Power System Flexible Operation By Using Continuous-time Optimization Theory

Under the carbon neutrality target,the increasing penetration of renewable generation,such as wind power,induces a sharper and more uncertain net load,which raises higher requirements on the flexibility of power systems.As an important part of power system operation,day-ahead scheduling plays a critical role in preparing flexibility resources in power systems.Existing day-ahead scheduling methods are mainly based on discrete-time optimization and model power variation as step curves that assume intra-period power to be unchanged and assume power variation between adjacent periods to be steps,which can not accurately describe power variation and may thus induce a less proper scheduling solution.Continuous-time optimization models power variation as smooth and continuous trajectories and can take intra-period power variation into account,for which the flexibility supply and requirements can be better considered and flexibility resources can be properly prepared.Therefore,continuous-time optimization is promising in the flexible operation of power systems.Based on the comprehensive review of state-of-the-art works,this paper conducts comprehensive studies on power system flexible operation by using continuous-time optimization.The main research contents include:(1)To fully realize the flexibility potentials of existing assets in power systems,a flexibility-enhanced continuous-time day-ahead scheduling is proposed.The continuoustime optimization theory and its solution method are revisited and the flexibility loss during existing Bernstein polynomial(BP)spline-based solution space transformation is exposed.According to de Casteljau’s algorithm,the enhancement matrix is derived and the enhanced solution space transformation is proposed to activate the potential flexibility.Simulation results show that the potential flexibility can be exploited by the proposed method and more scheduling solutions can be identified,for which a more proper solution may be found to improve power system operation.(2)To improve intra-period operational security,a continuous-time robust unit commitment considering beyond-the-resolution wind uncertainty is proposed.The continuous-time robust unit commitment is established,in which the beyond-theresolution uncertainty set is analyzed.Solution space transformation is utilized to shift the proposed continuous-time robust optimization into algebraic space and the column-andconstraint generation algorithm is then used for calculation.Simulation results show that beyond-the-resolution uncertainties can be taken into account,which significantly enhances the intra-period robustness of the solved unit commitment.(3)To fully use the complementarity of battery energy storage(BES)and linepack gas storage(LGS),a continuous-time unit commitment considering electric-gas multienergy storage(MES)is proposed.MES is formulated in function space and the dynamics of LGS are described by partial differential equations(PDE),for which the problem is formulated as PDE-constrained optimization.Combined with the operational matrices of BP,solution space transformation is extended to continuous spatial-temporal functions and the proposed optimization can be shifted into algebraic space for calculation.Simulation results validate the correctness of the proposed method and the complementarity of MES can be utilized to enhance the operational economy.(4)To improve the revenue of the energy storage station(ESS)and to reduce the power supply shortage risks of renewable power plants(RPP),a shared energy storage right-based hybrid discrete-time and continuous-time(HT)day-ahead flexibility trading is proposed.The flexibility package is proposed,which is comprised of energy/power/ramping capacity rights and initial/final stored energy.The HT bilevel optimization is proposed,which decides the arbitrage schedule of ESS,the bidding strategies of RPPs,and the flexibility trading.Simulation results show that the proposed method can facilitate flexibility trading to increase the revenue of ESS and help RPPs to select proper bidding and trading strategies to reduce power supply shortage risks.