Dynamics-aware optimal power flow

Abstract

Abstract-The development of open electricity markets has led to a decoupling between the market clearing procedure that defines the power dispatch and the security analysis that enforces predefined stability margins. This gap results in market inefficiencies introduced by corrections to the market solution to accommodate stability requirements. In this paper we present an optimal power flow formulation that aims to close this gap. First, we show that the pseudospectral abscissa can be used as a unifying stability measure to characterize both poorly damped oscillations and voltage stability margins. This leads to two novel optimization problems that can find operation points which minimize oscillations or maximize voltage stability margins, and make apparent the implicit tradeoff between these two stability requirements. Finally, we combine these optimization problems to generate a dynamics-aware optimal power flow formulation that provides voltage as well as small signal stability guarantees.

Distributed Minimization of the Power Generation Cost in Prosumer-Based Distribution Networks

“…Next, a distributed feedback control algorithm will be devised to minimize the power generation cost. The generation cost is often chosen to be a polynomial, e.g., a quadratic function of the type [4], [12], [13]…”

Coupling Load-Following Control With OPF

“…The spectral abscissa, that is, the largest real part of system state matrix eigenvalues, is upper bounded by a negative number in [17], yielding a non-smooth OPF. A simpler optimization problem is pursued in [18] using the pseudo-spectral abscissa as stability measure. Based on Lyapunov's stability theorem and the system state matrix, [19] incorporates small-signal stability constraints into the OPF.…”

“…The assumption on invertibility of h a (x 0 , a 0 ) is very mild in the sense that it holds for practical networks and for various operating points; see also [18] and references therein for sufficient conditions in a similar construction. Then, substituting ( 6) in (5a) yields…”

“…The standard OPF problem typically only considers the algebraic variable a s and is given as min a s c(a s ) subj. to (18) and a s ∈ A.…”

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“…Case studies are presented showcasing the performance of the L∞ controllers in comparison with automatic generation control and H∞ control methods. studies the design of grid operating points for generators with lower operational costs and desirable stability properties [2], [3]. The third category pertains to the design of economic incentives and demand-response methods that drive users to consume less energy, thereby impacting the overall grid generation and the stability of the grid [4].…”