Table 1 Comprehensive list of symbols, parameters, decision variables, and acronyms used throughout the paper.
Symbol/Acronym | Description |
|---|---|
Sets | |
\(\mathcal {G}\) | Set of grid nodes or buses |
\(\mathcal {L}\) | Set of transmission lines |
\(\mathcal {A}\) | Set of agents (producers, consumers, aggregators) |
\(\mathcal {T}\) | Set of time periods in the planning horizon |
\(\mathcal {S}\) | Set of uncertainty scenarios or parameters |
\(\mathcal {R}\) | Set of regulatory signals or incentives |
Parameters | |
\(C_i^{\text {gen}}\) | Marginal generation cost of agent i |
\(C_i^{\text {stor}}\) | Storage or degradation cost for agent i |
\(L_{ij}^{\max }\) | Maximum transmission capacity between node i and j |
\(D_i^{t}\) | Demand at node i at time t |
\(\eta _i^{\text {ch}}\) | Charging efficiency of storage for agent i |
\(\eta _i^{\text {dis}}\) | Discharging efficiency of storage for agent i |
\(\xi\) | Uncertain parameter vector (e.g. renewable output, demand) |
\(\Gamma\) | Budget of uncertainty controlling robustness level |
\(\alpha _i\) | Penalty or incentive coefficient for agent i |
\(\Delta t\) | Time step duration |
Decision variables | |
\(P_i^{t}\) | Power generated by agent i at time t |
\(P_{ij}^{t}\) | Power flow on line (i, j) at time t |
\(S_i^{t}\) | State of charge of storage for agent i at time t |
\(x_i^{t}\) | Decision variable representing agent i’s strategy at time t |
\(y^{t}\) | Upper-layer regulatory signal at time t |
\(\lambda _i^{t}\) | Dual variable for nodal balance constraint of agent i |
\(\mu _{ij}^{t}\) | Shadow price of line capacity constraint between node i and j |
Acronyms | |
ISO | Independent system operator |
VPP | Virtual power plant |
DER | Distributed energy resource |
DRL | Deep reinforcement learning |
PPO | Proximal policy optimization |
DRO | Distributionally robust optimization |
BoU | Budget-of-uncertainty |
LLM | Large language model |
