1. Chengming Zhu ‘13 Summer Research Assistant PENSA, Princeton laboratory for Energy Systems Analysis

2. 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

4. Coal Oil Gas

5. 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)

6. Coal Gas Coal Gas OR

7.  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

8. Coal Gas

9. 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

11. Demand Market A Supply Market ADemand Market B Supply Market B Price Quantity P_A0 P_A1 P_B0 P_B1

12. 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

13. Challenge:  Closed-Form?  Closed-Form Approximation?  Simulation: Too many different situations to consider and calculate

14. 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