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
Coal Oil Gas
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, X_i)
Coal Gas Coal Gas OR
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 output = Id; end
Coal Gas
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
Demand Market A Supply Market ADemand Market B Supply Market B Price Quantity P_A0 P_A1 P_B0 P_B1
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)} Simulation Closed-Form
Challenge: Closed-Form? Closed-Form Approximation? Simulation: Too many different situations to consider and calculate
Why does the research matter? 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 Market Coupling increase the efficiency in European power market, and enhance the aggregate welfare