Nomenclature
This section provides an overview of the formulations and optimization models used in the package.
Indexes
\(g\) |
Generator index |
\(\mathcal{G}_n\) |
Set of generators at bus \(n\) |
\(n, m\) |
Bus indices |
\(l\) |
Transmission line index |
Parameters
\(S_{\text{base}}\) |
Base power [MVA] |
\(a_{g}, b_{g}, c_{g}\) |
Cost coefficients for \(g\) |
\(\overline{p}_g, \underline{p}_g\) |
Active power generation limits for \(g\) [MW] |
\(\overline{q}_g, \underline{q}_g\) |
Reactive power generation limits for \(g\) [MW] |
\(p^d_n, q^d_n\) |
Active and reactive power demand at node \(n\) [MW, MVAr] |
\(\overline{\theta}_n, \underline{\theta}_n\) |
Voltage angle limits at bus \(n\) [radians] |
\(\underline{v}_n, \overline{v}_n\) |
Voltage magnitude limits at node \(n\) [p.u.] |
\(G^{sh}_n, B^{sh}_n\) |
Shunt conductance and susceptance at node \(n\) [p.u.] |
\(r_l, x_l\) |
Series resistance and reactance of branch \(l\) [p.u.] |
\(b_l\) |
Total charging susceptance of branch \(l\) [p.u.] |
\(\tau_l, \gamma_l\) |
Tap ratio magnitude and phase shift angle of branch \(l\) |
\(\overline{s}_l\) |
Apparent power flow limit for branch \(l\) [MVA] |
\(F_{l,n}, T_{l,n}\) |
Incidence matrices for “from” and “to” buses of line \(l\) |
We also define the following parameters for the branch \(l\):
Variables
\(p_g\) |
Active power generation of \(g\) [MW] |
\(q_g\) |
Reactive power generation of \(g\) [MVAr] |
\(v_n\) |
Voltage magnitude at node \(n\) [p.u.] |
\(\theta_n\) |
Voltage angle at bus \(n\) [radians] |
\(v_n^{(2)}\) |
Voltage magnitude squared at node \(n\) [p.u.] |
\(e_n, f_n\) |
Real and imaginary parts of voltage at node \(n\) [p.u.] |
\(p^f_l, p^t_l\) |
Active power flow on branch \(l\) (from/to) [MW] |
\(q^f_l, q^t_l\) |
Reactive power flow on branch \(l\) (from/to) [MVAr] |