# Minimum Frequency and Voltage Stability Constrained Unit Commitment for AC/DC Transmission Systems
## 6 Conclusions
\begin{tabular}{l l} \(N_{\text{B}}\) & Number of buses \\ \(C_{\text{sum}}\) & The total operation cost \\ \(u_{i}^{t}\) & On/off state of generating unit \(i\) at time \(t\) \\ \(P_{L,m^{\prime}}^{t},Q_{L,m}^{t}\) & Real and reactive load of bus \(m\) at time \(t\) \\ \(t_{i}^{t}\) & Reserve capacity of unit \(i\) at time \(t\) \\ \(\overline{P}_{i,\text{max}}\), \(\underline{P}_{i,\text{min}}\) & Upper and lower output limit considering ramp capacity of unit \(i\) \\ \(\overline{Q}_{G,i,\text{max}}\)/\(\overline{Q}_{G,i,\text{min}}\) & Upper/lower reactive power limit of unit \(i\) \\ \(HST_{i}\), \(CST_{i}\) & Hot and cold start-up cost of unit \(i\) \\ \(T_{i,\text{omr}}^{t}\), \(T_{i,\text{off}}^{t}\) & Continuous on/off time of unit \(i\) at time \(t\) \\ \(UR_{i}\), \(DR_{i}\) & Ramp up and down capacity of unit \(i\) \\ \(\Delta f_{\text{max}}\) & Maximal allowed frequency deviation \\ \(K_{L}\) & First frequency regulation coefficient of load \\ \(\eta_{VSM}\) & Voltage stability margin of power grid \\ \(P_{l0}\) & Initial real load of power grid \\ \(X_{\text{mn}}\) & Line reactance between bus \(m\) and \(n\) \\ \(\overline{P}_{d}^{t}\) & Maximum HVDC transmission power at time \(t\) \\ \(p_{\text{loss}}^{t}\) & Real power loss of power grid at time \(t\) \\ \(V_{m,s}^{t}\), \(V_{n,s}^{t}\) & Voltage of AC bus \(m/n\) at time t after second frequency regulation \\ \(PL_{mm,s}^{t}\) & Transmission power between bus \(m\) and \(n\) \\ \(MP_{1}\), \(MP_{2}\), \(MQ_{1}\), \(MQ_{2}\), \(MPL_{1}\), \(MP_{2}\), \(MPD_{1}\), \(MPD_{2}\) & Mismatch vectors \\ \(\Delta V\), \(\Delta\theta\) & Vector of units' amplitude and phase increments \\ \(dP\), \(dQ\) & Mismatch vector of real and reactive power of AC buses \\ \(dP\), \(dQ_{\text{dc}}\) & Mismatch vector of real and reactive power of HVDC \\ \(\Delta PL\) & Vector of AC transmission power \\ \(H\), \(N\), \(J\), \(L\), \(W\), \(S\), \(O\), \(D\), \(E\), \(F\) & Jacobian matrices \\ \(\Delta Q_{\text{min}}\), \(\Delta Q_{\text{max}}\) & Vector of units' reactive power limits with increments \\ \(\Delta V_{\text{min}}\), \(\Delta V_{\text{max}}\) & Vector of voltage limits with increments \\ \(\Delta X_{\text{dc,min}}\), \(\Delta X_{\text{dc,max}}\) & Vector of dc variables limits with increments \\ \(\Pi_{\text{max}}\) & Maximum number of iteration \\ \(I_{d}\) & DC current \\ \(\alpha\) & Trigger delay angle \\ \(V_{m}^{(t)}\), \(V_{n}^{(t)}\) & Voltage of AC bus \(m/n\) (at time t) \\ \(n_{R}\), \(n_{I}\) & Bridge number of rectifier/inverter \\ \(p_{\text{dR}}\), \(P_{\text{dI}}\) & Real power of rectifier/inverter \\ \(Q_{\text{CR}}\), \(Q_{\text{CI}}\) & Reactive power compensation of rectifier/inverter substation \\ \(i\) & Index of units \\ \(t\) & Index of hours \\ \(T\) & Number of scheduling periods \\ \(N_{\text{L}}\) & Number of HVDC \\ \(C_{\text{i}}\) & Cost function of unit \(i\), \(Ci=a_{\text{i}}(P_{G,i}^{t})^{2}+b_{\text{i}}P_{G,i}^{t}+c_{\text{i}}\) \\ \(a_{i}b_{i,\text{c}}c_{i}\) & Coefficients of cost function \\ \(P_{G,i}^{t}\), \(Q_{G,i}^{t}\) & Real/reactive generation of unit \(i\) \\ \(P_{d,I^{\prime}}^{t}\), \(Q_{d,I}^{t}\) & Real and reactive power of DC \(l\) at time \(t\) \\ \(\overline{P}_{G,i,\text{max}}\), \(\underline{P}_{G,i,\text{min}}\) & Upper and lower real power limit of unit \(i\) \\ \(PL_{mm}^{t}\) & Transmission power between bus \(m\) and \(n\) \\ \(ST_{i}^{t}\) & Start up cost of unit \(i\) at time \(t\) \\ \(T_{i,\text{upr}}\), \(T_{i,\text{down}}\) & Minimum continuous on/off time of unit \(i\) \\ \(T_{i,\text{cold}}\) & Cold start up time of unit \(i\) \\ \end{tabular}