Table 1 Variables, parameters and constants of the EV optimization problem
From: National-scale bi-directional EV fleet control for ancillary service provision
Name | Type | Dim. | Description |
|---|---|---|---|
c | Var | \(\mathbb {Z}^{T \times n_v}_{\{0,1 \}}\) | Ev connected to charger |
\(x_{c}\) | Var | \(\mathbb {Z}^{T \times n_v}_{\{0, 1\}}\) | Plug state |
x | Var | \(\mathbb {R}^{T+1 \times n_{v}}\) | Batteries state [kWh] |
\(u_c, u_d\) | Var | \(\mathbb {R}^{T \times n_{v}}\) | Charging / discharging power [kW] |
y | Var | \(\mathbb {R}^{T}\) | Energy costs [£] |
r | Par | \(\mathbb {R}^{T}\) | Reference profile |
l | Par | \(\mathbb {Z}^{T \times n_{v}}\) | Location matrix |
\(n_{max, s}\) | Par | \(\mathbb {Z}^{n_{s}}\) | Stations’ chargers |
\(p_{s, max}\) | Par | \(\mathbb {R}^{n_{s}}\) | Stations’ max power |
\(\psi _{buy}\), \(\psi _{sell}\) | Par | \(\mathbb {R}^T\) | Buying and selling prices [£/kWh] |
e | Par | \(\mathbb {R}^{T\times n_v}\) | Energy constraint matrix [kWh] |
\(\Delta e\) | Par | \(\mathbb {R}^{T\times n_v}\) | \(\Delta\) energy at arrival [kWh] |
\(\hat{p}\) | Par | \(\mathbb {R}^T\) | Forecasted station power [kW] |
\(\hat{p}_{pv}\) | Par | \(\mathbb {R}^{T}\) | Forecasted PV profile |
\(x_{start}\) | Par | \(\mathbb {R}^{n_v}\) | Initial battery state [kWh] |
\(x_{min}, x_{max}\) | Par | \(\mathbb {R}^{n_v}\) | Capacity limits [kWh] |
\(u_{d, min}, u_{d, max}\) | Par | \(\mathbb {R}^{n_v \times 2}\) | Discharging limits [kW] |
\(u_{c, min}, u_{c, max}\) | Par | \(\mathbb {R}^{n_v \times 2}\) | Charging limits [kW] |