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1 Economics of Electricity Generation Economic Dispatch EBF 483 Spring 2014
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Economics of Electricity Generation
Economic Dispatch
EBF 483
Spring 2014
Economic Dispatch Topics
• System marginal cost curve and “system lambda”
• Economic Dispatch without transmission constraints
• CorrecDng the Economic Dispatch in the presence of transmission congesDon.
Economic Dispatch for a VerDcally-‐Integrated Electric UDlity
• The uDlity’s (short-‐run) objecDve is to minimize the total generaDon cost of meeDng electricity demand.
• Economic Dispatch is the procedure by which the uDlity selects which of its generators it will use to meet electricity demand. Basically, economic dispatch is like clearing the electricity market.
Economic Dispatch Procedure • The uDlity constructs a marginal cost (supply) curve for its enDre system.
• Demand is oUen assumed to be price-‐inelasDc (verDcal demand curve).
• The marginal cost of generaDon at the market-‐clearing point (supply = demand) is called the “System Lambda.”
• The generator whose output serves the marginal kWh of electricity demand is called the “marginal unit.”
Modeling Supply Curves for Electricity
Two common models for modeling electricity supply curves:
1. QuadraDc total cost; linear marginal cost (more realisDc but harder)
2. Linear total cost of generaDon; constant marginal cost (less realisDc but oUen Dmes the best you can do with exisDng data)
Constant Generator Costs
• We often model generators as having constant marginal costs of operation. (This is not entirely accurate, but detailed production cost data is hard to get.)
• We model constant marginal costs with linear total cost functions
• Ex. TC(g)=32+5g – MC(g)= $5/MWh
Example: Constant Marginal Cost
• The system operator’s objective is to minimize the total cost of electricity generation, subject to a constraint that total supply = demand.
Generator Max Output Marginal Cost 1 100 MW $10/MWh 2 75 MW $30/MWh 3 20 MW $60/MWh
Constant Cost Example (II)
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Demand = 60 MWh λsystem = $10/MWh
Calculate Total Cost
• At Demand = 60 MWh, Generator 1 produces 60 MWh; the other generators produce 0 MWh (they are not dispatched).
• Total Cost: 60 × $10 + 0 × $30 + 0 × $60 = $600 + Fixed Costs
Constant Cost Example (III)
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Demand = 185 MWh λsystem = $60/MWh
Calculate Total Cost (Again)
• At Demand = 185 MWh, Generator 1 produces 100 MWh; Generator 2 produces 75 MWh; Generator 3 produces 10 MWh.
• Total Cost: 100 × $10 + 75 × $30 + 10 × $60 = $1000 + $2250 + $600 = $3850 + Fixed Costs
Again, with Fixed Costs!
• We will now add Qixed costs into the problem, as follows:
• Fixed costs take units of dollars (not dollars per MWh)
Generator Max
Output Marginal Cost Fixed Cost
1 100 MW $10/MWh $5 2 75 MW $30/MWh $10 3 20 MW $60/MWh $15
Fixed Cost Example
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Demand = 110 MWh λsystem = $30/MWh
Calculate Total Cost (Once Again)
• At Demand = 110 MWh, Generator 1 produces 100 MWh; Generator 2 produces 10 MWh; Generator 3 produces 0 MWh.
• Total Cost = Marginal + Fixed Costs = 100 × $10 + 10 × $30 + 0 × $60 + $5 + $10 + $15 = $1,300 + $30 = $1,330
The Fixed Cost Trap
• Be careful! Don’t forget to include Qixed costs for all generators, even those that do not produce any electricity!
• Since this is the short-‐run, we assume that Qixed costs must be paid for all plants in the system.
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Economic Dispatch With Congestion
Topics
• Transmission limits and transmission congesDon
• Economic Dispatch with transmission congesDon
Physical Transmission Limits
Transmission lines can become constrained or “congested” in several different ways:
1. Thermal limits (most important for us) 2. ReacDve power 3. Stability limits
Thermal Transmission Limits
• Remember that when current flows along a transmission line, the line heats up.
• When things heat up, they expand.
• When power lines heat up, the expansion causes the power line to “sag.” If the line sags too much, it could touch a nearby tree.
Some Cool Videos
• Boom! (video @2:30 hlp://www.youtube.com/watch?v=O9WOyHoD2yU)
• Zap! hlp://www.youtube.com/watch?v=vqgNrj6oEdc&feature=fvwrel
Thermal Transmission Limits
• To prevent “sag,” limits on transmission line power flow are established. These are someDmes called path ra2ngs.
• These are limits on the number of MW that the line can carry at any given moment.
• Path raDngs can change by season, Dme of day, or with system condiDons.
Kirchhoff vs. Economics!
• Path raDngs on transmission lines are constraints that system operators aren’t supposed to violate.
• Because of Kirchhoff’s Laws, the system operator can’t simply tell electrons to follow uncongested paths.
Kirchhoff vs. Economics!
• If the transmission system is congested, then the system operator can’t use a perfect economic dispatch.
• The system operator must tell some generators to back off, and tell others to increase power. This is called out-‐of-‐merit dispatch.
Example
G1 L
• MC(G1) = $10/MWh • MC(G2) = $30/MWh • Load demands 100 MWh. • Ignore capacity limits on the generators, for now. If there is no limit on transmission, G1=100 MWh and G2 = 0 MWh. Total system cost is 100 MWh * $10/MWh = $1,000.
G2 Node 1 Node 2
Example
G1 L
• If the limit on the transmission line is 80 MW, then G1 cannot produce any more than 80 MW before the system operator says “back off!” The remaining 20 MWh must be produced by G2.
• Total system cost: (80 MWh * $10/MWh) + (20 MWh * $30/MWh) = $1,400.
G2 Node 1 Node 2
Limit = 80 MW
Cost of Transmission Congestion
The system cost of transmission congesDon is defined as: (Total system cost with congesDon) – (Total system cost if all transmission constraints were eliminated) In our example, the system cost of transmission congesDon is $1,400 -‐ $1000 = $400. This is also the value to the system of increasing the flow limit on the transmission line.
