23 problems

The two approaches are scenario generation and rare-event sampling with Fleming–Viot biasing for robust stochastic programming; let the number of scenarios tend to infinity, and co…

A stochastic distribution network reconfiguration (SDNR) problem is a mixed-integer nonlinear optimization problem whose constraints and decision variables include binary switch va…

Let $al V_L$ be the set of load buses, with $P_{si}^0$ and $lpha_i$ denoting the active-power load parameters and $Q_{si}^0$ and $eta_i$ denoting the reactive-power load parameters…

Suppose Assumption 1 and Assumption 2 hold. Consider a differential-algebraic equation system with all loads purely static. Let $al V_t$ denote the generator buses and $al V_L$ the…

Let a power-system differential-algebraic equation model satisfy the assumptions used in the paper, and let the condition obtained for the specific four-bus system be given. Hisken…

The two-bus power flow system uses the load parameter and the associated maximization formulation to identify a maximal saddle-node bifurcation point. Generalization conjecture. Th…

A synchronous machine (SM) is a conventional generator, while a grid-forming converter (GFC) is a power converter that can establish the grid voltage and frequency. Consider a tran…

Combined linear optimization conjecture. For an abrupt power loss, the optimal placement of a fixed total amount of inertia and primary control that minimizes $\mathcal{M}_b$ is ob…

State-variation conjecture. Probing the grid to effect larger state variations across $\mathcal{T}$ should yield smaller condition numbers for…

Let $G=(B,E)$ be a graph with $B=\{0,1,\dots,|B|-1\}$, and let $P_{G,Y}$ be the system of $2n$ algebraic load flow equations in the variables $(v_1,\dots,v_n,u_1,\dots,u_n)$, where…

Let a power distribution network have one slack bus and $n$ PQ loads, and let it be described by the relaxed branch flow model. In the voltage stability region, set … where…

Scaling-performance conjecture. The better performance observed in the 30-bus model may be related either to the greater density of the Polish system, which requires linearizing a…

Consider distributed averaging control for secondary frequency regulation in a microgrid, where the communication graph and controller parameters may have degrees of freedom beyond…

Consider an approximate version of the lossless AC power-flow feasibility system in which the equation … is replaced by … where $\epsilon>0$ is part of the input. Approximate feasi…

Let the sufficient infeasibility test cited in the source be a test that guarantees power-flow infeasibility but is not asserted there to be necessary, and suppose the convex appro…

Let the convexity domain be the domain on which the energy function is convex, and let the power-flow equations be the equations defining power-flow solutions. Convexity-domain exi…

Let the principal region be the region enclosed by the Principal Singular Surface for a lossless power network, and call a power-flow solution stable when it is dynamically stable.…

Normal-operating-conditions conjecture. Under normal operating conditions, the SDP relaxation is tight.

Let $\mathbf{A}$ be the matrix in the dual formulation of the power-flow optimization, and consider systems for which … The multiple-bifurcation explanation conjecture. Similar exp…

Let $V_{slack}^{min}$ denote the minimum slack-bus voltage, and let $\mathbf{A}$ be the matrix in the dual formulation of the power-flow optimization. Suppose that more than two so…

Let $V_{slack}^{min}$ denote the minimum slack-bus voltage, and let $\mathbf{A}$ be the matrix in the dual formulation of the power-flow optimization. Suppose the minimum slack-bus…

Let $\mathbf{A}$ be the matrix in the dual formulation of the power-flow optimization, and let the controlled voltages be decreased so that solutions of the power-flow equations me…

Let instances of the system, differing for example in their configurations of load, be drawn from a reasonable distribution representing a typical regime, such as a morning of an o…