P L. Power Systems Laboratory. Andrés Vargas Serrano

Transcription

1 P L Power Systems Laboratory Andrés Vargas Serrano Economic Benefit Analysis of Retrofitting a Fixed-Speed Pumped Storage Hydropower Plant with an Adjustable-Speed Machine Master Thesis PSL 1617 Power Systems Laboratory High Voltage Laboratory Swiss Federal Institute of Technology (ETH) Zurich Examiner: Prof. Dr. Gabriela Hug Supervisors: Andrew Hamann, Sören Hedtke Zurich, April 14, 2017

2 Abstract Most pumped storage hydropower plants use a fixed-speed synchronous machine connected to a pump-turbine. In pump/motor mode, the pump-turbine operates at fixed load. In turbine/generate mode, the pump-turbine operates between 40 and 100% of rated power. If the motor-generator is replaced with an adjustable-speed machine, increased flexibility in pump mode facilitates the provision of reserve power ancillary services, among other benefits. This thesis assesses the potential impact on revenues of converting an existing fixed-speed pumped storage hydropower plant to adjustable speed. A test case of a four-unit Swiss pumped storage hydropower plant participating in the energy and secondary and tertiary reserve ancillary service markets is conducted. The operation of the plant is simulated using a multimarket bidding optimization for the reserve markets and a mixed-integer linear programming model to replan hydropower generation and consumption. The model replicates operation and uncertainties of Swiss reserve markets. If all four units are converted to adjustable speed, revenue is estimated to increase 58%. i

3 Contents List of Acronyms iv 1 Introduction Motivation Thesis Objectives Grimsel 2 Pumped Storage Plant Swiss Electricity Markets Energy-only Markets Derivatives Market Spot Markets Balancing Market Operating Reserve Markets for Reserve Capacity Compensation for Activation of Reserve Literature Review 12 4 Simulation Procedure Overview of the Simulation Procedure Week-Ahead Reserve Planning Opportunity Cost of Providing Reserve Stochastic Bid Curve Optimization Reserve Market Clearing Week-Ahead Planning Day-Ahead Planning Optimization Problem Formulation Deterministic Plant Optimization Stochastic Bid Curve Optimization Simulation Environment and Solution Time ii

4 CONTENTS iii 6 Plant Model Reservoirs Pump Model Fixed-Speed Operation Adjustable-Speed Operation Turbine Model Turbine Efficiency Curve Piecewise Linearized Turbine Power-to-Discharge Curves Generator/Motor and Grid Interface Alternatives and Losses 41 7 Case Study Plant Configuration Alternatives Sensitivity Analysis Results Plant Configuration Alternatives Sensitivity Analysis Conclusions Summary Conclusions Outlook A Available Data 53 A.1 Pumped Storage Plant Data A.2 Market Data B Simulated Permutations of Reserve Capacity 55 C Reserve Capacity Demand Curves 57 D Weekly and Daily Head Range 62 E Market Data Plots 64 F Pump Adjustable-Speed Efficiency 67 G Results for Each Scenario 69 Bibliography 72

5 List of Acronyms AS DFAM EEX EPEX SPOT FC FS HVAC HVDC KWO SCR SCRE SCRE + SM SwissIX TCR TCR + TCRE TCRE + Adjustable Speed Doubly Fed Asynchronous Machine European Energy Exchange The European Power Exchange SE Full-Power Converter Fixed Speed High-Voltage Alternating Current High-Voltage Direct Current Kraftwerke Oberhasli AG Secondary Control Reserve Secondary Control Reserve Negative Activation Energy Secondary Control Reserve Positive Activation Energy Synchronous Machine European Power Exchange Swiss Electricity Price Index Negative Tertiary Control Reserve Positive Tertiary Control Reserve Negative Tertiary Control Reserve Activation Energy Positive Tertiary Control Reserve Activation Energy iv

6 Chapter 1 Introduction 1.1 Motivation Price and energy arbitrage has typically been seen as the main source of income for pumped storage hydropower plants. This business model has become less attractive in electricity markets where high shares of wind and solar power have been installed, because of a decrease in overall energy prices and in the spread between peak and off-peak prices [1]. Consequently, pumped storage plants must increasingly look to other sources of revenue, particularly ancillary services [2]. A conventional pumped storage plant is generally built with a fixedspeed synchronous machine connected to a pump and turbine or a reversible pump-turbine. In turbine/generator mode, the pump-turbine typically operates between 40 and 100% of rated power [3]. In pump/motor mode, the pump-turbine operates at fixed load. The inability to regulate pump loading constrains the plant s ability to provide reserve or load-following ancillary services. However, modern adjustable-speed electrical machines and drives increase the flexibility of pumped storage plants and enable the regulation of pump load. Adjustable-speed plants can regulate pumping power within a range of 50-60% of rated power [3], extend turbine operating range, increase efficiency, and more quickly adjust generation [4]. As of 2012, there were 270 pumped storage plants operating or under construction around the globe, with a combined generating capacity of 127 GW [5]. Even though a majority of new plants are currently adopting adjustable-speed technology [6], 119 of these 127 GW are fixed speed. This raises interest in the conversion of fixed-speed plants to adjustable speed. Two retrofitting options are typically considered [7]: the conversion of the electric machine to a doubly-fed asynchronous machine (DFAM), through the replacement of the rotor with a wound rotor that is fed from a frequency converter; or the installation of a full-power frequency converter to feed the synchronous machine with a controlled frequency. 1

7 CHAPTER 1. INTRODUCTION 2 DFAMs have the advantage of requiring a lower converter rating, in the order of 10% of the rating of a full converter, which results in lower converter cost and less conversion losses. The main disadvantage of a DFAM is the higher cost, lower reliability and decreased efficiency of the machine. With either solution, the overall cost and efficiency is case-dependent. Nevertheless, a full converter is generally preferred for units of up to 100 MW, and a rotor replacement is preferred for larger units [8]. Worldwide experience in upgrading existing pumped storage plants to adjustable speed through a rotor replacement includes two 320 MVA units of the Okutataragi plant in Japan [9] and one 270 MVA unit at the Le Cheylas pumped storage plant [10]. Both these projects are scheduled for completion in The approach of installing a full-power frequency converter was chosen at the Grimsel 2 pumped storage plant in Switzerland, where one 100 MVA unit was retrofitted in A third alternative would be possible in the case of plants being connected to an HVDC line, by the use of a converter station capable of controlling the electrical frequency supplied to the motor-generator. This solution has been proposed in the context of a research project that studies the expansion of power transmission capacity in Switzerland through the conversion of existing overhead transmission lines to hybrid HVAC/HVDC 1. While it might be possible to adopt any of these adjustable-speed solutions with minimal changes to other powerhouse equipment, the upgrade costs must still be justified by increased revenue from energy and ancillary service sales. In one study, done for a single-unit pumped storage plant in Spain, electricity market income increased by 25 30% [11]. A similar analysis done for a Portuguese adjustable-speed plant estimated that participating in the spinning reserve market could double revenue [12]. Another Portuguese study indicated that revenue-maximizing operations will lead to almost exclusive reliance on spinning reserve sales, with electricity sales in the day-ahead market resulting in a net loss [13]. For a fixed-speed plant, one Swiss case study estimates that selling ancillary services increases profit by only 1-2% [14]. These results demonstrate that the business case for building an adjustable-speed plant will depend largely on ancillary service revenue, especially when compared to fixed-speed operations. 1.2 Thesis Objectives The goal of this thesis is to estimate the potential impact on energy and reserve market revenues from retrofitting an existing pumped storage plant with adjustable-speed technology by performing a test case on a Swiss pumped 1 Hybrid Overhead Power Lines project, which is part of the Energiewende program of the Swiss National Science Foundation. Further information can be found at

8 CHAPTER 1. INTRODUCTION 3 storage plant. Four pumped storage equipment configurations, shown in Fig. 1.1, are considered: 1. Fixed speed (base case) 2. Synchronous machine with a full-power back-to-back frequency converter. 3. Doubly-fed asynchronous machine. 4. Synchronous machine connected to an HVDC converter station with frequency control capability. Each of these configurations has unique pump-turbine production curves and operating ranges that affect the market strategy and revenue. The market operation during the hydrological year is simulated for the Grimsel 2 pumped storage plant, located in the Berner Oberland region of Switzerland. The different unit configuration alternatives are modeled, and the revenue potential of each plant configuration is compared to that of the base case. The model proposed in this thesis considers participation in the dayahead energy and week-ahead secondary and tertiary reserve markets in Switzerland. For modeling purposes, day-ahead markets for tertiary reserve are not directly considered; rather, these trades are incorporated into the simulated week-ahead tertiary reserve market using average volumes and prices. Primary reserve sales are neglected because the available spinning capacity is offered for secondary regulation, which for the period under study results in a higher expected revenue. Grimsel 2 is modeled as an energy price taker, but market depth is considered in the lower volume week-ahead reserve markets. Since equipment costs are confidential and unique to each hydropower installation, this thesis does not analyze costs. Instead, it emphasizes an accurate estimation of the potential revenue and operational benefits of each plant configuration. The specific contribution of this thesis is a method for the evaluation of the multi-market revenue of fixed and adjustable-speed pumped storage plant configurations. While the multi-market simulation method developed draws on the existing literature, it makes several improvements, including modeling a plant with multiple units, and simultaneously offering both spinning and non-spinning reserves. 1.3 Grimsel 2 Pumped Storage Plant Grimsel 2 is part of a large hydroelectric complex owned by Kraftwerke Oberhasli (KWO). Technical specifications and historical operation data of

9 CHAPTER 1. INTRODUCTION 4 Conventional (Fixed Speed) Pump/ Turbine SM Motor/ Generator Full Back-To-Back Frequency Converter Transformer AC Transmission Line SM Frequency Converter AC Transmission Line Doubly-Fed Asynchronous Machine DFAM AC Transmission Line HVDC SM Converter Station HVDC Transmission Line Figure 1.1: Sketch of a conventional pumped storage plant drive, and of the adjustable-speed equipment configurations covered in this thesis. Grimsel 2 were provided by KWO for this study. A list of the data supplied by KWO can be found in Appendix A. The plant has four pump-turbine units, each with an independent pump and turbine connected to a common shaft. The components and layout of each unit are depicted in Fig The rated generation capacity of Grimsel 2 is 348 MW, with a total discharge capacity of 93 m 3 /s. The maximum power consumption in fixed-speed pump mode is 363 MW, with a total pumping capacity of 80 m 3 /s [15]. The upper and lower reservoir of Grimsel 2 are Lake Oberaar and Lake Grimsel, respectively. The head difference between the two reservoirs ranges between 350 and 410 meters. In 2008, Unit 1 of Grimsel 2 was retrofitted with a full-power frequency converter, enabling adjustable-speed operation in pump mode. The pumping capacity of Unit 1 increased with an adjustable-speed operation, and a continuous pumping range between 67.5 MW and 100 MW was achieved. The adjustable-speed operation of the turbine would not compensate the converter losses, and therefore in turbine mode the frequency converter of Unit 1 is bypassed and the generator is operated at fixed speed.

10 CHAPTER 1. INTRODUCTION 5 1. High pressure shaft (to upper reservoir) 2. Low pressure shaft (to lower reservoir) 3. Manifold 4. Butterfly valves 5. Spherical valves 6. Francis turbine 7. Francis pump 8. Synchronous motor/generator Figure 1.2: Layout of a unit within Grimsel 2, including pump, turbine and generator (Source: [16]).

11 Chapter 2 Swiss Electricity Markets This chapter reviews Swiss energy and reserve electricity markets. Details can be found in [17], [18], [19], [20] and [21]. 2.1 Energy-only Markets Four main energy markets exist for Switzerland. 1. Derivative Market 2. Day-ahead Spot Market 3. Intra-day Spot Market 4. Balancing Market Fig. 2.1 summarizes the sequential operation of these markets and their classification according to the time scope and purpose of the products traded in them. DERIVATIVE MARKET DAY-AHEAD MARKET INTRADAY MARKET BALANCING MARKET Control exposure to price risk for future demand/supply Match production with consumption Match production with consumption System security Long and mid-term, years to weeks Short-term, one day in advance Very short-term, hours in advance Real-time Figure 2.1: Sequential operation, main purpose, and timing of the energyonly electricity markets. Adapted from [22]. 6

12 CHAPTER 2. SWISS ELECTRICITY MARKETS Derivatives Market Derivatives are financial instruments whose values are based on the value of an underlying asset. The Swiss energy derivatives market is operated by the European Energy Exchange (EEX). The products available in this market include futures, for the agreement of a mutually binding underlying energy asset price; options, where only one of the parties is obliged to fulfill the transaction; and location spreads, where the underlying is the spread between energy futures prices in two regions. Long- (anual) and mid-term (monthly) futures contracts are traded for Switzerland. The underlying products of futures contracts are products traded on the European Power Exchange (EPEX SPOT) market. Derivative contracts are settled and the financial exchange between parties occurs once the prices of the underlying products are available; that is, once the underlying products have been traded at EPEX SPOT Spot Markets The energy spot markets allow participants with energy surplus and shortage to trade their position. Both the day-ahead and the intra-day spot markets are organized by EPEX SPOT. For Switzerland, these markets represent a volume equal to 40% of the national consumption. Day-ahead spot market: The day-ahead spot market is a blind auction with hourly bids. It allows block orders, which link several hours. The market is cleared the day before delivery at 11:00 am. The price index for this market is known as SwissIX. Intra-day spot market: The intra-day spot market is a continuous trading market with hourly and 15-minute resolution. It opens the previous day at 15:00 and ends 45 minutes before delivery. This market is mainly used to balance outages and forecast errors. Since the traded volume is only about 10% of that traded in the day-ahead spot market, prices are relatively volatile Balancing Market In order to explain the balancing market it is first necessary to introduce balance groups, which are a key structure in the Swiss Electricity Market. A balance group is a virtual entity that combines consumers and generators in one group for billing purposes. The production and consumption from every generator and load in Switzerland is assigned to a specific balance group at the transmission level. There are approximately 130 balance groups in Switzerland.

13 CHAPTER 2. SWISS ELECTRICITY MARKETS 8 The transmission system operator, Swissgrid, receives a daily schedule from each balance group the day before delivery. The schedules considers all over-the-counter and spot market agreements the balance groups have. Balance groups may adjustments their schedules with 15 (45) minutes lead time for national (international) exchanges, and also ex-post. Swissgrid verifies that the schedules of the different balance groups match, and there is no scheduled surplus or deficit. After ex-post adjustments, Swissgrid calculates the deviations of the balance groups from their schedules. The remaining excess in realized consumption (generation) must be purchased (sold) by each balance group from Swissgrid in the balancing market. Swissgrid establishes regulating power and energy markets to make certain that there is available capacity to cover deviations, and supplies energy for the balancing market from these reserve markets. The cost of energy in the balancing markets depends on whether reserve energy from the secondary or tertiary control reserve markets, introduced in Section 2.2, was required: Excessive consumption or shortfall in generation are charged: 1.1 [max { SwissIX, λ SCRE+, λ TCRE+} + 10 e /MWh], (2.1) where SwissIX is the hourly spot price and λ SCRE+ and λ TCRE+ are the prices for positive secondary and tertiary reserve energy, if positive secondary or tertiary reserve was activated. Excessive generation or shortfall in consumption are paid: 0.9 [min { SwissIX, λ SCRE, λ TCRE } 5 e /MWh], (2.2) where λ SCRE and λ TCRE are the prices for negative secondary and tertiary reserve energy, if negative secondary or tertiary reserve was activated. 2.2 Operating Reserve For the real time operation of the power system, the availability of standby power capacity is required to compensate for deviations from scheduled generation and consumption. This reserve capacity must be capable of reacting within a certain time frame. The requirements in this respect determine three different types of reserve in Switzerland: 1. Primary control reserve, also referred to as frequency containment reserve. It is contracted as a symmetrical power product and implemented as an automatic frequency droop in a ±200 mhz band; that is, the total contracted capacity must be provided if the grid frequency deviation is of ±200 mhz or larger. Response is required within 15

14 CHAPTER 2. SWISS ELECTRICITY MARKETS 9 seconds. Primary reserve is activated throughout the continental European synchronized grid, independent of the location of the frequency disruption. 2. Secondary control reserve, also referred to as frequency restoration reserve or spinning reserve. It is a symmetrical product. Secondary reserve is automatically dispatched by Swissgrid on online power, with dispatch proportional to contracted capacity. It is activated within seconds of the triggering event and requires response within 5 minutes. Secondary reserve gives way to tertiary if the disturbance persists beyond 15 minutes. 3. Tertiary control reserve, also referred to as replacement reserve, or non-spinning reserve. It is activated for the full contracted capacity and requires response within 15 minutes. This allows enough time for generators to provide tertiary reserve even if they are offline. Swissgrid dispatches tertiary reserve by or phone call. Dispatch is by merit order of energy price; that is, units with cheapest energy are dispatched until completing the required power. Power [MW] Primary Secondary Online (spinning) Large power plant outage occurs Tertiary Spinning or non-spinning Time [minutes] Figure 2.2: Primary, secondary and tertiary control reserve response after the outage of a large power plant. Typical deployment times and total contracted volumes are depicted. Adapted from [18] Markets for Reserve Capacity Swissgrid solicits competitive tenders for primary, secondary and tertiary control reserve and awards capacity on a merit-order base. The main characteristics of these tenders are detailed in Table 2.1. In order to participate a bid must be submitted, which is composed of combinations of power quantity and price per MW (e/mw for primary, and CHF/MW for secondary and tertiary). Swissgrid encourages participants to enter bids with as many combinations as possible. The power-quantity-and-price combinations in a bid are monotonically non-decreasing with resolution of 1 MW. Swissgrid

15 CHAPTER 2. SWISS ELECTRICITY MARKETS 10 Primary Power Secondary Power Tertiary Power Week-Ahead tender Day-Ahead tender Product type Symmetric Symmetric Separate positive and negative products Typical demand 74 MW MW between daily and weekly on average the total is +400 MW/-200 MW Contract length 1 week 1 week 1 week 4 hours Payment pay-as-bid pay-as-bid pay-as-bid pay-as-bid Minimum bid 1 MW 5 MW 5 MW Maximum bid 25 MW 50 MW 100 MW Gate closure week-ahead week-ahead week-ahead 2 days-ahead Tuesday 15:00 Tuesday 13:00 Tuesday 13:00 14:30 Table 2.1: Overview of Swiss reserve markets. Adapted from [17]. clears at most one combination from a bid. An example bid is shown in Fig Price [CHF/(MW)] Combination selected by Swissgrid No combinations offered for some power levels Quantity [MW] Figure 2.3: Example bid for positive tertiary reserve Compensation for Activation of Reserve The compensation for reserve energy activated by Swissgrid varies among the different products; Primary reserve energy use is not compensated. Secondary reserve positive (negative) energy is averaged over 15-minute periods and paid (charged) for with a price indexed to the hourly SwissIX spot price 2 : Positive secondary reserve energy is remunerated with the maximum between 1 Supplied in a combined auction between Austria, Germany, the Netherlands and Switzerland with a total volume of 800 MW, though transmission limits exist to the provision from each country. A share of 74 MW is required from Swissgrid. 2 In the case of negative SwissIX prices, the margins are reversed, i.e., positive (negative) energy delivery receives the hourly price with a margin of -20% (20%).

16 CHAPTER 2. SWISS ELECTRICITY MARKETS 11 the weekly base price and 1.2 times the hourly SwissIX spot price. Negative secondary reserve energy is charged with the minimum between the weekly base price and 0.8 times the hourly SwissIX spot price. For tertiary reserve, providers must submit energy price offers for the complete period (day or week), in 4-hour blocks. Prices can be modified up to one hour before the start of each 4-hour period. Dispatch of tertiary reserve capacity is determined by merit order auctions. Positive tertiary reserve energy is sold to Swissgrid and negative reserve energy is purchased from Swissgrid. Interestingly, negative tertiary reserve energy has, on average, a negative price, meaning Swissgrid actually pays reserve providers to consume additional energy.

17 Chapter 3 Literature Review A summary of the main related work on the market simulation of pumped storage power plants is given in this chapter. The goal is to understand the simulation frameworks commonly used for the multi-market operation of a pumped storage plant. A complete review of scheduling models for optimizing the market operation of pumped storage power plants can be found in [2]. [23] studies a fixed-speed pumped storage cascaded plant participating as a price taker in the German day-ahead and intraday energy markets. The plant does not offer ancillary services. Four grid generation capacity expansion scenarios are considered (base, high penetration of renewable energy sources, high storage capacity and high energy efficiency) to construct dayahead market price scenarios. A multiple linear regression model is developed from historical data for the simulation of the intra-day market based on dayahead market prices and the amount of generation from renewable energy sources. The model accounts for the clearing sequence of the day-ahead and intra-day markets. This way, the decision for the day-ahead market is made for all the hours of the day in one step, whereas the decision for the intra-day market takes place for each hour sequentially, knowing the actual intra-day prices and decisions made in previous hours. At each stage a revenue-to-go function is calculated for a set of discrete reservoir levels, which is used to calculate the previous stage revenue-to-go functions, and the solution procedure advances backwards. The upper reservoir is assumed to be at its lowest level at the beginning and at the end of the one-year simulation period. [11] assesses the participation of a closed loop adjustable-speed pumped storage plant in the Spanish day-ahead energy and secondary reserve markets. A calculation of maximum theoretical revenue is performed, assuming perfect knowledge of market prices and secondary reserve activation. A two-year period is simulated, imposing that the water level of the reservoirs is the same at the end of each day. The model uses historical energy and secondary reserve prices, and historical secondary reserve activation. The authors 12

18 CHAPTER 3. LITERATURE REVIEW 13 Four 35-year day-ahead price scenarios evaluated independently, 1 year at a time Deterministic Inflows 2 intra-day price scenarios, each hour disclosed sequentially Day-Ahead Optimization 24 hours at a time, starting at the end of the year Day-Ahead commitment for ten discrete total-discharge levels Intra-Day Optimization 1 hour at a time, from the beginning of the day Revenue-to-go function for 12 reservoir levels, with all scenarios taken as equiprobable Figure 3.1: Diagram of the simulation method proposed in [23]. compare different flow regulation capacities in pumping mode. Adjustablespeed operation in generating mode is not considered. Results show that an adjustable-speed drive increased total energy and ancillary service income for a pumped storage plant by approximately 30%. A similar study for the Portuguese market concludes that revenue-maximizing operation of an adjustable-speed plant leads to almost exclusive reliance on ancillary services sales, with electricity sales in the energy market actually resulting in a net loss [13]. Initial and final reservoir level each day (always the same) 2 years of day-ahead and secondary reserve prices, and secondary energy usage Day-Ahead Energy & Secondary Reserve Optimization 730 days Each day is optimized independently Total Revenue Figure 3.2: Diagram of the simulation method proposed in [11]. Building on [11], [12] studies an adjustable-speed pumped storage plant in Portugal. In this publication a bidding strategy is developed for participation in day-ahead energy and secondary reserve markets. Using this strategy, the authors compare market revenue from an adjustable-speed plant with a fixedspeed plant that does not provide secondary reserve. Forecasts of natural water inflows and energy and secondary reserve prices are used. The model they propose is divided into three modules: Mid-term Optimization: This module allocates the water from natural inflows considering a one year time horizon. It uses weekly forecasts for the average market price and natural water inflows. The initial and final level of the reservoir are set at the middle level. Outcome is the optimal weekly reservoir level for the entire year for each scenario. The average of all scenarios for the reservoir level at the end of the

19 CHAPTER 3. LITERATURE REVIEW 14 first week is then used to define the reservoir level at the end of the short-term optimization. Short Term Optimization: This module maximizes revenue from energy and secondary reserve markets for a period of one week (168 hours). It uses forecasts for natural water inflows and for energy and secondary reserve prices. Only capacity (not activation) revenue for secondary reserve is represented in the objective function, but a portion of the reservoir is allocated for the purpose of secondary reserve activation. The first 24 hours of the short term optimization are used for bidding. Evaluation Module: This module calculates the revenue from energy and secondary reserve markets and the revenue from secondary reserve activation. It uses real data for energy and reserve market prices, reserve activation, and inflows. The activation is taken from the ratio between total system-wide activation and available secondary reserve capacity. The reservoir level is updated using the information of inflows and activation of secondary reserve. The end-of-day reservoir level obtained from the evaluation module is used as the initial state for the following day in the mid-term model. Weekly average day-ahead energy price forecast Weekly sum of water inflows Day-Ahead and secondary reserve price forecasts Water inflows forecast Realized values - Day-Ahead energy prices - Secondary reserve prices - Water inflows - Secondary reserve activation Reservoir initial and final state (mid-level) Medium Term Optimization Reservoir level at the end of the first week Short Term Optimization Market Bids Operational Setpoints Evaluation Revenue 52 Weeks (1 year) 168 hours (1 week) 24 hours End-of-day reservoir level Figure 3.3: Diagram of the simulation method proposed in [12]. Diagram adapted from the original publication. The study in [12] concludes that upgrading to adjustable speed could double revenue, mainly from increased spinning reserve sales. For comparison, [14] assesses the operation of a fixed-speed pumped storage plant in the Swiss day-ahead energy and week-ahead secondary reserve markets. The simulation method determines the end-of-week revenue-to-go at each reservoir level recursively using weekly time steps from the end of the time horizon to the beginning, taking empty basins as the initial and final border conditions. For each week a two stage algorithm is proposed: in stage one, the price and amount of secondary reserve to offer for the week is decided by maximizing the expected profit over the secondary reserve and energy market price scenarios; in the second stage the algorithm optimally

20 CHAPTER 3. LITERATURE REVIEW 15 produces electricity and pumps water, using the then known deterministic prices. Results show that for a fixed-speed plant the consideration of secondary reserve has a small impact on revenues, in the order of 1-2%. Deterministic inflows 8 secondary reserve power scenarios 5 secondary reserve price scenarios 2 to 3 day-ahead energy price scenarios Realized values - Day-Ahead energy prices - Secondary reserve prices Revenue-to-go Calculation From end of horizon, weekly time steps Weekly secondary power Water value 1 week Day-Ahead Optimization Initial reservoir level for next week Figure 3.4: Diagram of the simulation method proposed in [14]. This thesis draws on the work in the literature and adds two contributions by modeling (1) a plant with multiple units that (2) simultaneously offers spinning and non-spinning reserve.

21 Chapter 4 Simulation Procedure This chapter describes the plant simulation procedure. It begins with a general overview and then dedicates a section to each stage that composes the simulation procedure. Figure 4.1: Weekly procedure for the multi-market simulation. 4.1 Overview of the Simulation Procedure The simulation model considers plant participation in the week-ahead secondary and tertiary reserve markets and in the day-ahead energy market. The sequential structure of the procedure is illustrated in Fig The simulation of each week begins with a week-ahead reserve planning procedure that calculates bid curves for each reserve market. Then, a reserve market clearing procedure determines the cleared quantities from the reserve bid curves using historical reserve market conditions. A week-ahead planning procedure uses the awarded reserve computed in the previous step and plans the water use in the energy market throughout the week assuming that a certain fraction of reserve will be activated. Finally, the day-ahead 16

22 CHAPTER 4. SIMULATION PROCEDURE 17 planning module calculates the participation in the energy market for each day and the activation of reserve. The total revenue of the plant is the sum of the pay-as-bid revenue from reserve sales, the energy market revenue, and the reserve activation revenue. Fig. 4.2 shows a summary of the input data and output variables of the different stages. These stages use two mixed-integer linear optimizations programs: a deterministic plant optimization model, that optimizes the operation in the energy market, given certain reserve obligations, and a stochastic bid curve optimization that uses the opportunity cost of providing reserve to optimize the reserve bid curves over a set of reserve price scenarios. 4.2 Week-Ahead Reserve Planning The week-ahead reserve planning routine computes bid curves for secondary, positive tertiary and negative tertiary reserve. Construction of the bid curves is a two-step process. First, it calculates the opportunity cost of providing secondary, positive tertiary and negative tertiary reserve. Second, it uses those opportunity costs in a stochastic optimization to compute optimal bid curves Opportunity Cost of Providing Reserve The first step in the week-ahead ancillary service planning is to estimate the opportunity cost of providing reserve. This is done by running a set of simulations to calculate the energy market revenue of the plant for different awarded reserve quantities. For each secondary, positive tertiary and negative tertiary reserve combination a deterministic plant optimization is performed. The results of those optimizations describe how the energy market profit varies with the level of secondary, positive tertiary, and negative tertiary reserve. A linear regression of the results gives coefficients that represent the marginal opportunity cost of providing secondary, positive tertiary, and negative tertiary reserve. The method is summarized in Fig Appendix B includes a list of the permutations of reserve capacity that are tested to calculate the cost of providing reserve. An example of the reserve-capacityto-energy-market-revenue function and its linear approximation is shown in Fig. 4.4 for two different levels of secondary reserve. The deterministic plant optimization allocates an amount of water for the activation of reserve that is proportional to the awarded reserve, assuming expected energy requirement. It calculates the reserve energy requirement from an average historical activation of reserve as a fraction of the contracted reserve capacity (7% for positive secondary reserve, 6% for negative secondary, 4% for positive tertiary, and 8% for negative tertiary). For example, if the plant provides 100 MW of positive tertiary reserve, the expected energy for

23 CHAPTER 4. SIMULATION PROCEDURE 18 Model Inputs H Historical values (2014/2015) S Stochastic variables (scenarios from 2013/2014) F Deterministic forecasts (historical average values) H - Reservoir end of week target level - Net hourly water inflows - Day-Ahead and secondary energy prices S F - Secondary and tertiary power clearing prices - Secondary and tertiary activation - Tertiary energy prices Week-Ahead Reserve Planning Reserve bid curves H - Secondary and tertiary power demand curves Reserve Market Clearing Revenue from reserve availability Awarded reserve capacities H - Secondary energy prices F H - Secondary and tertiary activation - Tertiary energy prices - Daily total secondary and tertiary energy demand - Daily average secondary and tertiary energy prices Week-Ahead Planning Day-Ahead Planning x 7 Daily reservoir volumes for participation in the day-ahead market Revenue from the energy market and reserve activation Initial reservoir levels for the following week Figure 4.2: Diagram of the multistage optimization procedure displaying the input data and output variables from each stage.

24 CHAPTER 4. SIMULATION PROCEDURE 19 π π Figure 4.3: Calculation of opportunity cost of providing reserve. positive tertiary reserve activation is 4% 100 MW 168 h = 672 MWh, which can be converted to an equivalent water volume. In Fig. 4.4, the cost of providing negative tertiary reserve is low compared to positive tertiary. This is because the activation of negative tertiary reserve implies having additional available water that may be sold in the energy market. Before each execution of the deterministic plant optimization, the program tests whether the plant fulfills the reserve obligations with a total plant consumption of at least the minimum pumping power of one unit. This removes cases in which it is not possible to pump water; and empirically predicts most infeasible cases. Nevertheless, some cases with maximum secondary reserve (50 MW) do not reach a solution within the time limit and are treated as infeasible. The program avoids producing bid curves that could result in infeasible combination of reserve capacity by limiting the capacity offered in the least profitable reserve market. It calculated the limits after running the set of reserve capacity permutations. The limit for the least profitable reserve product is the maximum capacity that is feasible with any combination of the remaining two reserve types. The least profitable reserve market is the one with the lowest expected net revenue per MW. For the test case, secondary reserve is the least profitable.

25 CHAPTER 4. SIMULATION PROCEDURE 20 Figure 4.4: Energy market revenue as a function of positive (TCR + ) and negative (TCR ) tertiary reserve capacity, for a configuration with four adjustable-speed units. Secondary reserve capacity is 0 MW (left) and 10 MW (right). The meshed surface is the linear regression fit to the underlying surface shown in grey Stochastic Bid Curve Optimization The second step in the week-ahead ancillary service planning is a bid curve optimization. This is a stochastic optimization program which constructs bid curves that maximize the average revenue over a set of reserve price scenarios. Reserve price scenarios are taken from historical prices from the year immediately prior to the simulation year. The bid curve optimization model formulation is detailed in Chapter Reserve Market Clearing The reserve market clearing routine uses the historical demand curves provided by Swissgrid. Swissgrid clears at most one capacity/price combination from each bid and remunerates it pay-as-bid, as shown in Fig Week-Ahead Planning The week-ahead planning optimizes plant operations considering awarded secondary and tertiary reserve quantities. It uses the deterministic plant optimization model with the same assumptions for activation of reserve as the week-ahead ancillary service planning. The result of this stage allocates the available water volume to each day of the week, in such a way that energy market revenue is maximized.

26 CHAPTER 4. SIMULATION PROCEDURE 21 Figure 4.5: Clearing of reserve bids. 4.5 Day-Ahead Planning The day-ahead planning simulates the actual participation of the plant in the energy market. It computes reservoir elevations, reserve deployment, pump-turbine utilization, and revenue based on scheduled generation and reserve capacity obligations. This is done with the deterministic plant optimization model adapted to a day-ahead planning horizon, with appropriate reservoir initial and target levels. The diagram in Fig. 4.6 depicts how the daily water volumes and the volume required for reserve activation are considered. The volume at the beginning of each day is the final volume of the previous day minus the volume required the previous day for reserve activations. The day-ahead planning estimates the plant s activation of reserve from the ratio of total daily reserve activation over total cleared capacity in Switzerland. For example, if a certain day 10 MWh were activated from a total system-wide available capacity of 100 MW, this ratio is 0.1 MWh of activation energy for each MW of reserve capacity. The end-of-week reservoir levels are slightly different from the target levels by the error in the reserve activation forecast of the week-ahead planning. This implies that reservoir volumes at the end of the complete year of simulation are not equal among the different scenarios due to the forecast error in the last week. Historical activation of reserve in the last week is 9.4% for positive secondary, 3.8% for negative secondary, 3.0% for positive tertiary, and 1.4% for negative tertiary. The percentage point difference between the forecast and the historical activation is -2.4% for positive sec-

27 CHAPTER 4. SIMULATION PROCEDURE 22 Initial volume Day 1 Day 2 Day 3 Day 7 Weekly simulation Upper Reservoir Volume [m³] Actual reserve energy water volume use on day 1 Actual use on day 2 V DA Day 3 V DA Day 3 Volume available for the energy market Daily simulation Estimated water volume use for reserve activation (week-ahead planning) Historical final volume (target) Final upper reservoir volume (initial volume for the next week) Figure 4.6: Water volume allocation considering reserve activation. ondary, 2.2% for negative secondary, 1.0% for positive tertiary, and 6.6% for negative tertiary. This results in scenarios with higher awarded reserve having a lower final upper reservoir volume. The maximum difference is between a scenario with no awarded reserve and a scenario with maximum awarded reserve. In the first case the final reservoir level is equal to the historical level. In the case with maximum awarded reserve (50 MW secondary reserve, 100 MW positive tertiary and 100 MW negative tertiary), the forecast error is 168 (( 2.4% 2.2%) % % 100) = 1327 MWh. The average energy price of the last week is 47.1 CHF/MWh. An approximate value in the energy market of the maximum forecast error is = CHF. This value represents 0.2% of the total revenue for a scenario with five units, where maximum reserve capacity is offered. A lower error as percentage of total revenue is obtained in the scenarios with four units. No measure is taken to compensate for this error. The accuracy of the plant model in the day-ahead planning is higher than that of the week-ahead planning, as the unit characteristics are calculated for the daily average head level instead of the weekly average head level. Plots of the weekly and daily variation of head level are shown in Appendix D.

28 Chapter 5 Optimization Problem Formulation This chapter gives the mathematical formulation of the two mixed-integer linear programs used in the simulation procedure: the deterministic optimization of the participation of the plant in the energy market, and the stochastic optimization of the reserve market bid curves. 5.1 Deterministic Plant Optimization The deterministic plant optimization model calculates the profit maximizing strategy in the energy market considering reserve obligations. It assumes that the plant is a price taker. The problem is formulated as a mixed-integer linear program, with the objective max p E s K [ λ E (k) p E s (k) ]. (5.1) k=1 where p E (k) is the power generation (if positive) or consumption (if negative) of the plant in hour k, and λ E (k) is the energy price in hour k. The length of the optimization period is denoted by K. Hence, K is equal to 168 and 24 for week-ahead and day-ahead planning, respectively. The objective function is subject to the following constraints. Non-simultaneous pump and turbine operation. When turbine j is online (u j = 1) in hour k, pump j must be offline (y j = 0). The inverse is also true. If u j and y j are binary variables, this constraint can be written as u j (k) + y j (k) 1. (5.2) Minimum offline time. The plant requires a changeover time of minutes when switching from pump to turbine mode or viceversa. Although changeover time for an adjustable-speed unit is lower, 23

29 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 24 it does not meet the 10-minute limit allowed in Switzerland for ramping changes in scheduled generation [24]. In order to make sure the ramping limit is met, it is necessary to leave a one-hour period of no generation when changing between modes [25]. During the one-hour changeover period neither the pump nor turbine is online. Mathematically, u j (k) + y j (k + 1) 1 j, k [2..169] (5.3a) y j (k) + u j (k + 1) 1 j, k [2..169]. (5.3b) Power limits. Pump consumption p pump j (k) and turbine generation p turbine j (k) are constrained by minimum and maximum power limits. Mathematically, u j (k) p min,turbine j p turbine j (k) u j (k) p max,turbine j j, k (5.4a) y j (k) p min,pump j p pump j (k) y j (k) p max,pump j j, k. (5.4b) Power production. Power production is the sum of pump consumption and turbine generation. Mathematically, p E (k) = J [ j=1 p turbine j ] (k) p pump j (k). (5.5) Water balance. Hydraulic coupling between the upper and lower reservoirs is modeled considering natural inflows w(k), power production, and reservoir storage v(k). Power-to-discharge functions for the pump and turbine, denoted by Q pump j and Q turbine j, model the volume of water that is pumped or turbined for a given amount of load or generation. Dynamic head effects are not considered, and initial reservoir storages are fixed. Water balance equations are similar for both reservoirs. For the upper reservoir, the water balance equation is v upper (k + 1) = v upper (k) + w upper (k) J ( ) J Q turbine j p turbine j (k) + j=1 j=1 ( Q pump j p pump j ) (k). (5.6) Details on the implementation of the pump and turbine discharge functions can be found in Chapter 6. Q turbine j is formulated as a piecewise linear function [26] and Q pump j is a linear function. The deterministic plant optimization problem considers the pump and turbine discharge functions assuming an average expected head.

30 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 25 Storage limits. Both reservoirs must operate between their minimum and maximum elevations. Mathematically, v min,upper v upper (k) v max,upper v min,lower v lower (k) v max,lower (5.7a) (5.7b) End-of-period reservoir storage. For week-ahead planning, endof-week upper reservoir storage v target cannot be lower than it was historically. Ancillary service water consumption is incorporated into this constraint by assuming that a certain fraction of reserve capacity will be activated. These water volumes are given by v SCR, v TCR+, and v TCR- for secondary, positive tertiary, and negative tertiary reserve, respectively, and are computed from historical data of reserve activation for a particular week or day. For day-ahead planning, v target is an output of the week-ahead optimization adjusted for actual reserve activations. The end-of-period reservoir storage constraint can be written as v target v upper (K + 1) v SCR v TCR+ + v TCR-. (5.8) Priority commitment. If units are identical, the optimization problem will have multiple solutions since unique unit schedules with the same number of online pumps and turbines will have equivalent water consumption and power production. To mitigate this, priority constraints set the order in which pumps and turbines are scheduled. They are only imposed in scenarios were all units are of one type, either fixed or adjustable speed. For a plant with J identical units, this constraint is written u j 1 (k) u j (k) 0 j 2, 3... J (5.9a) y j (k) y j 1 (k) 0 j 2, 3... J. (5.9b) Spinning reserve. Available positive and negative spinning reserve must be greater than or equal to the secondary reserve obligation p SCR. Mathematically, p SCR p SCR J j=1 + J [ j=1 + [ u j (k) p max,turbine j J [ j=1 p turbine j J j=1 p pump j ] p turbine j (k) ] (k) y j (k) p min,pump j ] (k) u j (k) p min,turbine j [ y j (k) p max,pump j ] p pump j (k) (5.10a) (5.10b)

31 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 26 Feasible regions. When tertiary reserve is activated, the new operating point (either p E (k) + p TCR+ or p E (k) p TCR- ) must have sufficient spinning reserve to meet the secondary reserve obligation. Feasible operating regions that fulfill this condition are calculated during preprocessing with fixed reserve obligations. The constraint that restricts operation to within these regions is, L l=1 [ zl p min ] l p E (k) L l=1 [z l p max l ] and L z l = 1 (5.11) where p max l and p min l bound region l. The binary variable z l determines which feasible region is active. Fig. 5.1 illustrates this constraint. In the example, the plant is generating 150 MW, and it has ±40 MW of secondary and ±100 MW of tertiary reserve obligations. Regardless of whether or not tertiary reserve has been activated, the plant must provide 40 MW of spinning reserve. Hence, it should have 40 MW of spinning reserve available when operating at 150 MW, 250 MW (positive tertiary activated), Feasible and Operating 50 MW (negative Regions tertiary activated). In theplant figure, Configuration L = 3 and z 2 With = 1. 1 AS and 3 FS Units, Head = 400 m Example with: Energy: 150 MW SCR: ±40 MW TCR + : 100 MW TCR : 100 MW Turbines Online Pumps Online l=1 Range of power with specified units online Operating point (150 MW) Range for SCR (±40 MW) Operating point with TCR + activated (250 MW) Operating point with TCR activated (50 MW) Feasible operating regions with reserve constraints Plant Total Power Output [MW] Figure 5.1: Calculation of feasible operating regions with one adjustable-speed and three fixed-speed units. All combinations with units in pump mode are drawn assuming the adjustable-speed pump is used. The following procedure is used to determine the feasible regions:

32 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION Calculate the operating range of all possible combinations of online and offline units in pump and turbine mode. 2. Subtract the spinning (secondary) reserve requirement from both extremes of each operating range. 3. Calculate the intersection of the full set of operating ranges with the full set of operating ranges shifted to the right by the negative tertiary reserve obligation, and with the full set of operating ranges shifted to the left by the positive tertiary reserve obligation. In the example in Fig. 5.1, the output of this algorithm is the three narrow regions highlighted in red. The figure also depicts why the spinning reserve constraint (5.10) is not redundant. For instance, operating with two turbines online satisfies the feasible regions constraint but not the spinning reserve constraint. 5.2 Stochastic Bid Curve Optimization The stochastic bid curve optimization routine computes reserve bid curves for the pay-as-bid secondary, positive tertiary, and negative tertiary reserve auctions. It considers the cost of providing each reserve product. Since the cost factors are independent and the clearing prices for secondary, positive tertiary and negative tertiary reserve were assumed to be uncorrelated (see Appendix E), the bid curve for each reserve product is calculated separately. The optimization procedure accounts for how reserve capacity is cleared and remunerated, where at most one combination of quantity and price is awarded from each bid and revenue is pay-as-bid. The objective is to maximize expected net revenue from energy and reserve sales over a set of reserve auction cut-off price scenarios, mathematically, max π i p i { 1 S S s=1 i=1 I [ cis p i (π i β r λ )]} (5.12) where π i is the price and p i is the quantity of block i of the bid curve. In the inner sum, the binary variable c is is the commitment status for block i in scenario s, β is the cost factor for this reserve product, r is the average activation percentage for this reserve product (evaluated from historical data), and λ is the expected energy price for this reserve product. The total profit in scenario s is thus the revenue from providing reserve minus the opportunity cost of providing reserve (in terms of foregone energy market revenue) plus the revenue from Swissgrid activating the reserve. While the objective function specified in (5.12) is nonlinear, it can be simplified and solved with mixed-integer linear programming. In the linear formulation, the commitment status c is and the bid block quantity p i are

33 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 28 combined into one variable, and bid block prices π i are taken from a fixed set of discrete prices. The fixed set of prices for the bid blocks are the scenario cut-off prices. Any bid with prices different to the scenario cut-off prices will offer a lower expected revenue as a consequence of revenue being pay-as-bid. For example, if only one price scenario is considered and its cut-off price is higher than the net cost 1 of providing reserve, the optimum bid curve is a single bid block for the maximum quantity offered at the scenario cut-off price. A lower price gives a lower expected revenue (the pay-as-bid revenue decreases proportionally) and a higher price results in zero expected revenue (the bid is not awarded). Offering a quantity below the maximum would also reduce the expected revenue. Note that this behavior is because cost functions are linear; quadratic or nonlinear cost curves would not necessarily exhibit this behavior. The optimization program determines the quantity awarded in each scenario. The bid curve is derived from these quantities. This is possible because bid curves are specified for integer quantities, with monotonically non-decreasing prices. For example, assume there are two price scenarios, with 100 MW awarded in the higher-price scenario and 99 MW in the lowerprice scenario. These values represent the awarded quantities for a bid curve with two bid blocks: 100 MW offered at the cut-off price of the higher-priced scenario, and 99 MW offered at the lower price. If instead 100 MW are awarded in both scenarios, this means 100 MW is offered at the cut-off price of the lower-priced scenario. The linear formulation of the bid curve optimization problem for each reserve product (secondary, positive tertiary, or negative tertiary reserve) extends this logic to any number of scenarios, with the following input parameters, S Number of price scenarios λ(n) nth lowest scenario cut-off price, with n 1... S, [CHF/MW] where λ(1) is the lowest and λ(s) is the highest scenario price p max Maximum quantity that can be offered [MW] β Opportunity cost factor for the reserve product [CHF/MW] r Activation percentage for the reserve product % of reserve λ Expected energy price for the reserve product [CHF/MW] The problem variables are, 1 Opportunity cost of providing reserve minus revenue from reserve activation.

34 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 29 p(n) b(n) γbid block si ρbid block si Quantity awarded in scenario n, where p is an integer variable with p p max Binary variable that models which scenario prices and awarded quantities are offered as bid blocks. If b(n) = 1, the nth lowest cut-off price λ(n) defines a bid block together with the awarded quantity p(n) for scenario n Binary variable that models whether the bid block defined with the ith lowest cut-off price is awarded in the scenario with the sth lowest cut-off price, with s 1... S and i s Integer variable that models the quantity from the bid block defined with the ith lowest cut-off price that is awarded in the scenario with the sth lowest cut-off price, with s 1... S and i s [MW] [MW] The objective (5.12) reformulated with these variables is, { 1 S s [ max S bid block ρsi (λ(i) β r λ )]}. (5.13) s=1 i=1 Since scenarios are sorted by price, the total awarded quantity in each scenario is monotonically non-decreasing, that is, p(s 1) p(s) s 2... S (5.14) A bid block is implicitly defined for index i if the quantity p(i) awarded in the scenario with cut-off price λ(i) is higher than the quantity p(i 1) awarded in the scenario with the next lowest cut-off price λ(i 1). Therefore, the binary variable b(i) is only 1 if p(i) p(i 1). Mathematically, p(i) p(i 1) b(i) i 1... S (defining p(0) = 0) (5.15) Only valid combinations may be awarded. Mathematically, bid block b(i) γsi i s, s 1... S (5.16) with scenario index s 1... S identifying the scenario with cut-off price λ(s) and bid block index i identifying the quantity and price combination p(i) and λ(i). The quantity ρbid block si from bid block i awarded in the scenario with cut-off price λ(s) is the bid block quantity p(i) if the corresponding binary variable γbid block is 1. Mathematically, si bid block ρsi p max bid block γ si bid block bid block ρsi i s, s 1... S (5.17a) + p max γsi p(i) + p max i s, s 1... S (5.17b)

35 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 30 An additional constraint verifies that at most one combination is awarded in each scenario. Mathematically, s i=1 bid block γsi 1 s 1... S (5.18) Also, a constraint models the minimum bid block quantity of 5 MW. Mathematically, p(i) 5 b(i) i 1... S (5.19) For example, if this method is applied to the set of price scenarios {500, 510, 520, 530, 535}, that is, λ(1) = 500, λ(2) = 510, etc., with a net cost of β 168 r λ = 100 CHF/MW, and a maximum quantity of 100 MW, the solution is p(n) = { 97, 98, 99, 100, 100} b(n) = { 1, 1, 1, 1, 0} bid block index i γbid block si = scenario index s ρbid block si = bid block index i scenario index s where the dashes represent combinations for which the scenario cut-off price is below the bid block price. It is not necessary to include these combinations in the formulation, as they are never awarded. The value of the objective function is (i.e., the expected value of the revenue from reserve availability

36 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 31 and activation, minus the cost of providing reserve), 1 5 S s=1 i=1 s [ ] bid block ρsi (λ(i) 100) = 1 [97 ( ) ( ) 430] 5 = CHF The information contained in p(n), b(n), and λ(n) determines bid block combinations defined in 1 MW steps down from the maximum quantity. This corresponds to the upper portion of the bid curve. The curve is extended down to the minimum of 5 MW by offering the lower quantities at the price of the lowest-price bid block. The bid curve resulting from this example is shown in Fig Price [CHF/MW] Quantity [MW] 100 Figure 5.2: Example of reserve bid obtained from the optimization algorithm. The curve is extended down to the minimum of 5 MW at the price of the lowest-price bid block. The cut-off price scenarios are defined using reserve prices from the previous year (2013/2014), considering the maximum quantity the plant offers. The historical awarded bids are sorted by price and the cut-off price is set as the price of the most expensive bid for which the sum of awarded capacity of equal or higher price equals at least the maximum quantity offered by the plant. The result of this calculation is the maximum price at which the maximum quantity would be awarded. This step approximates market depth

37 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 32 and mitigates the risk of the bid being out-of-money. For example, if the maximum negative tertiary reserve quantity offered is 100 MW and Swissgrid procures 300 MW of negative tertiary reserve from four 75 MW bids of 5, 10, 15, and 20 CHF/MW, λ(s) is 15 CHF/MW. The bid quantity will only be smaller than the maximum bid size 2 in cases where the quantity offered in some of the reserve markets has been limited to avoid a combination of awarded capacity that is inviable for the plant. The price λ for positive secondary reserve energy in the bid curve optimization is assumed to be 120% of the average energy price, λ E. For negative secondary reserve energy it is assumed to be 80% of the average energy market price. Tertiary reserve energy prices are modeled as: Tertiary positive λ = 1.4 λ E [CHF/MWh] (5.20a) Tertiary negative λ = 1.2 λ E 80 [CHF/MWh] (5.20b) The value used for the average activation percentage r for positive secondary reserve is 7%, for negative secondary 6%, for positive tertiary 4% and for negative tertiary 8%. 5.3 Simulation Environment and Solution Time The algorithm was implemented in Matlab, using the CPLEX 12.2 solver called via the TOMLAB optimization interface. The simulations were executed on a computer server with two Intel Xeon X GHz processors and 96 GB of RAM. On this platform, the stochastic bid curve optimization is timed out after 1 minute. A solution within the allowed gap is usually reached before this time. In any case, the solution does not change significantly if execution continues beyond 1 minute. The deterministic plant optimization requires between 1 and 10 minutes, the latter in case of a large provision of reserve. A complete simulation for 51 weeks requires 12 to 24 hours of computer time. This is achieved by running the week-ahead set of permutations in parallel. It was necessary to adjust the solver s final gap in order to reach a solution in a reasonable time. The gap is the difference between the best integer objective and the non-integer objective of the best remaining node. The default setting of 0.01% is too demanding for this problem. In fact, the objective does not improve appreciably once a gap of 1% has been reached. This is consistent with what is reported in [27] and [28]. We set a tolerance of 0.5%, meaning that the optimization is stopped when the gap falls below this value. We also set time limits for the week-ahead planning problem for simulations with four units: 500 seconds for each deterministic plant 2 In Switzerland, the maximum possible bid size for secondary and tertiary reserve is 50 MW and 100 MW, respectively.

38 CHAPTER 5. OPTIMIZATION PROBLEM FORMULATION 33 optimization and 60 seconds for the stochastic bid curve optimization. In both cases solutions do not improve significantly beyond those times. For the deterministic optimization we observe that, after 500 seconds, either a reasonably good solution has been found or the problem is infeasible. When optimizing a plant with additional units, these time limits are adjusted accordingly.

39 Chapter 6 Plant Model The deterministic plant optimization problem models the following components: upper and lower reservoir, pump, turbine, and losses in the chosen electric machine and grid interface. This chapter explains the mathematical models for each component and how they differ for the different unit configurations. Grid Interface Upper Reservoir Generator/ Motor Pump Turbine Lower Reservoir Figure 6.1: Components of the plant model. 6.1 Reservoirs The deterministic plant optimization problem calculates average head from hourly reservoir levels. For week-ahead planning it uses historical reservoir levels; for day-ahead planning it uses reservoir levels calculated in the weekahead planning. Head is calculated using upper (Lake Oberaar) and lower (Lake Grimsel) reservoir volumes with volume-to-elevation curves. These curves are plotted in Fig. 6.2 and were provided by KWO. 34

40 CHAPTER 6. PLANT MODEL 35 Figure 6.2: Upper (Lake Oberaar) and lower (Lake Grimsel) reservoir storage curves. 6.2 Pump Model Separate models for fixed-speed and adjustable-speed pumps were derived using historical operation data from Unit 1 of the Grimsel 2 pumped storage plant. These models were used to determine pump power-to-discharge functions for the deterministic plant optimization Fixed-Speed Operation For fixed-speed operation, there is a clear linear relationship between head and power (and discharge). These dependencies are shown in Figs. 6.3 and 6.4, which plots one year of 15-minute data for one of the fixed-speed units. The hours in which Unit 1 was operated at fixed speed were used to derive the model. These hours are characterized by increased efficiency and constant power. Linear models for the fixed-speed power and discharge as a function of the head were then calculated, obtaining, p FS,pump = H d FS,pump = H (6.1a) (6.1b) with p FS,pump in MW, d FS,pump in m 3 /s, and H in meters. These linear functions translate to an efficiency in the range of 83% 85%.

41 CHAPTER 6. PLANT MODEL 36 Figure 6.3: Historical pump power to head data from Grimsel 2 for the operation of a fixed-speed unit (Unit 2). Figure 6.4: Historical pump discharge to head data from Grimsel 2 for the operation of a fixed-speed unit (Unit 2).

42 CHAPTER 6. PLANT MODEL Adjustable-Speed Operation The adjustable-speed pump model considers pump power-to-discharge curves and speed dependent power limits. Pump Power to Discharge The historical adjustable-speed operation data of Unit 1 shows that the pump efficiency is relatively stable and does not have clear power or head dependencies. This is shown in Appendix F. For the sake of simplicity and computational speed, a constant adjustable-speed pump efficiency of 83.7% is used to model discharge d AS,pump as a function of power p AS,pump and head H, mathematically, d AS,pump [m 3 /s] = η configuration 1000 p AS,pump [MW] 9.8 H [m] (6.2) where the unit configuration efficiency η configuration incorporates additional losses from the adjustable-speed conversion, the gravitational acceleration is 9.8 m/s 2, and the 1000 factor is a power unit conversion to kilowatts. The values for each configuration are given in Section 6.4. Speed Dependent Power Limits The upper operating limits of the pump are: maximum motor power of 100 MW determined by pump shaft admissible torque and frequency converter power [16]; maximum discharge of 25 m 3 /s; and maximum rotational speed. The lower operating limits are: minimum rotational speed; and cavitation limit of 67.5 MW. The theoretical cavitation limit of the units in Grimsel 2 is 60 MW [16], but in practice the pumps are not operated below 67.5 MW. The motor power, discharge and cavitation limits are configuration independent. On the other hand, the type of adjustable-speed drive determines rotational speed limits. The dependence of power limits on speed range was estimated based on the adjustable-speed characteristics provided by KWO, from tests on a scale model of the pump. The power-to-speed characteristic around the fixed-speed operating point is a function of head. Within a small range of speeds, this relation is linear. Furthermore, the power-to-speed slope is linearly dependent on head H. The equation for the power-to-speed slope m p as a function of head H is, m p [MW/rpm] = H (6.3) with a value given in MW/rpm. Fig. 6.5 shows how this relationship was obtained. The power-to-speed slope models upper and lower motor consumption limits. Mathematically, P max pump [MW] = p FS,pump + m p speed P min pump [MW] = p FS,pump m p speed (6.4a) (6.4b)

43 CHAPTER 6. PLANT MODEL 38 Figure 6.5: Dependence of pump power-to-speed slope m p on head. For example, if the fixed-speed power of the pump is 90 MW and the powerto-speed slope is 0.5 MW/rpm, a speed range of ±10 rpm will allow this pump to operate between 85 and 95 MW. The pump power limits are summarized in Fig. 6.6, which shows the power limits for different speed ranges speed. Doubly-fed asynchronous machines are typically characterized by such speed capabilities. In the case of the full converter configurations, they are not restricted by the speed range, only by the maximum power limit and cavitation limit. 6.3 Turbine Model Turbine Efficiency Curve The turbine efficiency curve was obtained from historical data, and is modeled as a function of head and turbine power. Fig. 6.7 shows an example efficiency curve, for a head of 390 ±5 m. The dependence of the efficiency on power is approximated by the function drawn in yellow, which is a quadratic function. Parameters are a function of head, and were determined by fitting quadratic polynomials to the data for discrete head levels and regressing the parameters of these polynomials to head. The intercept of the polynomial is determined through another regression, for the maximum efficiency η max turbine

44 CHAPTER 6. PLANT MODEL 39 Figure 6.6: Pump adjustable-speed operating limits. to head dependence. This formulation guarantees a smooth and consistent behavior throughout the head range. Turbine efficiency η turbine is calculated using, η turbine = a p 2 turbine + b p turbine + b 2 / (4 a) + η max turbine (6.5) where, a = H H b = H H η max turbine = H H (6.6a) (6.6b) (6.6c) (6.6d) The operating limits of the turbine are: maximum generator power of 85 MW; full gate maximum power; and cavitation minimum power. The hill chart of a hydraulic model of the turbine was used to derive the functions for the full gate and cavitation limits, full gate Limit p turbine [MW] = H 65.0 (6.7a) cavitation Limit pturbine [MW] = H (6.7b) Fig. 6.8 shows the complete fixed-speed turbine characteristic described by (6.5), (6.6) and (6.7). A study conducted by KWO concluded that the efficiency gained by operating the turbine in adjustable speed would not compensate converter

45 CHAPTER 6. PLANT MODEL 40 Figure 6.7: Turbine efficiency when head is 390 meters. Figure 6.8: Turbine operating limits and efficiency.

46 CHAPTER 6. PLANT MODEL 41 losses [16]. Hence, in turbine mode, the frequency converter is bypassed and the generator is operated at fixed rotational speed. Additionally, adjustablespeed operation of a unit in which pump and turbine are separate machines should not affect the turbine power limits significantly [4]. Therefore, we model fixed-speed and adjustable-speed turbine units the same Piecewise Linearized Turbine Power-to-Discharge Curves The power-to-discharge function is, d turbine [m 3 /s] = η turbine (p turbine ) η configuration 1000 p turbine [MW] 9.8 H [m] (6.8) where the turbine efficiency curve η turbine (p turbine ) is calculated with Eq. (6.5), the gravitational acceleration is 9.8 m/s 2, and the 1000 factor is a power unit conversion to kilowatts. The unit configuration efficiency η configuration incorporates additional losses from the adjustable-speed conversion and its values are given in Section 6.4. The power-to-discharge function (6.8) is cubic, convex, and is implemented through a piecewise linearization. An example of piecewise linearized functions for three different head levels is shown in Fig The gain in precision by increasing the number of segments diminishes with each additional segment. Three linear segments were used for the piecewise linearization. With three segments, the maximum error in the linearized function is below 0.5%. The end points of the piecewise linear function are given by the turbine power limits. The two vertices are calculated to minimize the sum-of-squares error. 6.4 Generator/Motor and Grid Interface Alternatives and Losses The pump and turbine models do not consider the additional losses of the components involved in the adjustable-speed upgrade. Losses were limited in this study to those that are expected from the frequency converter and/or wound rotor. Additional losses are considered in the deterministic optimization model with: 99.1% efficiency factor for pump and turbine operation of DFAM units, taken from a fixed-speed/adjustable-speed comparative analysis performed in [29]; 99.2% efficiency factor for the pump and turbine operation of units connected through an HVDC converter [30]; and 98.6% efficiency factor for full-converter units, obtained by comparing the efficiency with and without a converter around the fixed-speed operating point. The full-converter efficiency is in line with the values published in [31], and was considered to be constant in the power range of interest based on the results of [32] and [30]. The full-converter losses are taken to only affect the pump, as it was assumed that the converter is bypassed in turbine operation.

47 CHAPTER 6. PLANT MODEL 42 Figure 6.9: Piecewise linearization of turbine performance curves with three segments for the performance curve at three different head levels. The deterministic optimization incorporates these efficiency factors through the pump and turbine power-to-discharge functions. The efficiency factor multiplies the discharge volume in pump mode and divides the discharge volume in turbine mode. Fig shows the unit configuration alternatives with their main components, converter or DFAM efficiency, and grid interface location.

48 CHAPTER 6. PLANT MODEL 43 Conventional (Fixed Speed) Power measurement Pump/ Turbine SM Motor/ Generator Full Back-To-Back Frequency Converter Transformer MWh No additional losses, base case AC Transmission Line SM Frequency Converter Doubly-Fed Asynchronous Machine MWh Pump: 98.6% Turbine: 100% AC Transmission Line DFAM MWh 99.1% efficiency AC Transmission Line HVDC SM Converter Station MWh 99.2% efficiency HVDC Transmission Line Figure 6.10: Adjustable-speed technologies considered in the case study.

49 Chapter 7 Case Study This chapter describes the plant configuration scenarios evaluated in the case study, and explains the energy price sensitivity analysis that was performed. 7.1 Plant Configuration Alternatives The case study simulated Grimsel 2 operations from October 6, 2014 to September 27, Different plant configurations based on the adjustablespeed options shown in Fig were studied. The base case is the scenario with four fixed-speed units. The effect of converting anywhere from one to all four units to adjustable speed with full back-to-back frequency converter technology was evaluated. Additionally, the conversion of all units to adjustable speed by means of a DFAM was evaluated for different ranges of adjustable-speed capability. Finally, an HVDC connected adjustable-speed plant was evaluated. If an HVAC line is converted to HVDC, it could be possible to increase transmission capacity significantly without expanding right-of-way or installing new transmission towers [33]. To assess the potential benefits of an HVDC-enabled expansion of the plant capacity, additional studies with one or two additional adjustable-speed units were conducted. Table 7.1 shows the twelve resulting equipment scenarios. 7.2 Sensitivity Analysis To test the sensitivity of results to energy prices, the case study was repeated for the configuration with four full-converter units using scaled 2014/2015 energy prices. When scaling prices, it was assumed that reserve prices do not change since there is little correlation between energy and reserve prices. Hence, secondary and tertiary reserve prices were taken to be the same as those of the year 2014/2015. Reserve activation energy prices are correlated with energy prices, however, and were adjusted accordingly. Secondary and positive tertiary activation energy prices were scaled directly with the same 44

50 CHAPTER 7. CASE STUDY 45 Technology Number of Adjustable-Speed Units Number of Fixed-Speed Units Additional Adjustable-Speed Losses Base Case 0 4 Full Converter % Full Converter % Full Converter % Full Converter % DFAM ±1% % DFAM ±3% % DFAM ±5% % DFAM ±7% % HVDC (FC) % HVDC (FC) % HVDC (FC) % Table 7.1: Case study equipment configuration scenarios. factor as energy prices. Negative tertiary activation energy prices were scaled based on their regression to energy prices. A positive correlation with an intercept of -80 CHF/MWh was determined from this regression. The intercept was maintained when scaling, mathematically, ( ) λ TCRE scaled = λ TCRE 2014/ x 80, (7.1) with scaling factor x, and 2014/2015 negative tertiary daily average energy price λ TCRE 2014/2015. A fifth price scenario was simulated using energy and reserve prices from the 2012/2013 hydrological year. Since Swissgrid does not provide tertiary activation energy prices for 2012/2013, a time series was synthesized based on energy prices. The average energy and reserve prices for the complete set of price scenarios are summarized in Table 7.2. The four price-scaling scenarios are defined with a scaling factor of x = 0.5, 1, 1.5 and 2.

51 CHAPTER 7. CASE STUDY 46 Price scenario Average energy price Average secondary cutoff price Average positive tertiary cutoff price Average negative tertiary cutoff price 2014/2015, x = 1 Scaled, x = { 1 2, 3 2, 2} x / Table 7.2: Average energy and reserve prices. Values in CHF/MW h.

52 Chapter 8 Results 8.1 Plant Configuration Alternatives Fig. 8.1 and Table 8.1 summarize the results from each simulation. The light gray region in the background of the figure shows the energy market revenue assuming no reserve sales. The dark gray region shows the value of net water inflows for each scenario, assuming no reserve sales and no pump operation; this demonstrates that pumping water produces the majority of energy market revenue. The stacked bars show the revenue assuming energy and reserve market sales, broken down into energy, reserve capacity and reserve activation revenues. Total revenue increases 58% for a plant with four units retrofitted with full-power back-to-back frequency converter. This increase is 50% for four DFAM units with ±7% speed range and 53% for the four-unit HVDC configuration. Turbine and pump capacity factors and cycling increase substantially with adjustable-speed equipment because the plant provides spinning reserve, which requires units to be online. The configuration with only fixed-speed units has a 30% capacity factor, the different adjustable-speed configurations have a 38 44% capacity factor. Turbine cycling with adjustable-speed units increases 30% to 40% and pump cycling increases 50% to 90% relative to the situation with all fixed-speed. The pump and turbine capacity factors are detailed in Appendix G. The bids for positive and negative tertiary reserve in configurations with two or more adjustable-speed units are generally for the maximum bid size. The average bid sizes and awarded capacities in each scenario are detailed in Appendix G. If a fifth unit is added the additional flexibility allows the plant to also offer full-sized (50 MW) bids for secondary reserve in most weeks, thereby almost reaching the limit in the participation in each reserve market and increasing the total revenue by 23%. If a sixth unit is added, revenue increases an additional 10%, primarily from additional price arbitrage. 47

53 CHAPTER 8. RESULTS 48 Figure 8.1: Revenue with each configuration. Figure 8.2: Energy price sensitivity for configuration with 4 full-converter units.

54 CHAPTER 8. RESULTS 49 Adjustable Speed Configuration Scenario Results # of Adjustable Speed Units # of Fixed Speed Units Addition Adustable Speed Losses Revenue 10 6 CHF Turbine Starts Pump Starts Turbine Capacity Factor Pump Capacity Factor Base Case % 16% Full Converter % % 24% Full Converter % % 22% Full Converter % % 23% Full Converter % % 24% DFAM ±1% % % 20% DFAM ±3% % % 21% DFAM ±5% % % 22% DFAM ±7% % % 22% HVDC (FC) % % 23% HVDC (FC) % % 26% HVDC (FC) % % 27% Table 8.1: Case study results.

55 CHAPTER 8. RESULTS 50 Scenario Price Year Scaling Factor Revenue 10 6 CHF Turbine Starts Results Pump Starts Turbine Capacity Factor Pump Capacity Factor 2014/ % 24% 2014/ % 24% 2014/ % 22% 2014/ % 22% 2012/ % 24% Table 8.2: Price sensitivity results. 8.2 Sensitivity Analysis Fig. 8.2 shows the results of the sensitivity analysis. As energy prices increase, revenue from tertiary reserve remains stable while revenue from secondary reserve decreases, due to higher opportunity costs for providing secondary. Higher energy prices increase revenue from positive tertiary activation and decrease revenue from negative tertiary activation because activation energy and energy market prices are correlated. The revenue of the plant from participation only in the energy market scales proportionally to energy prices. With the provision of reserve capacity, increases in energy prices have a reduced impact on total revenue (price elasticity of revenue of 0.38), because a substantial and consistent revenue is earned from reserve capacity sales and reserve activation. For the 2012/2013 simulation negative tertiary activation has a minor revenue as a consequence of the relatively high energy prices of that period.

56 Chapter 9 Conclusions 9.1 Summary This thesis estimated the financial benefits of retrofitting a pumped storage hydropower plant with adjustable-speed technology. A method was developed for optimizing the operation in the day-ahead energy and week-ahead ancillary service markets, which was used to study the case of a Swiss hydropower plant that has been (hypothetically) upgraded from fixed speed to adjustable speed. 9.2 Conclusions The results showed that the benefit of adjustable-speed equipment is minor for a plant that only participates in the energy market (revenue increased 4%), but is much more significant when participating in the energy and reserve power markets. A maximum revenue increase of 58% was seen for a plant with four units retrofitted with a full converter configuration. A fixed-speed plant is capable of offering tertiary reserve, but with a large impact on the energy market revenue. With one or more adjustablespeed units, a plant is able to offer tertiary reserve while retaining close to maximum profit in the energy market. On the other hand, the provision of significant secondary reserve was shown to require large plant flexibility, in the form of at least two adjustable-speed units, and a large speed range. A higher profit was seen for a back-to-back frequency converter configuration, however, the revenues for the DFAM and HVDC scenarios were affected by the assumption of additional losses in turbine mode. In a real implementation these losses are compensated or reverted by the adjustablespeed operation of the turbine, which was not considered here. Ultimately, the potential benefits depend more on the converter and electric machine efficiency than on the choice of technology. None of the adjustable-speed technologies is inherently more efficient than the other, and the efficiency will 51

57 CHAPTER 9. CONCLUSIONS 52 depend on equipment specifications. Nevertheless, cost and other attributes, like reactive power control and switching times, must also be considered when selecting a technology. The results depend strongly on ancillary service sales. Due to the small size and low liquidity of the reserve markets in Switzerland, bidding strategy can have a significant and unpredictable impact on market performance. Hence, while results clearly demonstrate the benefits of adjustable-speed pumped storage hydropower, the study is inherently uncertain and care should be taken before applying these conclusions to other situations and scenarios. 9.3 Outlook Further research should focus on improving the bidding strategy for ancillary services, incorporating tactics such as placing multiple bids for the same pumped storage plant or integrating market dynamics into the bid curve optimization, and on reducing the uncertainty of revenue estimates by considering more energy and reserve price scenarios.

58 Appendix A Available Data A.1 Pumped Storage Plant Data Technical specifications of the units in Grimsel 2, water level-volume characteristic of both reservoirs, and historical operation data were provided by Kraftwerke Oberhasli (KWO), the plant operator. The historical data covers from October 2013 to September 2014 and includes, with hourly resolution: Power generation/consumption of each unit. Water discharge of each unit in turbine and pumping mode. Upper and lower reservoir water level. Inflows and outflows from both reservoirs. Spot energy price. Participation in reserve markets. Other plants in the hydroelectric complex make use of the upper and lower reservoir of Grimsel 2, therefore the inflow information provided by KWO does not account for the water actually used by Grimsel 2. For this reason the hourly net inflow time series used for the simulations were built from the reservoir level time series by using the water level-volume characteristics and adding the discharge volumes of Grimsel 2. In this way, the calculated inflows are the net hourly positive or negative water volumes that were effectively available for Grimsel 2. A.2 Market Data The data for ancillary services is available on the Swissgrid website. This includes: 53

59 APPENDIX A. AVAILABLE DATA 54 Cleared bids for weekly secondary reserve capacity. Cleared and non-cleared bids for daily and weekly positive and negative tertiary reserve capacity. 15-minute total positive and negative secondary energy demand and cost. 15-minute total positive and negative tertiary energy demand and cost. All reserve and energy prices were converted from Euros to Swiss Francs using the exchange rates published by the European Central Bank.

60 Appendix B Simulated Permutations of Reserve Capacity 55

61 APPENDIX B. SIMULATED PERMUTATIONS OF RESERVE CAPACITY56 Table B.1: Simulated permutations of reserve capacity in the week-ahead ancillary service planning routine. Secondary Positive Tertiary Negative Tertiary

62 Appendix C Reserve Capacity Demand Curves In this work, only the week-ahead positive and negative tertiary reserve market is modeled, but demand that was supplied in the day-ahead positive and negative tertiary reserve market is included in the demand curves. It is represented as a demand block for the average capacity and price of the day-ahead market over the week. This is necessary because the total capacity required by the transmission system operator is usually distributed among the week-ahead and the day-ahead market, and not considering the demand from the day-ahead market would result in some weeks of very low demand. In fact, the sum of the average total tertiary reserve capacity demanded each week from both markets is relatively stable, as is shown in Fig. C.1 and in Fig. C.2. Also, prices in the week-ahead market are inversely correlated to the prices in the day-ahead market because when a low power is supplied in one of the markets, high power must be supplied in the other, thus driving prices in opposite directions. Figs. C.3 C.5 show the demand curves used for the simulation of the reserve markets. Demand curves from the hydrological years 2012/2013 and 2014/2015 are used for the simulation of the operation in these years. Demand curves from the hydrological year 2013/2014 are used to determine the cut off price scenarios in the stochastic bid curve optimization. 57

63 APPENDIX C. RESERVE CAPACITY DEMAND CURVES 58 Figure C.1: Sum of average over each week of positive tertiary reserve capacity cleared in the day-ahead and week-ahead market. Figure C.2: Sum of average over each week of negative tertiary reserve capacity cleared in the day-ahead and week-ahead market.