Key Takeaways & Executive Findings
- •• • The TRD expands in a stepwise manner with regulation cost investment and exhibits diminishing marginal returns; identifying the stepwise growth point provides a reliable reference for cost optimization, enabling operators to avoid overinvestment beyond the point where additional cost yields negligible domain expansion. • • As renewable penetration increases, the TRD follows a steep-rise, plateau, and sharp-drop pattern; the critical penetration threshold identified via this evolution can guide renewable construction to avoid triggering system security violations, with the sharp drop indicating a hard limit on inverter-based resource integration. • • The prior-constraint-guided deep neural network achieves efficient and accurate boundary characterization for high-dimensional TRDs, overcoming the curse of dimensionality that causes exponential growth in computational complexity for point-search methods such as point-wise simulation and vertex search. • • The TRD model incorporates intertemporal coupling constraints across multi-period, multi-type resources, enabling global assessment of regulation capability that point-based evaluation cannot provide, thereby supporting scheduling and resource allocation decisions with quantified feasible space.
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Abstract
The rapid proliferation of inverter-based renewables in new-type power systems has exposed the inadequacy of conventional point-based regulation capability assessments, which evaluate a single operating point and fail to capture the temporally coupled feasible space required for scheduling and resource allocation. This paper introduces the temporal regulation domain (TRD) as a global construct that maps all feasible system states satisfying intertemporal constraints into an observation space. A compact TRD model is formulated incorporating ramping, state-of-charge, power balance, security, and regulation cost budget constraints. Topological analysis establishes that the TRD is bounded, closed, and monotonically non-decreasing with respect to the cost budget. To overcome the curse of dimensionality in boundary characterization, a prior-constraint-guided deep neural network is developed, embedding monotonicity priors into the loss function. Simulations on a modified IEEE 118-bus system demonstrate that the proposed method efficiently and accurately delineates high-dimensional TRD boundaries. The TRD expands in a stepwise manner with regulation cost investment, exhibiting diminishing marginal returns; identifying the stepwise growth point provides a reliable reference for cost optimization. As renewable penetration increases, the TRD follows a steep-rise, plateau, and sharp-drop pattern, enabling identification of critical penetration thresholds to guide renewable deployment without violating security boundaries.
1. Introduction
Existing regulation capability assessment methods for power systems fall into two categories: renewable accommodation capacity and flexibility evaluation. Accommodation studies rely on time-series production simulation with power flow constraints or stability constraints to compute maximum renewable hosting capacity, while flexibility studies design indices based on ramping rates and unit capacities to quantify upward and downward insufficiency. Both approaches perform point evaluation at specific operating points, failing to characterize the complete feasible regulation space under intertemporal coupling constraints. This limitation stems from the temporal interdependence of regulation actions—measures taken in one period directly affect available resources in subsequent periods—and the high-dimensional decision space formed by multi-type resources coordinated across multiple periods, where solution complexity grows exponentially with dimensionality.
Domain theory offers a global perspective by mapping all feasible states satisfying intertemporal constraints into an observation space. Prior domain constructs include security region, dispatchable region, wind power accommodation region, and flexibility operating region, but none systematically address the temporal regulation capability of new-type power systems. The temporal regulation domain (TRD) introduced here fills this gap by incorporating ramping, state-of-charge, power balance, security, and regulation cost budget constraints into a compact model. Topological properties—boundedness, closedness, and monotonic non-decreasing behavior with respect to cost budget—are proven to provide theoretical support for boundary solution algorithms. A prior-constraint-guided deep neural network embeds monotonicity priors into the loss function, enabling efficient and accurate boundary characterization for high-dimensional domains, as validated on a modified IEEE 118-bus system.
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REN Ji, REN Zhouyang, FENG Jianbing, LUO Yufan, ZHAO Ruifeng, GUO Wenxin, CHEN Zhiwei (2026). Temporal Regulation Domain for New-Type Power Systems: Concept and Methodology. Power Automation Equipment. https://doi.org/10.16081/j.epae.202605005
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Frequently Asked Questions
What specific failure mechanism in existing point-based assessment methods does the temporal regulation domain address, and what empirical evidence demonstrates the improvement?
Point-based methods evaluate regulation capability at a single operating point, ignoring intertemporal coupling where current-period actions constrain future-period resources. This leads to incomplete characterization of the feasible regulation space, as demonstrated by the inability of point evaluation to capture the stepwise growth and diminishing marginal returns of the TRD with respect to cost investment. The TRD model, validated on a modified IEEE 118-bus system, reveals that the domain expands in a stepwise manner and exhibits a steep-rise, plateau, and sharp-drop pattern as renewable penetration increases, providing critical thresholds that point-based methods cannot identify.
How does the prior-constraint-guided deep neural network overcome the curse of dimensionality that plagues point-search methods, and what are the computational trade-offs?
Point-search methods such as point-wise simulation and vertex search require optimizing a large number of sample points, with computational complexity growing exponentially with dimensionality. The proposed method embeds monotonicity priors into the loss function of a deep neural network, constraining the solution space to physically valid regions and enabling efficient boundary characterization. This reduces the number of required samples and avoids exhaustive search, achieving high accuracy for high-dimensional TRD boundaries. The trade-off is the need for training data and network architecture design, but the method maintains interpretability by incorporating power system operating mechanisms.
What are the quantitative thresholds for regulation cost investment and renewable penetration that trigger nonlinear domain behavior, and how can operators use them?
The TRD exhibits a stepwise growth point where additional cost investment yields a sudden expansion of the feasible regulation space, followed by diminishing marginal returns. Operators can identify this point to optimize cost allocation, avoiding overinvestment beyond the step. For renewable penetration, the TRD follows a steep-rise, plateau, and sharp-drop pattern; the critical penetration threshold at the onset of the sharp drop indicates a hard limit beyond which system security constraints are violated. These thresholds are derived from simulations on the modified IEEE 118-bus system and provide actionable guidance for renewable deployment and cost budgeting.
How does the TRD model handle the non-convexity introduced by binary decision variables such as unit commitment and storage charging states?
The TRD model includes binary variables for thermal unit on/off states and storage charge/discharge states, making the feasible region non-convex. The paper addresses this by decomposing the problem into subproblems for each possible binary configuration, defining subproblem feasible regions that are then projected onto the continuous decision space. The union of these projections forms the overall TRD. The prior-constraint-guided neural network is trained to approximate the boundary of this union, effectively handling the non-convexity while maintaining computational tractability.
What validation metrics and baseline comparisons confirm the superiority of the proposed boundary solution method over existing approaches like analytical methods, hyperplane methods, and convex hull methods?
The paper validates the method on a modified IEEE 118-bus system, comparing against analytical methods, point-wise simulation, hyperplane approximation, convex hull approximation, and standard neural network methods. The proposed prior-constraint-guided neural network achieves higher accuracy in boundary characterization for high-dimensional TRDs, as evidenced by its ability to capture the stepwise growth and diminishing marginal returns features that other methods either smooth over or miss. The method also satisfies the monotonicity property, ensuring results align with power system operating principles, unlike purely data-driven neural networks that lack interpretability.
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