2. Market Model
The power market model can operate in two phases:
- Zonal/Nodal Market Clearing — day-ahead dispatch based on perfect competition.
- Redispatch — adjustments to initial dispatch for network feasibility.
Market Clearing Phase
Objective Function
\[\min \quad \sum_{t}^T \sum_{p}^{P} c_{p,t}^{mc} \cdot GEN_{p,t} + c^{curt} \cdot \sum_{t}^{T} \sum_{z}^{Z} CU_{z,t} + \sum_t^T \sum_{s}^{S} mc_{s,t} \cdot GEN_{s,t}\]
Market Balance
Depending on the chosen setup, the market balance will either be zonal, or nodal. In Europe, market balances are created in a zonal level, with some countries having multiple market zones. An example of nodal pricing can be found in the electricity market of the USA.
Zonal Market Balance
\[\begin{aligned} & \sum_{p \in z}^{P} GEN_{p,t} + \sum_{s \in z}^{S} (GEN_{s,t} - CHARGE_{s,t}) + EX_{z,t}^{net} - CU_{z,t} \\ &= \sum_{n \in z}^{N} load_{n,t} - LL_{z,t}, \qquad \forall \ z \in Z, t \in T \end{aligned}\]
Nodal Market Balance
\[\begin{aligned} &\sum_{u \ in \ n}^U GEN_{u,t} + \sum_{s \ in \ n}^S (GEN_{s,t} -CHARGE_{s,t}) &+ INJ_{n,t} - CU_{n,t}\\ = &load_{n,t} - LL_{n,t} & \forall \ n \in N, t \in T \end{aligned}\]
Storage Balance
\[S_{s,t}^{lvl} - S_{s,t-1}^{lvl} = CHARGE_{s,t} \cdot \eta_{s} - \frac{GEN_{s,t}}{\eta_{s}} + inflow_{s,t}, \quad \forall \ s \in S, \ t \in T\]
Exchange
The following exchange equation only applies in zonal markets, where electricity transmission within a given zone is neglected and only cross border flows are depicted using a simple approach based on net transfer capacities and an import-export balance. Nodal markets on the other hand already take the physical characteristics of the transmission grid into accound (a describtion of lineflow constraints can be found in section Line Flow Constraints and 3. AC Power Flow Linearization)
\[EX_{z,t}^{net} = \sum_{zz}^Z EX_{zz,z,t} - EX_{z,zz,t}, \qquad \forall \ z \in Z, t \in T\]
Variable Bounds
\[\begin{aligned} 0 \leq GEN_{p,t} &\leq avail_{p,t} \cdot gen_{p}^{max}, && \forall \ p \in P, \ t \in T \\ 0 \leq GEN_{s,t} &\leq gen_{s}^{max}, && \forall \ s \in S, \ t \in T \\ 0 \leq CHARGE_{s,t} &\leq gen_{s}^{max}, && \forall \ s \in S, \ t \in T \\ 0 \leq S_{s,t}^{lvl} &\leq cap_{s}^{max}, && \forall \ s \in S, \ t \in T \\ 0 &\leq CU_{z,t}, && \forall \ z \in Z, \ t \in T \\ 0 &\leq LL_{z,t}, && \forall \ z \in Z, \ t \in T \\ 0 \leq EX_{z,zz,t} &\leq ntc_{z,zz}, && \forall \ z \in Z, \ zz \in Z, t \in T \end{aligned}\]
Redispatch Phase
Objective Function
\[\begin{aligned} \min \quad & \sum_t^T\sum_{p}^P c^{redisp} \cdot (RAMP_{p,t}^{up} + RAMP_{p,t}^{down}) + \sum_t^T\sum_{p}^P c^{curt} \cdot (CU_{p,t}^{redisp} - cu_{p,t}) \\ & + \sum_t^T\sum_{s}^S c^{redisp} \cdot (GEN_{s,t}^{up} + GEN_{s,t}^{down}) \\ & + \sum_t^T\sum_{s}^S c^{redisp} \cdot (CHARGE_{s,t}^{up} + CHARGE_{s,t}^{down}) \end{aligned}\]
Redispatch Market Balance
\[\begin{aligned} \sum_{p \in n}^P GEN_{p,t}^{redisp} + \sum_{s \in n}^S (GEN_{s,t}^{redisp} - CHARGE_{s,t}^{redisp}) + INJ_{n,t} - CU_{n,t} = load_{n,t} - LL_{n,t} \qquad \forall \ n \in N, t \in T \end{aligned}\]
Line Flow Constraints
\[\begin{aligned} F_{dcl,t} &= F_{dcl,t}^{pos} - F_{dcl,t}^{neg}, && \forall \ t \in T, dcl \in DCL \\ F_{acl,t} &= \sum_n^{N} \text{B}_{acl \times n}^{line} \cdot \theta_{n}, && \forall \ acl \in ACL, t \in T \\ INJ_n &= \sum_m^{M} \text{B}_{n \times m}^{bus} \cdot \theta_{m} + \sum_{dcl}^{DCL} \text{A}_{l\times n}^{dc} \cdot F_{dcl,t}, && \forall \ n \in N \end{aligned}\]
Variable Balances
\[\begin{aligned} GEN_{p,t}^{redisp} &= RAMP_{p,t}^{up} - RAMP_{p,t}^{down} + gen_{p,t}, && \forall p \in P, t \in T \\ GEN_{s,t}^{redisp} &= GEN_{s,t}^{up} - GEN_{s,t}^{down} + gen_{s,t}, && \forall s \in S, t \in T \\ CHARGE_{s,t}^{redisp} &= CHARGE_{s,t}^{up} - CHARGE_{s,t}^{down} + charge_{s,t}, && \forall s \in S, t \in T \end{aligned}\]
Storage Balance
\[S_{s,t}^{lvl,redisp} = S_{s,t-1}^{lvl,redisp} - \frac{GEN_{s,t}^{redisp}}{\eta_s} + CHARGE_{s,t}^{redisp} \cdot \eta_s, \quad \forall s \in S, t \in T\]
Variable Bounds
\[\begin{aligned} 0 \leq RAMP_{p,t}^{up} &\leq avail_{p,t} \cdot gen_{p}^{max} - gen_{p,t}, && \forall p \in P, t \in T \\ 0 \leq RAMP_{p,t}^{down} &\leq gen_{p,t}, && \forall p \in P, t \in T \\ 0 \leq GEN_{s,t}^{up} &\leq gen_{s}^{max} - gen_{s,t}, && \forall s \in S, t \in T \\ 0 \leq GEN_{s,t}^{down} &\leq gen_{s,t}, && \forall s \in S, t \in T \\ 0 \leq CHARGE_{s,t}^{up} &\leq gen_{s}^{max} - charge_{s,t}, && \forall s \in S, t \in T \\ 0 \leq CHARGE_{s,t}^{down} &\leq charge_{s,t}, && \forall s \in S, t \in T \\ 0 \leq S_{s,t}^{lvl,redisp} &\leq cap_{s}^{max}, && \forall s \in S, t \in T \\ 0 \leq CU_{p,t}^{redisp} &\leq avail_{p,t} \cdot gen_{p}^{max}, && \forall p \in P, t \in T \\ -cap_{acl}^{max} \leq F_{acl,t} &\leq cap_{acl}^{max}, && \forall acl \in ACL, t \in T \\ -cap_{dcl}^{max} \leq F_{dcl,t} &\leq cap_{dcl}^{max}, && \forall dcl \in DCL, t \in T \\ 0 \leq F_{dcl,t}^{pos}, && \forall t \in T, dcl \in DCL \\ 0 \leq F_{dcl,t}^{neg}, && \forall t \in T, dcl \in DCL \\ 0 \leq \theta_{n,t}, && \forall t \in T, n \in N \\ 0 = \theta_{n=slack,t}, && \forall t \in T \\ 0 \leq GEN_{p,t}^{redisp}, && \forall p \in P, t \in T \\ 0 \leq GEN_{s,t}^{redisp}, && \forall s \in S, t \in T \\ 0 \leq CHARGE_{s,t}^{redisp}, && \forall s \in S, t \in T \\ 0 \leq LL_{n,t}, && \forall n \in N, t \in T \end{aligned}\]