Transcript presentation

Chengming Zhu ‘13
Summer Research Assistant
PENSA, Princeton laboratory for Energy Systems Analysis
Predict electricity forward price based on
 Fuel forward prices
 Stochastic electricity demand
Intuition behind:
 Electricity production cost is largely affected by fuel prices
 Fluctuation in demand create price spiking in peak hours
Gas
Oil
Coal
Fuel Forward Price as:
P = F * exp(k + m * X)
 P=Price of Fuel
 F=Fuel Forward coeff
 X=Quantity
 k, m both coeff for calibration
The inverse function is:
X = 1/m * (log(P/F)-k)
The log function allows us to easily calculate: X_i+X_j, S(X_i)
Coal
OR
Gas
Coal
Gas
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Id=zeros(N,2);
for i=1:2*N
if Demand(i)<D
if rem(IX(i),2)==1
Id((round((IX(i)+1)/2)),1)=1;
else
Id((round(IX(i)/2)),2)=1;
end
end
end
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output = Id;
end
Gas
Coal
Difficult to solve for 3 or more than 3 fuel types
Solution:
 Approximate by:
 Pair-wise + Weighted Average
Example:
 Coal; Oil; Gas
 Then closed-form solution ≈ weight*P(Coal+Oil) + weight*P(Oil+Gas)
 NOTE: Still an approximation
Price
Price
Supply Market A
Demand Market B
Supply Market B
Demand Market A
P_B0
P_A1
P_A0
P_B1
Quantity
Quantity
France & Germany:
 P = Price after Mkt Coupling
 B = Electricity price function
 X= Electricity Supply
 K_f_g = Transmission capacity from France to Germany
P_f = max{ min{B_f(X_f-K_f_g), B_f+g(X_f+X_g)}, B_f(X_f+K_g_f)}
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Simulation
Closed-Form
Challenge:
 Closed-Form?
 Closed-Form Approximation?
 Simulation: Too many different situations to consider and calculate
Why does the research matter?
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Carbon trade will affect the electricity price essentially as a production cost.
Therefore, we can tweak the model to study the effect of carbon trade
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Market Coupling increase the efficiency in European power market, and
enhance the aggregate welfare