On the Construction of Linear Approximations of Line Flow Constraints for AC Optimal Power Flow

A Novel Approximation of Security-Constrained Optimal Power Flow With Incorporation of Generator Frequency and Voltage Control Response

“…As was observed in [21], which solved an OPF with all lines linearized, the problem is solved faster only for highly stressed systems; on average, the linearization slows down the solution process. Furthermore, convergence issues were observed in our simulations when linearizing too many lines, attributed to the voltage control constraints, ( 17)- (18), "clashing" with the large number of introduced voltage-angle constraints (see [21]). As such, only a percentage of power flows can be linearized, in order to avoid such cases.…”

“…The linearization achieves a small speed improvement (on average, about 7.5%) owing to the simplification of the CVE and SCOPF modules. However, the large number of introduced linear constraints (see [21]), coupled with the required voltage constraints, ( 17)- (18), does not allow for further improvement. The objective value is about 0.5% higher.…”

“…Each such constraint is replaced by a series of linear constraints (convex envelopes are created for each branch flow limit), representing different behavioral patterns concerning the branch voltage magnitudes and angles at the limit boundary. The utilized methodology is inspired from [21], and adapted to this work to address partial power system linearization and constraint differentiation between CCs. Performing this simplification for a high number of lines decreases the problem complexity of the problem and could lead to faster solution times.…”

“…Performing this simplification for a high number of lines decreases the problem complexity of the problem and could lead to faster solution times. The reader is referred to [21] for an in-depth explanation of the linearization procedure.…”

“…• A simple but effective heuristic to get rid of the overwhelming slack variables from the problem formulation. • A significant adaptation of a previously proposed line flow convex approximations method [21], developed for AC OPF, which makes it for the first time applicable to the AC SCOPF problem. The remainder of this paper is structured as follows.…”