n-k Operational Security Problem

The $N-k$ problem is a Mixed-Integer Non-Linear Program (MINLP), usually intractable, since the combinatorial combinations of binary variables representing component fails (even for small values of $k$) in addition to the non-linear modeling of power flow physics, make this problem a non convex one.

Although in many cases the use of linear approximations in power systems is sufficient, when trying to model possible cascading effects such models are not appropriate.

In this repository we explore several formulations to solve the problem.

Solutions for 14 Bus System

Big M	Sol	Gap	time (ms)	N sols
0.95	2	0	35	3
0.9	3	0	39.7	2
0.85	4	0	59.6	3
0.8	4	0	66.9	3
0.75	5	0	79.3	4
0.7	6	0	80.5	3

lambda_i	Sol	Gap	time (ms)	N sols
0.95	2	0	88.2	3
0.9	3	0	70.9	3
0.85	4	0	121	4
0.8	4	0	92.5	4
0.75	5	0	105	5
0.7	6	0	160	3

NL	Sol	round	Term Code	time (ms)
0.95	2.96	3	optimal	55.2
0.9	4.82	5	optimal	62.1
0.85	4.86	5	optimal	83.2
0.8	4.91	5	optimal	102
0.75	8.93	9	optimal	360
0.7	9.93	10	optimal	98.0

Solutions for 118 Bus System

Big M	Sol	Gap	time (s)	N sols
0.95	2	0	7.2	2
0.9	4	0	251	5
0.85	5	40%	3600	4
0.8	7	57.14%	3600	5
0.75	9	66.67%	3600	5
0.7	11	72.72%	3600	4

lambda_i	Sol	Gap	time (s)	N sols
0.95	2	0	20.2	3
0.9	4	0	209	3
0.85	5	40 %	3600	8
0.8	7	57.14%	3600	8
0.75	9	66.67%	3600	8
0.7	12	66.67%	3600	7

NL	Sol	round	Term Code	time (s)
0.95	3.77	4	optimal	1.04
0.9	3.97	4	optimal	1.13
0.85	6.91	7	optimal	1.21
0.8	11.3	11	optimal	1.16
0.75	14.9	15	optimal	1.2
0.7	16.23	16	acceptable	10.6