Participation of Renewables¶
Market Participants¶
- Price taker: Decisions and resulting offers (buying/selling) does not affect market outcomes
- Price maker: Decisions and resulting offers (buying/selling) affects market outcomes
Market Participation Strategy¶
- Increase your offer
| \(E_i\) | Limitations | |
|---|---|---|
| Trust the forecast Directly take forecasts and make offers | \(\hat E_i\) | Susceptible to balancing costs from under-producing |
| Increase your offer | \(\tau \hat E_i\) \(\tau > 1\) | |
| Be bold and just max out generation | Unrealistic (Requires knowledge of future balancing prices) |
Revenue Analysis¶
Performance Ratio $$ \begin{aligned} \gamma &= (R_\text{DA} + R_B)/R^*_\text{DA} \ \gamma & \in (0, 1) \end{aligned} $$ where
- \(R_\text{DA} =\) revenue from day-ahead
- \(R_\text{DA} =\) revenue from balancing market
- \(R_\text{DA} =\) Optimal revenue
News vendor problem¶
How much should news vendor buy from printing store to maximize expected revenue
Bank cashflow problem: how much a bank should keep in reserves to satisfy request for withdrawal
Requirements¶
- One shot opportunity to decide on quantity of interest
- Uncertain outcome
- Known marginal revenue, profit, loss
- Objective: maximize expected revenue
Solution¶
Optimal number \(n^*\) such that $$ \begin{aligned} \alpha^* &= \dfrac{\pi+}{\pi+ + \pi^-} \ n^* &= F{-1}(\alpha*) \end{aligned} $$ where
- \(\pi^+ = \lambda^R - \lambda^P =\) unit cost of buying less than needed
- \(\pi^- = \lambda^P - \lambda^T =\) unit cost of buying more than needed
- \(\alpha^* =\) Normal level of original CDF F
Uncertainty¶
\[ n^* = \hat F^{-1}(\hat \alpha^*) \\ \implies n_t^* = \hat F_t^{-1}(\hat \alpha_t^*) \]
Notes¶
The optimal strategy can change over time