Dual Analysis of Continuous-time Economic Dispatch and Its Price Implications
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| Format: | Preprint |
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2026
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| _version_ | 1866918307770138624 |
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| author | Zhang, Menghan Wang, Caisheng |
| author_facet | Zhang, Menghan Wang, Caisheng |
| contents | As load varies continuously over time, it is essential to provide continuous-time price signals that accurately reflect supply-demand balance. However, conventional discrete-time economic dispatch fails to capture the intra-temporal variations in load and generation. Its dual solution--the marginal price--may distort economic signals, leading to inefficient market incentives. To analyze these issues, this paper develops a continuous-time dispatch model and derives its dual formulation for price analysis. The continuous-time dispatch produces dual variables that can be interpreted as price signals. Piecewise time-indexed generation and price trajectories are then constructed through a parametric programming approach. The resulting price, represented by the Lagrange multiplier of the system-wide power balance constraint, evolves piecewise along the continuous-time load profile. Each segment corresponds to a critical region characterized by a set of active constraints. Furthermore, we discuss the impact of unit-specific ramping constraints on price implications. Results indicate that continuous-time generation and price trajectories provide deeper insights into the price distortions and inefficient incentives inherent in discrete-time formulations. The proposed methodology is validated on an illustrative 5-bus system and a modified IEEE RTS-2019. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dual Analysis of Continuous-time Economic Dispatch and Its Price Implications Zhang, Menghan Wang, Caisheng Systems and Control As load varies continuously over time, it is essential to provide continuous-time price signals that accurately reflect supply-demand balance. However, conventional discrete-time economic dispatch fails to capture the intra-temporal variations in load and generation. Its dual solution--the marginal price--may distort economic signals, leading to inefficient market incentives. To analyze these issues, this paper develops a continuous-time dispatch model and derives its dual formulation for price analysis. The continuous-time dispatch produces dual variables that can be interpreted as price signals. Piecewise time-indexed generation and price trajectories are then constructed through a parametric programming approach. The resulting price, represented by the Lagrange multiplier of the system-wide power balance constraint, evolves piecewise along the continuous-time load profile. Each segment corresponds to a critical region characterized by a set of active constraints. Furthermore, we discuss the impact of unit-specific ramping constraints on price implications. Results indicate that continuous-time generation and price trajectories provide deeper insights into the price distortions and inefficient incentives inherent in discrete-time formulations. The proposed methodology is validated on an illustrative 5-bus system and a modified IEEE RTS-2019. |
| title | Dual Analysis of Continuous-time Economic Dispatch and Its Price Implications |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2601.19095 |