Analysis of a dc bus system with a nonlinear constant power load and its delayed feedback control

Abstract

This paper tackles a destabilizing problem of a direct-current (dc) bus system with constant power loads, which can be considered a fundamental problem of dc power grid networks. The present paper clarifies scenarios of the destabilization and applies the well-known delayed-feedback control to the stabilization of the destabilized bus system on the basis of nonlinear science. Further, we propose a systematic procedure for designing the delayed feedback controller. This controller can converge the bus voltage exactly on an unstable operating point without accurate information and can track it using tiny control energy even when a system parameter, such as the power consumption of the load, is slowly varied. These features demonstrate that delayed feedback control can be considered a strong candidate for solving the destabilizing problem.

Dynamics of dc bus networks and their stabilization by decentralized delayed feedback

“…3. A ccording to our previous result [16], for no param eter m ism atch p = 0, a stand-alone bus system has stable p + if a < «hp for b ^ 1 and a < asN for b ^ 1, where a hp and asN denote the H opf (HP) and saddle-node (SN) bifurcation points, respectively. The region w ith param eter m ism atch shrinks in com parison w ith the region w ith no param eter m ism atch.…”

“…T his is because for a nom inal param eter set (a,b) ju st below bifurcation curves, som e buses can have the param eter set (an,b") above the curves due to random choice. On the other hand, this num erical result suggests that our previous result [16] is useful for design o f the nom inal param eters (a,b,e) such that the bus system netw orks are stable even w ith som e param eter m ism atch.…”

“…From X\ = 0 in Eq. (7), system s (9) include Z\ = A(x±)Z\, w hich does not depend on L and e. This suggests that if A(x±) is unstable, then the state X*± is unstable for any L and for any e. Since A (x * ) is always unstable [16], the state X*_ is unstable, independent o f L and e. Furtherm ore, note that if A (x * ) is unstable, the state X \ is unstable, independent o f L and s. ■ L em m a 1 restricts our attention to dynam ics around the state X* . Thus, the present paper w ill deal only w ith the dynam ics o f system s (9) w ith A (x * ), show n in Fig.…”

“…In a previous study, we demonstrated that bifurcation theory analytically clarifies the dynamics of a simplified dc bus system [16], Furthermore, a delayed-feedback control [17] was used to overcome the drawback regarding potential instability. The application of a delayed-feedback control to the simplified dc bus system allows us to noninvasively stabilize an unstable operating point without using the location of the point.…”

Sliding mode control of a bidirectional DC/DC converter with constant power load

“…The stabilization of DC bus becomes more challenging in the presence of CPLs due its nonlinear nature. Some of the techniques, among many other, proposed in the literature for the stabilization of the CPL induced instabilities are power shaping based BraytonMoser's mixed potential function [10], coupling induced open loop stabilization [11], [12] and sliding mode control (SMC). SMC is a well known technique to design controllers which are robust to system parameter variations and input and load disturbance [13].…”