Non-Anticipatory Coordinated Dispatch Framework

• The framework is a hierarchical, non-anticipatory strategy that decomposes multi-area dispatch into local subproblems coordinated via coupling variables.
• It employs multi-parametric programming and iterative updates to enable privacy-preserving communication of aggregated cost and sensitivity data.
• By relying solely on present and historical data, the approach robustly integrates long-term planning with short-term operations to achieve global convergence.

A non-anticipatory long-short-term coordinated dispatch framework is a hierarchical operational and optimization paradigm that enables secure, efficient, and privacy-preserving real-time dispatch of multi-area or multi-resource power systems, while explicitly addressing the uncertainty and temporal coupling inherent to long-term planning and short-term operational needs. The defining characteristic is that dispatch decisions at each timescale are made based strictly on currently available and past information—never on foresight of future uncertainties—through carefully structured coordination, limited information exchange, and algorithmic strategies spanning multi-parametric programming, distributed optimization, and scenario-based robust methods.

1. Hierarchical Decomposition and Coupling Variables

The framework decomposes the multi-area economic dispatch problem into local subproblems, each parameterized by coupling variables that represent physical or operational “boundaries” between areas or subsystems. For instance, in multi-area power systems, the coupling variables are typically boundary phase angles $\theta$ shared across the interface buses. Each area $i$ then solves a local optimization problem: $$\min_{x_i}\; f_i(x_i) \quad \text{subject to} \quad A_i x_i + B_i \theta = b_i, \; x_i \in X_i,$$ where $x_i$ denotes the area’s internal dispatchable variables.

The local optimum from each area can be represented as a parametric optimal value function $V_i(\theta)$, which, under convexity, is piecewise affine or quadratic with respect to $\theta$. The global problem is thereby recast as a coordination over $\theta$: $$\min_{\theta \in \text{Feasible}} \sum_{i} V_i(\theta),$$ with boundary constraints handled collectively.

2. Non-Anticipatory Decision Structure

The essence of non-anticipation is that, at each decision instant, dispatch policies and updates use only information available up to the present—current measurements, aggregated forecast data, and local sensitivities—explicitly precluding knowledge of future uncertainty realizations:

• In the long-term coordination phase, central decisions (e.g., boundary angles, scheduled tie-line flows) are formed from limited communicated data such as local cost sensitivities or gradients evaluated at the present state; no attempt is made to "guess" future contingency outcomes.
• In the short-term operational phase, each local operator updates its dispatch and possibly recalculates sensitivities given the latest boundary variable—again strictly based on present data.

This structure is aligned with real-world operation and regulatory realities, where forward-looking commitments must be robust, and operational controls must adapt rapidly without overreliance on uncertain forecasts.

3. Iterative Coordination via Multi-Parametric Programming

Coordination is implemented in an iterative, privacy-preserving loop that alternates between central and local agents:

1. Initialization: The coordinator proposes a candidate value for the coupling variables $\theta^{(0)}$.
2. Local Solution: Each area $i$ solves its parameterized local problem for $\theta^{(k)}$, computing both the optimal cost $V_i(\theta^{(k)})$ and associated coupling-constraint multipliers $\lambda_i$.
3. Communication: Local areas transmit only aggregated information—cost values, gradients, or dual variables—thereby preserving system security and operator privacy.
4. Master Update: The coordinator updates $\theta$ by solving the global master problem, often via subgradient, cutting-plane, or primal-dual schemes, e.g.,

$$\theta^{(k+1)} = \theta^{(k)} - \alpha^{(k)} \sum_{i} B_i^\top \lambda_i$$

where $\alpha^{(k)}$ is a step size.

This cycle repeats until first-order optimality is achieved for all areas, guaranteeing global convergence under convexity assumptions. The piecewise structure of $V_i(\theta)$ means each local agent need only supply summary data for the relevant “critical region” in $\theta$ space, maximizing computational and communication efficiency.

4. Critical Regions and Efficient Information Exchange

A distinguishing innovation is explicit exploitation of “critical regions” in multi-parametric programming—the polytopic domains of coupling-variable space where the set of active constraints (and thus the form of the optimal solution) is invariant for each local area. Within each region:

• The local optimal value functions and sensitivity maps are explicit affine or quadratic forms.
• Operators can “lookup” responses for new $\theta$ values without repeatedly solving nonlinear programs.
• Communication overhead is reduced since only region-level summaries or cost/sensitivity coefficients must be exchanged instead of full constraint sets or state vectors.

This critical region structure underlies the computational efficiency and scalability of the coordinated dispatch process.

5. Limited Information Sharing and Data Privacy

The framework is designed for minimal, aggregated information exchange:

• Local operators communicate only high-level operational summaries—typically cost values $V_i(\theta)$ and Lagrange multipliers associated with boundary constraints—for current $\theta$.
• Full cost functions, constraint details, or resource schedules are not revealed, protecting sensitive local data.
• The coordinator’s decisions thus rest on sufficiently rich, but non-intrusive, aggregated data, reflecting a non-anticipatory, privacy-informed operational stance.

This limited exchange is both a technical and regulatory imperative, fostering decentralized participation and trust in multi-area or multi-operator systems.

6. Convergence Properties and Optimality

Under standard convexity and regularity assumptions:

• When each local subproblem is convex and the interface constraints are linear in the coupling variables, the iterative process converges to a globally optimal solution.
• The piecewise structure and critical region decomposition ensure that the global problem remains convex and that strong optimality conditions (including stationarity and complementary slackness) are satisfied at each step.
• Convergence in a finite number of steps is established when the number of critical regions is finite and the boundary variables settle within a region where optimal responses are invariant.

This guarantees both computational performance and operational reliability.

7. Long- and Short-Term Roles in Modern Power Systems

The non-anticipatory long-short-term coordinated dispatch framework underpins a wide array of hierarchical, multi-timescale operational strategies:

• Long-term phase: Supports robust scheduling (e.g., day-ahead boundary profiles, tie-line coordination) under forecast uncertainty using only presently available aggregated information. The coordinator relies on parametric cost/sensitivity data to form robustly optimal setpoints.
• Short-term phase: Enables rapid reaction to real-time deviations via localized re-optimization, updating dispatch and sensitivities based on the most recent central guidance, again without access to future information.

This layered approach facilitates seamless integration of planning and operational timescales in large, dynamic, and uncertain power systems.

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In summary, the non-anticipatory long-short-term coordinated dispatch framework combines multi-parametric programming, iterative boundary coordination, and rigorous privacy strategies to yield a scalable, robust, and information-efficient solution for multi-area dispatch problems. By adhering to non-anticipatory principles—making decisions based solely on current and historical data—the framework achieves both operational reliability and practical deployability in complex, modern power system environments.