In this paper, we propose a projection-free power-limiting droop control for grid-connected power electronics and an associated constrained flow problem. In contrast to projection-based power-limiting droop control, the novel projection-free power-limiting droop control results in networked dynamics that are semi-globally exponentially stable with respect to the set of optimizers of the constrained flow problem. Under a change to edge coordinates, the overall networked dynamics arising from projection-free power-limiting droop control coincide with the projection-free primal-dual dynamics associated with an augmented Lagrangian of the constrained flow problem. Leveraging this result, we (i) provide a bound on the convergence rate of the projection-free networked dynamics, (ii) propose a tuning method for controller parameters to improve the bound on the convergence rate, and (iii) analyze the relationship of the bound on the convergence rate and connectivity of the network. Finally, the analytical results are illustrated using an Electromagnetic transient (EMT) simulation.
The ongoing shift from synchronous machine-based power generation towards power electronics-interfaced generation and energy storage results in significant changes to power system frequency dynamics. Specifically, grid-connected power electronics differ from conventional synchronous generators in terms of their fast response (i.e., milliseconds to seconds) and resource constraints (e.g. power and current limits). Accordingly, incorporating renewable generation resources into large-scale power system challenges standard operating and control paradigm and jeopardizes system stability [1], [2]. For instance, stability analysis of emerging power systems crucially requires considering the constraints of power converters and renewable generation resources such as power limit.
Today, most renewables are interfaced by dc/ac voltage source converters (VSC) use so-called grid-following control. This control paradigm requires a stable and slowly changing ac voltage (i.e., magnitude and frequency) and jeopardizes grid stability when disturbance occur [3]. Since grid-following explicitly controls the converter current/power, incorporating power limits is straightforward. In contrast, grid-forming converters, that are commonly envisioned to be the cornerstone of future power systems, impose stable and self-synchronizing ac voltage dynamics at their grid terminals. Although prevalent grid-forming controls including droop control [4], virtual synchronous machine control (VSM) [5], and dispatchable virtual oscillator control (dVOC) [6] have been investigated in detail constraints are not accounted for in their analysis [7]- [11].
However, from a practical point of view, resource and converter constraints are a significant concern. The majority of works on grid-forming control under constraints in the application oriented literature has focused on currentlimiting (see [12] for a recent survey). Only few works investigate dc voltage [13] or power limits [14]. Notably, power-limiting droop control combines conventional droop control with proportional-integral controls that activate when the converter reaches its power limit [14].
Continuous-time primal-dual gradient descent dynamics [15] have been widely used to study system-level controls for multi-machine systems such as automatic generation control and economic dispatch [16]. Moreover, primal-dual dynamics have been used to design novel distributed power flow controls [17]. The focus of these works are predominantly equality constrained optimization problems that arise from secondary and tertiary control of power systems.
In contrast, this work leverages projection-free primaldual dynamics [18] to develop a novel decentralized powerlimiting primary control for grid-connected power electronics and analyze the resulting multi-converter system frequency dynamics. Our novel projection-free power-limiting droop control is distinct from power-limiting droop control [14], [19] and enables rigorous bounds on the convergence rate of the multi-converter system frequency to the optimal solution of an associated constrained network flow problem.
Compared with conventional grid-forming droop control [4], power-limiting droop control [14], [19] explicitly accounts for active power limits of resources interfaced by power converters. Moreover, the frequency dynamics of a network of VSCs using power-limiting droop control can be expressed as projected dynamical system [19]. To characterize the steady-states of these networked dynamics, a generic constrained network flow problem can be formulated whose associated primal-dual dynamics are distinct from the networked dynamics and cannot be implemented using only local information [19]. However, leveraging a change of coordinates to edge coordinates [20], the Carathéodory solutions of the projected networked dynamics turn out to be asymptotically stable with respect to Karush-Kuhn-Tucker (KKT) points of the constrained flow problem in edge coordinates. Specifically, in edge coordinates, the primal-dual dynamics associated with the constrained flow problem and the projected networked dynamics coincide. This, enables to represent the networked dynamics a primal-dual dynamics and apply well-known stability results [15]. Notably, the networked dynamics in nodal coordinates are globally asymptotically stable with respect to the set of optimizers of its associated constrained network problem in nodal coordinates [19]. This result directly establishes frequency stability and synchronization of networks of converters using powerlimiting grid-forming droop control. In addition, upon convergence, the converters exhibit power-sharing properties similar to so-called power-sharing in unconstrained droop control [21].
However, the discontinuity of power-limiting droop control hinders convergence analysis and no convergence rate is provided in [19]. In particular, while the stability of the common primal-dual gradient descent is well-studied as a discon
This content is AI-processed based on open access ArXiv data.