gas and coal is of order of 4% and 7% respectively but 80% for PS. Clearly the impact of operating reserve requirements on PS utilization is proportionately the greatest.


Introduction
The UK with many other nations aims at net zero emissions by 2050 (HM Government, 2021).That requires the power sector to be decarbonized by 2035 (CCC, 2019).This target requires high levels of renewable generation.In 2020, renewable 1 electricity provided 46% of the total annual supply, while the expected levels of renewable generation in 2035 are required to increase to at least 68% 2 of total supply with rest met by nuclear and other low carbon generation (CCC, 2020).While a high renewables scenario satisfies one leg of the UK's 'energy trilemma' (WEC, 2016), electricity markets also need to provide energy supply at least-cost and ensure reliability of supply.
Reliability requires continuing to operate "within equipment and electric system thermal, voltage, and stability limits so that instability, uncontrolled separation, or cascading failures of such system will not occur as a result of a sudden disturbance, including a cybersecurity incident, or unanticipated failure of system elements" (NERC, 2017).Ensuring reliability in these high renewables scenarios is challenging considering the intermittency and seasonal variability of wind and solar PV (variable renewable energy, VRE).If VRE output is low the power system must be able to replace it with alternative supply from flexible generation, demand reduction, imports or storage, whereas if output is high then the system must be able to accommodate the residual output, either through storage, export or curtailing (spilling) the excess (Newbery, 2018(Newbery, , 2021)).
The GB energy regulator, Ofgem, defines a flexible source as one that has "the ability to ramp generation or demand up or down quickly in response to changing market conditions" (Ofgem, 2015).Examples include gas-fired power (both closed-cycle and open-cycle gas turbines, CCGT, OCGT), diesel or gas-fired reciprocating engines, pumped and battery storage and interconnectors, and, increasingly important, demand response.These need to be available in sufficient volumes to respond to the sudden and also persistent swings to maintain the specified reliability, such as controlled demand reductions not more than 3 h per year on average.
A desirable market design of a future electricity system with high level of renewables is one that meets the targeted emissions reduction, provides the security of supply needed and is delivered at least cost to consumers.
Many energy models have been developed and calibrated for the UK (surveyed e.g. in Hall and Buckley, 2016;Strachan and Li, 2021).While these models have been widely used, there are fewer models of the GB electricity system specifically.Given that, and the role of the power system to deliver ambitious emissions reduction efforts, this paper has two research objectives: (i) to formulate a simple unit commitment and economic dispatch (UCED) model (see Appendi×1: Model Formulation), and (ii) apply it to analyse the role of hydro pumped storage (PS) as a source of flexible response in the GB electricity market with a high share of VRE.
The paper contributes to the energy policy and modelling literature in the following ways.The model's distinctive features are that it handles a reasonable range of generation technologies at plant or unit level and storage capability at an hourly dispatch resolution while keeping the solution time on a PC to manageable times so that it can explore a range of fuel and carbon prices and levels of renewables penetration.To this end, we publish the source code and input data used for this research for other scholars to use, extend and update our model for own research purposes. 3On the policy side, we contribute by analysing the economics of PS and their role in high-VRE GB electricity system.We examine key drivers of PS economics, such as a rising share of VRE on price arbitrage opportunities and on operating reserve requirements, and PS interactions with conventional supply sources (coal, gas and interconnectors).The rest of our paper is organised as follows: the next section provides a literature review.Section 3 describes our analytical framework and scenarios while section 4 presents key results and discussion.The final section concludes with the main findings and suggestions for future work.

Literature review
This section aims to provide a brief overview of the literature on energy market models as well as on the role of flexibility, especially storage, in power systems with high share of renewables.
As the proportion of VRE sources has increased to meet decarbonisation objectives so interest in its economic impacts has grown (Holttinen, 2005;Milligan et al., 2011;Katzenstein and Apt, 2012).Bachner et al. (2018) use a computable general equilibrium (CGE) model to quantify the macroeconomic costs of higher VREs in the European Union (EU) and find that the welfare effects of VRE depend on relative costs and capital intensities of generation technologies, and to a large extent on 'integration costs' of VRE (see e.g., Nicolosi, 2012;Hirth et al., 2015).They add to the top-down modelling literature which evaluates energy systems from a long-term, system-wide perspective (including a vector of energy carriers and related impacts of energy use) (see e.g.Chen et al., 2016;Annicchiarico et al., 2017).A key advantage of the CGE models is the ability to understand and model substitution and complementarities amongst various inputs and energy sources (see e.g., Jia and Lin, 2022 and studies mentioned there).A class of partial equilibrium energy system models, such as MARKAL (Fishbone and Abilock, 1981) and TIMES models (Loulou et al., 2005), have become a benchmark in energy policy analyses.These models are most often used to understand possible energy and climate 'pathways' under various assumptions related to economic growth, technology evolution and policy objectives, but offer limited understanding of operating a flexible electricity system.For example, Hobbs et al. (2001), Pfenninger and Keirstead (2015), Tapia-Ahumada et al. (2015), MIT Energy Initiative (2016), andHowlader et al. (2020) conclude that proper assessment of impacts of VRE needs bottom-up, spatiotemporally explicit power system models capturing system reliability and adequacy constraints.
Unit commitment and economic dispatch (UCED) models can accurately capture the techno-economic features of power system and has been instrumental in supporting analytical work on developments of liberalised power markets.The reader is referred to Hobbs et al. (2001) and Abujarad et al. (2017) for an excellent review of the history of UCED models.There has been proliferation of open-source energy models, including UCEDs models, recently in terms of scope (i.e., modelled features), sectoral coverage, time resolution and geographic focus (see e. g., a growing list of open-source models published by openmod, 4 a grass root initiative of academic modellers across the world).At the time of writing only three open-source models, out of 83 reviewed by these authors, were applied to the UK energy policy context: (i) "Calliope -UK" (Pfenninger and Keirstead, 2015), (ii) "EXO-XEL" (Heuberger et al., 2017), and (iii) "HighRES" (Zeyringer et al., 2018).Thus, we contribute our model, as an open-source tool, with ready-available baseline data and detailed documentation of data collection processes and assumptions (Appendix 2) to simulate GB 5 power market.While these existing open-source models may have advanced features (such as capacity expansion), our model differ from these as follows: 1. We model synchronized and non-synchronized spinning reserve provided by conventional generation and hydro pumped storage units; 2. We model endogenous interconnector flows and their ramp rates; 3. We calibrate the model and provide extensive sensitivity analysis to quality assure the model and provide detailed analysis of economic behaviour of the model using different scenarios and case studies.
We believe this is a contribution that can further support research on energy policy and facilitate teaching as a tool to explain how key economic drivers, technical and policy limitations interact in an electricity market with high share of renewables.Thus, we aim to provide researchers and students with a tool, which has a detailed explanation of how it works, its economic intuition, detailed documentation on data gathering and calibration processes and that can be used straightaway.The rest of this section focuses on the role of flexibility, especially storage, in power systems with high share of renewables, as our second contribution to the energy policy literature.
The strain of literature investigating technologies to support VRE integration is vast.Zerrahn and Schill (2017) present a systematic review of economics and engineering literature treating storage's role in power system flexibility.They also introduce the Dispatch and Investment Evaluation Tool with Endogenous Renewables (DIETER), which minimizes cost of combinations of generation, demand-side response, and power storage capacities as well as their optimal dispatch.
The flexibility that conventional thermal units can economically provide depends on wider system characteristics and their technological constraints.Ummels et al. (2007) point out that in the combined heat and power (CHP) dependent Dutch system minimum load problems may occur with increasing wind power, as CHP units must operate to provide heat even when they are not generating power.Newbery (2021) points out that Non-Synchronous (including VRE) System Penetration will typically need to be limited to maintain adequate inertia.Fossil fuel-based thermal plants are limited by technological constraints on cycling and ramping rates, which affect capital and operating expenses, efficiency loss (increased emissions) and increased probability of outages (Henderson, 2014;Hirth et al., 2015).To improve viability thermal plants may have to undergo retrofits which enhance ramping rates and the ability to operate at lower loads, which incurs its own costs. 6Gas and biomass-fired thermal power plants have lower technological constraints on ramping than coal and nuclear plants, and are thus, found to play larger roles in providing flexibility (Hong et al., 2012;Göransson et al., 2017).Wang and Hobbs (2014) analysed the effects of "Flexiramp" products by modelling them in a deterministic dispatch model and comparing outcomes with stochastic dispatch.They find that with flexibility products, out-of-merit-order dispatch is made in earlier periods so that flexible capacity is scheduled for later periods, to reduce the probability of price spikes.This finding is corroborated using an equilibrium program with equilibrium constraints (EPEC) approach by Gharibpour and Aminifar (2019).Wang and Hobbs (2014) also show that penalties for non-provision of services, marginal costs of flexible units and the magnitude of ramping capacity procured impact market efficiency improvements offered by ramping products. 7 Comparing deterministic with stochastic UCED models for the GB system, Qadrdan et al. (2014) find a higher usage of pumped storage (PS) in the stochastic scenario, highlighting storage as an important source of flexibility.Tuohy and O'Malley (2011) analyse the role of hydro PS in reducing wind curtailment in the Irish system, while other studies have analysed operation of batteries in conjunction with VRE for baseload generation (Denholm and Sioshansi, 2009;Hittinger et al., 2010).Managing the participation of storage in traditional markets has been difficult due to lack of efficient and transparent prices for some services, or bundling of prices due to overlapping timescale of services (Castillo and Gayme, 2014;Greenwood et al., 2017).However, as markets have been restructured the independent value of storage has been evaluated.Pozo et al. (2014) and Hemmati and Saboori (2016) use UCED models 8 and find that it can reduce system costs and enable greater VRE integration through load levelling and by acting as reserves for surplus demand and generation.Virasjoki et al. (2016) and Shahmohammadi et al. (2018) show that in competitive settings storage can economically mitigate out-of-merit-order dispatch of conventional sources.Jiang et al. (2012) use a robust optimization method to show that use of PS can reduce total costs imposed due to uncertainty of weather conditions in a high VRE system.This represents a closely studied application of storage and one of the modelling case studies presented in this paper, that of arbitrage: buying cheap (for charging) and selling high (when discharging).Graves et al. (1999) and Walawalkar et al. (2007) present early studies of intra-day arbitrage opportunity for storage, showing that price-taking storage units' net revenues are sensitive to round-trip efficiency, as low efficiency implies longer charging periods and reduced chances of a full recharge at low prices.The price-taking assumption is popular in the literature as storage is unlikely to be a large enough share of demand to affect prices (Bathurst and Strbac, 2003;Ekman and Jensen, 2010;Barbour et al., 2012).Although arbitrage may seem to be a profitable application for storage, Newbery (2018) shows that most of the revenue earnt by battery and PS has been from ancillary services.Analysing hourly pricing data for 2005-15 in Ontario, Canada using Fast Fourier Transform (FFT), Bassett et al. (2018) show that although hourly price spreads contribute a large share of the annual revenue of storage systems, participation in ancillary services is necessary to make an economically viable case for grid-scale storage.Zafirakis et al. (2016) use spot price data for 2007-10 in five EU electricity markets (Nord Pool, UK, Spain, Greece and EEX) to estimate PS and air storage arbitrage revenues under different strategies.They find that buying/selling at the lowest/highest weekly spot prices fetched maximum revenue, but it was still inadequate to cover lifecycle costs.Further, markets which are dependent on imports for energy requirements and where inefficiencies exist, arbitrage opportunities may be higher.Karhinen and Huuki (2019) investigate PS profitability with changing wind energy penetration levels on the system (up to 15%) to simulate long-term changes, and conclude that as wind share increases participation in the balancing market rather than the day-ahead market becomes more profitable, under certain assumptions on capital costs and discount rates.
A technology neutral analysis of inter-day arbitrage by Sioshansi et al. (2009) also shows that the magnitude of the arbitrage opportunity may be dependent on the wider system fuel-mix and locational constraints, which are reflected in marginal peak and off-peak prices.Further, Locatelli et al. (2015) model the arbitrage and operating reserve revenues by considering the number of hours having day-ahead price spreads (in the UK market) wide enough for operating cost recovery.Optimizing the storage size for given costs and price spreads, they find that storage has NPVs which are less negative in cases where they also provide reserves than when they rely only on arbitrage.They conclude that along with cost reduction and participation in reserve markets, storage also needs wider price spreads to be profitable.
Other sources of flexibility explored in the literature are interconnectors and demand-side response (DSR).For example, improving coordination between utilities and increasing the size of balancing areas have been shown to cost-optimally enhance flexibility as they make use of diversity and reduce the need for backup and storage (DeCesaro et al., 2009;Rodriguez et al., 2015;Child et al., 2019).Newbery et al. (2019) show that interconnectors have provided capacity value since their inclusion in the GB capacity markets in 2015, and flexibility value through an option to reduce imports in off-peak hours.Newbery (2018) shows that although prices in the UK and Continental European markets have converged, reducing arbitrage profits for interconnectors, participation in the ancillary service markets promises attractive revenues.DSR is recognised as a potential method to affect grid control through locational and time-of-use pricing, load-switching and demand-bidding techniques (Strbac, 2008;Heydarian-Forushani et al., 2014;Magnago et al., 2015;Vijay et al., 2017).However, the realisation of DSR is still held up by high costs (Newbery, 2018) and technological and policy issues, due to which smart meter rollouts in multiple jurisdictions have fallen behind schedule (Gompertz, 2019).
To sum up, what distinguish our case studies is that we examine interactions between flexible sources, in particular PS and gas-fired generation (CCGT), and their role in integrating further wind and solar resources.While the literature that we summarised above focuses on individual solutions such as batteries, PS, etc., to best of our knowledge, the interactions between PS and CCGT in the presence of growing share of intermittent (wind and solar) and inflexible (coal) generation has not been explored using a detailed, hourly UCED model.

Analytical framework
In this section, we describe our scenarios, sensitivity analysis and analytical approach to meet our research objectives.First, we calibrate the model to the 2015 GB electricity market data and then subject the model to numerous tests and sensitivity analysis to check its robustness (for details, see §A.1.4.Calibration & §A.1.5.Sensitivity analysis).The primary objective of this calibration and sensitivity analysis is to give us confidence that the model gives robust results.The calibrated 2015 GB electricity market model forms our baseline scenario for the analysis (see §3.1).Using the model, we attempt to answer the question 'what are key drivers of PS profitability?' (see §3.2).We then take this analysis further by changing key input assumptions to calibrate to the 2025 GB 6 See Hentschel et al. (2016) for an impact analysis of enhanced ramping rates and sub-optimal load operation on power plant viability.National Grid ESO, 2021) as well as undertaking sensitivity analysis to test robustness of our modelling results (see §3.1).The rationale for modelling a 2025 GB electricity system is to capture the potential impact of a different generation mix and fuel prices on PS profitability.

Scenarios and sensitivity analysis
For our analysis, we developed two scenarios: (i) a baseline scenario that uses 2015 GB electricity system data to calibrate the UCED, and (ii) a 2025 GB electricity system following National Grid's Five Year Forecast of supply mix (National Grid ESO, 2021).We then conduct three sensitivity analysis.For the 2015 baseline scenario, we conduct two sets of sensitivity analysis to measure the potential impact of (i) higher share of VRE, and (ii) changing operating reserve requirements on hydro PS economics.We also conduct one further sensitivity analysis to measure the potential impact of higher share of VRE on hydro PS in a 2025 GB electricity system.
To measure the impact of a higher share of VRE on PS private cost and benefit, we vary wind and solar production by up to 200% from the baseline production level (i.e., tripling wind and solar production relative to 2015).To put this increase in wind and solar in the context of GB's electricity system, a 200% increase in wind and solar production (relative to 2015) is ca.123 TWh of electricity, which is 37% of 2015 generation in GB.Thus, pushing up the level of wind and solar we can measure the role of PS in integrating VRE and consequently its profitability.Varying wind and solar production changes the residual demand to be met by conventional generation (e.g., coal and gas) and PS but also changes the operating reserve requirement (Appendix 2, A.2.3).Both changes could substantially impact PS through price arbitrage opportunities as well as a balancing tool.
Table 1 shows the evolution of GB's electricity generation mix and Table 2 gives fuel and carbon prices for 2015 and 2025.One can see that our modelled scenarios (2015 baseline and 2025) captures a range of generation mix.For example, by 2025 there is an expectation that coal will be completely phased out while wind and solar capacity should increase by almost a factor of 2.5.

Calculating PS profitability
Annual profit, R PS j,t , for PS units are defined as profit from price arbitrage (first term) and received payments from the provision of spinning up reserve (second term) less ongoing fixed O&M as well as transmission grid connection costs (FC j ): where * denotes optimal values from the solution to the unit commitment problem (see Appendix 1), p * t is the system marginal price, p * t is the spinning up reserve price, V j,1 is the value of energy stored in the first time period valued at the wholesale price of that time period, and V j,8760 is the value of energy stored in the last time period valued at the price of that time period.All other parameters and variables are as in the notation section in Appendix 1.Thus, the first bracketed term represents revenue from price arbitrage, while the second term is revenue from bidding into the spinning reserve market.

Results and discussion
This section discusses the key findings from the modelling.We first analyse the impact of higher wind and solar on PS profitability.Then we explore the sensitivity of PS position to the assumption around spinning reserve requirements.Next, we contextualise the simulated PS profitability with the actual revenue from GB's balancing and ancillary services market for 2015-2022.We then explore the potential impact of coal divestment and uptake in flexibility sources (more gas, interconnectors and batteries) on PS profitability by analysing the expected 2025 GB generation mix.Finally, we discuss revenues streams against ongoing costs of existing PS as well as in the context of investment in a new PS station.

Does wind and solar generation increase the economic value of hydro PS?
Table 3 reports the modelling results that highlight the impact of higher share of VRE on profitability of PS.The profitability of pumped storage units improves with more wind and solar on the system: as the share of wind and solar in total generation increases (from 12% to 37%) aggregate profit of all GB's existing PS increases from ca. £-3 mn/yr to more than £124 mn/yr.This re-confirms the finding from the literature about the importance of bulk energy storage solutions (like PS) to manage increasing share of VRE (Tuohy and O'Malley, 2011;Rasmussen et al., 2012;Qadrdan et al., 2014;Pozo et al., 2014;Hemmati and Saboori, 2016;Thomaβen et al., 2022).Total energy discharged from PS increases by 120% (line 5, Table 3) when wind and solar increases by 200% relative to the baseline.
The table shows that the increase in wind and solar generation   Chyong et al. (2020) and can be further explained by looking at the results from the sensitivity analysis reported in §A.1.5.3.In short, because of much higher start-up costs, longer on and offline commitments and slower ramping rates, coal was effectively cheaper in our baseline scenario than gas, and, hence, when wind and solar generation increases they displace more expensive (and flexible) generation units firstthe so-called merit order effect (see e.g., Cludius et al., 2014;Bublitz et al., 2017;Gianfreda et al., 2018).Indeed, in the baseline, the simulated SMP is £39.5/MWh while at a higher VRE share (37% of total generation) the SMP drops to £24.3/ MWh, or 40% decrease for an increase of 200% of wind and solar.At the same time, SMP volatility (measured as coefficient of variations, CV) increase dramatically, from 25% to 121%.Thus, as the share of VRE increases in the generation mix, wholesale price volatility may become the main driver of PS profitability, that is, from price arbitrage opportunities.Fig. 1 shows the split of revenue from the price arbitrage (first bracket term in eq. ( 1)) and from provision of spinning reserve (second term in eq. ( 1)) under various wind and solar scenarios.Worth noting also that aggregate profitability of all PS is positive and increases as we get more instances of negative prices (line 17, Table 3).
An important implication of displacing gas and ICs flows is that PS and other electric storage solutions (e.g., batteries) will likely dominate the flexibility market which we will explore in more depth in §4.5.While with the increasing share of VRE, arbitrage profit of PS increases the modelled revenue from spinning reserve market is important (especially at lower levels of VRE).Thus, next section explores the role of spinning reserve on the PS operations.

The impact of operating reserve on hydro PS
Dimensioning (sizing) spinning reserve requirements is important in that it could greatly influence the dispatch order.For example, spin-up reserve requirement will make sure that a certain amount of reserve capacity will be 'taken off' the dispatch order (supply curve).Traditionally, the spin-up reserve is equal to the capacity of the largest generation (or interconnector) plus a percentage of demand to reflect possible errors in demand forecasting.But with the rapid uptake of VRE, the spin-up requirement also needs to consider forecast errors of the VRE PS discharge 1.9 1.9 2.0 2.2 2.3 2.5 2.9 4.0 Net interconnector flows 20.3 20.0 19.5 18.4 17.0 15.1 9.7 3.9 [8] Britned 7.9 7.9 7.7 7.4 6.9 6.4 4.8 3.1  resources (wind and solar).This means that operating reserves will become increasingly volatile.The volatility will be dependent on VRE capacity but also how much assurance a system operator wants to have to hedge against forecasts errors.For example, the assurance will involve a decision whether to hedge against 99% of possible swings in demand and VRE generation forecast errors (three standard deviations of forecast errors) or less (more) (see Appendix 1: Model Formulation).This section examines the impact on PS economics of (i) sizing of the operating reserve, and (ii) the types of units that can fulfil reserve requirements.In the baseline we define spinning up requirement as the sum of the capacity of the largest generator plus three standard deviations (SD or σ) of demand and wind forecast errors (see eq. A.6 in Appendix 1).Three SDs will cover 99% of the distribution of errors, four SDs will cover 99.99%, while two SDs will cover 95%.Taking a zero SD means not considering errors in demand and VRE resource forecasts and only the largest generator.The operating reserve is then static over the entire modelling horizon and equal to the capacity of the largest generating unit connected to the system.We also model a case without operating reserve ("no reserve" case, equations A3 and A4).
In eq. ( A3) both synchronized and non-synchronized units can bid into the spinning up reserve market.Non-synchronized units are fast ramping generators that can spin up very quickly (usually within an hour to reach full capacity).We allow both hydro PS and gas-fired generation to bid as non-synchronized units.In a sensitivity analysis we allow only hydro PS to bid as non-synchronized units, thus excluding all fast-ramping gas units from this market.The rationale here is to see whether this will impact hydro PS utilization.
Table 4 reports our modelling results for different input assumptions around operating reserves.First, as we increase the 'coverage' of demand and VRE forecast errors in sizing of the operating reserve (from 0σ to 4σ), the volatility (measured as the coefficient of variation, CV) of hourly reserve requirements increases.Greater volatility implies a higher use of PS.With higher wind and solar penetration, the requirement for electric energy storage will likely increase, but more as a balancing and ancillary service provider rather than as purely price arbitrage.This can be seen by comparing the PS utilization in the "no reserve" case with the baseline.Furthermore, the importance of PS in providing ancillary services (in our case non-synchronous spin-up capability) can be seen in the case when we restrict PS to provide spin-up capability as non-synchronous units onlyin this case, the PS utilization is very close to the actual 2015 utilization level (in 2015, in charge mode, PS consumed 3.6 TWh and produced 2.7 TWh in discharged mode).
Second, higher volatility of reserve requirements means higher SMP volatility (compare baseline with 4SD and other cases in Table 4).It is also interesting that if PS is restricted to provide spin-up capability as the only non-synchronous units, the SMP volatility is the highest amongst all cases considered as it puts substantial pressure on synchronized units (coal and gas units who are already committed in the energy only market) to fulfil reserve requirements.
Third, in all our cases, non-synchronized gas-fired capacity will cover 99% of all spin-up reserve requirements (Table 5).It is only when we exclude non-synchronized gas-fired capacity from providing spin-up reserves is the spin up reserve market roughly equally divided between online coal and gas units as well as PS units.
In summary, defining operating reserve requirements is important as it will influence dispatch order and SMP.That said, our sensitivity analysis shows that the variations in annual output of gas and coal is of the order of 4% and 7% respectively and 80% for PS.Clearly, the impact on the PS utilization is the greatest.Thus, participation in operating reserve, balancing and ancillary services markets is important for PS profitability.The next section summarises other (than price arbitrage) revenue opportunities for PS in the GB electricity market by looking at balancing services reported by the GB's Electricity System Operator (ESO) for 2015-22.

Other revenue opportunities for hydro PS
Our modelling results suggest that at a moderate level of VRE (>21% of supply), the modelled revenues from purely price arbitrage and from the spinning-up service will likely be high enough to cover PS ongoing fixed connection charges.More wind and solar improves PS profit as arbitrage opportunities increase.Apart from the two revenue streams that we modelled (price arbitrage and spinning reserve market), there are other potential profit streams which PS can capture by providing the following services (ENTSO-E, 2016): 1. Balancing Mechanism (e.g., bid and offer instructions delivered within 60 s); 2. Frequency Response (e.g., primary, secondary, high); 3. Reactive Power (e.g, MVar lead and lag); 4. Reserve Services (e.g., Spin-Gen, Spin-Gen with Low Frequency (LF) Relay, Spin-Pump, Spin-Pump with High Frequency (HF) Relay, Pump De-Load, Rapid Start); 5. Black Start.
Note, therefore, that the second term in eq. ( 1) above can be used as a proxy to understand revenues from part of the item 4 (reserve service: spin-gen).It is worth noting that the above system services can be provided by many other storage solutions some of which could be potentially more cost and technologically appropriate than hydro PS (see Fig. 2).
Considering both the technical operational ranges of conventional PS and the timescales of power system operational issues means that bulk hydro PS would most likely operate to deal with transmission congestion, re-dispatch and operating reserve services (see Fig. 3).
In financial years (FY) 2015-22, total costs of managing constraints grew exponentially: in 2015 the cost was ca.£352 mn/year, or about 37% of the total balancing costs of the GB electricity system, but by the end of FY 2021/22 the constraints cost increased by a factor of 4.18 (318% increase relative to the 2015 level) reaching £1,474 mn/yr.Managing transmission constraints is the most expensive item in the balancing and ancillary services markets.Fig. 4 gives the breakdown of this cost by fuel and payment types.
We can see that, on average, gas receives 65% of the total constraint management payment, of which 61% is to rebalance the system; whereas coal receives about 9% of the net constraint payment.The category "others" contains all fuel types not reported separately and includes PS, hydro, OCGT, demand-side response, nuclear and oil.Thus, PS would have received not more than 12% of the constraint payments, on average, in 2015-22, or at most £52 mn/year in total.Unsurprisingly, given their wide geographic spread and flexibility, gas power stations dominate re-dispatch to deal with transmission constraints.
PS stations are, however, active in fast reserve, response and other reserve services with a combined market share of 18% in all these three ancillary services (Fig. 5: right panel).The total payment for all three services in FY 2021/22 was about £107 mn, of which 81% is the payment for fast reserve service (Fig. 5: left panel).This total revenue from ancillary services is ca.64% of the simulated revenue from price arbitrage in the case of +200% wind and solar.Apart from these reserve and response services PS can offer black start capability as well as reactive power services and participate in capacity market auctions.The simulated revenue from spinning reserve market amounts to £35-53 mn/yr, or only 33%-50% of actual total revenue from balancing and ancillary services markets for FY 2021/22.This underestimate should be taken into account when examining PS profitability.

Economic value of PS in a flexible power systemthe 2025 GB electricity system
One of the key conclusions from the above analysis is that PS competes with flexible generation, such as gas and interconnectors (ICs).But the above analysis took into account a large share of coal (which is less flexible than gas or ICs) in the GB electricity system (its share was 18% in GB's 2015 generation capacity) and therefore higher VRE share is likely more beneficial to the economics of PS (as wind and solar displaces gas and IC flows more than coal, see §4.1.)than in a system where there is no coal and most generation are flexible (e.g., gas, ICs, batteries etc.).This section explores this sensitivity by looking at the profitability of PS in a 2025 GB generation mix (see Table 1 for comparisons of generation mix in 2015 and 2025) without coal generationa policy objective in the UK and most of Europe.
Table 6 outlines the results of modelling the 2025 and baseline scenarios as well as wind and solar sensitivities analysis.Comparing these results reveals some very interesting insights: 1.An increase in the VRE (wind and solar) outputs have a greater positive impact on PS profitability when there is a large share of coal in the system (see line 20 in Table 6 for the Baseline scenario and wind and solar sensitivities).This is because coal is less flexible, with longer on and off commitment time, and therefore increasing VRE output causes larger SMP volatility (line 18, Table 6).This larger volatility then drives much of the increase in PS arbitrage revenue (see Fig. 1) and hence profitability.Arbitrage revenue increases, in particular, because of higher instances of negative SMPs when coal generation is still present in the system.2. In the 2025 scenario, when coal generation is phased out, PS profitability (in aggregate) is slightly above zero and is not comparable to the profitability levels under the +150% and higher increases in VRE in the baseline when coal is present (£0.7 mn/yr in 2025 vs £124.8 mn/yr in the +200% VRE sensitivity).Again, this much lower level of profitability is driven by the less volatile SMP (38% in the scenario vs. much higher C.V. in the sensitivities) and fewer instances of negative prices (only 47 h in 2025 vs 1,156 in the +200% wind and solar sensitivities).The lower SMP volatility (and instances of negative prices) is a result of removing inflexible coal and higher share of flexible supply sources: gas generation increases by 40% in 2025 relative to the baseline, ICsby 148%, storage (batteries) -by 122% (see Table 1).3. The increase in flexible capacity (gas, ICs and batteries) in while reducing inflexible coal helps to accommodate higher share of wind and solar (45% in total supply) by smoothing out its variability.This can be seen by comparing the SMPsin 2025 the average SMP is £36/MWh vs £39.5/MWh in the baseline vs £24.3/MWh in the baseline with +200% wind and solar.Thus, the merit order effect is much lower than in the baseline system in which there was less flexibility.

Stacking up revenue streams
If we add to the modelled revenue from price arbitrage the actual total 2021/22 balancing and ancillary services revenues (Fig. 5) against the ongoing fixed O&M and grid connection costs, then existing PS seem to be profitable under both the baseline and 2025 scenarios as well as under baseline wind and solar outputs sensitivities (Fig. 6).We see that the four existing PS stations can recover their ongoing costs and Note: CVcoefficient variation is determined as a ratio of standard deviation to the mean; 4σ means four standard deviations (SD) of demand and wind forecast errors; 3σ -three SD and so on.C.K. Chyong and D. Newbery depending on system configuration (with or without coal and the level of wind and solar penetration) that majority of the revenue to cover the costs comes from balancing and ancillary services marketsbetween 40% and 84%.However, if we compare the individual PS' profit (line 21-24, Table 6) with a capex of a new 600 MW PS station, which according to Leigh Fisher and Jacobs (2016) amounts to £67 mn/yr,10 , this suggests that the investment in new PS will be challenging. 11The gap in financing will have to come from either higher arbitrage revenue opportunities and/or more from balancing and ancillary services market opportunities.

Conclusion and policy implications
This paper outlined a simple unit commitment and economic dispatch model and applied it to the GB electricity market.The model reproduced the 2015 market data reasonably well on average.Using this calibrated 2015 baseline we carried out a number of sensitivity analyses to test the robustness of the model against changes in model structure, its main assumptions and data inputs.First, we tested performance and results against different model horizon lengths and found that increasing the model horizon has a dramatic increase in the solution time without any meaningful improvement in the 'quality' of the results.This highlights the importance of model compactness and its influence on the solution time.Fortunately, the model outputs are very robust to variations in the model time horizon.
We also tested the model's structural features related to plant flexibility, namely, ramping rates and commitment time, as well as start-up and shut-down decisions and their associated costs.We found that cycling characteristics (ramp rate and commitment time) can change the supply mix quite significantly.Coal's inflexibility disadvantages gas in the supply mix due to minimum up and down time requirements of coal plants and thus their inability to respond to fuel price dynamics quickly.Further, we found that total system operating cost under a simple economic dispatch model that ignores all the unit commitment and cycling decisions is just 2.7% less than the operating cost of the system under a UC model.The majority of cost savings is due to lower fuel and carbon costs.Start-up and shut-down costs represent just under 0.3% of total operating cost of the system.Hence, the impact of cycling is not so much on operating costs per se but on the way plants react to changes in demand and supply conditions and system marginal prices.
After model calibration and extensive testing we conducted an economic analysis of the four existing hydro pumped storage (PS) stations in GB.First, we found that more wind and solar increases PS arbitrage revenuespecifically, as the share of wind and solar in total generation increases (from 12% to 37%) aggregate profit of existing PS increases from ca. £-3 mn/yr to more than £124 mn/yr.Coal generation plays a key role in this profitability increase.This is because coal is less flexible and therefore increasing VRE output causes larger SMP volatility.This larger volatility drives much of the increase in PS arbitrage revenue and hence profitability.Second, we found that a higher volatility of reserve requirements means a higher utilization of PS.Higher wind and solar penetration will likely increase the requirement for electric energy storage, but more as a balancing and ancillary service provider rather than as purely price arbitrage.Further, when we restrict PS to provide (non-synchronized) spin-up capability only, its utilization is very close to the actual 2015 level underlying its importance in providing balancing and ancillary services.However, excluding gas-fired (non-synchronized) units from providing spin-up reserve means a very high SMP volatility as this puts a substantial pressure on synchronized units (coal and gas units who are already committed in the energy only market) as well as PS to fulfil reserve requirements.In all our analysis, non-synchronized gas-fired capacity will cover 99% of all spin-up reserve requirements.It is only when we exclude non-synchronized gas is the spin-up reserve market roughly equally divided between online coal and gas units.All in all, we found that defining operating reserve requirements is important as it will influence the dispatch order and SMPs.That said, our analysis shows that the variations in annual output of gas and coal is of order of 4% and 7% respectively and 80% for PS.Clearly the impact of spinning reserve requirements on PS utilization is proportionately the greatest.
Third, we could confirm that balancing and ancillary services revenue is important for the existing PS in the GB electricity market.By analysing the balancing market reports for 2015-22 we found that PS were not so active in constraint management, where about 65% of constraint payments went to gas-fired units.GB Gas stations dominate re-dispatch to deal with transmission constraints due to their geographic distribution and operational flexibility.However, most of PS (non-price arbitrage) revenue came from fast reserve, response and other reserve services.The total payment for all three services in 2021/22 was about £107 mn, of which 81% is the payment for fast reserve service.This total revenue from ancillary services is ca.64% of the simulated revenue from price arbitrage in the case of +200% wind and solar.We also found that the simulated revenue from spinning reserve market amounts to £35-53 mn/yr, or 33%-50% of actual total revenue from balancing and ancillary services markets in 2021/22.
Fourth, another key conclusion from our analysis is that VRE has a higher positive impact on PS profitability with a large share of coal (which is less flexible than gas, interconnectors or batteries).For example, in the 2025 scenario, when coal generation is phased out, PS profitability is slightly above zero and is not comparable to the profitability levels under the high share of VRE in the baseline when coal is present.This much lower level of profitability is driven by less volatile SMP and less instances of negative prices.Lower SMP volatility (and instances of negative prices) is a result of removing inflexible coal and higher share of flexible supply sources: gas generation increases by 40% in 2025 relative to the baseline, ICsby 148%, storage (batteries) -by 122%.Thus, the increase in flexible capacity in 2025, while reducing inflexible coal, helps to accommodate higher share of wind and solar (45% in total supply) by smoothing out its variability.For example, the average SMP in 2025 is £36/MWh vs £39.5/MWh in the baseline vs £24.3/MWh in the baseline with +200% wind and solar.Thus, the merit order effect is much lower than in the baseline system where there was less flexibility.
Finally, we found that adding the modelled revenue from price arbitrage to the 2021/22 balancing and ancillary services revenues and subtracting the ongoing fixed O&M and transmission connection costs suggests that the four existing PS stations are quite profitable.Most of the revenue to cover the costs comes from balancing and ancillary services markets.However, the revenues would not be enough to justify a new 600 MW PS station, making investment in any new PS challenging.
The gap in financing a new PS facility will have to come from balancing and ancillary services market opportunities and less from purely price arbitrage.This is true even with a very high share of VRE, unless a substantial portion of flexible generation capacity (gas, batteries and ICs) comes off line.This is because the existing PS competes with gas (and with ICs and batteries) in providing flexibility such as ramping.
To conclude, the unit commitment model with hourly resolution can reasonably capture the price arbitrage value of PS but analysing the economics of electrical energy storage requires a robust analysis of revenue opportunities in the balancing and ancillary services markets.Thus, for future research, it would be desirable to include ancillary services as well as conventional plant re-dispatch to deal with transmission constraints which requires explicitly dealing with forecast and plant uncertainty (especially VRE) over different time scales.However, the curse of dimensionality of stochastic models and more importantly data availability for calibration purposes might limit research in this direction.The final point to stress is that the model assumes perfect competition, and is not well-designed to deal with the exercise of market power.Incorporating market power in a traditional UC models, such as this, would potentially lead to an EPEC which, with just continuous decision variables, is well-known to be an extremely hard problem to solve.Lastly, simulation models has limited ability to predict extreme events such the recent Russo-Ukrainian War and its impact on fuel prices in Europe.Nevertheless, it is a useful policy analysis tool as its primary objective is to explore "what-if" scenario analysis, including extreme shocks and security of supply scenarios.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(continued ) The objective of this optimization problem is to minimize total power system costs (eq.( A1)).The optimization assumes a central planner who has perfect information about the cost structure of all generation units, the levels of demand and all other technical conditions and as such assumes perfect foresight over the modelling horizon T when searching for optimal commitment statuses and economic dispatch of generation units while meeting a set of constraints (eq.(A2)-A24).where m is number of rolling horizons that will be required to cover the annual modelling horizon (e.g. one year or 8760 h).Clearly m depends on s and q.For example, if K = 100 h and q = 30 h, hence s = 70 h then m = 8760/70 = 126 rolling horizons that need to be modelled and solved; that is, there will be 126 rolling horizons with 70 h each and the last 127th horizon will have only 60 h.However, since q = 30 h, every next rolling horizon the model 'resolves' the previous 30 h of the preceding horizon.This creates 'redundancy' but this is needed to ensure that solution of each horizon is optimal and would be as close to solving the entire 8760 h in one go as possible.In this sense, the larger is the q the closer to full optimality the combined results of each horizon would be.Sensitivity analysis regarding setting the parameter K will reveal the trade-off between total solution time needed to solve 8760 h and differences in results due to different values of K.
The inputs to the second simulation (T2) are the commitment and output status of every plant and the energy storage levels.This preserves the state of the system while the demand profile and other exogenous inputs for the new horizon are added.This process is repeated until the full modelling horizon (e.g. one year or 8760 h) is satisfied.

A.1.3.2. Time horizon and granularity
We simulate the GB electricity market at hourly resolution.The simulation time horizon is one year (8760 h for a normal year and 8784 for a leap year).The initial period was set to be one month prior to the modelling horizon; also, in order to minimize 'the end' of model horizon issues we set the model to run for one additional month after the model horizon.Thus, for the baseline scenario that we model (calibration to year 2015), the initial time period is the 1st hour of the December 1, 2014 while the last time period of the modelling is the last hour of the January 31, 2016.The model therefore runs for two additional months (14 months in total) such that we have 'optimal' starting and end points for each plant and storage levels.
In addition, we assume that at the initial period all pumped storage (PS) stations are fullthat is, in total, 23.9 GWh of electricity is available at the beginning of the modelling horizon.This assumption is not critical as the model runs for an additional month before the actual model timeframe so that the optimal storage level by the 1st hour of January 1, 2015 will be determined by the model.

A.1.4. Calibration
We chose to calibrate the model to 2015 as that was the latest comprehensive dataset of existing power plants (details in Appendix 2) reported by National Grid in its 2015Electricity Ten Year Statement (National Grid, 2015).That report also maps the plants to GB transmission zones and boundaries (where physical network constraints are likely to occur) as well as providing forecasts of plant additions and retirements from 2015 to 2035.The calibration for 2015 is consistent with this power plant dataset.We use the actual annual generation mix of 2015 as a benchmark against which we report all our calibration results.
A number of factors could influence dispatch decisions and hence, the resulting generation mix: 1. Fuel and interconnector prices, carbon and variable operating and maintenance costs (variable opex.)faced by a generating unit, 2. Generator's cycling cost (start-up and shut-down costs), 3. Generator's thermal efficiency and carbon intensity, 4. Generator's net versus gross output (parasitic loss factor) and its outage/capacity factor, 5. Operating reserve requirements, gross capacity of a unit and its ramping capability.
These techno-economic factors are the main ones which will determine the commitment status and dispatch order of plants.Some of these parameters are well defined (each unit's generation capacity, fuel prices and carbon cost).Others are subject to numerous uncertainties (e.g.cycling costs, variable opex., thermal efficiency and hence, carbon intensity).Some involve simplifications (e.g.operating reserve requirements, outage/ capacity factors, parasitic loss factors).Details of data sources and assumptions are given in Appendix 2 and other sections of this paper.The calibration process involves ensuring that the dispatch delivers the fuel mix observed (at least on average) and for that we only adjust two parameters: (i) the cost function of a generator, and (ii) wholesale prices of interconnected markets.
To manipulate the marginal cost functions of a generator we use multiplicative fuel mix calibration parameters, M j , as follows: For tractability and simplicity, this calibration parameter is changed either to all coal or all gas units and not individual plants, j.We change the historical hourly prices for interconnected markets by applying a similar multiplicative parameter for the whole year such that, on average, annual net interconnection flows match historically observed flows.
We use three sets of fuel prices to see the impact of price granularity on our generation mix and interconnector flows from the modelling.The fuel prices are the averages of the prices delivered to major power stations as reported by DUKES statistics, which include transport and gas network charges, making these prices higher than the spot traded prices (see Table A. 1).As we treat all similar plants as identical, average rather than plantspecific fuel prices are appropriate.coal and oil prices but daily National Balancing Point (NBP) gas prices adjusted to account for costs of delivering from the NBP to the power stations ("mark up over NBP", column 5, Table A. 1).Then, we find a set of M j for coal, gas and interconnectors such that the difference between the model and real 2015 supply mix (annual resolution) is minimized.
Using either annual or quarterly fuel prices we were unable to obtain satisfactory results for the supply mix of 2015 -we could not find the multiplicative calibration parameter M j that would get us close to the observed supply mix of 2015.However, using daily gas and interconnector prices with quarterly coal prices, Table A. 2 shows that there exists a set of M j that minimizes the differences between annual supply in 2015 and the model results.The result delivers the annual supply mix extremely close to the actual 2015 mix.

Table A 2
Calibration results for the year 2015 using daily gas prices and quarterly coal prices Annual supply, TWh Supply mix calibration parameter, Mj The differences between the modelling results and the observed data is within 4%, except for PS stations.Differences in hydro PS reflect the fact that in the model the PS results are driven only by price arbitrage and participation in spinning markets whereas in reality PS stations fulfil a number of balancing and ancillary services that are not captured in the current model.Further, Cruachan PS station has access to a catchment area and so enjoys natural inflows that might offer "free" storage.It is reported that 10% of annual electricity output from the Cruachan PS station is produced using rain and to that extent operates as a conventional run-of-river hydropower station (Scottish Power, 2011).
Finally, we compared the calibrated system marginal prices (SMP) with the 2015 GB day-ahead prices and found that, on average, our SMPs are 2% lower than the 2015 actual day-ahead prices (Figure A. 2).This is a result of 'marking up' fuel (coal by 2.75%) and interconnector prices to achieve the 2015 supply mix (see Table A. 2).
Applying these multiplicative fuel mix calibration parameters addresses the systematic biases in the quality of input data, such as fuel prices which are very heterogenous (specific to each plant and location), as well as systematic biases inherent to the modelling approach, such as determinism and perfect foresight.Using these multiplicative correction biases parameters for sensitivity and further scenario-based analysis appears defensible and more plausible than application of specific hourly mark-up parameter which is calibrated to historical data to get a very close match between model output and real data.In this regard, using this multiplicative correction biases parameter for sensitivity and further scenario-based analysis is more plausible than, for example, hourly mark-up parameters calibrated to historical data.

A.1.5. Sensitivity analysis
This section reports the sensitivity to structural features of the model.We take the calibrated baseline (Appendix 1: Model Formulation, §A.1.4.Calibration) as the reference point and change the model structure along two key dimensions: 1.The length of the rolling modelling horizon, 2. Binary and commitment decisions, plant flexibility parameters and simple economic dispatch solution without binary decisions.

A.1.5.1. Sensitivity of results and solution time to modelling horizon length
The baseline sets the rolling horizon at 100 h, that is, K = 100.The cut-off time is 30% of this, i.e. 30 h (see §A.1.3.2.).changing the number of hours in one rolling horizon.One can see that increasing the number of hours from 100 h (baseline) to 720 h (K720) increases the total solution time by a factor of five.However, the impact on the results is only a slight improvement in PS dispatch (i.e. an increase in PS utilization).This confirms our initial expectation that the number of hours in each horizon will most likely influence dispatch of units with intertemporal constraints such as eq.(A19-A20) for PS and conventional generation constraints related to minimum up and down time (eq.(A11)-A16).It is interesting that the higher PS utilization is associated with higher outputs from gas plants, probably because gas prices vary daily and hence, PS can realize daily arbitrage opportunities more efficiently compared to coal quarterly prices.
There is some non-linearity in the relationship between the number of hours and PS utilization -K180 seems to produce the highest PS utilization while in K48 we see the lowest PS utilization.Again, this might be due to fuel price dynamics (gas prices in particular) in that a moving 180-h optimization window might capture most of gas price volatility and hence, higher PS utilization rather than a moving 720-h window.Note: solve time is reported for the entire modelling horizon of 14 months or 10248 h.
All in all, one can see that a rather drastic change in the length of one modelling horizon from 48 h to 720 h produces results which are very similar.At least for this UC model of the GB electricity market the model time horizon should be 48-180 h to reduce the solution time.As noted earlier, practical uncertainty about future demand, renewables output and plant availability limit the time horizon over which systems actually optimize operations, so optimizing beyond a couple of days may not make much sense.
In general, the solution time increases linearly with the size of the optimization problem (Figure A. 3).However, the number of non-zeros (data that the model needs to process) slightly better explains the solution time than the number of constraints and variables.This highlights the importance of model's compactness and the influence of this has on the solution time.For example, comparing model characteristics for the baseline and K720 shows that while the number of constraints and variables increases by a factor of 7.2, the number of non-zeros increases by a factor of 22.8; and this increases the solution time by a factor of 4.7.The length of time horizon should be guided by the minimum up/down times as well as the total storage volume, as these parameters influence the optimality of each modelling horizon.For example, if coal stations have a minimum up (and down) time of 24 h then it would be desirable to model at least 25 h in one modelling horizon to ensure the model can decide on their commitment status.Similarly, if all PS stations can store up to 24 h' worth of energy then the modelling horizon should be at least twice 24 h to account for one cycle of charge and discharge.This will ensure that we are not constraining the model and the search space when it comes to PS dispatch decisions.
The baseline and all the sensitivities were modelled on a 64-bit Windows 7 PC with 32 GB of RAM and 2 multi-core Intel Xeon CPU E5-2650 2.6 GHz processors (16 cores in total). 13The baseline has also been modelled on two other machines with different specifications to see how sensitive the solution time is to the spec of the PC: 1. 64-bit Windows 10 PC with 8 GB of RAM and one multi-core (4 cores in total) i5-4590 with 3.3 GHz processor 14 2. 64-bit Windows 10 Laptop with 16 GB of RAM and one multi-core (4 cores in total) i7-4702HQ with 2.20 GHz processor. 15  We use AIMMS 16 as the modelling environment and CPLEX solver version 12.7.1 Rather surprisingly the solution time for the baseline on the i5-4590 machine was 593 s, almost twice as fast as the 2 multi-core processors machine.On a laptop, the solution time is significantly slower -10,665 s.Clearly CPU clock speed significantly influences the solution time rather than the number of cores.This is principally because our model calibrated to the 2015 GB electricity market has a relatively small branch and bound tree and hence the number of cores does not matter too much.

A.1.5.3. Plant flexibility and commitment
This section addresses a question of power system flexibility and what it means for dispatch and SMP.To this end, we run several sensitivities around the UC parameters such as: 1. Ramping limits and on/off commitment time, 2. Exclusion of binary variables dealing with start-up and shut down and commitment status of dispatchable generation from the optimization problem.
We define two sensitivities around the cycling characteristics for gas-and coal-fired power stations to represent a potentially 'highly' flexible power system and a highly 'inflexible' one.Baseline assumptions for cycling parameters are in Appendix 2, Table A. 8.For a flexible (inflexible) system we increase (reduce) ramping rates and reduce (increase) the minimum up/down time by a factor of two from the baseline cycling parameters.Under the inflexible power system sensitivity, we might see load shedding and power curtailment to deal with inflexibility imposed on generation units.
For the third sensitivity we exclude all binary variables (commitment status, start-up and shut-down variables) so the optimization problem is reduced to a simple linear program (LP) with the following set of equations: A1-A4 (objective function and system constraints), A5-A8 (thermal ramping limits), A17-A20 (bulk storage), A21-A24 (interconnector flows).Minimum generation term (u j,t P j ) is removed from eq. (A7) as commitment status was removed from this sensitivity analysis.This LP might represent a very flexible thermal power system and hence, the results could be similar to those from a UC model with highly flexible cycling parameters.As before, we benchmark the results from these sensitivities (Table A. 4) with the ones obtained for the baseline case.Note: * in the LP we do not model binary decisions and unit commitment constraints so start up and shut down cost is not relevant in this case.
Cycling characteristics can change the supply mix quite significantly.In both cases (flexible and inflexible) we see a clear shift to a gas-dominant supply mix with some marginal variations around how much coal generates from one sensitivity to another.Thus, in the inflexible case, coal generates about 32% more annually than it would generate under the flexible case, but 22% less than under the baseline.
The reason is that when coal is more flexible it responds to fuel price dynamics more compared to the situation when coal is less flexible (baseline or inflexible cases).This is evident by looking at hourly coal generation for the three cases (Figure A. 4).In summer months when coal is flexible it ramps up and down quite often (start-up and shut-down cost is £27 million vs £20 m in the baseline).When it is inflexible (red line) coal generates at minimum stable generation level and rarely cycles (start-up and shut-down costs are zero).In the baseline coal is more flexible and ramps up and down to the minimum stable generation.Because the minimum up and down time has been reduced dramatically for coal (and gas) under the flexible case, coal units do a lot of cycling (starts and shuts).  .5 shows the generation dynamics for coal across the year and for the three cases.It shows that winter and summer coal and gas price differentials change the merit order between CCGTs and coal units.In the winter coal stays ahead of gas.In the summer gas stays ahead of coal.This is the principal reason why the model optimizes coal dispatch during the year in response to relative coal and gas price dynamics in the more flexible case.Another way to examine this is to look at the coefficient of variations (CV) in outputs for all supply sources (see Appendix 3, Table A. 12).Coal output is much more variable under the flexible case whereas its output is less variable under the inflexible case.CCGTs become more baseload when flexible and ramp more in the baseline (but for some CCGTs, the magnitude of ramps is wider under the flexible case vs. the baseline case).
In the inflexible case, most CCGTs are baseload and PS utilization is very high, but variations in charge/discharge are lower than in the baseline or flexible case (see Appendix 3, Table A. 12).This suggests that PS stations are indeed used to address inflexibility but the hourly time resolution misses much of the short-term response.The output data show that PS responds more strongly than fossil plant in the first 5 min of variations in residual demand, but once more flexible fossil units (mostly gas) can ramp up, then PS is replaced by cheaper flexibility options in the balancing market, so that over a whole hour the valuable fast response of PS is largely hidden.PS is clearly valuable as flexible response, even if a deterministic hourly resolution UC model fails to give it adequate credit.
However, the combined profile of coal and gas generation did not change drastically (Figure A. 6).Coal and gas generation for the first half of January shows that the only notable difference is that under the inflexible case the trough in generation is always higher than in the other two cases.The primary reason for this is the increase in commitment timeminimum up and down times for both gas and coal.There are two important implications of the inflexibility case for the 2015 GB system (see Table A (Ofgem, 2015).Under the inflexible case, the modelling results show 314 GWh of wind power curtailment, or 1% of total wind generation.For this reason, the wholesale price, which reflects the opportunity cost of generation but also curtailment (being the FiT), is much lower than the other simulated cases (Table A . 4).As one would expect, the volatility of SMP is very high in the inflexible generation case compared to other cases.Finally, the results from the LP optimization confirms our hypothesis that its results will look like the results from the flexible case but more extremeignoring all the unit commitment constraints we find that although PS is hardly utilized, its variation is actually very high, suggesting very volatile PS utilization if a power system were to be completely flexible.However, rather surprisingly we found that the LP solution gives an average SMP which is higher than the SMP under the cases with the unit commitment constraints.This is because in the LP case, there are more interconnector imports and gas is dispatched more than coal.That said, the total operating cost of the system is the lowestnot surprisingly UC constraints have a cost.

Appendix 2. Data Input and Assumptions for the GB electricity market
This appendix details sources of the data used in this paper, the data handling processes, and the various assumptions made.Wherever possible we use the same notation as in the model formulation (see Appendix 1: Model Formulation) to denote the exogenous input parameters and functions that we use to calibrate the UC model to the 2015 GB electricity market.

A.2.1. Notation for data inputs and parameters
Below we define additional parameters required for calibrating the model to the GB electricity system.Total generation from all other sources: non-biomass thermal renewable generation, distribution connected oil-fired generation and other generation (steel works etc.)

A.2.2. GB electricity demand in 2015
Before the uptake of distributed renewable electricity supply (and especially PV) that is connected to distribution networks, finding the UK electricity demand was simple as it was published by the GB transmission system operator (TSO) National Grid.The uptake of embedded wind and solar generation means that the demand at the transmission level is net of embedded wind and solar power output.National demand should now be determined as: where ND t is our estimated GB electricity demand.CONV GEN t is national transmission-level net generation including net interconnector flows as reported by ELEXON, defined in (eq.( A27)): where WIND TR t is transmission level generation from all wind generators as reported by ELEXON (GridWatch, 2019); EMD WIND t is an estimate of the GB wind generation from wind farms which do not have Transmission System metering installed.These wind farms are embedded in the distribution network and "invisible" to National Grid.Their effect is to suppress the electricity demand during periods of high wind.The actual output of these generators is not known so an estimate is provided based on National Grid's best model (National Grid, 2018).Similarly, the EMD SOLAR t is National Grid's estimated embedded solar generation lacking transmission system metering.Both embedded wind and solar generation estimated were obtained from the National Grid website (National Grid, 2018).Finally, the residual demand, D t , that we model in eq.(A2) (Appendix 1) is defined as: where σ DF is the demand forecast and σ WF is wind forecast error standard deviation (Holttinen, 2005as cited in Gerber et al., 2011).Gerber et al.
(2011) noted that in a power system without significant variable renewable generation, operating reserve is determined by the capacity of the largest unit on the system as well as by load forecast errors.In their work, they have assumed 1.8 GW as the largest on line in 2020 in the GB (the next nuclear power station, not now expected much before 2025).We should note that σ DF and σ WF are standard deviation of hourly time series of load and wind generation respectively, as originally noted by Holttinen (2005).Hence the rationale for multiplying the square root term in eq. ( A30) by 3 is that it is standard deviation indicating that with a probability of 99% the expected combined variation of load and wind generation falls within their mean forecast error.Similarly, multiplying the square root term by 4 would indicate that 99.99% of the expected variations are within the mean value.We modify the last term of eq.(A30) as follows to reflect a general situation: where max j∈J(f ) CAP j is the largest plant in the model.
In lieu of the standard deviations of forecast (load and wind) errors, the two parameters σ DF and σ WF are determined as follows.As part of its role as system operator, National Grid forecasts and publishes short-term wind and demand forecasts (Ofgem, 2015).OFGEM sets a number of incentives schemes to motivate National Grid to outperform and improve the accuracy of these forecasts.For wind generation forecasts, the target is to get wind generation forecast errors consistently below 3% of actual wind generation during the summer (April to September) and 4.75% in winter (October to March).Thus, where tf t is the forecast error targets set by OFGEM (3% during the summer months and 4.75% during the winter months) and WIND t is total wind generation.
As for demand forecast error, σ DF , National Grid publishes mean absolute error of demand forecast for a number of timeframes (National Grid, Note that the operating reserve definition as given by eq. ( A33) is for secondary control only.In general, ENTSO-E defines reserve in three categories: primary, secondary and tertiary control (ENTSOE, 2015).Both primary and secondary reserve categories are designed with a respond time up to min.To restore the primary and secondary control units back to the reserve state, the tertiary control units are engaged: these are slower response units.Table A. 5 below summarises the operating reserve requirements based on GB data.Note that we assume downward reserve as 50% of upward reserve requirement.The minimum load at which a plant can operate consistently as well as ramp rate and minimum up/down time has been compiled from multiple sources by Schröder et al. (2013).The average of these values is taken and assigned to each plant in our plant database.Note that gas-and diesel-fired turbines (GT) are assumed completely flexibleno minimum load and up/down time and can ramp to full capacity within an hour (see Schröder et al., 2013).Further, once minimum stable generation is reached all generation technologies can ramp to maximum nameplate capacity within an hour (see Schröder et al., 2013).We assume that ramp down factor is the same as ramp up and shut ramp factor is equal to start ramp factor.
Due to potential inconsistencies between eqs.A5 and A7 in that eq.(A7) requires plants to reach minimum stable generation within an hour which could be larger than the start ramp rate (eq.( A5)).Indeed, the original data for CCGTs and Coal plants in Table A. 8 shows that minimum stable generation is greater than start ramp rate.To correct this, we assume that start ramp factor equals to min power output and note that CCGTs can ramp to full capacity in about 2 h while coal plantsabout 4 h.Hence, for CCGTs we adjust start ramp factor to a minimum power output of 0.40 of nameplate capacity while its ramping rate once they reach minimum stable generation is set to 1 (i.e., ramping to full capacity within 1 h).For coal plants, we set the start ramp factor to 0.38 (minimum stable generation) while their ramp factors are set to (1-0.38)/3 (first hour it ramps to 0.38 of maximum capacity, reaching minimum generation) because it will need another 3 h to reach maximum capacity.
Note that in eq.(A2) we adjust power output, p j,t , by the parasitic loss factor, PL j , since ELEXON generation data (GridWatch, 2019) that we use to define residual demand (eq.( A28)) is reported on the net basis, that is, gross generation less power consumed within the stations.We use data from DUKES (2018) "Table 5.6" to derive parasitic loss factor, PL j , which we use in the model.Table A. 9 reports DUKES (2018) annual generation data which includes both gross generation and parasitic loss, PL j .Source: DUKES (2018), "Table 5.6" Finally, net power output from all dispatchable plants including power discharged from hydro pumped storage stations are adjusted for transmission losses, TL, in eq.(A2).In 2015, transmission losses were 28.6 TWh while gross supply injected into the GB transmission grid was 339.6 TWh (DUKES, 2018 "Table 5.1.2");hence transmission losses represent 8.43% of gross supply and we use that loss factor in our modelling.Note that according to DUKES (2018) data the transmission loss factor fluctuates between 7.2 and 9.6% since 1970 to 2017 with an average value of 8.13% in that period.

A.2.5. Pumped Hydro Storage in GB
There are currently four pumped hydro storage (PS) stations in operation in GB with a total power capacity (discharge) of 2828 MW and about 23.9 C.K. Chyong and D. Newbery GWh of energy storage capacity Table A. 10).Source: Power and energy capacity are from DNV GL (2019); roundtrip efficiency, variable and fixed O&M cost as well as grid connection cost (TNUoS) is from Leigh Fisher and Jacobs ( 2016) report (medium values).
Data on the actual roundtrip efficiency of PS stations are not available in the public domain.Leigh Fisher and Jacobs (2016) suggest that modern PS stations might have an improved roundtrip efficiency of 75%, which we use as an input (parameter SE j in eq. ( A19)) for our simulations.Actual variable O&M costs are not available as well.LF (2016) suggests a variable O&M cost of £40/MWh e in their medium cost scenario.This includes an assumption of off-peak power price of £30/MWh e , hence, our assumption that stations' variable O&M cost is £10/MWh e .

A.2.6. Interconnectors
For the baseline scenario, we model four interconnectors (Table A. 11).Assumed interconnector capacity for calibration to 2015 was derived by taking the highest flow observed in 2015 18 .Ramping limits are derived using 2015 flows as reported by National Grid (2018b). 19Interconnector prices that we use in the model are obtained from the Bloomberg terminal and reported as in Fig. A. 10. 20    Note: Moyle has been operating at around half of its normal capacity due to subsea cable faults since 2012.

Fig. 4 .
Fig. 4. Breakdown of constraint costs by fuel type (2015-2022 Financial Years) Note: Payment to manage constraints is the cost incurred by National Grid to pay generators to be constrained off whereas payment to rebalance the system is the cost incurred by National Grid to bring the system back into balance, which includes not just energy balance, but also to readdress the level of reserve available on the system; Positive values show the costs to National Grid, negative values show receipts; "Other" includes all fuel types not reported separately and includes hydro, open-cycle gas turbine (OCGT), demand side suppliers, and nuclear.Source: NG ESO (2022): System balancing reports for 2015-2022.

Fig. A 3 .
Fig. A 3. Solution time and the size of the unit commitment problem 14 3.3 GHz base frequency and 3.7 GHz max turbo frequency. 152.2 GHz base frequency and 3.2 GHz max turbo frequency. 16https://aimms.com/.

Fig. A. 4 .
Fig. A.4. Coal generation under the baseline and two flexibility cases

Fig. A. 5 .
Fig. A.5. Merit order with January and July coal and gas prices Note: CCGT_HE -high efficiency CCGT units; CCGT_LE -low efficiency units. .
4):(i) it could result in surplus electricity being pushed to neighbouring markets (net imports under the inflexible case is 44% of the baseline level), and (ii) as noted above, PS utilization is very high compared to the baseline (or 2015 actual data) (seeFigure A. 7).

Fig. A. 6 .
Fig. A.6.Coal and gas generation under Flexible, Inflexible and Baseline cases.

Figure
Figure A. 7 shows differences in coal and gas generation ('delta fossil generation'), PS net charge ('delta PS') and net interconnector flows ('delta IC') between inflexible and flexible cases for a sample of the first 100 h in January.One can see that the 'excess' (or the difference) in coal and gas generation is being absorbed by interconnector and PS.Interesting to note is that in hour 29 one can see that combined export and PS charge capacity is not enough to absorb all excess generation.This results in curtailment of 677 MWh of wind generation and hence a negative wholesale price of £47.22/MWh (Figure A. 8), which reflects the average value of ROC in 2018/19(Ofgem, 2015).Under the inflexible case, the modelling results show 314 GWh of wind power curtailment, or 1% of total wind generation.For this reason, the wholesale price, which reflects the opportunity cost of generation but also curtailment (being the FiT), is much lower than the other simulated cases (TableA.4).As one would expect, the volatility of SMP is very high in the inflexible generation case compared to other cases.

Fig
Fig. A.7. 'Excess' fossil fuel generation due to inflexibility and where it goes Note: delta fossil generation: fossil fuel generation in flexible case less fossil fuel generation in inflexible case; delta IC: net interconnector flows ("-" export, "+" imports) in inflexible case less net interconnector flows in flexible case; delta PS: net PS discharge ("-" charge, "+" discharge) in inflexible case less net PS discharge in flexible case..

(
Fig. A.9. Demand Forecast Errors Source: National Grid (2018b).An alternative approach to defining operating reserve requirement is outlined by Quoilin et al. (2017) who follow ENTSO-E's operational guidelines definition of positive operating reserve requirements as: ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ amax h (Demand h ) + b 2 √ − b (A33)

Fig. A. 10 .
Fig. A.10.Price duration curves we use for the baseline modellingNote: reported prices cover the period from the Dec 1, 2014 until the Jan 31, 2016 to cover all 14 months of modelling; in SEM, there were 143 h when prices >£100/ MWh; in GB, there were 12 h when prices >£100/MWh; max hourly price for NL and FR was £80/MWh and £90/MWh respectively.Source: Bloomberg terminal.

Table 3
Impact of wind and solar generation on supply, system marginal price and PS profitability.

Table 4
Impact of operating reserve requirements on modelling results.

Table 5
Provision of reserves by technology type, MW/hour (as % of hourly average reserve requirement).
Note: for each scenario, summing up all bids for spin (down) up reserve should be equal to average hourly spin up (down) reserve requirement reported in Table4.C.K.Chyong and D. Newbery

Table 6
Comparing the Baseline scenario, wind and solar sensitivities and 2025 scenario.
C.K.Chyong and D. Newbery

Table A 3
Impact of modelling horizon length on results

Table A .4
Impact of thermal generation flexibility on modelling results

system operating cost, £ mn, of which:
ND t − (WIND TR t + EMD WIND t + EMD SOLAR t ) − (HYDRO t + NUCLEAR t + OIL t + BIOMASS t + OTHER GEN t ) C.K.Chyong and D. Newbery

Table A
Schröder et al. (2013)factors are reported as ratios of plant capacity that can be reach within an hour.Source:Schröder et al. (2013); ramp up factor, start ramp factor, and minimum power output factor are reported as proportion of installed capacity while minimum up and down time are in hours. Note

Table A .9
Electricity generation by sources: gross and parasitic loss

Table A .
10 Operational Pumped Hydro Storage Stations in GB

Table A12 :
Economics (2013)ad applied.This is a weighted average of VoLL at winter peak for just domestic customers and an average value for SMEs from LondonEconomics (2013).MWh VR+Value of loss load applied to upward operating reserve requirement constraint.The parameter was derived through calibration such that SMP is close to the actual 2015 day-ahead prices £75/MWh V R− Value of loss load applied to downward operating reserve requirement constraint.The parameter was derived through calibration such that SMP is close to the actual 2015 day-ahead prices Coefficient variations of generation, interconnectors and hydro PS under flexibility sensitivities A.2.7.Other costs t Carbon cost which for the calendar year 2015 includes both EU ETS price and GB carbon price support £22/tCO 2 V D (continued on next page) 18 https://www.ofgem.gov.uk/electricity/transmission-networks/electricity-interconnectors. 19https://researchbriefings.files.parliament.uk/documents/SN05927/SN05927.pdf. 20by the proportion of electricity generation SMEs and domestic consumers respectively.