Ultimate boundedness of droop controlled Microgrids with secondary loops

In this paper we study theoretical properties of inverter-based microgrids controlled via primary and secondary loops. Stability of these microgrids has been the subject of a number of recent studies. Conventional approaches based on standard hierarchical control rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. In this paper we show that (i) frequency regulation can be ensured without assuming time-scale separation and, (ii) ultimate boundedness of the trajectories starting inside a region of the state space can be guaranteed under a condition on the inverters power injection errors. The trajectory ultimate bound can be computed by simple iterations of a nonlinear mapping and provides a certificate of the overall performance of the controlled microgrid.Comment: 8 pages, 1 figur

Robust Operating Envelopes for DER Integration in Unbalanced Distribution Networks

Operating envelopes (OEs) have been introduced in recent years as a means to manage the operation of distributed energy resources (DERs) within the network operational constraints. OEs can be used by network operators to communicate DER dispatchable capacity to aggregators without further consideration of network constraints and are thus viewed as a key enabler for demand-side participation in future electricity markets and for ensuring the integrity of distribution networks. While a number of approaches have been developed to calculate OEs, uncertainties in system data are typically ignored, which can lead to unreliable results and introduce security risks in network operations. This paper presents a deterministic procedure to calculate robust OEs (ROEs) explicitly hedged against uncertainty and variability in customers' loads and generations. The approach is based on a geometric construction strictly included within the feasible region of a linear unbalanced three-phase optimal power flow problem that specifies the network operational constraints. The paper analyses and rigorously shows that the proposed approach also delivers proportional fairness in capacity allocations, and demonstrates how the ROEs can be enlarged by (i) exploiting the knowledge of customer operational statuses, and (ii) by optimising customers' controllable reactive powers. Two case studies based on an illustrative distribution network and an Australian representative low-voltage distribution network illustrate the efficiency and compliance of the proposed approach.Comment: Submitted to IEEE Transactions on Power System

Robust Dynamic Operating Envelopes via Superellipsoid-based Convex Optimisation in Unbalanced Distribution Networks

Dynamic operating envelopes (DOEs) have been introduced to integrate distributed energy resources (DER) in distribution networks via real-time management of network capacity limits. Recent research demonstrates that uncertainties in DOE calculations should be carefully considered to ensure network integrity while minimising curtailment of consumer DERs. This letter proposes a novel approach to calculating DOEs that is robust against uncertainties in the utilisation of allocated capacity limits and demonstrates that the reported solution can attain close to global optimality performance compared with existing approaches.Comment: Accepted by by IEEE Transactions on Power Systems (PES Engineering Letters Section

Robust Dynamic Operating Envelopes with Uncertain Demands and Impedances in Unbalanced Distribution Networks

Dynamic operating envelopes (DOEs), as a key enabler to facilitate DER integration, have attracted increasing attention in the past years. However, uncertainties, which may come from load forecast errors or inaccurate network parameters, have been rarely discussed in DOE calculation, leading to compromised quality of the hosting capacity allocation strategy. This letter studies how to calculate DOEs that are immune to such uncertainties based on a linearised unbalanced three-phase optimal power flow (UTOPF) model. With uncertain parameters constrained by norm balls, formulations for calculating Robust DOEs (RDOEs) are presented along with discussions on their tractability. Two cases, including a 2-bus illustrative network and a representative Australian network, have been tested to demonstrate the effectiveness and efficiency of the proposed approach.Comment: Under review by Journal of Modern Power Systems and Clean Energ

Frequency domain analysis of sampled-data control systems

This thesis is aimed at analysis of sampled-data feedback systems. Our approach is in the frequency-domain, and stresses the study of sensitivity and complementary sensitivity operators. Frequency-domain methods have proven very successful in the analysis and design of linear time-invariant control systems, for which the importance and utility of sensitivity operators is well-recognized. The extension of these methods to sampled-data systems, however, is not straightforward, since they are inherently time-varying due to the intrinsic sample and hold operations. In this thesis we present a systematic frequency-domain framework to describe sampled-data systems considering full-time information. Using this framework, we develop a theory of design limitations for sampled-data systems. This theory allows us to quantify the essential constraints in design imposed by inherent open-loop characteristics of the analog plant. Our results show that: (i) sampled-data systems inherit the difficulty imposed upon analog feedback design by the plant's non-minimum phase zeros, unstable poles, and time-delays, independently of the type of hold used; (ii) sampled-data systems are subject to additional design limitations imposed by potential non-minimum phase zeros of the hold device; and (iii) sampled-data systems, unlike analog systems, are subject to limits upon the ability of high compensator gain to achieve disturbance rejection. As an application, we quantitatively analyze the sensitivity and robustness characteristics of digital control schemes that rely on the use of generalized sampled-data hold functions, whose frequency-response properties we describe in detail. In addition, we derive closed-form expressions to compute the L2-induced norms of the sampled-data sensitivity and complementary sensitivity operators. These expressions are important both in analysis and design, particularly when uncertainty in the model of the plant is considered. Our methods provide some interesting interpretations in terms of signal spaces, and admit straightforward implementation in a numerically reliable fashion.PhD Doctorat

Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability

We address the stabilization of switching linear systems (SLSs) with control inputs under arbitrary switching. A sufficient condition for the stability of autonomous (without control inputs) SLSs is that the individual subsystems are stable and the Lie algebra generated by their evolution matrices is solvable. This sufficient condition for stability is known to be extremely restrictive and therefore of very limited applicability. Our main contribution is to show that, in contrast to the autonomous case, when control inputs are present the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices satisfy the aforementioned Lie-algebraic stability condition can become a generic property, hence substantially improving the applicability of such Lie-algebraic techniques in some cases. Since the validity of this Lie-algebraic stability condition implies the existence of a common quadratic Lyapunov function (CQLF) for the SLS, our results yield an analytic sufficient condition for the generic existence of a control CQLF for the SLS

Level crossing sampling in feedback stabilization under data-rate constraints

This paper introduces a novel event-driven sampled-data feedback scheme where the plant output samples are triggered by the crossings - with hysteresis - of the signal through its quantization levels. The plant and controller communicate over binary channels that operate asynchronously and are assumed to be error and delay-free. The paper proposes two systematic output feedback control design strategies. The first strategy consists in the digital emulation of a previously designed analog controller. The second strategy is a simple direct design that drives the plant state to the origin in finite time after a total transmission of 2n + 2 bits, where n is the order of the plan