## Abbreviations  
\(P_{net,t}\) net load of systems with wind power integration in hour \(t\)  
\(P_{load,t}\) forecast value of load demand in hour \(t\)  
\(P_{wind,t}\) forecast output of wind farm in hour \(t\)  
\(R_{amp,t}^{up}/R_{amp,t}^{dn}\) up/down ramp demand of the net load in hour \(t\)  
\(p_{sim}^{\max}/p_{sim}^{\min}\) maximum/minimum output of unit \(i\)  
\(u_{it}\) on-off state of unit \(i\) in hour \(t\)  
\(P_{g,i}\) output of unit \(i\) in hour \(t\)  
\(\triangle P_{load,t}\) spinning reserve demand of the load demand in hour \(t\)  
\(\Delta P_{wind,t}^{up}/\Delta P_{wind,t}^{dn}\) upper and down limitation of wind prediction interval  
\(N_{g}\) number of conventional units  
\(P_{online,max}/P_{online,min}\) upper/lower limitation of the online units  
\(P_{online,total}\) total output of the online conventional units  
\(P_{net}\) net load of systems with wind farm configuration BESS  
\(R\) total spinning reserve capacity required by the system  
\(P_{cap}\) rated power of BESS  
\(S_{cap}\) rate capacity of BESS  
\(C_{serve}\) difference auxiliary service cost of systems with and without BESS  
\(C_{fixed}\) fixed cost item of auxiliary service  
\(C_{unry}\) variable cost item of auxiliary service  
\(C_{AI}\) daily investment cost per capacity of conventional units  
\(P_{g}^{N}\) rated power of the conventional unit \(i\)  
\(p_{g,i}^{bs}\) output of unit \(i\) with configuration BESS in hour \(t\)  
\(M^{BESS}/M\) number of units participating the auxiliary service with/without BESS  
\(c_{g}^{BESS}/c_{g}^{Wind}\) unit coal cost of conventional units with/without BESS  
\(T\) one scheduling period  
\(L_{cyc,D}\) cycle life of BESS under the charge/discharge depth of \(D\)  
\(L_{cyc,N}\) cycle life of BESS with fully charge/discharge  
\(N_{B}\) charge/discharge number of BESS though the life cycle  
\(T_{life}\) equivalent operation years of BESS  
\(P_{g,t}\) output of BESS in hour \(t\)  
\(p_{min,t}\) output of wind energy union system in hour \(t\)  
\(S_{soc,t}\) state of charge (SOC) of BESS in hour \(t\)  
\(\triangle t\) scheduled interval  
\(\lambda_{t}\) charge/discharge status of BESS at time \(t\)  
\(\eta_{s}\) charge/discharge effectiveness of BESS  
\(C_{ost}\) total investment cost of BESS  
\(S_{ave}\) directly benefit from saving wind curtailed energy  
\(C_{c}(p,n)\) capital recovery factor with annual interest rate \(p\)  
\(C_{E}\) unit capacity cost of BESS  
\(C_{OM}\) unit operation and maintenance cost of BESS  
\(a^{s}\) amortized power cost per year  
\(\beta^{s}\) amortized capacity cost per year  
\(r\) kW\(\cdot\)h/kW cost ratio of BESS\(\rho^{\text{in}}\)  
on-grid price of wind power  
\(P_{\text{inloss},t}/P^{\text{B}_{\text{inloss},t}}\)  
curtailed wind energy with and without BESS in hour \(t\)  
\(C_{\text{serve}}^{\text{Wind}}/C_{\text{serve}}^{\text{BESS}}\)  
auxiliary service cost caused by wind power with/without BESS  
\(R_{i}\)  
ramping ability of unit \(i\)  
\(T_{i,\text{max}}^{\text{on}}/T_{i,\text{min}}^{\text{on}}\)  
maximum/minimum online time of unit \(i\)  
\(C_{Gnt}\)  
operating cost function of conventional units  
\(R/P_{gilt}\))  
quadratic fuel cost function with coefficients \(a_{i}\), \(b_{i}\), \(c_{i}\)  
\(S_{i}\)  
on-off cost of unit \(i\)  
\(q\)  
curtailed rate of wind power  
\(N_{\text{cyc}}\)  
equivalent cycle numbers of BESS though a scheduling period  
\(\varepsilon_{s}\)  
reserve level provided by BESS for the uncertainty of wind power