Related papers: A differential analysis of the power flow equation…
The classical optimal power flow problem optimizes the power flow in a power network considering the associated flow and operating constraints. In this paper, we investigate optimal power flow in the context of utility-maximizing demand…
Part I of this paper embeds the AC power flow problem with voltage control and exponential load model in the complex plane. Modeling the action of network controllers that regulate the magnitude of voltage phasors is a challenging task in…
Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is…
Power flow in a low voltage direct current grid (LVDC) is a non-linear problem just as its counterpart ac. This paper demonstrates that, unlike in ac grids, convergence and uniqueness of the solution can be guaranteed in this type of grids.…
With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC…
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all…
Many power system operation and planning problems use the DC power flow approximation to address computational challenges from the nonlinearity of the AC power flow equations. The DC power flow simplifies the AC power flow equations to a…
Non-convex AC optimal power flow (AC-OPF) is a fundamental optimization problem in power system analysis. The computational complexity of conventional solvers is typically high and not suitable for large-scale networks in real-time…
The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear…
The AC optimal power flow (AC-OPF) problem is essential for power system operations, but its non-convex nature makes it challenging to solve. A widely used simplification is the linearized DC optimal power flow (DC-OPF) problem, which can…
Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained…
The solvability set of a power network - the set of all power injection vectors for which the corresponding Power Flow equations admit a solution - is central to power systems stability and security, as well as to the tightness of Optimal…
For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic equations has no solution. This sufficient…
Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…
The existence of multiple solutions to AC optimal power flow (ACOPF) problems has been noted for decades. Existing solvers are generally successful in finding local solutions, which are stationary points but may not be globally optimal. In…
Convex relaxations of the AC Optimal Power Flow (OPF) problem are essential not only for identifying the globally optimal solution but also for enabling the use of OPF formulations in Bilevel Programming and Mathematical Programs with…
The existence of multiple solutions to AC optimal power flow (ACOPF) problems has been noted for decades. Existing solvers are generally successful in finding local solutions, which satisfy first and second order optimality conditions, but…
The DC optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of…
Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the optimal power flow (OPF) problem. Meanwhile, convex relaxed power flow equations are also prerequisites for efficiently solving a wide…
The increasing penetration of renewable energy resources, paired with the fact that load can vary significantly, introduce a high degree of uncertainty in the behavior of modern power grids. Given that classical dispatch solutions are…