Use of PLEXOS® Software to Calculate and Dispatch Power Prices

Use of PLEXOS® Software to Calculate and Dispatch Power Prices
Dr Christos Papadopoulos Regional Manager Europe Energy Exemplar (Europe) Ltd 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Energy Exemplar® Commercial since 1999
Focused on PLEXOS® for Power Systems software Global client base served from three locations: Adelaide, Australia London, UK California, USA 20% staff with Ph.D. level qualifications spanning Operations Research, Electrical Engineering, Economics, Mathematics and Statistics Client base growing >20% p.a. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

PLEXOS Overview of Features and Uses
5/11/2011 PLEXOS® Modelling Tour PLEXOS Overview of Features and Uses 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

PLEXOS® for Power Systems – Market Simulation & Analysis
Proven power market simulation tool Uses mathematical programming, optimisation and stochastic techniques Robust analytical framework, used by: Energy Producers, Traders and Retailers Transmission System /Market Operators Energy Regulators/Commissions Consultants, Analysts and Research Institutions Power Plant Manufacturers and Construction companies Power system model scalable to thousands of generators and transmission lines and nodes 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Scalability System size: Simulation interval:
From single generator to 1000’s From single transmission node to 10000’s Largest system studied: Eastern Interconnect (US) nodes 7000+ generators Simulation interval: Switch easily between hourly, half-hourly and 1-minute (or any other timeframe) with a simple option 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

What can be achieved with PLEXOS®
Power Market Modelling, Simulation and Analysis - short & long term: Price Forecasts based on power system operational constraints and market fundamentals, at nodal and regional level. Detailed operational planning and dispatch optimization while modelling complex renewable-hydro-thermal and transmission Renewable integration analysis Investment planning and analysis Optimise new generation and transmission builds and retirements – what, when, where? Assessing the effectiveness of investment decisions and policies Portfolio optimization and valuation 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

What can be Achieved with PLEXOS® (2)
Risk management via scenario analysis, stochastic modelling and optimization: Optimal resource allocation decisions (fuel, heat, capacity) over the long or short term subject to uncertainty (e.g. volatility in fuel prices, wind, hydro inflows, demand) Fuel, Emissions and hedge contract evaluation and analysis Transmission and Ancillary Services/Balancing Analysis Regional, Zonal or Nodal Congestion Forecast and Management Security Constrained Dispatch (N-x) Co-optimization of ancillary services/reserve and energy dispatch Optimal power flow modelling Interconnector Modelling 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

PLEXOS® Gas Modelling (2013)
22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

PLEXOS® Electricity and Gas Modelling
Goal is to provide modellers an integrated gas and electricity model that is straight-forward for electric market modellers to understand and use. Initially the details of pipeline pressures and pressure drop functions not modelled. Storage volumes, pipeline flows and gas demands can be expressed in potential energy terms. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

PLEXOS® Electricity and Gas Modelling (2)
Short and long term simulations Both system-planner (cost minimisation) and strategic (maximise profit) solutions Investment planning: Gas field, storage, and pipeline potential candidates defined with: Capital cost of construction (builds cost, WACC, economic life, project start date, min/max build constraints) Operating costs (fixed and variable) Co-optimisation of both Electricity and Gas Markets!! 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Features: Overview Generation Optimal capacity expansion
Unit commitment Heat rate model Maintenance optimization Monte Carlo simulation Fuel constraints Emission constraints Technical limits Auxiliary use Ancillary services CCGT & CHP SCUC (Contingency) Transmission Radial and meshed networks Regional pricing Nodal pricing Large-scale networks Interface limits Losses LMP decomposition Wheeling charges Pricing methods Contingencies and SC-OPF SCUC (Contingency) ISO level outputs Renewables All types Energy constraints Must-run limits External profiles Cascading Hydro Pumped Storage Uncertainty Markets/Portfolio Optimisation Energy Ancillary Services Heat Fuel Capacity Integrated Gas/Fuel Modelling Field Storage Pipeline Node Financials Financial contracts CfD & FTR Generator bid formation Gaming models Pricing and Uplift Escalators Stochastics Variable inputs Correlations Stochastic optimization Monte Carlo Timeframes 5-minutes to 10’s of years Constraint decomposition LDC model Chronological model Time Slices Visualisation Geospatial user requested results graphs Google Earth Customizations Generic constraints Programming API Automation Data retrieval Demand Bidding/Participation Energy Ancillary Services 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Simulation and Analysis tools in PLEXOS – Seamless Integration
LT Plan – Long Term Optimal Investment PASA – Optimal Maintenance Scheduling MT Schedule – Medium Term Decomposition ST Schedule – Short Term Chronological 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Simulation Phases in PLEXOS®
Step Size: years Capacity Expansion LT Plan Step Size:1 year at a time Maintenance Planning PASA Step Size:1+ years at a time Constraint Decomposition MT Schedule Step Size: 5 minute – 1 week at a time Chronological Simulation ST Schedule 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

LT Plan - Long Term Capacity Expansion Planning
Finds the optimal combination of generation and transmission new builds and retirements that minimizes the net present value of the total costs (incl. fixed and variable operating costs) of the system over a long-term planning horizon. The following types of expansion/retirements and features are supported: Building and retiring generating plants and transmission lines Multi-stage build projects Expanding the capacity on existing transmission interfaces Taking up new physical load /generation contracts Deterministic or stochastic optimization 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

PASA - Projected Assessment of System Adequacy
PASA is a simulation that focuses on the balance of supply and demand in the medium term. When used in combination with MT Schedule and/or ST Schedule, the primary purpose of the PASA is to determine, where and when maintenance outages should occur. It can model planned and random outages of generation plants and transmission lines, and its severity In multi-region models PASA calculates the optimal amount of reserve that should be shared between regions using the transmission network. (Equalizing regional capacity reserves done using quadratic programming formulation.) 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

MT Schedule - Medium Term Scheduling and Simulation
MT Schedule is used to give fast results for medium to long-term studies. The MT Schedule handles all user-defined constraints including those that span several weeks, months, or years. This might include: Fuel off-take commitments e.g. gas take-or-pay contracts Energy limits, Emission quotas Long-term storage management taking into account inflow uncertainty MT Schedule: Gives the option of Load Duration Curves or Chronological modelling approach, similar to that in LT Plan. Each constraint is optimised over its original timeframe and the MT Schedule to ST Schedule Bridge algorithm converts the solution obtained, e.g. a storage trajectory, to targets or allocations for use in the shorter step of ST Schedule Can model competitive behaviour of portfolios over the medium term. (Sophisticated game-theoretic behaviours like Nash-Cournot competition or ‘simply’ recovery of fixed costs.) 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

ST Schedule ST Schedule is mixed-integer programming (MIP) based chronological optimization. It can emulate the dispatch and pricing of real market-clearing engines, but it provides a wealth of additional functionality to deal with: unit commitment; constraint modelling; financial/portfolio optimization; and Monte Carlo simulation. ST Schedule provides two methods for modelling the chronology: Full Chronology Every trading period (interval) inside the ST Schedule horizon is modelled explicitly. (Interval can be 1min to 24hrs in length.) Typical Week One week is modelled each per month in the horizon and results are applied to the other weeks. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Modelling of All Renewable Energy Sources
Hydro/Pump Wind Solar (PV, CSP) Geothermal Bio-energy Marine + others 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Features: Thermal Unit Commitment
Highly detailed thermal unit commitment model: Polynomial heat rate functions Minimum up and down time constraints Energy ramping constraints Starts costs variable by cooling state Run up and down periods Rough-running zones Combined-cycle model: Genuine optimisation of CCGT operation Models of GT and steam units Combined heat and power 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Features: Emissions and Fuels
Scope: Any number and types of fuels and emissions across any set of Generators Fuel Contracts Optimal capacity expansion, dispatch and pricing reflect all constraints Constraints and pricing: Minimums (take-or-pay) and maximum constraints Emission limits across any timeframe including multi-annual constraints Fuel constraints across any timeframe (interval, day, week, month, year, multi-annual) Fuel and emission shadow and accounting prices 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Features: Hydro Multiple phase simulation (LT>MT>ST):
Long-term storage decomposition via targets or water values to shorter-term (more detailed) phases Ensures optimal use of storage down to chronological level Cascading networks: Major and minor storages and junctions Natural inflows and spillways and canals Constraints: Minimum releases for environment Operational constraints and hydro generation efficiency functions Monte Carlo or Stochastic optimisation: Any number of iterations with variation in any input 2-stage stochastic optimisation for better modelling of storage release policies under uncertainty Applications worldwide 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Comparison – Pump operation and price
Pump storage unit pumps during low price periods and generates at high prices periods as required. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

PLEXOS® and Policy Analysis
PLEXOS® has a proven track record in the area of policy analysis and development. Common policy analysis with PLEXOS® includes: The design, analysis, and benchmarking of electricity market rules and effect on market participants. Assessing the effectiveness of renewable technology policies and resulting impact on carbon emissions, prices, transmission grid operations and investment incentives. Forecasting market entry and assessing future technology and fuel mixes as well as examining the development of system adequacy. Examining market competitiveness and market power. Evaluating generation or transmission investments. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Analysis tools in PLEXOS®
Capacity Expansion Planning Minimization the NPV of: Cost of new builds Cost of retirements Fixed operating costs Variable operating costs Outputs: Generation new builds and retirements Long term operational results New Transmission line builds e.g. DC lines Transmission interface upgrades Physical contract purchases (generation or load) Indicators: LOLP, EENS 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Capacity Expansion Planning Optimal Expansion Plan Generator Build Cost ($/kW) WACC (%) Economic Life (years) Existing New_CCGT 1750 12 25 New_GT 1100 Generator Property Value Units Scenario New_CCGT Max Units Built 5 - Allow Expansion Build Non-anticipativity -1 $/MW New_GT 100 LOLP Data Configure Results 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Market Analysis - Resource allocation: PLEXOS solves the operational problem in each phase (i.e. LT, MT or ST). MT phase solves “long term” constraints problem such as: Storage release policies. Emission allowance. Fuel-Energy limits. Allocate any resource via custom constraints. ST solves detailed period-by-period chronological Unit commitment problems (considering the resource allocation from MT) 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Market Analysis – Price Forecast: From Long & Medium Term pricing LRMC Recovery Algorithm Shadow Pricing (Bertrand game) Nash- Cournot Competition Residual Supply Index (RSI) Uplift mechanisms To Short Term (Day ahead/Real Time/AS) pricing 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Forecasting of Electricity Power Prices
Use of PLEXOS® Software to Calculate and Dispatch Power Prices Forecasting of Electricity Power Prices

BACKGROUND Wholesale Electricity Markets
Source: ISO New England 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Wholesale Electricity Markets

Marginal Pricing Price Forecasting from Fundamental (Production Cost)
5/11/2011 Price Forecasting from Fundamental (Production Cost) & Market Equilibrium Modelling (Hybrid Models) Marginal Pricing Power markets run on marginal pricing thus it is the “cost” of the marginal (or last) unit of load that sets the energy price. NOTE: This sometimes equates to the SRMC of the marginal generating unit. Not so often though cause generators usually bid above their SRMC. Every linear programming problem, referred to as a primal problem, can be converted into a dual problem, which provides an upper bound to the optimal value of the primal problem. The dual problem deals with economic values. Price is exactly the optimal value of the dual variable associated with the primal constraint that forces generation and load to match. As such, it is referred as the “Shadow Price” of the primal energy balance constraint. Energy Prices are the Shadow Prices of the Constraint that matches supply & demand Shadow Prices: How much my Obj Function changes if I make a change in the RHS of the constraint that matches supply & demand 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

What is Nodal Pricing? Nodal Pricing or Locational Marginal Pricing (LMP) or Locational Based Marginal Pricing (LBMP). Nodal Pricing is a method of determining prices in which market clearing prices are calculated for a number of locations (nodes) on the transmission grid. Each node represents the physical location on the transmission system where energy is injected by generators or withdrawn by loads. Price at each node represents the locational value of energy (or else the cost to the system as a whole of a unit change in load at the bus) which includes the cost of the energy and the cost of delivering it, i.e., losses and congestion. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Locational Marginal Pricing (LMP) in PLEXOS®
λ ι = λ αι βι LMP Marginal Cost of Generation at reference bus Marginal Cost of Transmission Congestion Marginal Cost of Losses = + + λ is the system “lambda” αι is the node’s congestion charge βι is the node’s marginal loss charge αι : is the congestion charge at node i ωj: is the shadow price on the thermal limit constraints for path j Xi,k: is the angle reference matrix element ωκ: is the shadow price on the node phase angle constraints for node k βi: is the marginal loss charge at node i rj: is the resistance on line j fj’: is the flow on the line j at the optimal solution 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

PLEXOS® Mechanism for Calculating Market Price
The market price of energy is the marginal cost (as represented by generators price/quantity offers) of serving consumption at each node or region. The marginal cost is found by simulating the least-cost economic dispatch of the entire market, emulating the steps followed by a Market Operator, subject to all: Generation technical characteristics and constraints; Transmission technical characteristics and constraints; and Forecast of load/demand and renewable generation The market price is made up of the marginal cost of: Generation; Transmission losses, to that node; and Transmission congestion, to that node PLEXOS therefore can fully replicate the Nodal or Locational Marginal Pricing (LMP) market rules. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Solving SC UC/ED using MIP in PLEXOS®
Unit Commitment and Economical Dispatch can be formulated as a linear problem (after linearization) with integer variables of generator on-line status Unit Commitment (UC): What combination of units will produce the load demand (MW) at minimum cost? Objective: Minimisation of Cost Minimize Cost = generator fuel cost + VOM cost + generator start cost + contract purchase cost – contract sale saving + transmission wheeling + energy / AS / fuel / capacity market purchase cost – energy / AS / fuel / capacity market sale revenue 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Unit Commitment (UC) subject to constraints:
Solving SC UC/ED using MIP in PLEXOS® (cont) Unit Commitment (UC) subject to constraints: Energy balance constraints Operation reserve constraints Generator and contract chronological constraints: ramp, min up/down, min capacity, etc. Generator and contract energy limits: hourly / daily / weekly / … Transmission limits Fuel limits: pipeline, daily / weekly/ … Emission limits: daily / weekly / … Others 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Economic Dispatch is what determines the LMPs
Solving SC UC/ED using MIP in PLEXOS® (cont) Energy Dispatch (ED): How much should each unit in that combination generate? Objective: Maximisation of Social Welfare Economic Dispatch is what determines the LMPs (not the commitment) 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Supply/Demand Curve Source: ISO New England 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Producer/Consumer Surplus

Social Surplus (Welfare)

Pricing in PLEXOS® Load settlement method and generator settlement method can be adjusted Locational Marginal Pricing (Nodal Pricing) (value = 0) Loads pay the locational marginal price at the node. Regional Reference Pricing (value = 1) Loads pay the regional reference price i.e. the locational marginal price at the regional reference node. Regional Load Weighted Price (value = 2) Loads pay the load-weighted price in their region. Uniform Pricing (value = 4) Loads pay the single market price (uniform pricing). None (value = 5) The loads make no payment for energy purchased. Custom (value = 6) 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Use of Stochastic Modelling for Electricity price prediction 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Coping with Uncertainty
Price Prediction is a process that inherently carries uncertainty. PLEXOS® offers three distinct approaches to coping with uncertainty: Scenario analysis Monte Carlo simulation Stochastic optimisation 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Stochastic Variables In PLEXOS® any input parameter can be stochastic.
Set of uncertain inputs ω can contain any property that can be made variable in PLEXOS: Load Fuel prices Electric prices Ancillary services prices Hydro inflows Wind energy, etc Number of samples S limited only by computing memory First-stage variables depend on the simulation phase Remainder of the formulation is repeated S times 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Stochastic Variables To model input values as stochastic drivers
Define stochastic Variables in Variable class Specify stochastic characteristics Specify number of iterations for stochastic sampling and simulation Properties of the Stochastic object Assign Variables to stochastic drivers Need to decide period of stochastic change Every Minute, Hourly, Daily, Weekly, Monthly, Annually 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Define Stochastic Variables
Two methods to define stochastic Variables: Exogenous sampling: user-defined profile samples (with assigned probability for each sample) Endogenous sampling: user-defined expected profile that will be scaled up and down by random samples with random numbers with user-specified distribution 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Random Sampling Methods
Exogenous sampling: Directly define a set of chronological sequences that can be randomly selected when sampling - these sequences can be correlated e.g. the demand in two regions may be correlated, but each can be supplied with a set of demand trances with various associated probabilities. Endogenous Sampling: Define the expected value and information on how errors are distributed and allow the PLEXOS engine to generate the required samples. Simple autocorrelation. Brownian motion with mean reversion. Box-Jenkins methods ARMA - Autoregressive moving average model. ARIMA - Autoregressive integrated moving average model. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Stochastic Wind Modelling
ARIMA Sampling ARIMA (or two-parameter form ARMA) is highly suitable for generating random errors in wind speed forecast With suitable parameter settings also a good model for other inputs such as long term fuel price forecasts ARIMA related properties are Variable [ARIMA alpha], Variable [ARIMA beta], and Variable [ARIMA d] Lookup table Using the Variable class you can define a lookup table to translate raw sample values to values used in simulation For wind modeling the look-up table can be used to define a power curve with ARIMA used to generate random wind speed samples Lookup table properties are Variable [Lookup x], Variable [Lookup y], and Variable. [Lookup Unit] This model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. Variable Lookup x defines the x values for a look-up table used to translate raw sample values to final values used in the simulation. This is a multi-band property used in conjunction with Lookup y and optionally Lookup Unit. Sample values that fall between the lookup table x values are linearly interpolated into y values. Values that fall outside the range of defined x values are truncated to the nearest y value. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Stochastic Gas Forward Price.csv
Exogenous Sampling User-defined profile samples (with assigned probability for each sample) Property Value Units Band Data File Random Number Seed 2 - 1 Sampling Method Profile 10 Stochastic Gas Forward Price.csv Year Month Day Period 1 2 3 4 5 6 7 8 9 10 2005 6.45 7.32 6.96 6.58 8.19 7.25 7.15 7.38 7.08 7.93 6.04 5.86 7.43 6.02 7.14 6.55 6.8 7.79 6.17 6.27 6.37 6.85 8.21 6.65 6.78 5.94 8.45 7.72 6.09 6.05 8.3 5.78 6.08 7.99 7.05 6.34 7.28 6.12 6.46 8.39 8.25 6.91 7.22 5.89 6.79 7.53 8.15 … 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Wind Generation Profile
Endogenous Sampling User-defined expected profile that will be scaled up and down by random number samples with user-specified distribution Normal distribution Expected profile Property Value Units Band Data File Scenario Random Number Seed 3 - 1 Stochastic runs Sampling Method 2 Distribution Type Profile Wind Generation Profile Error Std Dev 50 % Min Value Max Value Mean Reversion 0.2 Auto Correlation 80 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Define Correlations Stochastic variables can be correlated, e.g. high load might be associated with high fuel prices Two ways to specify correlations Specify Variable [Variables] [Correlation] in the data grid pane Specify Variable [Variables] [Correlation] in correlation matrix Highlight Variable class and right-click In shortcut menu, select Correlation Matrix Fill the correlation matrix table Variables with the same sample frequency (Profile / Profile Day / Profile Week / Profile Month / Profile Year) can be correlated Only endogenous sampling can be correlated Stochastic variables can be correlated. For example, high load might be associated with high fuel prices. The correlation matrix for all defined Variable objects is edited via the right-mouse button pop-up Correlation Matrix option of the Variables collection. When sampling a normal distribution across a set of correlated variable it is required that the correlation matrix is positive semi-definite. Often this precludes use of negative correlations, but PLEXOS includes an algorithm for modifying the correlation matrix so that it is guaranteed to be positive semi-definite. This modification is performed internally at runtime. The higher the autocorrelation, the more the 'randomness' of the errors is dampened and smoothed out over time. The higher the standard deviation, the greater the volatility of the errors. Because the error function can produce any positive or negative value (at least in theory) it is often necessary to bound the profile sample values produced by this method. The Variable properties Min Value and Max Value are used for this purpose. The actual sample value used at any time is simply the sum of the profile value and the error (which may be positive or negative) bounded by the min and max values. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Stochastic Modelling - Monte Carlo vs. Optimisation
Monte Carlo simulation (Parallel Option) assumes perfect foresight for each stochastic sample PLEXOS then computes the optimal decision for each of a number of possible stochastic samples independently Stochastic Optimisation Simultaneously considers all the possible stochastic samples and associated probabilities PLEXOS computes a single optimal decision that is best hedged for the uncertainty represented by the stochastic samples 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Stochastic Optimization (SO)
Fix perfect foresight issue Monte Carlo simulation can tell us what the optimal decision is for each of a number of possible outcomes assuming perfect foresight for each scenario independently; It cannot answer the question: what decision should I make now given the uncertainty in the inputs? Stochastic Programming The goal of SO is to find some policy that is feasible for all (or almost all) the possible data instances and maximize the expectation of some function of the decisions and the random variables PLEXOS® uses scenario-wise decomposition 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Stochastic Modelling – Monte Carlo
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Stochastic Modelling – SO

Value of water and uncertainty
Stochastic Optimization “Short-sighted” solution Looking ahead Leaving for “tomorrow” what is needed More conservative releasing approach 1) Independent Samples 3) Stochastic Solution with enough foresight Again, it is draining the storage at the end of the horizon (full resource usage) Looks like an average, but it is not! It is the optimal level 2) Stochastic Solution 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Stochastic Runs and Monte Carlo
5/11/2011 Stochastic Runs and Monte Carlo Number of samples for each Variable object: Exogenous: Number of randomly selected sequences (in bands) Endogenous: Number of sequence drawn for each variable Number randomly generated Forced Outages. Forced Outages: Tells PLEXOS if random outages should be drawn for all phases Maintenance: Tells PLEXOS if maintenance outage should be generated by PASA. Monte Carlo: Force Outages frequency are distributed according to a Weibull pdf. Convergent Monte Carlo: ‘Winning’ Outage Pattern after Chi-square test The total number of independent samples executions or scenarios for each SO run is always the number of Stochastic Samples if Variable objects are defined. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Estimating correct cross-border flows with expert transmission analysis. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Transmission Analysis
Regional, Zonal or Nodal: Locational Marginal Prices Transmission Losses Transmission Congestion Regional and Zonal TLFs Security-Constrained Unit Commitment Region: Outer Container Zone: Inner Container Nodes: Transmission ends DC Lines AC Lines Transformers Interfaces Phase Shifters Lines 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Transmission Network Modelling
Two kinds of power flow can be modelled Transportation model Power flows as directed flows Transmission network (Kirchhoff's law must be obeyed) More power flow in lower reactance transmission lines Direct-Current Optimal Power Flow (DC-OPF) method is used to solve the power flow in the transmission network 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

DC – Optimal Power Flow (OPF) Methods
Refers to the generator dispatch and resulting AC power flows that is minimum cost and feasible with respect to thermal limits on the AC transmission lines. The OPF might include other constraints such as interface limits, and other decisions such as the optimal flow on DC lines and phase shifter angles. The OPF using a linearisation of the power flow equations which considers only real power flows and assumes voltages are all 1 p.u. It is important not to confuse Linearised DC-OPF with a transportation solution. In a transportation model the flow on all lines is controllable, but in a DC-OPF the KVL constraints are applied so basically flows mimic AC flows. PLEXOS® provides two DC-OPF formulations: set by the option Transmission [OPF Method]: 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

DC – Optimal Power Flow (OPF) Methods
Fixed Shift Factor OPF Network shift-factors are pre-computed and used to create “side-constraints” to enforce transmission constraints and model transmission losses. Variable Shift Factor OPF Bus (node) phase angles and branch (line) flows are decision variables in the optimisation, thus the shift-factors are implicit and no pre-computation is required, but the formulation size is potentially very large. These options represent the two most commonly used DC-OPF formulations with some unique and powerful enhancements in modelling losses and security-constrained optimal power flow. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Cross-border flows - Interconnectors
Generally market interconnectors are modelled as simple DC lines (transportation model) with thermal limits. Available Transfer Capacity (ATC) modelling - Simple DC lines with max flow set at ATC values Flow Based (FB) modelling - Allows for more flexible use of interconnectors. Use rules published by TSO to either: Create custom constraint on line flows Use interface objects with flow coefficients and RHS values. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

SC UC/ED with OPF transmission analysis.
SC UC/ED with OPF finds the optimal unit commitment and dispatch solution subject to the transmission being feasible if any defined contingency (such as the loss of a line or generator) should occur. The SC UC/ED with OPF algorithm in PLEXOS® computes Contingency Shift Factors - CSFs (also called generation-shift sensitivity factors) which define how much of the flow lost during a contingency will appear on other lines in the network. These factors are used to monitor and enforce the contingency constraints. The resulting dispatch is more conservative and at higher cost, but reflects more accurately the actual system operation. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Grid Congestion & Pricing
A nodal price represents the cost to the system as a whole of a unit change in load at the bus. In the absence of either constraints or losses all nodal prices will be equal. This uniform price is referred to as the system lambda or network energy charge. No matter where we perturb load in the network, the marginal impact on total system cost would be the same. As we introduce constraints on the transmission flows (either on individual branches or combinations of flows), the nodal prices diverge. Congestions and Losses are reflected by the separation/differences of nodal (LM) prices across the network. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Interconnector modelling - Example
Compare modelling interconnectors on ATC or FB basis: ATC: Two interconnectors with thermal limit 300MW in winter and 400MW in summer FB: Two interconnectors with sum of flow limited to 600MW winter and 800MW summer. Flow on each interconnector limited 450MW winter and 600MW summer. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Comparison – Imports and exports
Greater flexibility of FB allows both greater export and import of energy. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Comparison – Prices Flow based rules result in lower prices on average. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Interconnector modelling - Expansion
PLEXOS can be used to optimise the expansion of transmission lines. For this exercise we simply examine the results of increasing the CH-DE interconnector capacity. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Comparison – Imports and exports
Greater interconnector capacity increases both imports and exports 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Comparison – Average monthly prices
Greater interconnector capacity reduces price – greater price convergence 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Adjusting PLEXOS to the right time frame
Forecasting of Electricity Power Prices Adjusting PLEXOS to the right time frame 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Price Forecasting timeframes in PLEXOS®
LT Optimal Expansion Plan MT LRMC RSI Nash-Cournot ST Cost-based Efficiency Bertrand Nash-Cournot Game Uplift ex-post price Energy prices Capacity payments (prices) LT prices Company (player) revenue targets Adjust bids: Mark-ups MT prices Hourly (period) price forecast ST prices 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Case Study - NWE Price Forecast MT vs ST LRMC Northwest Europe:
5 regions (BE, DE, FR, NL, NO) 861 generators 6 interconnectors Model initially set up to run MT Schedule with LRMC Price forecasting over 15 years. Average price from LRMC is acceptable but the shape of the curve is too flat: it is missing the overnight effects of unit commitment and the affects of peaking generation costs in the day. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Case Study - NWE Price Forecast MT vs ST LRMC
Northwest Europe: 5 regions (BE, DE, FR, NL, NO) 861 generators 6 interconnectors Model initially set up to run MT Schedule with LRMC Price forecasting over 15 years. Just turning on ST Schedule without adding appropriate unit commitment data and algorithms 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Case Study - NWE Price Forecast MT vs ST LRMC
Northwest Europe: 5 regions (BE, DE, FR, NL, NO) 861 generators 6 interconnectors Model initially set up to run MT Schedule with LRMC Price forecasting over 15 years. Modelling unit commitment correctly has given us realistic peak to off-peak price differentials 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Case Study - NWE Price Forecast (automatic bidding):
RSI means “Residual Supply Index”: Measure of the size of the largest supplier relative to the load The higher the RSI the less competitive the market RSI defines markup index (Lerner Index) as a formula based on the RSI (and other indicators) in any hour: Lerner Index = (P – C) / P P is observed market price, C is cost-based price RSI has mixed reviews as a general price forecasting method; however The PLEXOS version provides for a number of regression terms such as [Load Capacity Ratio] not just RSI 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Case Study - NWE Price Forecast MT vs ST RSI
Northwest Europe: 5 regions (BE, DE, FR, NL, NO) 861 generators 6 interconnectors Model initially set up to run MT Schedule with RSI Price forecasting over 15 years. RSI produces very similar prices to LRMC but with ST Schedule showing a better peak to off-peak price ratio 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Balancing Renewables Volatility with PLEXOS®
Incorporating volatility in day-ahead and intraday markets 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

DA/ID/RPM/RT – ST Markets Overview
The day-ahead market (spot market): Physical market in which prices and amounts are based on supply and demand. The resulting prices and the overall amounts traded are made public. The spot market is a day-ahead market where bidding closes at noon for deliveries from midnight and 24 hours ahead. The intraday market: There is quite a time difference between close of bidding on the day-ahead market and on the regulating power market (below). The intraday market was therefore introduced as an ‘in between market’, where participants in the day-ahead market can trade on the next one-hour long power. Prices are published and based on supply and demand. The regulating power market (RPM): A real-time market covering operation within the hour. The main function of the RPM is to provide power regulation to counteract imbalances related to day-ahead planned operation. The demand side of this market is made up of transmission system operators (TSOs) alone, and approved participants on the supply side include both electricity producers and consumers. The balancing (RT) market: This market is linked to the RPM and handles participant imbalances recorded during the previous 24-hour period of operation. The TSO acts alone on the supply side to settle imbalances. Participants with imbalances on the spot market are price takers on the RPM/balance market. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Volatility in DA/ID power Markets
Wind power is unpredictable by nature. Due to its increased volatility within day, imbalances between day-ahead contracts and produced volume often need to be offset within very short time intervals. Apart from the Day-ahead market, Intraday and Regulating power markets are becoming increasingly important for the development and integration of Wind/PV power in the power systems. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Volatility in DA/ID Unit Commitment and Energy/Price Dispatch
Stochastic Unit Commitment for System Operator: On/off decisions for thermal units Minimise total system cost SO can provide more robust DA schedule Price-based Unit Commitment (PBUC): On/off decisions for thermal Use of contracts Maximise profit SO can increase return on investment and help manage constraints such as fuel budgets 22/09/2018 3rd European Electricity Ancillary Services & Balancing Forum Workshop

SO in Unit Commitment (cont)
Assumption is that we must make certain commitment decisions ‘now’; and cannot perfectly anticipate certain variables such as load or wind dispatch. Simulating a number of independent samples can give ambiguous results because each sample has perfect foresight: units on in some samples and off in others; or starting and stopping at different times Thus we wish to find the optimal on/off decisions for selected generating units over a given “non-anticipativity window” given our knowledge of the uncertainty 22/09/2018 3rd European Electricity Ancillary Services & Balancing Forum Workshop

System Operator Day-ahead Unit Commitment Example
CAPACITY TECHNICAL LIMITATIONS MINIMUM PRODUCTION PRODUCTION COST 2x100 [MW] -12hrs off -8hrs on [65] MW 10$/MWh 100 [MW] -4hrs on -2hrs off [10] MW 50$/MWh 0-100 [MW] uncertain Must-run! - 0$/MWh How to efficiently schedule thermal power plants with technical restrictions if we don’t know how much wind (and/or load) is going to be available? 22/09/2018 3rd European Electricity Ancillary Services & Balancing Forum Workshop

Day-ahead Unit Commitment, Continued
No wind generation is available Assume for example a worst-case scenario analysis. First, the wind is absent during the entire day (pessimistic) Two base load “slow” units can be scheduled Fast units are required just in order to meet the load 22/09/2018 3rd European Electricity Ancillary Services & Balancing Forum Workshop

Now assume an optimistic scenario analysis. Wind is going to be available during the entire day High wind resources Fast units in order to avoid unserved energy One base load “slow” unit pre-schedule The question is: If we don’t know how the wind is going to be… what to do? Dispatch one or two slow base units? 22/09/2018 3rd European Electricity Ancillary Services & Balancing Forum Workshop

Stochastic Optimisation: Two stage scenario-wise decomposition Take the optimal decision 2 Expected cost of decisions 1+2 Is there a better Decision 1? Take Decision 1 Reveal the many possible outcomes Stage 1: Commit 1 or 2 or none of the “slow” generators Stage 2: There are hundreds of possible wind speeds. For each wind profile, decide the optimal commitment of the other units and dispatch of all units RESULT: Optimal unit commitment for “slow” generator 22/09/2018 3rd European Electricity Ancillary Services & Balancing Forum Workshop

In conclusion: SO solution provides a more conservative and robust unit commitment solution for the day-ahead market Because SO is embedded at the deepest level of the optimisation the outcomes respect all input constraints including security-constrained transmission, fuel, emissions, etc, so one expects the SO-based DA schedule to yield in real-time dispatch: Less congestion Less use of emergency generation/load management solutions More conservative/robust ancillary services dispatch 22/09/2018 3rd European Electricity Ancillary Services & Balancing Forum Workshop

Photovoltaic and wind intermittency causes and response. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

How does wind power and photovoltaic influence the power price on the spot market?
The impact of wind power generation on the day-ahead spot prices can be quite substantial, something that have been reported in a number of related studies. Particularly, adding wind into the power mix has a significant influence on the resulting price of electricity, the so called Merit Order Effect (MOE). Wind power does contribute to the reduction in prices but also interconnector capacities play a very significant role in bringing the price to zero at time. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

In general, Wind & PV power influence prices on the spot market in two ways: A) Wind/PV power normally has a low marginal cost (zero fuel costs) and therefore enters near the bottom of the supply (stack) curve. Graphically, this shifts the supply curve to the right (see next Figure), resulting in a lower power price, depending on the price elasticity of the power demand. In general, the price of power is expected to be lower during periods with high wind than in periods with low wind. This is called the ‘Merit Order Effect’. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

The way in which Wind/PV power integration influences the power spot price due to its low marginal cost. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

B) There may be congestion in power transmission, especially during periods with high Wind power generation. Thus, if the available transmission capacity cannot cope with the required power export, the supply area is separated from the rest of the power market (market splitting) and constitutes its own pricing area. With an excess supply of power in this area, conventional power plants have to reduce their production, since it is generally not economically or environmentally desirable to limit the power production of wind. In most cases, this will lead to a lower power price in the sub-market. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

MIBEL Price Collapse & Market Splitting - 31/10/ PLEXOS® 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

The impact of wind power on market prices depends on the time of the day. If there is plenty of wind power at midday, during the peak power demand, most of the available generation will be used. This implies that we are at the steep part of the supply curve (see next figure) and, consequently, wind power will have a strong impact, reducing the spot power price significantly (from Price A to Price B). But if there is plenty of wind-produced electricity during the night, when power demand is low and most power is produced on base load plants, we are at the flat part of the supply curve and consequently the impact of wind power on the spot price is low. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Wind power & Photovoltaic influence on the power prices on the spot markets
Many studies have shown that an increase in amount of wind power reduces the periods of constant production and the duration of these periods. The capacity factor of units with low start-up and turn down performances and high minimum stable level will decrease more than the capacity factor of units with high start and turn down performance and/or low minimum stable level. With increased wind power volatile fed in the power price becomes increasingly volatile as well. While the short term effect of wind is lowering prices, in the long term there is an effect on the conventional capacity as well. Therefore, the result of the RES-E integration with a relatively low capacity credit is an increase in peak load capacity and decrease in base load capacity. The slope of the merit-order curve will also change in the long run due to this. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Wind power & Photovoltaic influence on the power prices on the spot markets
In general, an increased penetration of wind power reduces wholesale spot prices. In countries, where the target is to have a high percentage of the electricity consumption from Wind/PV, there will be more instances of zero spot prices. This will have an effect on new generation investments by making investments in future capacities less attractive. The share of RES will play an crucial role in future development of the market structure. During periods of low demand, the technology that sets the price in the wholesale market is usually hard coal in most European countries. It has been observed that Wind replaces hard coal power plants during hours of low demand and gas fired power plants during hours of high demand. For the time being, Lignite and nuclear have no MOE so Gas and hard coal had the highest MOE MOE effect has been reported to range from 3 to 23 €/MWh 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

5/10-minute price dispatch rates

PLEXOS Program Scope 1 min 30 years+

PLEXOS Can model 1-minute or greater time step
Real-time markets Sequential Day-ahead and Real-Time markets simulation to capture the Renewables / load variability and uncertainty DA simulation produces unit commitment schedules using forecasted Renewable generations and loads RT simulation reveals the ramp capacity adequacy using “actual” Renewable generations and loads 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Background Need to include short-term variability of renewables in price forecasting, and emerging trend of markets operating at sub-hourly level… Leads to requirement to model with very short intervals e.g. 5/10-minutes Here we explore modelling 5-minute dispatch and consequences for pricing behaviour of generators via PLEXOS simulator and later 10-minute dispatch in association with game theoretic models… 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

5/10-minute Dispatch PLEXOS configurable from 1-minute up to 1-hour (or coarser) resolution In 5/10-minute dispatch models we can simulate: Run up and down time for generators: Affect of cooling on run up and ramping rates: Combined ramp and ancillary services limits: 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Fundamental Model Inputs
Load and Renewables: Forecast and error parameters Thermal Generation: Fuel costs Heat rate curves Technical constraints (next slide) Outage factors Transmission: Interchange capability and costs 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Generator Technical Limits
Hot Ramp Rate Cold Ramp Rate Run Up Rate Min Stable Level Min Up Time 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Wind and Dynamic Constraints
Wind resources require significant ramping capability in the system PLEXOS allows for the specification of ramp rates which must be obeyed (or can be violated at a penalty) In the long run ramp rates ensure that enough flexible capacity is built to meet the ramping requirement imposed by wind energy In the short run of DA & RT Markets this ensures PLEXOS commits enough fast ramping plant to meet requirements 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

EXAMPLE - Modelling Details
Unit Commitment In hourly modelling it is convenient to assume that generators ‘jump’ from zero generation to Min Stable Level in the one hour and back again when shutting down. This simplifies the unit commitment problem because only operation inside the normal operating range (Min Stable Level to Max Capacity) needs to be modelled. In 5/10-minute modelling the time taken for a unit to run up is important both because of simulation accuracy and also because units cannot provide regulation or other ancillary services while running up or down. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

EXAMPLE - Modelling Details
Property Value Units Max Capacity 100 MW Min Stable Level 40 Max Ramp Up 1 MW/min. Run Up Rate 0.5 A more detailed alternative to constant Run Up Rate is a Start Profile. In the following definition “P” indicates the interval number after the unit is commenced start up: Property Value Units Timeslice Start Profile 5 MW P01 10 P02 15 P03 20 P04-13 25 P14 30 P15 35 P16 40 P17 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

5-minute modelling in PLEXOS®
This chart shows the start up of a generator using two alternative inputs: a constant run up rate or a more detailed profile of start up 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

This effect is largely lost in hourly modelling
5-minute modelling in PLEXOS® Why is 5-minute modelling important? During the run up and down period the generator is completely inflexible No spinning or regulation reserve response can be provided Sudden changes in wind production (up or down) can only be covered by flexible units operating in their normal range This effect is largely lost in hourly modelling 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

5-minute Modelling & Reserves Response
A ‘basic’ model of spinning reserve response assumes that response is defined only by the constraint: Response <= Spare Capacity In reality (and in 5/10-minute modelling) response is limited by the rate of response in the timeframe the reserve is required in: Response <= Timeframe × Energy Ramp Rate Further, energy ramping subtracts from available reserve response, but not necessarily at a 1:1. The reserve response can be faster than the energy ramping rate: Ramp + [Response Ratio] × Response <= Timeframe × Ramp Rate In addition, no response is possible during the run up or down period. In the following example the [Response Ratio] parameter is set to 0.5. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

5-minute Modelling & Reserves Response
Firstly the unit cannot provide response during run up, but also while it continues to ramp up through its normal operating range the available response is limited because energy ramping subtracts from reserve ramping. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Game Theoretic Models with PLEXOS: an in depth presentation
Balancing Renewables Volatility with PLEXOS® Game Theoretic Models with PLEXOS: an in depth presentation 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Game Theoretic Models with PLEXOS®
Game theory is the study of multi-person or multi-firm decision-making problems. In the field of industrial organisation in economics, game theory is used extensively to study auction behaviour, bargaining, principal-agent relationships, product differentiation, and strategic behaviour by firms. Companies are the primary objects used to define competitive entities in the PLEXOS gaming models such as Nash-Cournot Competition, Bertrand Competition, Residual Supply Analysis, and LRMC (Revenue Recovery) methods. You must group generators into Companies to use these models. The extent to which a Company participates in gaming is controlled by the level of Financial Contract cover and/or the setting of the Strategic property. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Company Strategic property can be used to control the extent of participation by a Company in the automated gaming models. Values of Strategic above zero and up to 100% are used to approximate the effect of contracts on gaming behaviour. Strategic = 0 will 'switch off' the Company from participation in these games i.e. their generator offers are then prepared on a short-run marginal cost basis. Each Company object contains collections for ownership of Generators, Purchasers, and Lines. A Company may contain any number and combination of these members, and any Generator, Purchaser, or Line may belong to multiple Companies i.e. companies may share ownership of assets and hence share in their reported generation, revenue, costs, etc. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

A way to group the Game models is by the type of interaction that they assume about the behaviour of power markets participants (primarily, but not limited to, generators): Competitive – firms are price-takers and possess no market power Cournot – quantity is the strategic variable, and firms choose quantities simultaneously, under the assumption that other firms’ quantities are fixed Bertrand – price is the strategic variable, and firms choose prices simultaneously, assuming that other firms’ prices are fixed Supply Function Equilibrium (SFE) – entire bid functions are the strategic variables, and firms choose their supply functions simultaneously, under the assumption that other firms’ supply functions are fixed; a market mechanism, e.g. an ISO, then determines price and sets the quantity. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

LRMC Recovery Method 5/11/2011 One way to model the recovery of fixed costs is for the analyst to input a set of energy offers that in some way reflect fixed cost charges. This could be based on historical offering patterns – if they seem to result in recovery of those costs – or some another method. This approach can be implemented with PLEXOS but has several drawbacks. To address this, PLEXOS can model fixed cost recovery in a totally dynamic and automatic fashion, accounting for natural rents earned across a long period of time and all system constraints and opportunities that arise due to outages, as well as the dynamics of cost recovery across a portfolio of assets. All that is required is for the analyst to input the fixed cost requirements on each generator or transmission line, and invoke the fixed cost recovery model as a model option. Historical patterns are more often than not poor indicators of medium term future patterns, particularly because they do not account for growth in load, new generator entry, new transmission expansion, or any short-term simulated event such as outages. The same disadvantages apply to user-defined offers, plus they can be very time-consuming to prepare. Neither offers based on historical patterns nor user-defined offers can easily ‘target’ the level of fixed cost recovery required for each portfolio of plant. 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Fixed versus Variable Costs
The variable portion of generation cost is set by fuel prices, generator efficiencies and any opportunity costs implied by other constraints. Generators trading in the market expect to recover their variable costs of operation in every period – referred to as their short-run marginal cost (SRMC). In the medium term, however, they must also cover fixed operating costs, make contributions to debt servicing, and return a profit to shareholders. These fixed cost charges together can be expressed as a per kW capacity charge across some period of time, generally one year. The combined charge (variable plus fixed) is often referred to as long-run marginal cost (LRMC) 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Calculating Fixed Cost Charges
5/11/2011 Calculating Fixed Cost Charges For convenience, PLEXOS divides the total annual fixed cost charge into three components: Fixed Operations and Maintenance Charge (FO&M Charge) Equity Charge Debt Charge Because this is a medium term equilibrium model, it requires that MT Schedule is selected in the Simulation Horizon. Cost recovery is performed across portfolios, thus every generator or line that is involved in cost recovery must belong to a Company. The FO&M Charge is equal to the total fixed operations and maintenance cost divided by the installed kilowatts at the generator e.g.if the total annual cost is $66 million and the generator has 2640 MW installed capacity, then the FO&M Charge is: FO&M Charge = 66,000,000 / 2,640,000 = $25 /kW/year 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop 22/09/2018

Price Forecast – Nash Cournot MT Schedule solves an annual Cournot game in aggregate quantities i.e. not hourly because there is no demand function by hour but there is by year. Accounts for contract position, and transmission Interprets the Cournot solution as a set of volume and revenue expectations by Company Calculates mark-ups using modified LRMC algorithm Decomposes MT Schedule solution into a set of mark-ups for ST Schedule ST Schedule proceeds with calculated mark-ups Most suitable for Merger & Acquisition analysis, though it produces plausible price results on some markets e.g. Australian NEM Will receive more development in the near future: has a lot of potential as a price forecasting method 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Nash-Cournot game The demand function is linear function with intercept in units of price (e.g. $/MWh). The higher the intercept relative to the Demand Slope, the less elastic the demand function. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Price Forecast – Uplift PLEXOS specifically allows for definition of a custom “uplift” (Design settings) This uplift could be a ‘real’ uplift method or simply a method for adding a premium to the market price to synthesise observed mark-ups (similar to RSI) Mark-ups can also be changed programmatically Both of these customisation methods use OpenPLEXOS 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Focus of this presentation
Game Theoretic Models Long Term years LRMC Medium Term 1 year Nash-Cournot Short Term 5-min. – 1 hour Bertrand Focus of this presentation 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

PLEXOS® Experience PLEXOS simulation applied to:
California 25% and 33% renewable generation integration studies: Public dataset available Cluster computing Mid-west ISO / Manitoba Hydro renewable generation integration study: Full transmission system (OPF) Detailed hydro network 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Solution Method Mixed-integer programming with Monte Carlo simulation of load, wind, solar, outages Solved in two passes: Scheduling Run: Hourly resolution Daily time steps Determine unit commitment for slow-start plant Real-time Simulation: 10-minute resolution 4-hour time steps Dispatch intermediate and fast-start units 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Bertrand – Shadow Pricing
The core mechanism of the Bertrand Game is 'Shadow Pricing' i.e. pricing generation up to the next generator's offer price in the merit order. 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Bertrand – Out-of-merit-order
Where the next generator in the merit order has a small volume it can be optimal to price above that generator and sacrifice the volume for a higher overall profit 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Bertrand – 10-minute Modelling
Out-of-merit-order pricing is possible when generators are running up – they cannot respond if generators lower in the merit order price above them Similarly when generators are ramp-up constrained their competitors may price above them Conclusion: not just peak load periods will have mark-ups but also high ramp periods 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Case Study Spanish System, March 2020: Scheduling Run: Real-time Run:
52 GW peak load 35GW wind 7GW PV 1,9GW Biomass Scheduling Run: MIP with non-zeros, 9500 integers 1 hour/month solve time Real-time Run: MIP with non-zeros, 8500 integers 10-minutes/month solve time 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Cost-based and Gamed Prices
Many instances of extreme pricing. Let’s zoom in on a day and find out why… Simulation Results Orange = Cost-based prices Blue = Bertrand prices 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Load and Renewables Generation
Simulation Results Wind and solar both drop before the evening peak Wind goes away in the early morning No solar till 7:00 AM 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Residual load has two peaks and exaggerated ramp
Simulation Results 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Steam Unit Generation Simulation Results

CCGT Generation Simulation Results

OCGT Generation Simulation Results

Thermal Unit Starts Simulation Results Starts during morning ramp
and evening ramp 2.5 GW dip in renewable production 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Cost-based and Gamed Prices
Price spike in peak time Simulation Results Price spike in evening ramp Price spike in morning ramp Orange = Cost-based prices Blue = Bertrand prices 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Price Duration Curves Simulation Results
Bertrand shifts PDC to the right Orange = Cost-based prices Blue = Bertrand prices 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Predicting Price Spikes
When do high mark-ups occur? High load? Low generation availability? High residual load ramp? Residual Supply Index? Question: Can we derive a statistical relationship between Bertrand-derived mark-ups and any of these parameters? Answer: No. There are no significant correlations in these results… 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

Conclusions Integration of wind and solar leads to:
Double-peak residual load profile Greater demand for flexibility More frequent cycling of thermal units Frequent binding of ramp and start-up constraints Gaming opportunities away from peak load times Game theoretic models integrated into a fundamental model can capture these effects Difficult to predict gaming behaviour using empirical models Fundamental simulation at sub-hourly resolution a key tool in modern price forecasting 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

1 Hour v 5 Minute Simulation – FLEX units

PLEXOS® Applications Price forecasting
Power market simulation and analysis Capacity expansion planning Co-optimisation of ancillary services Transmission analysis Portfolio optimisation Risk management and stochastic optimisation Renewable integration analysis 22/09/2018 3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

European Electricity Ancillary service & Balancing Forum- Berlin 2012
Thank you for your time, attention and the opportunity. 22/09/2018 European Electricity Ancillary service & Balancing Forum- Berlin 2012

Use of PLEXOS® Software to Calculate and Dispatch Power Prices

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Use of PLEXOS® Software to Calculate and Dispatch Power Prices

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Presentation on theme: "Use of PLEXOS® Software to Calculate and Dispatch Power Prices"— Presentation transcript:

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