Modelling Profit Maximisation in Deregulated
Power Markets by Equilibrium Constraints
Mariano Ventosa
Andrés Ramos Michel Rivier
13thPSCC
Trondheim, 29 June 1999
Outline
• Introduction
• Modelling Approaches
• Model Description:
Ñ Model Overview
Ñ Scheme of a production cost model with
Equilibrium Constraints
Ñ How the Equilibrium Constraints work
• Case Study
• Model Applications
• Conclusion
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 2
Introduction (I)
• Changes in global electric industry:
Ñ
Deregulation
Ñ
Competition
• Spanish electricity market
Ñ
Beginning in January, 1998
Ñ
Based on a simple merit order of the bids
Ñ
Market clearing price is the highest accepted bid
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 3
Introduction (II)
• New Framework: Deregulated Power Market
Ñ Increased opportunities and increased risks
Ñ New responsibilities:
• Unit commitment
• Hydrothermal coordination
• Biding prices and quantities
• Electric companies need original models that
consider:
Ñ The technical operation constraints
Ñ The new competitive framework:
• Profit maximisation behaviour
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 4
Modelling Approaches
• Other modelling approaches:
Ñ Based on the market equilibrium
Ñ Theoretical and practical advances
Ñ However, with some limitations
• Our approach:
Ñ Detailed modelling operation of thermal, hydro
and pumped units
Ñ Single shot optimisation procedure
Ñ Competitive behaviour of the market
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 5
Model Overview (I):
Traditional Production Cost Models
• Traditional Production Cost Models:
Ñ Medium term operation planning studies
Ñ Minimum generation cost subject to operating
constraints
• Two relevant characteristics of these models:
Ñ A detailed representation of the electric system
operation
Ñ Their main decision variables are the generation
output levels offered to the market
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 6
Model Overview (II):
Equilibrium Constraints
• Equilibrium Constraints
reproduce the first order
optimality conditions of the
firms’ profit maximisation
objective
Profit
Profit E. C.
Market Equilibrium with
Cost Minimization and
Equilibrium Constraints
Profit C.M .
Market Equilibrium
with
Cost Minimization
Pr ofit firm = Pr ice ⋅ Powerfirm − Cost firm
Power E.C . Power C.M .
∂ Pr ofit firm
∂ Powerfirm
Price
=0
Electricity demand
function
Marginal Cost
Price E. C.
Market Equilibrium
with
Cost Minimization
Price C.M .
Pr ice + Powerfirm ⋅
∂ Pr ice
= M arg inal Cost firm
∂ Powerfirm
Marginal Revenue
Output = Power
Marginal Revenue
Power E.C . Power C.M .
Output = Power
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 7
Scheme of the production cost model with
Equilibrium Constraints
Minimisation of:
Total Generation Variable Costs +
+ Costs of non accepted demand bids
Objective
Function
Subject to:
Operating
Constraints
Market
Constraints
Interperiod Constraints
Intraperiod Constraints
Equilibrium Constraints
Price equation
Market Share Constraints
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 8
Objective Function
Minimisation of:
Objective
Objective
Function
Function
Total Generation Variable Costs +
+ Costs of non accepted demand bids
Subject to:
Operating
Constraints
Market
Constraints
Fuel Costs
+
O&M
Interperiod
Constraints
variable costs
+
Intraperiod
Constraints
Start-up costs
+
Penalty
unmet reserve
margin
by
Equilibrium
Constraints
+
non
Price
equation
Costs of
accepted
demand bids
Market Share Constraints
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 9
Operating Constraints
Minimisation of:
Total Generation Variable Costs +
+ Costs of non accepted demand bids
Objective
Function
Subject to:
Interperiod
Operating
Operating Interperiod Constraints
Constraints
Hydro management
Constraints
Intraperiod
Constraints
Constraints
Seasonal operation of pumped-hydro
units
Fuel management
Maintenance scheduling
Equilibrium Constraints
Intraperiod
Constraints
Market
Balance
between
generation and demand
Price
equation
Generation Limits
Constraints
Daily/Weekly
pumped-storage
units
Market
Share Constraints
Reserve Margin
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 10
Market Constraints
Minimisation of:
Total Generation Variable Costs +
+ Costs of non accepted demand bids
Objective
Function
Subject to:
Equilibrium Constraints
Operating
Constraints
Marginal revenues equal marginal cost for each
firm
Interperiod Constraints
strategic
Marginal cost of each firm as a function of its
Intraperiod
Constraints
committed
units
System Marginal Price equation
The price is a function of the served demand
Equilibrium
Market Market Share
Constraints Constraints
Market
The market
share of
each leader in quantity
Constraints
Price
equation
Constraints
must be equal to its market share objective
Market Share Constraints
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 11
How the Equilibrium Constraints Work
The Cost Minimisation achieves
the cheapest feasible scheduling
of hydro generation of each firm
for the entire scope
Total Output
of Firm e
For each firm,
the Equilibrium Constraints
choose the output
that maximises
its profits for each load level
Thermal
Unit 2
Thermal Unit 1
Must run thermal generation
Run-of-the-river generation
The Cost Minimisation achieves
the cheapest feasible
commitment of thermal units of
each firm for each load level
Time
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 12
Case Study
• Our model has been applied to the Spanish power
market: 73 thermal units and 30 equivalent hydro units.
• The size of the MIP is 25,000 continuous variables,
2,000 binary variables and 33,000 constraints.
System
Marginal
Price
with
Cost Minimisation
and
Total Output
with
Cost
Minimisation
and with
with
Equilibrium
Constraints
Equilibrium Constraints
System Marginal Price
Total($/MWh)
Output (GW)
Price C.C.M.
Output
M.
Price E.E.C.
Output
C.
630
60
525
50
420
40
315
30
210
20
15
10
00
0
0
800 1500 2700 3900 4700 5200
800
1500 2700 3900 4700 5200
6100
6100
6900
6900
7800
7800
8500
8500
Time (h)
(h)
Time
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 13
Model Applications
• Use of results for analysing strategies:
Ñ In the long term, it is essential to find
specific quantities in order to maximise
the profit
Ñ In the short term, forecasted prices help
in defining bidding tactics in the wholesale
market
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 14
Conclusion
• Power market approach based on MPEC
• Maximise the producer profit while taking
into account operating constraints
• The equilibrium constraints implies only
minor modifications to traditional models
Modelling Profit Maximisation in Deregulated Power Markets by Equilibrium Constraints - 15