Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos

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Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
Forecasting power and gas prices on various
time frames and resolutions with PLEXOS®

Dr Christos Papadopoulos
Regional Director Europe       5th Annual Electricity Price Modelling
                               and Forecasting Forum
Energy Exemplar (Europe) Ltd
Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
Energy Exemplar &
PLEXOS® Integrated Energy Model
Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
About Energy Exemplar
 PLEXOS® Integrated Energy Model - Released in 1999
    Continuously Developed to meet Challenges of a Dynamic Environment
 A Global Leader in Energy Market Simulation Software.
 Offices in Adelaide, AUSTRALIA; London, UK; California, USA-WC; Connecticut, USA-EC,
  Johannesburg, SOUTH AFRICA.
 High Growth Rate in Customers and Installations
 30% staff with Ph.D. level qualifications spanning
  Operations Research, Electrical Engineering,
  Economics, Mathematics and Statistics
 European Office:
    Software Sales
    Customer Support
    Training
    Consulting
    European Systems/Markets &
        Countries Datasets
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Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
Energy Exemplar
Portfolio of clients in all five continents                                         Energy Exemplar Europe

As of the end of July 2014, worldwide installations of PLEXOS have exceeded 850
at over 145 sites in 35 countries.

      11-Sept-14                            Energy Exemplar - 5th Annual EPM & FF                       4
Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
PLEXOS® Integrated Energy Model for Energy (Power & Gas)
         Systems & Markets Simulation, Optimisation & Analysis.
 Proven power market simulation tool &
  Integrated Energy Model
 Uses cutting-edge Mathematical Programming
  based Constrained Optimisation techniques
  (LP/MILP/DP/SP),
 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 systems’ models scalable to thousands of
  generators and transmission lines and nodes
     11-Sept-14                               Energy Exemplar - 5th Annual EPM & FF   5
Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
PLEXOS® Integrated Energy Model

 Recently it was released and was integrated within PLEXOS® the
  NEW Gas (modelling) Module. The new PLEXOS® Gas module
  provides the capability to model the costs and constraints of gas
  delivery from its source fields via a network of pipelines,
  through storages and on to meet demands, including those
  associated with the Power production model.
 More importantly though, it is now possible in PLEXOS®, the
  Integrated Modelling of both Natural Gas and Power Systems &
  associated Markets.

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Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
PLEXOS® Integrated Energy Model

GAS ELECTRIC
COOPTIMIZATION &
PRICE FORECASTING

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Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
PLEXOS® Integrated Energy Model
 That practically means that, it can be now also used in:

  Simulation of electricity and natural gas prices in short term to long term.
  Natural gas network price formation linked to Gas Powered Generation
   fuel costs
  Pipeline congestion pricing from Well Heads to Natural Gas Hubs
  Gas market integrated with competitive electricity market production
   cost models
  Market driven production outputs for both gas and electricity sources
  Fundamentals of Supply and Demand modelling for gas and electric
  Hourly and sub hourly price forecasting for Day Ahead, Intraday & Real
   Time Markets
  Flexibility for assessments for gas electric systems
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Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
Natural Gas and Electric System Coordination
Coordination of both the Natural Gas and Electric sectors is critical for:

 Least cost co-optimization of OPEX and CAPEX of gas and electric system
  expansion
 Combined economic benefit analysis for gas and electric rate payers
 Strategic energy development for public policy and renewables integration
 Valuation of gas and electric storage opportunities and dual fuel
  optimizations
 Evaluation of gas and or electric contingencies that can impact reliability
 Derating of gas powered generators due to gas network constraints
 Assessing emerging gas constraints with generation retirements
 Interregional market and asset development planning for gas and electric

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Forecasting power and gas prices on various time frames and resolutions with PLEXOS - Dr Christos Papadopoulos
Integrating quantitative and fundamental
     price forecasting with PLEXOS®
A General Classification of Models

                  Specific vs Generic
             Estimation vs Principal Laws
                Numerical vs Analytical
              Stochastic vs Deterministic
             Microscopic vs Macroscopic
                Discrete vs Continuous
              Qualitative vs Quantitative
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Power Markets’ Models Classification – Statistical
 Statistical (or technical analysis) Models,
Statistical approaches aim at finding the optimal model for electricity prices
in terms of its forecasting capabilities. They are either direct applications of
the statistical techniques of load forecasting or power market
implementations of econometric models. Most popular methods include
multivariate regression, time series models and smoothing techniques.
While the efficiency and usefulness of such “technical analysis” tools in
financial markets is often questioned, in power markets these methods do
stand a better chance. The main reason is the seasonality prevailing in
electricity price processes during normal (non-spiky) periods. This makes
the electricity prices more predictable than those of “very randomly”
fluctuating financial assets. In order to enhance their performance, they
often incorporate fundamental factors, like loads or fuel prices.
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Power Markets’ Models Classification – Artificial Intelligence
 Artificial intelligence-based (or non-parametric, ANN, Fuzzy Logic,
  Genetic Algorithms) Models:

Artificial intelligence-based (AI-based) models, are employ pattern
recognition type of techniques, modelling price processes via non-
parametric tools such as artificial neural networks (ANNs), expert systems,
fuzzy logic and support vector machines. AI based models tend to be
flexible and can handle complexity and non-linearity. This makes them
promising for short-term predictions

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Power Markets’ Models Classification – Quantitative
 Quantitative (Econometric, Reduced-form) models:

Quantitative models characterize the statistical properties and dynamics of
electricity prices over time, with the ultimate objective of derivatives
evaluation and risk management.
They aim to recover the main characteristics of electricity prices, typically
at the hourly/daily time scale and monthly time horizons.
Although in this context the models’ simplicity and analytical tractability
are an advantage, in accurately forecasting e.g. hourly prices is a serious
limitation, while the recovery of their main underlying characteristics is an
excessive luxury.

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Power Markets’ Models Classification – Fundamental
 Fundamental Models:
Fundamental methods are based on the most basic economic principles of
supply and demand describing price dynamics and modelling the impact of
important physical and economic factors on the market equilibrium price of
electricity. The fundamental inputs (loads, weather conditions, system
parameters) are independently modelled and predicted, often employing
statistical, econometric or non-parametric techniques.
Because of the nature of fundamental data which is typically collected over
relatively long time intervals and the data availability issues, pure
fundamental models are mostly used for medium to long-term analysis and
predictions.

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Fundamental Models’ Classification – Production Cost
 Production Cost (or cost-based) models:

Pure production-cost models simulate the operation of generating units
aiming to satisfy demand at minimum cost. They may have the capability to
also forecast prices on an hour-by-hour, bus-by-bus level, however, when
ignore market’s operational principles and strategic bidding practices are
not well suited for today’s competitive markets.

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Fundamental Models’ Classification – Market Equilibrium
Equilibrium (Game Theoretic) approaches may be viewed as generalizations of cost-based
models amended with strategic bidding considerations. They may give good insight into whether
prices will be above marginal costs and how this might influence the players’ outcomes.
Various types of equilibrium approaches have been proposed:
Perfect Equilibrium – Firms are price-takers, biding in their SRMC and possess no market power
Cournot-Nash Game – Quantity is the strategic variable, and firms choose quantities
simultaneously, under the assumption that other firms’ quantities are fixed
Bertrand Game – 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. Cournot-Nash framework tends to provide higher prices than those observed in reality
and the supply function equilibrium framework requires considerable numerical computations
and consequently, has limited applicability in day to-day market operations.

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Fundamentals vs Quantitative modelling
Fundamental Models                                     Quantitative Models
   Prices are determined by supply and
    demand principles                                     Prices depend mostly on historical prices
   Replicates actual market design and                    and random processes
    intended behaviour meeting economic                   Usually     probabilistic,    explore     the
    and operational constraints                            distribution properties of prices
   Can capture technical constraints on
    physical assets operating within the                  Can suffer from in-sample bias of historical
    market                                                 data
   Allows any type of “what if” analysis into            Scenarios only with parameters and/or
    the future                                             explanatory variables
   Can allow co-optimisation of other
    requirements such as ancillary services               Most models cannot handle negative prices
    and/or district heating load etc.                     Result focuses on prices only
   Produce results that reflect future                   Limited understanding of what particular
    structural changes e.g. carbon price
    impacts, changes to market rules,                      input could be causing the resulting price
    renewable integration

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Common criticisms of Fundamental Market models
     in replicating short term prices (trading)
 Emphasis on a deterministic outcome
 Failure to capture bidding strategies by players in the market
  (pure production cost models)
 Assumptions of perfect market theory
 Failure to capture the peak price volatility (pure equilibrium
  models)
 Run times not conducive of using a large market model within
  a trading environment when regular updating of inputs is
  required.
 However the recent advances in computing power have led
  to their adoption for short-term predictions.
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Fundamentals vs Quantitative modelling

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Uncertainties and Risks involved
With the advent of power markets and the evolution of market
mechanisms both financial and physical positions have uncertainty that
requires quantification to better plan for the future.
In today’s power sector transmission competes with generation and load
competes with generation and transmission.
How so?
 Active demand response and energy efficiency can reduce the need for
    generation capacity as well as transmission requirements.
 A load pocket can be served with transmission or local generation.
Physical asset developers must evaluate all the risks of physical competition
to see how competitive their solutions are and then shortlist the most
competitive ones and use limited corporate resources to focus on the more
likely winners.
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PLEXOS® Modelling Framework
PLEXOS provides a framework for testing various pricing options for
assets valuations in markets where competition can emerge in the
form of load, transmission or generation solutions. Likewise for natural
gas infrastructure development, PLEXOS® provides a comprehensive
valuation methodology that considers both electrical and gas sector
gas demands.
For financial risk evaluation PLEXOS® mixes both statistical risk
models with fundamentals models.
Statistical risk methods depend on historical data and can suffer from
in-sample bias where fundamentals models can generate price paths
that can reflect structural change such as carbon price impacts, change
in market rules, retirements and new entries of power plants, changes
in demand forecasts and fuel forecasts and price paths subject to
other uncertainty.
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PLEXOS® Modelling Framework

The combination of statistical methods and
fundamentals is the preferred approach of today’s risk
managers.
In addition, PLEXOS® also offers the power of stochastic
optimization which enables the risk manager to forecast
robust forecasts for generation assets, market prices,
and other quantities.

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PLEXOS® Modelling Framework

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2 Day Forecast ARMA (3,0,3)(1,0,1)

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PLEXOS® Modelling Framework

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Two fundamental modelling approaches in PLEXOS®
Input Bid based Stack model:                      Generation Cost based Stack model:
 Each generator is represented with offer        Each cost element that makes up a
   price/quantity files which must be known in    generators offer into the market can be
   advance (“backasting - calibration”) or        separately inputted
   inferred.                                      Each generator offer price/quantity is
 Easier to setup, no need to calculate each      calculated based on SRMC plus any mark-ups,
   element that makes up a generators SRMC.       so it is finally transformed to a Bid-stack model.
 Can link price/quantity files to an external    Allows more flexibility when modelling the
   source     to     update     regularly   and   overall effect of changes of certain generator
   automatically                                  values (fuel costs, heat rates, outage rates etc.)
 Unit commitment decisions will still be         Harder to gain accurate technical and
   optimised by PLEXOS such as MUT, MDT,          commercial characteristics on competitors
   ramp limits, start profiles etc. However min   plant.
   stable level and max capacity of units need    If inputs are realistic, a more useful model for
   to be defined.                                 price “forecasting” when compared to a Bid
                                                  stack model, at the cost of increased run time
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                    BID STACK                             GENERATION (SRMC) STACK               27
Impact of Growing Generation from RES on Supply Stack & the Wholesale
   Power Price
                  Supported RES generation brings volatile and less predictable          Demand
                  supply
                  The spot prices decline (not the final price for the consumer!)
                                                                                          Gas
                  Negative impact also - Lower utilization of non-RES generation

                                                                      Hard coal
             75                                    Lignite

             50

                              Nuclear

             25

                      RES

             0
                            20                40                 60                  80
                                                                                                Source: CEZ
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Supply (bid) Curves of multiple generators
             Daily development of the supply curves submitted to the California Power
             Exchange during a 24-hour period

                                                          Energy Laboratory Publication # MIT_EL 00-004

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Plants’ Bid Stack vs Generation (SRMC) Stack

             Bid Stack                                           Generation Stack

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Fundamental Hybrid modelling for price formation in PLEXOS®
   - Marginal Pricing
Power markets run on “marginal pricing” thus it is the “cost” of the
marginal (or last) unit of serviced load that sets the energy price.
NOTE: Under Perfect Competition price must be equal to the SRMC of the
marginal generating unit. In reality, generators 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 (Shadow Prices).
Solving a linear program usually provides more information about an
optimal solution than merely the values of the decision variables.
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The different timeframes and resolution
           phases of PLEXOS®
Europe’s electricity providers face an existential threat
  (The Economist 12/10/2013)

New Era
The decline of Europe’s utilities has certainly been startling. At their peak in 2008, the top
20 energy utilities were worth roughly €1 trillion ($1.3 trillion).
Now, less than half that.
Under the “old” system, electricity prices spiked during the middle of the day and early
evening, falling at night with lower demand. So, companies made all their money during
peak periods.
Now the middle of the day belongs to solar generation that has competed away the price
spike.
In Germany in 2008, according to the Fraunhofer Institute for Solar Energy Systems, peak-
hour prices were €14 per MWh above baseload prices.
In the first six months of 2013, the premium was €3 per MWh.
    So not only have average electricity prices fallen by half since 2008, but the peak
                       premium has also fallen by almost four-fifths.
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Historical price analysis slowly becoming less relevant

    Fundamental changes in the energy markets are already
     effecting prices
            Changing government policies (EMR)
            Change in market design (coupling of markets)
            Renewable Integration/Subsidies
            Drop in energy demand and growth due to economic crisis
            Falling CO2 price
            Spark spreads going to negative and falling (expensive Gas)
            Dark spreads going positive (cheap imported coal)

    What do we have to consider next?
            Demand Side Management
            Energy Storage technologies
            Capacity markets or more importance on reserves and balancing
            Increased electrification of rail networks
            Government legislation and policies

    Understanding renewables profiles and potential variations is
     becoming more critical in forecasting daily prices
                                 Strong decrease of the weight in the
                                  peak hours in a typical daily profile
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Price Forecasting: What Price(s)?
 When we normally talk about Electricity Price Modelling and
Forecasting we imply Electricity Price and particularly Spot (DA)
Prices.
               Are still the only important ones?

 There is a whole list of electricity associated market products
that their significance is continuously revealed day by day and their
pricing and associated price forecasting will be become even more
important in the years to come.
 Reserves (AS) and Balancing Prices and related Price Forecasting.
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Price Forecasting: What Timeframes and at what
  Resolution?
  PLEXOS®
                                                                      Energy prices
             • Optimal Expansion Plan
                                                                      Capacity payments (prices)
    LT                                                                •LT prices

             • LRMC Recovery Method
             • RSI                                                    Company (player) revenue targets
   MT        • Nash-Cournot Game                                      Adjust bids: Mark-ups

             • Cost-based Efficiency                                  •MT prices
             • Bertrand Game
                                                                      Hourly (period) energy price forecast
             • Nash-Cournot Game
    ST       • Uplift ex-post price                                   (RT) Energy & Ancillary Services prices
                                                                      •ST prices

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Generation: Fixed v 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)

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PLEXOS® Equilibrium Model Mechanism for Calculating Market Price
 The market price of energy is the marginal cost, as represented by
  generators’ price/quantity offers (usually, somewhere between SRMC &
  LRMC) 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, at Nodal Level (LMP) 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.
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Locational (Nodal) Marginal Pricing (LMP) in PLEXOS®
λι     =       λ     +     αι       +      βι
                   Marginal Cost                  Marginal Cost
LMP          =     of Generation            +          of                      +   Marginal Cost
                    at reference                  Transmission                      of Losses
                         bus                       Congestion

  λ is the system “lambda”              αι : is the congestion charge at node i
                                                                                    βi: is the marginal loss charge at
  αι is the node’s congestion charge ωj: is the shadow price on the thermal         node i
  βι is the node’s marginal loss charge limit constraints for path j                rj: is the resistance on line j
                                        Xi,k: is the angle reference matrix
                                                                                    fj’: is the flow on the line j at the
                                        element
                                                                                    optimal solution
                                        ωκ: is the shadow price on the node
                                        phase angle constraints for node k

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Market Equilibrium
 LMP prices based on marginal costs do not include:
                                                                     While short term solutions
        Start Cost
                                                                     for start and no-load costs
        No-load cost                                                are typically included in
        Fixed Costs                                                 generator bids, Long-term
                                                                     cost recovery (fixed costs)
 Therefore, units do not collect all of their costs, and electric
                                                                     is seldom met in an
     prices are artificially low                                     energy-only market model.
        Baseload and intermediate units can collect some of
           these costs because they collect above marginal costs     This phenomena has been
           while peakers are running                                 dubbed      “the Missing
                                                                     Money Problem”.
        Peakers do not collect these costs                          Absent a solution, the
 Market Solutions                                                   market           generates
        External (i.e. Resource Adequacy)                           insufficient revenue to
                                                                     sustain operations
        Price Uplift
        Revenue Adequacy Energy Exemplar - 5th Annual EPM & FF
11-Sept-14                                                                                 40
What about Reserves (AS) & Balancing Prices Forecasting?
 Utilities and grid operators must be prepared to account for power plants
or transmission lines that unexpectedly go out of service, or for unforeseen
increases or decreases in electricity supply and/or demand.
 In addition, as utilities and grid operators increase their reliance on
intermittent renewable generation capacity like wind and solar power,
additional balancing resources are required to address any inconsistencies in
generation (e.g. when sufficient wind and sun are not available).
 The existing’ products address these short-term imbalances in
electricitAncillary Servicesy markets by dispatching resources within seconds
or minutes of an unacceptable imbalance, but the question is, will these
existing AS products be enough in this challenging new environment?
  Due to all these and the increased role of AS, a significant diversification
   between DA and RT (balancing prices) might be expected in the future.
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What about Ancillary Services & Balancing Prices Forecasting?
 System Reserves include among others, coordinated system operation,
  frequency regulation, energy balance, voltage support and generation
  reserves.
 Ancillary Services features of PLEXOS® are used in order to:
    Optimise the uptake of renewables given this additional burden
    Ensure provision of reserves in dispatch and expansion planning
    But more importantly, to calculate the cost to the system and the
      effect on energy prices of the additional reserve requirements and to
    Calculate and forecast expected ancillary service prices and test any
      new ancillary services provisions.
 This analysis takes advantage of PLEXOS® ability to set dynamic reserve
  requirements based on generators’, load or line contingencies.
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Co-optimization–Towards an Integrated solution

Co-optimisation & Pricing in Integrated Markets/Systems

 Co-optimization is necessary to minimize the total costs of
coordinating generation, transmission and reserves to meet
demand and ensure reliability.
 Electricity and Reserves Shadow prices derived from the
constrained optimization accurately reflect the system-wide
opportunity costs of associated scarce resources, both inter-
temporally and spatially.
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Ancillary Services Pricing & Price Forecasting

 When requirements for reserves are considered, the optimal trade-off
  between energy and reserve provision must be determined.
 The AS marginal price for an AS in a region is the incremental (Marginal)
  cost for meeting an additional MW of the requirement for the AS in this
  region.
 If no additional compensation were required to cover the cost of a plant
  operating at lower efficiency to provide reserves, the required
  compensation is given by the opportunity cost of backing off generation
  to provide reserves.
 In PLEXOS® this compensation will be automatically embodied in the
  reserves price, which is equal to the dual variable associated with the
  constraint defining the required quantity of reserves.

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Opportunity Costs
Under the Co-optimisation of Energy and multiple AS, the market clearing prices for the multiple
products have the following 3 characteristics:
 LMP for energy gives a precise representation of the cause-effect relationship that is
    consistent with grid reliability management
 Higher Prices for higher quality (more Flexible) Ancillary Services.
Spinning Raise Prices = Shadow Price (Clearing Price) of Spinning Reserve requirement constraint +
Shadow Price (Clearing Price) of Regulation Raise requirement constraint
 There is Marginal Equity between Energy and Reserves Prices
      Energy LMP - Shadow Price (Clearing Price) of Regulation Raise requirement constraint =
         Marginal Cost (Shadow Price) of combined Energy and Regulation Reserves provision at
         the node, when SR=0 and RR>0.
      Energy LMP - Shadow Price (Clearing Price) of Regulation Raise requirement constraint -
         Shadow Price (Clearing Price) of Spinning Reserve requirement constraint = Marginal Cost
         (Shadow Price) of combined Energy, Spinning and Regulation Reserves provision at the
         node, when SR>0.
 11-Sept-14                        Energy Exemplar - 5th Annual EPM & FF                        45
Modelling & Forecasting DA/ID/RT Prices
Energy Exemplar performs a few renewable generation integration studies
using the 3-stage DA-HA-RT sequential simulation approach. This approach
can be illustrated in the following flow-chart.

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Available Pricing Methods in PLEXOS®
 Locational Marginal Pricing (Nodal Pricing) (value = 0)
  Generators receive the locational marginal price (LMP) at the node(s) they are connected to. If a generator is connected
  to multiple nodes it receives the generation-weighted average price at those nodes according to the defined generation
  participation factors.
 Regional (Reference Node Pricing) (value = 1)
  Generators receive the regional reference price modified by the generators’ marginal loss factor.
 Regional Weighted Price (value = 2)
  Generators receive the load-weighted price in the region(s) they belong to.
 Pay-as-Bid (value = 3)
  Generators receive the offer price for each megawatt of generation cleared.
 Uniform Pricing (value = 4)
  Generators receive the single market price (uniform price).
 Most Expensive Dispatched (value = 7)
  The price is set at the SRMC of the most expensive dispatched Generator regardless of whether or not that Generator is
  truly marginal.
 None (value = 5)
  Generators receive no payment for generation. This option is useful where generators sell their output into an external
  energy market and revenues accrue to the trading portfolio (company) rather than the individual generating units.
 Custom (value = 6)
  PLEXOS® makes a call to Open PLEXOS® to calculate pricing. This method allows the user to implement custom pricing.

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Bertrand Competition Modelling in short-term price
     Forecasting?
 Bertrand Competition is a game theoretic model in which firms
manipulate the price component of their generation offer and keep
quantities fixed.
 It is generally accepted that Bertrand Competition does not yield
high enough average prices to recover generator investment costs,
but that it is a useful method for modelling short-term pricing
especially in the way it can capture gaming behaviour in times of
tight supply-demand balance and/or transmission congestion.

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Bertrand Competition in Modelling short-term
     pricing?
 PLEXOS® simulator implements a heuristic shadow pricing scheme that mimics
Bertrand Competition. In this game generators choose prices for their output in
order to maximize profit making opportunities in a one-round game.

 The Bertrand game is simulated independently for each dispatch interval e.g.
hour, half-hour, etc.
     The advantage of this is that the Bertrand Game can be run for any horizon
    length from a single interval up.
     The disadvantage is that the game makes no reference to the medium term
    effect of the pricing results i.e. it ignores the price elasticity of demand.

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Bertrand Game -'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. This is
illustrated in Figure 1. The stack of
generation is shown for three                         Figure 1: Generation bid-stack

independent generators (G1, G2, G3).
Figure 2 shows the offer prices that
result from a simple shadow pricing
policy:
"G1" bids up to "G2" price less epsilon
"G2" bids up to "G3" price less epsilon
"G3" bids up to shortage price less
epsilon
                                                      Figure 2: Generation bid-stack after Shadow Pricing
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Daily Bertrand v Real Energy Prices - Germany

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Hourly Bertrand v Real Energy Prices - Germany

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Daily Bertand v Real Energy Prices – France

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Hourly Bertrand v Real Energy Prices - France

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Thank you for your time and the
         opportunity
For further Information, please do not hesitate to contact EE Europe:

Dr Christos Papadopoulos
Regional Director Europe
christos.papadopoulos@energyexemplar.com

                       www.energyexemplar.com
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