Price Taker Problem

This problem is defined at period $t$ and scenario $\omega$ for an asset owner $i$.

Sets

Lists new or modified sets, not present in the centralized operation subproblem.

• $J^T_i$: Set of thermal units owned by asset owner $i$.
• $J^H_i$: Set of hydro units owned by asset owner $i$.
• $J^R_i$: Set of renewable units owned by asset owner $i$.
• $J^B_i$: Set of battery units owned by asset owner $i$.

Parameters

Lists new or modified parameters, not present in the centralized operation subproblem.

• $\pi_{n, \tau}(\omega)$: Price of electricity on network node $n$ during subperiod $\tau$ and scenario $\omega$.

Variables

Lists new variables, not present in the centralized operation subproblem.

• $e_{n, \tau}$: Asset owner's total generation on network node $n$ during subperiod $\tau$.

Subproblem Constraints

The following constraints are defined for a subproblem at period $t$ and scenario $\omega$ for an asset owner $i$.

Asset owner's total generation

\[ e_{n, \tau} = \sum_{j \in J^T_i(n)}{g^T_{j, \tau}} + \sum_{j \in J^H_i(n)}{\rho_j (u_{j, \tau})} + \sum_{j \in J^R_i(n)}{g^R_{j, \tau}} + \sum_{j \in J^B_i(n)}{g^B_{j, \tau}} \\ \quad \forall n \in N, \tau \in B(t)\]

The remaining constraints are a subset of the centralized operation problem, but only for the asset owner's assets. Notably, network, demand balance and deficit constraints are not included.

Hydro Balance

Intra-period balance

\[ v_{j, \tau+1} = v_{j, \tau} - u_{j, \tau} - z_{j, \tau} + \sum_{n \in J^H_U(j)}{u_{n, \tau}} + \sum_{n \in J^H_Z(j)}{z_{n, \tau}} + a_{j, \tau} \quad \forall j \in J^H_i, \tau \in B(t)\]

Inter-period balance

\[ v^{S_{in}}_j = v_{j, 1} \quad \forall j \in J^H_i\]

\[ v^{S_{out}}_j = v_{j, |B(t)| + 1} \quad \forall j \in J^H_i\]

Renewable Balance

\[ g^R_{j, \tau} + y^r_{j, \tau} = G^R_{j, \tau}(\omega) \quad \forall j \in J^R_i, \tau \in B(t)\]

Battery Unit Balance

Intra-period balance

\[ s^b_{j, \tau+1} = s^b_{j, \tau} - g^B_{j, \tau} \quad \forall j \in J^B_i, \tau \in B(t)\]

Inter-period balance

\[ s^{B_{in}}_j = s^b_{j, 1} \quad \forall j \in J^B_i\]

\[ s^{B_{out}}_j = s^b_{j, |B(t)| + 1} \quad \forall j \in J^B_i\]

Hydro Bounds

Volume bounds

\[ 0 \leq v_{j, \tau} \leq V_j, \quad \forall j \in J^H_i, \tau = 1, ..., |B(t)| + 1\]

Other bounds

\[ 0 \leq u_{j, \tau} \leq U_j, \quad 0 \leq z_{j, \tau} , \quad \forall j \in J^H_i, \tau \in B(t)\]

Thermal Bounds

\[ 0 \leq g^T_{j, \tau} \leq G^T_j, \quad \forall j \in J^T_i, \tau \in B(t)\]

Renewable bounds

\[ 0 \leq g^R_{j, \tau} \leq G^R_j, \quad 0 \leq y^r_{j, \tau} \leq G^R_j, \quad \forall j \in J^R_i\]

Battery Unit bounds

\[ -G^B_j \leq g^B_{j, \tau} \leq G^B_j, \quad 0 \leq s^b_{j, \tau} \leq S^B_j, \quad \forall j \in J^B_i, \tau \in B(t)\]

Objective Function

\[ min{ \sum_{\tau \in B(t)}{( - \sum_{n \in N}{\pi_{n, \tau}(\omega) e_{n, \tau}} + \sum_{j \in J^T_i}{C^T_j g^T_{j, \tau}} + \sum_{j \in J^R_i}{C^R_j y^r_{j, \tau}} )} }\]