1. PLEXOS®: Game Theoretic Models and 10-Minute Dispatch in Price Forecasting
Dr Christos Papadopoulos
Regional Manager Europe
Energy Exemplar (Europe) Ltd
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop
18/09/2018

2. 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
18/09/2018

3. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

4. 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
18/09/2018

5. 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
18/09/2018

6. 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
18/09/2018

7. 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
18/09/2018

8. Using PLEXOS® for Price Forecasting
PLEXOS®: Game Theoretic Models and 10-Minute Dispatch in Price Forecasting
Using PLEXOS® for Price Forecasting

9. Analysis tools in PLEXOS®
Market Analysis – Price Forecast
From Long & Medium Term pricing
LRMC Recovery Algorithm
Shadow Pricing (Bertrand game)
Nash- Cournot Competition Game
Residual Supply Index (RSI)
Uplift mechanisms
To Short Term (Day ahead/Real Time/AS) pricing
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

10. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

11. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

12. 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.
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

13. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

14. 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
18/09/2018

15. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

16. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

17. 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)
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

18. 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
18/09/2018

19. 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.
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

20. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

21. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

22. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

23. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

24. Renewables analysis: detailed 5-minute renewable production analysis

25. PLEXOS Program Scope 1 min 30 years+
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop
18/09/2018

26. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

27. 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-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…
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

28. 5-minute Dispatch
PLEXOS configurable from 1-minute up to 1-hour (or coarser) resolution
In 5-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:
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

29. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

30. Generator Technical Limits
Hot Ramp Rate
Cold Ramp Rate
Run Up Rate
Min Stable Level
Min Up Time
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

31. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

32. 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-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.
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

33. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

34. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

35. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

36. 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.
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

37. 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.
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

38. Smart load modelling

39. Smart Loads
The concept of the Smart Grid is to perform live two-way communication between the grid (or system operator) and consumers (industrial and residential) such that loads can respond in real-time to price signals
Smart loads are those that have some ability to shift consumption between hours of the day but perhaps not reduce consumption in aggregate
Examples include refrigeration, washing machines, heating (night-store being an old-school example)
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

40. Smart Load Scenario in PLEXOS
For example, a class of customers normally consumes 800 MW per hour on average or 19.2 GWh per day
We can define this load as high-priced bids with the typical hourly shape and then add a Constraint on the Purchasers [Demand Coefficient] as in the following…
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

41. Smart Load Scenario in PLEXOS
Add a smart load with a scenario
Create Purchaser called ‘Smart Load’ at load center (node 3)
Set bid quantity of 50MW (the maximum simultaneous off take)
Set bid price of $1000 (the maximum price at which is will off take load)
Create constraint object
Setup membership to purchaser and set load coefficient of 1
Set RHS day of <= 0.3 (average of 25MW per hour)
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

42. Smart Load Scenario Price Responsive Load Inelastic Load
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

43. Price dispatch every 10 minutes

44. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

45. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

46. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

47. Residual load has two peaks and exaggerated ramp
Simulation Results
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

48. Steam Unit Generation Simulation Results
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

49. CCGT Generation Simulation Results
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

50. OCGT Generation Simulation Results
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

51. Thermal Unit Starts Simulation Results Starts during morning ramp
and evening ramp
2.5 GW dip in renewable production
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

52. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

53. Price Duration Curves Simulation Results
Bertrand shifts PDC to the right
Orange = Cost-based prices
Blue = Bertrand prices
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

54. 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…
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

55. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

56. Demand for flexibility
10 minute Dispatch
1 Hour Dispatch
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

57. Transmission Investment Analysis
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop
18/09/2018

58. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

59. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

60. 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
18/09/2018

61. 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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

62. Analysis tools in PLEXOS®
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
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

63. Comparison – Imports and exports
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.
Greater interconnector capacity increases both imports and exports
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

64. Comparison – Imports and exports
Greater interconnector capacity reduces price – greater price convergence
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop

65. Thank you for your time, attention opportunity.
and the
opportunity.
18/09/2018
3rd Annual European Electricity Price Modelling & Forecasting Forum Workshop