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ECO 435 Locational Transmission Pricing. Stoft Chapter 5. Chapter 5-1 Power Transmission and Losses. 5-1.1 DC power lines. AC: provides enormous advatages for long-distance transmission DC: the wave of the future; economical; more controllable. The Power Law.
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ECO 435 Locational Transmission Pricing Stoft Chapter 5
5-1.1 DC power lines • AC: provides enormous advatages for long-distance transmission • DC: the wave of the future; economical; more controllable
The Power Law • Power equals voltage times current (Volt*Amps) The electrical power, W, measured in watts, consumed by any element of an electrical circuit equals the voltage drop, V, across that element times the current, I, flowing through that element.
Ohm’s law • Voltage equals current times resistance (I*R) The electrical current, I, flowing through a conductor equals the voltage drop across the conductor, V, divided by the resistance, R, of the conductor: V=I*R.
Transmission Losses • Transmission losses are proportional to Power square/voltage square • where • Transmission losses, L, are proportional to the square of the power consumed by the load, and the line resistance, and inversely proportional to the square of the line voltage.
Transformers --make power markets possible by creating the high voltages needed for long-distance transmission and then reducing them to safe levels for consumption. --useful in changing the voltage.
Introduction • Without transmission limits, power markets would have ample competition and no need for congestion pricing. • Transmission limits: • Physical limits • Contingency limits --both can be expressed as a simple megawatt limit on power flow that is allowed over the power line or transformer.
5-2.1 Thermal limits on power lines • Power flow causes a loss of electrical power, and the “lost” power heats the power lines causing the copper to expand and the line to sag. • The system operator must know the line limits. • Electrical current determines line losses and thus the thermal limits on power. I=W/V
5-2.2 Reactive power and thermal limits • Reactive power --a necessary part of the transmission of real AC power and has no counterpart in DC power flows. • Real power --simply the normal electrical power traded in power markets
Real power only flows from generators to load, and it delivers the service of electric power. • Reactive power flows back and forth in equal amounts and supplies no energy.
Reactive power helps keep the voltage at the load end of the line at its proper level. • Reactive power contributes to losses.
Thermal limits • The primary source of heat: the friction of electric currents in the wires. • When there is both real power W and reactive power Q, current is proportional to --apparent power. • A thermal limit that involves both W and Q is not economically useful and should be reformulated.
Thermal limits depends on real and reactive power flows. • W<TLw*PF, where PF=W/
Use and production of reactive power • Loads and transmission tend to use more reactive power than they produce • Capacitors: require no external energy input 2. Synchronous Condensers: require no external fuel source, but it uses some real power • Generators • Motors and Transformers
Why AC power flows on transmission lines • Reactive power flow is characterized by a phase difference bw voltage and current at a given location • Power flow is driven by a phase difference bw two voltages at different locations. • The larger the phase difference, the greater the difference in voltage bw the two ends of the line, the greater the current and power flow on the line.
Physical impediments to trade cause competitive prices to differ; the difference is the price of congestion
5-3.1 Congestion pricing is competitive pricing • Tradable physical transmission rights can be used by a classic, decentralized market to solve the congestion problem. • Objective: find what prices would emerge from such an ideal and fully decentralized competitive market. • Bilateral trading; nodal pricing
The price of transmission rights (TRs) • TRs are not bundles with energy but are traded separately. • In a competitive market, city customers can buy what they need at the city price; remote generators can sell what they want at the remote price. • This will drive up the price. (to energy price difference bw the remote bus and the city bus) Pab=Pb- Pa
The price of power • Def: congestion • In a competitive market, the path from A to B is congested if the price of transmission rights from A to B is positive. • This is equivalent to the price of power at b being greater than the price of power at A. • If a line would be overused if its limit were not enforced, it is congested.
If congested, there will be two different prices • If not, the line limit is irrelevant and there is a single price of power. • Assume: not congested; determine how much it would be used; if overused, it is congested.
The PJM, CLPs are called locational marginal prices (LMPs) • CLPs equal marginal costs at the relevant location
5-3.2 Benefits of competitive locational prices • CLPs cause suppliers to minimize the total cost of production, and are the only free-market prices capable of doing this. • CLPs send the right signals to consumers
Production cost minimization • If generators choose their production levels freely, based on market prices, only competitive locational prices will minimize total production costs by inducing the right set of generators to produce.
Demand side efficiency • A general property of competitive locational prices: The CLP at location X equals the system marginal cost of supplying an additional megawatt at X. • CLPs are the only prices that send the right signals to consumers.
The point of central calculation is to find the perfectly competitive, bilateral-market prices.
5-4.1 Centralized computation of CLPs • Provided that generators and their customers tell the ISO their true supply and demand curves, the ISO will find the same CLPs that a bilateral market would find.
How central computation works • With central calculation, there is no need to issue transmission rights; there is only an energy market.—simpler than bilateral market. • Another simplification: traders need not look for trading partners or engage in comparison shopping in the market.—everyone trades with the ISO. • Every load customer automatically gets the benefit of every supply bid, and every supplier benefits from every demand bid.
Each generator and every load customer submits a bid to the ISO which specifies the location at which they will take or provide power. • If load does not bid, the ISO simply bids for the load based on its best expectation of real-time demand. • Accepts bids: ISO maximizes total surplus and sets price equal to marginal surplus at every location.
The three-line example • Loop flow • Radial: a network that is not looped • AB: take more than one path • Impedance: a generalization of resistance; describes how difficult it is for power to flow over a certain path.
Power flows are approximately additive • If a balanced trade causes power flows (F1,…,Fn) on lines 1 through N, and another balanced trade causes flows (G1,…Gn), when the two trades take place simultaneously, the flows on the lines will be (F1+G1,…,Fn+Gn)
Checking the computed prices • Checking the optimization: If load could be supplied more cheaply, it would be possible to back down an expensive generator and produce more with a cheaper generator. • Checking the prices: price at each location is the value of an additional free megawatt at that location.
5-4.2 Bilateral pricing compared to centralized pricing • Are the centralized trades the best bilateral trades? Each bus is examined in turn. The most convenient set has been picked as the reference set.
Conclusion: • There would be no profitable trades remaining. • A perfect central computation finds exactly the same prices as a perfect bilateral market.
Competitive bilateral prices equal centralized locational prices • Market prices in a perfectly competitive bilateral market would equal, at every location, perfectly competitive centralized nodal prices. • This common set of prices is called the competitive locational prices, CLPs.
The bilateral-nodal debate • Against: Prices; fail to realize the central computation computes the prices that would be produced by the ideal competitive markets. • Debate questions: Which system would arrive at the prices more accurately? Which system was more susceptible to market power or bureaucratic rigidity? Which system would give rise to more innovations?
