Transcript Chapter 5-1 Power Transmission and Losses

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
• 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
• L  aW 2 where a  RT /V 2
• 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.
Chapter 5-2 Physical
Transmission Limits
Introduction
•
Without transmission limits, power markets would have
ample competition and no need for congestion pricing.
•
1.
2.
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
1.
Reactive power
--a necessary part of the transmission of real AC power
and has no counterpart in DC power flows.
2.
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 W  Q
--apparent power.
2
2
• 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/
W 2  Q2
Use and production of reactive
power
•
1.
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
3 Generators
4 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.
Chapter 5-3 Congestion
Pricing Fundamentals
• 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.
Competitive locational prices
(CLPs) in context
Commodity
Symbol
Price
Power at the city
bus (Bus 2)
P2
$46/MWh
Power at remote
bus (Bus1)
P1
$32/MWh
Transmission
rights from Bus 1
to Bus 2
P12
$14/MWh
• 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.
Chapter 5-4 Congestion
Pricing Methods
• 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
B
C
• AB: take more than one path
• Impedance: a generalization of
resistance; describes how
difficult it is for power to flow
over a certain path.
A
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.
Figure 5-4.1
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.
Table 5-4.1 Bilateral trades compatible with
Figure 5-4.1
Trade#
MW
From
To
Sale
Price
TRs
1
150
A
B
$45
100MW
2
300
A
A
$35
0
3
450
B
B
$45
0
4
600
A&B
C
$40
0
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?