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Managing Risk using Rolling Forecasts in Energy-Limited and Stochastic Energy Systems

Thomas Mortimer, Robert Mieth

TL;DR

The paper tackles risk-aware operational control of an energy system with stochastic wind, storage, and limited fuel under rolling forecasts. It introduces a parameter-modified cost function to enforce $\mathrm{CVaR}_{\alpha}$ of total costs and $\mathrm{BPoE}$ reliability targets, yielding a deterministic look-ahead policy with offline-tuned discount parameter. A case study demonstrates that a constant or look-up-table tuned $\theta$ in the wind-forecast modification can closely match risk-aware performance while dramatically reducing computation compared with full stochastic risk integration, and it provides explicit reliability guarantees through $\mathrm{BPoE}$. The approach offers a scalable tool for risk management in energy-limited, stochastic systems and informs wind/solar time-series discounting in planning contexts.

Abstract

We study risk-aware linear policy approximations for the optimal operation of an energy system with stochastic wind power, storage, and limited fuel. The resulting problem is a sequential decision-making problem with rolling forecasts. In addition to a risk-neutral objective, this paper formulates two risk-aware objectives that control the conditional value-at-risk of system cost and the buffered probability of exceeding a predefined threshold of unserved load. The resulting policy uses a parameter-modified cost function approximation that reduces the computational load compared to the direct inclusion of those risk measures in the problem objective. We demonstrate our method on a numerical case study.

Managing Risk using Rolling Forecasts in Energy-Limited and Stochastic Energy Systems

TL;DR

The paper tackles risk-aware operational control of an energy system with stochastic wind, storage, and limited fuel under rolling forecasts. It introduces a parameter-modified cost function to enforce of total costs and reliability targets, yielding a deterministic look-ahead policy with offline-tuned discount parameter. A case study demonstrates that a constant or look-up-table tuned in the wind-forecast modification can closely match risk-aware performance while dramatically reducing computation compared with full stochastic risk integration, and it provides explicit reliability guarantees through . The approach offers a scalable tool for risk management in energy-limited, stochastic systems and informs wind/solar time-series discounting in planning contexts.

Abstract

We study risk-aware linear policy approximations for the optimal operation of an energy system with stochastic wind power, storage, and limited fuel. The resulting problem is a sequential decision-making problem with rolling forecasts. In addition to a risk-neutral objective, this paper formulates two risk-aware objectives that control the conditional value-at-risk of system cost and the buffered probability of exceeding a predefined threshold of unserved load. The resulting policy uses a parameter-modified cost function approximation that reduces the computational load compared to the direct inclusion of those risk measures in the problem objective. We demonstrate our method on a numerical case study.
Paper Structure (15 sections, 21 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 15 sections, 21 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Energy System Model
  4. Risk-aware decision-making
  5. Risk Measure: Conditional Value-at-Risk
  6. Risk Measure: Buffered Probability-of-Exceedance
  7. Risk-aware policies for energy system model
  8. Stochastic risk-aware policies
  9. Parameter-modified cost function approximation policies
  10. Parameter tuning
  11. Case Study with numerical results
  12. Constant parameter tuning
  13. Look-up table parameter modification
  14. Influence of $\theta$ in reducing energy shortfalls
  15. Conclusion

Figures (4)

  • Figure 1: Energy system model with power exchange between system components as decision variables. Arrows indicate variable signs.
  • Figure 2: Probability density function of a continuous random variable $X$. For a threshold $\zeta \in \mathbb{R}$, $p_x(X)$ equals $\mathbb{P}(X > z)$, which is the cumulative density (hashed area). For the same threshold $\zeta$, $\bar{p}_{\zeta}(X)$ is the cumulative density (solid+hashed area). The expectation of the worst-case $1 - \alpha = \bar{p}_{\zeta}(X)$ outcomes equals $\zeta = \bar{q}_{\alpha}(X)$.
  • Figure 3: Rolling horizon illustration
  • Figure 4: Influence of a constant $\theta$ on the $\mathop{\mathrm{BPoE}}\nolimits$ of shortfall events.