Ioannis Lestas

Liam Hallinan, Ioannis Lestas

Recent small-signal stability studies of AC grids have shifted towards analysing power systems as interconnections of subsystems and leveraging their input-output properties to derive scalable stability certificates. Two subsystem representations appear frequently in the literature: the PQ model, coupling powers to phase angle and voltage magnitude, and the IV model, coupling currents to voltages. In this paper, we derive both models without simplifying the bus or line dynamics and show that a loop transformation relates the two. One of the main results in the paper is to then show analytically that each representation may exhibit unstable poles depending primarily on the operating point (IV model) or the presence of high-frequency passive dynamics (PQ model). In particular, such unstable poles in the subsystems can occur even when the aggregate interconnection is stable and well-behaved. These effects are validated numerically, including a case study using the full-order dynamics of a synchronous generator with an exciter and transformer. Our results highlight that care must be taken when choosing a subsystem representation, as neglecting high-frequency dynamics or device operating points may obscure unstable poles that must be stabilised by the network interconnection and must be accounted for in system identification.

Andreas Kasis, Eoin Devane, Ioannis Lestas

We present a method to design distributed generation and demand control schemes for primary frequency regulation in power networks that guarantee asymptotic stability and ensure fairness of allocation. We impose a passivity condition on net power supply variables and provide explicit steady state conditions on a general class of generation and demand control dynamics that ensure convergence of solutions to equilibria that solve an appropriately constructed network optimization problem. We also show that the inclusion of controllable demand results in a drop in steady state frequency deviations. We discuss how various classes of dynamics used in recent studies fit within our framework and show that this allows for less conservative stability and optimality conditions. We illustrate our results with simulations on the IEEE 68 bus system and observe that both static and dynamic demand response schemes that fit within our framework offer improved transient and steady state behavior compared with control of generation alone. The dynamic scheme is also seen to enhance the robustness of the system to time-delays.

Andreas Kasis, Nima Monshizadeh, Eoin Devane et al.

We present a systematic method for designing distributed generation and demand control schemes for secondary frequency regulation in power networks such that stability and an economically optimal power allocation can be guaranteed. A dissipativity condition is imposed on net power supply variables to provide stability guarantees. Furthermore, economic optimality is achieved by explicit decentralized steady state conditions on the generation and controllable demand. We discuss how various classes of dynamics used in recent studies fit within our framework and give examples of higher order generation and controllable demand dynamics that can be included within our analysis. In case of linear dynamics, we discuss how the proposed dissipativity condition can be efficiently verified using an appropriate linear matrix inequality. Moreover, it is shown how the addition of a suitable observer layer can relax the requirement for demand measurements in the employed controller. The efficiency and practicality of the proposed results are demonstrated with a simulation on the Northeast Power Coordinating Council (NPCC) 140-bus system.

Andreas Kasis, Nima Monshizadeh, Ioannis Lestas

We study the problem of decentralized secondary frequency regulation in power networks where ancillary services are provided via on-off load-side participation. We initially consider on-off loads that switch when prescribed frequency thresholds are exceeded, together with a large class of passive continuous dynamics for generation and demand. The considered on-off loads are able to assist existing secondary frequency control mechanisms and return to their nominal operation when the power system is restored to its normal operation, a highly desirable feature which minimizes users disruption. We show that system stability is not compromised despite the switching nature of the loads. However, such control policies are prone to chattering, which limits the practicality of these schemes. As a remedy to this problem, we propose a hysteretic on-off policy where loads switch on and off at different frequency thresholds and show that stability guarantees are retained when the same decentralized passivity conditions for continuous generation and demand hold. Several relevant examples are discussed to demonstrate the applicability of the proposed results. Furthermore, we verify our analytic results with numerical investigations on the Northeast Power Coordinating Council (NPCC) 140-bus system.

Jeremy D. Watson, Ioannis Lestas

Hybrid AC/DC networks are a key technology for future electrical power systems, due to the increasing number of converter-based loads and distributed energy resources. In this paper, we consider the design of control schemes for hybrid AC/DC networks, focusing especially on the control of the interlinking converters (ILC(s)). We present two control schemes: firstly for decentralized primary control, and secondly, a distributed secondary controller. In the primary case, the stability of the controlled system is proven in a general hybrid AC/DC network which may include asynchronous AC subsystems. Furthermore, it is demonstrated that power-sharing across the AC/DC network is significantly improved compared to previously proposed dual droop control. The proposed scheme for secondary control guarantees the convergence of the AC system frequencies and the average DC voltage of each DC subsystem to their nominal values respectively. An optimal power allocation is also achieved at steady-state. The applicability and effectiveness of the proposed algorithms are verified by simulation on a test hybrid AC/DC network in MATLAB / Simscape Power Systems.

Thomas Holding, Ioannis Lestas

In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of subgradient dynamics that provide a restriction in an arbitrary convex domain. We show that despite the nonlinear and non-smooth character of these dynamics their $ω$-limit set is comprised of solutions to only linear ODEs. In particular, we show that the latter are solutions to subgradient dynamics on affine subspaces which is a smooth class of dynamics the asymptotic properties of which have been exactly characterized in part I. Various convergence criteria are formulated using these results and several examples and applications are also discussed throughout the manuscript.

Meng Chen, Yufei Xi, Frede Blaabjerg et al.

A common assumption in both grid-following (GFL) and grid-forming (GFM) control systems is that they are open-loop (OL) stable in the vicinity of high-frequency resonances. Hence classical loop-shaping approaches are often used for establishing stability margins and designing active damping (AD) strategies. This paper shows that single-loop GFM (SL-GFM) control schemes incorporating a widely used class of reactive power (RAP) control, referred to as droop-I control, can lead to OL unstable poles. This finding reveals a novel instability mechanism resulting in a reduced stability margin and robustness at high frequencies. The sensitivity of this phenomenon to both RAP and electrical parameters is analyzed in detail. An AD design that explicitly accounts for the newly identified instability mechanism is proposed. We also provide a comparison between such SL-GFM and well-studied GFL control schemes, highlighting quite different resonance features between them. Validation is performed through experiments.

Andreas Kasis, Nima Monshizadeh, Ioannis Lestas

We consider the problem of distributed secondary frequency regulation in power networks such that stability and an optimal power allocation are attained. This is a problem that has been widely studied in the literature, and two main control schemes have been proposed, usually referred to as 'primal-dual' and 'distributed averaging proportional-integral (DAPI)' respectively. However, each has its limitations, with the former requiring knowledge of uncontrollable demand, which can be difficult to obtain in real time, and with the existing literature on the latter being based on static models for generation and demand. We propose a novel control scheme that overcomes these issues by making use of generation measurements in the control policy. In particular, our analysis allows distributed stability and optimality guarantees to be deduced with practical measurement requirements and permits a broad range of linear generation dynamics, that can be of higher order, to be incorporated in the power network. We show how the controller parameters can be selected in a computationally efficient way by solving appropriate linear matrix inequalities (LMIs). Furthermore, we demonstrate how the proposed analysis applies to several examples of turbine governor models. The practicality of our analysis is demonstrated with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system that verify that our proposed controller achieves convergence to the nominal frequency and an economically optimal power allocation.

Xinyi Yi, Ioannis Lestas

District heating systems (DHSs) require coordinated economic dispatch and temperature regulation under uncertain operating conditions. Existing DHS operation strategies often rely on disturbance forecasts and nominal models, so their economic and thermal performance may degrade when predictive information or model knowledge is inaccurate. This paper develops a data-driven online control framework for DHS operation by embedding steady-state economic optimality conditions into the temperature dynamics, so that the closed-loop system converges to the economically optimal operating point without relying on disturbance forecasts. Based on this formulation, we develop a Data-Enabled Policy Optimization (DeePO)-based online learning controller and incorporate Adaptive Moment Estimation (ADAM) to improve closed-loop performance. We further establish convergence and performance guarantees for the resulting closed-loop system. Simulations on an industrial-park DHS in Northern China show that the proposed method achieves stable near-optimal operation and strong empirical robustness to both static and time-varying model mismatch under practical disturbance conditions.