Robust Continuous-Time Generation Scheduling under Power Demand Uncertainty: An Affine Decision Rule Approach
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913769321398272 |
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| author | Cho, Youngchae Yang, Insoon Ishizaki, Takayuki |
| author_facet | Cho, Youngchae Yang, Insoon Ishizaki, Takayuki |
| contents | Most existing generation scheduling models for power systems under demand uncertainty rely on energy-based formulations with a finite number of time periods, which may fail to ensure that power supply and demand are balanced continuously over time. To address this issue, we propose a robust generation scheduling model in a continuous-time framework, employing a decision rule approach. First, for a given set of demand trajectories, we formulate a general robust generation scheduling problem to determine a decision rule that maps these demand trajectories and time points to the power outputs of generators. Subsequently, we derive a surrogate of it as our model by carefully designing a class of decision rules that are affine in the current demand, with coefficients invariant over time and constant terms that are continuous piecewise affine functions of time. As a result, our model can be recast as a finite-dimensional linear program to determine the coefficients and the function values of the constant terms at each breakpoint, solvable via the cutting-plane method. Our model is non-anticipative unlike most existing continuous-time models, which use Bernstein polynomials, making it more practical. We also provide illustrative numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Continuous-Time Generation Scheduling under Power Demand Uncertainty: An Affine Decision Rule Approach Cho, Youngchae Yang, Insoon Ishizaki, Takayuki Optimization and Control Systems and Control Most existing generation scheduling models for power systems under demand uncertainty rely on energy-based formulations with a finite number of time periods, which may fail to ensure that power supply and demand are balanced continuously over time. To address this issue, we propose a robust generation scheduling model in a continuous-time framework, employing a decision rule approach. First, for a given set of demand trajectories, we formulate a general robust generation scheduling problem to determine a decision rule that maps these demand trajectories and time points to the power outputs of generators. Subsequently, we derive a surrogate of it as our model by carefully designing a class of decision rules that are affine in the current demand, with coefficients invariant over time and constant terms that are continuous piecewise affine functions of time. As a result, our model can be recast as a finite-dimensional linear program to determine the coefficients and the function values of the constant terms at each breakpoint, solvable via the cutting-plane method. Our model is non-anticipative unlike most existing continuous-time models, which use Bernstein polynomials, making it more practical. We also provide illustrative numerical examples. |
| title | Robust Continuous-Time Generation Scheduling under Power Demand Uncertainty: An Affine Decision Rule Approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2504.00390 |