Risk-Aware Value-Oriented Net Demand Forecasting for Virtual Power Plants

TL;DR

This paper tackles the risk of excessive operation costs in virtual power plants by training net-demand forecasts to be risk-aware. It introduces a bilevel framework where the upper level optimizes forecast parameters to minimize the CVaR$_{\beta}$ of the total day-ahead and real-time costs, while the lower level performs the DA/RT dispatch given the forecast. A key contribution is deriving an analytical, convex, piecewise-linear function linking the forecast to the overall cost via DA/RT cost partitions, enabling a convex reformulation when the forecast is linear. A case study shows the approach reduces high-cost risk compared with risk-neutral baselines and remains computationally efficient, closely approaching the performance of an ideal stochastic benchmark. This yields more robust VPP operations under RES variability and uncertainty.

Abstract

This paper develops a risk-aware net demand forecasting product for virtual power plants, which helps reduce the risk of high operation costs. At the training phase, a bilevel program for parameter estimation is formulated, where the upper level optimizes over the forecast model parameter to minimize the conditional value-at-risk (a risk metric) of operation costs. The lower level solves the operation problems given the forecast. Leveraging the specific structure of the operation problem, we show that the bilevel program is equivalent to a convex program when the forecast model is linear. Numerical results show that our approach effectively reduces the risk of high costs compared to the forecasting approach developed for risk-neutral decision makers.

Figures (4)

• Figure 1: The illustration of $\text{CVaR}_\beta$. The dashed area measures $\beta$. $\text{VaR}_\beta$ is the $\beta$-quantile of the cost. $\text{CVaR}_\beta$ is the expected value of the cost above $\text{VaR}_\beta$.
• Figure 2: Illustration of a cost-merit order dispatch. (a) In the DA operation, there are two generators with marginal costs $\rho_1^{\text{DA}},\rho_2^{\text{DA}}$ and capacities $\overline{p}_1^{\text{DA}},\overline{p}_2^{\text{DA}}$. The blue solid line represents the net demand forecast $\hat{y}_{d,\tau}$. Since the generator 1 is the cheapest one, it is dispatched to full capacity. The generator 2 is partially dispatched until the net demand is settled. (b) In the RT operation, flexible resources 1 and 2 addressing energy deficit with marginal cost $\rho_1^{+},\rho_2^{+}$ and capacities $\overline{p}_1^{+},\overline{p}_2^{+}$. Flexible resources 3 and 4 address energy surplus with marginal utility $\rho_1^{-},\rho_2^{-}$ and capacities $\overline{p}_1^{-},\overline{p}_2^{-}$. The orange solid line represents the negative forecast deviation $y_{d,\tau}-\hat{y}_{d,\tau} < 0$. Since flexible resource 3 has a higher marginal utility, it is dispatched to the full capacity. The flexible resource 4 is partially dispatched until the deviation is settled.
• Figure 3: Illustration of the function between the overall operation cost and the forecast. In the DA operation, there are two generators with marginal costs $\rho_1^{\text{DA}}=25 \$/kW,\rho_2^{\text{DA}}=30 \$/kW$. In the RT operation, flexible resources 1 and 2 addressing energy deficit with marginal cost $\rho_1^{+}=55 \$/kW,\rho_2^{+}=60 \$/kW$. Flexible resources 3 and 4 address energy surplus with marginal utility $\rho_1^{-}=18 \$/kW,\rho_2^{-}=16 \$/kW$. The function has 8 segments.
• Figure 4: The 6-day net demand forecast profiles, when the marginal cost of flexible resources addressing energy deficit in RT is larger than the marginal utilities of flexible resources addressing energy surplus. $\beta$ is set as 0.5.

Theorems & Definitions (6)

• Definition 1
• Proposition 1
• proof
• Theorem 1
• Proposition 2
• proof