Solution techniques for transient stability‐constrained optimal power flow – Part I

A Survey of Relaxations and Approximations of the Power Flow Equations

“…Moreover, while much of the literature develops power flow representations in the context of certain applications, this monograph focuses on the power flow representations themselves rather than specific problems. The reader interested in a specific problem or solution algorithm is referred to the surveys and tutorials that exist for power flow [8,9], different formulations of optimal power flow [10][11][12][13][14][15][16][17][18][19][20][21] (and various extensions to consider, e.g., security constraints [22][23][24][25] and transient-stability constraints [26,27]), unit commitment [28][29][30][31], state estimation [32][33][34][35], transmission switching [36], infrastructure planning [19], voltage stability analysis [37][38][39][40], cascading failure [41], distributed optimization and control methods [42][43][44][45], complex network theory [46], and more general power system stability concepts [6]. Several recent references of particular relevance are the surveys in …”

Analysis of Numerical Methods to Include Dynamic Constraints in an Optimal Power Flow Model

“…TSCOPF models combine a classical optimal power flow with dynamic constraints that make it possible to ensure that the optimal solution is transiently stable. During the last decade, a significant number of papers have been published on the subject and different approaches have been proposed [1][2][3][4].…”

“…Simultaneous discretization is one of the main paths followed in TSCOPF. It includes in a single non-linear optimization model: (1) the equations that represent the steady state operation of the power system and its operational constraints; and (2) the discretized differential equations that represent the dynamics of the system during one or several incidents and the corresponding transient stability limits. The model is completed with the objective function to minimize.…”

“…The trapezoidal rule is widely used in TSCOPF studies to integrate the dynamic equations [1,[8][9][10][11]. However, the impact of the numerical integration method and the corresponding time step requires deeper studies but has not been addressed in detail yet.…”

Optimal Curtailment of Non-Synchronous Renewable Generation on the Island of Tenerife Considering Steady State and Transient Stability Constraints

“…Given the size and complexity of TSCOPF optimization models, the necessary trade-off between model detail and computational time has produced a number of different approaches [13]. Numerical methods that incorporate the discretized differential equations defining the dynamics of the power system into the formulation of the OPF [14,15] have several advantages, such as being able to robustly handle unstable systems with different constraints [13]. However, they produce large models with a number of variables and equality constraints that is impractical for large or medium-size systems.…”