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The emergence and spread of deadly pandemics has repeatedly occurred throughout history, causing widespread infections and loss of life. The rapid spread of pandemics have made governments across the world adopt a range of actions, including non-pharmaceutical measures to contain its impact. However, the dynamic nature of pandemics makes selecting intervention strategies challenging. Hence, the development of suitable monitoring and forecasting tools for tracking infected cases is crucial for designing and implementing effective measures. Motivated by this, we present a hybrid pandemic infection forecasting methodology that integrates compartmental model and learning-based approaches. In particular, we develop a compartmental model that includes time-varying infection rates, which are the key parameters that determine the pandemic's evolution. To identify the time-dependent infection rates, we establish a hybrid methodology that combines the developed compartmental model and tools from optimization and neural networks. Specifically, the proposed methodology estimates the infection rates by fitting the model to available data, regarding the COVID-19 pandemic in Cyprus, and then predicting their future values through either a) extrapolation, or b) feeding them to neural networks. The developed approach exhibits strong accuracy in predicting infections seven days in advance, achieving low average percentage errors both using the extrapolation (9.90%) and neural network (5.04%) approaches., Comment: 13 pages, 7 figures, 12 tables

A major transition in modern power systems is the replacement of conventional generation units with renewable sources of energy. The latter results in lower rotational inertia which compromises the stability of the power system, as testified by the growing number of frequency incidents. To resolve this problem, numerous studies have proposed the use of virtual inertia to improve the stability properties of the power grid. In this study, we consider how inertia variations, resulting from the application of control action associated with virtual inertia and fluctuations in renewable generation, may affect the stability properties of the power network within the primary frequency control timeframe. We consider the interaction between the frequency dynamics and a broad class of power supply dynamics in the presence of time-varying inertia and provide locally verifiable conditions, that enable scalable designs, such that stability is guaranteed. To complement the presented stability analysis and highlight the dangers arising from varying inertia, we provide analytic conditions that enable to deduce instability from single-bus inertia fluctuations. Our analytical results are validated with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system, where we demonstrate how inertia variations may induce large frequency oscillations and show that the application of the proposed conditions yields a stable response., Comment: 14 pages, 8 figures

Price based demand response schemes may significantly improve power system efficiency. Additionally, it is desired that such schemes yield improved power operation, by reducing the peak consumption. This paper proposes the Intraday Block Pricing (IBP) scheme, aiming to promote effective demand response among consumers by charging their electricity usage based on intraday time-slots. To design the prices associated with the proposed scheme, we formulate a bilevel optimization problem that aims to minimize the Peak-to-Average Ratio (PAR) and simultaneously benefit the consumers and the utility company. The bilevel problem is converted into a single-level Mathematical Program with Equilibrium Constraints (MPEC). The resulting MPEC is non-convex and includes nonlinear constraints. Hence, to obtain a solution, it is relaxed into a Mixed Integer Linear Program by dealing with all nonlinearities. To evaluate the conservativeness of the proposed approach, a lower bound to the cost of the original bilevel problem is obtained. The applicability of the proposed scheme is demonstrated with simulations on various case studies, which exhibit a significant reduction in PAR and economic gains for the utility company and consumers. Moreover, simulation results show that the solutions of the original and relaxed problems are equivalent, demonstrating the effectiveness of the proposed solution approach. Further simulation results demonstrate significant advantages in the performance of the IBP scheme when compared to existing schemes in the literature., Comment: 16 pages, 12 figures, 1 table

The increasing participation of local generation and controllable demand units within the power network motivates the use of distributed schemes for their control. Simultaneously, it raises two issues; achieving an optimal power allocation among these units, and securing the privacy of the generation/demand profiles. This study considers the problem of designing distributed optimality schemes that preserve the privacy of the generation and controllable demand units within the secondary frequency control timeframe. We propose a consensus scheme that includes the generation/demand profiles within its dynamics, keeping this information private when knowledge of its internal dynamics is not available. However, the prosumption profiles may be inferred using knowledge of its internal model. We resolve this by proposing a privacy-preserving scheme which ensures that the generation/demand cannot be inferred from the communicated signals. For both proposed schemes, we provide analytic stability, optimality and privacy guarantees and show that the secondary frequency control objectives are satisfied. The presented schemes are distributed, locally verifiable and applicable to arbitrary network topologies. Our analytic results are verified with simulations on a 140-bus system, where we demonstrate that the proposed schemes offer enhanced privacy properties, enable an optimal power allocation and preserve the stability of the power network., Comment: 13 pages, 6 figures, 2 tables

Load side participation can provide support to the power network by appropriately adapting the demand when required. In addition, it enables an economically improved power allocation. In this study, we consider the problem of providing an optimal power allocation among generation and on-off loads within the secondary frequency control timeframe. In particular, we consider a mixed integer optimization problem which ensures that the secondary frequency control objectives (i.e. generation/demand balance and the frequency attaining its nominal value at steady state) are satisfied. We present analytical conditions on the generation and on-off load profiles such that an $\epsilon$-optimality interpretation of the steady state power allocation is obtained, providing a non-conservative value for $\epsilon$. Moreover, we develop a hierarchical control scheme that provides on-off load values that satisfy the proposed conditions. We study the interaction of the proposed control scheme with the physical dynamics of the power network and provide analytic stability guarantees. Our results are verified with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system, where it is demonstrated that the proposed algorithm yields a close to optimal power allocation., Comment: 13 pages, 6 figures

Governments across the world are currently facing the task of selecting suitable intervention strategies to cope with the effects of the COVID-19 pandemic. This is a highly challenging task, since harsh measures may result in economic collapse while a relaxed strategy might lead to a high death toll. Motivated by this, we consider the problem of forming intervention strategies to mitigate the impact of the COVID-19 pandemic that optimize the trade-off between the number of deceases and the socio-economic costs. We demonstrate that the healthcare capacity and the testing rate highly affect the optimal intervention strategies. Moreover, we propose an approach that enables practical strategies, with a small number of policies and policy changes, that are close to optimal. In particular, we provide tools to decide which policies should be implemented and when should a government change to a different policy. Finally, we consider how the presented results are affected by uncertainty in the initial reproduction number and infection fatality rate and demonstrate that parametric uncertainty has a more substantial effect when stricter strategies are adopted., Comment: 30 pages, 31 figures, 3 tables

Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior which raises the risk that these could synchronize when coupled with the frequency dynamics of the power grid, i.e. simultaneously switch, inducing persistent and possibly catastrophic power oscillations. To address this problem, schemes with a randomized response time in their control policy have been proposed in the literature. However, such schemes introduce delays in the response of TCLs to frequency feedback that may limit their ability to provide fast support at urgencies. In this paper, we present a deterministic control mechanism for TCLs such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we provide analytic conditions which ensure that synchronization is avoided. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small. Our analytical results are verified with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system, which demonstrate that the proposed scheme offers improved frequency response compared to conventional implementations., Comment: 10 pages, 5 figures, 1 table

Load side participation can provide valuable support to the power network in case of urgencies. On many occasions, loads are naturally represented by on and off states. However, the use of on-off loads for frequency control can lead to chattering and undesirable limit cycle behavior, which are issues that need to be resolved for such loads to be used for network support. This paper considers the problem of primary frequency regulation with ancillary service from on-off loads in power networks and establishes conditions that lead to convergence guarantees and an appropriate power allocation within the network. In particular, in order to assist existing frequency control mechanisms, we consider loads that switch when prescribed frequency thresholds are exceeded. Such control policies are prone to chattering, which limits their practicality. To resolve this issue, we consider loads that follow a decentralized hysteretic on-off policy, and show that chattering is not observed within such a setting. Hysteretic loads may exhibit, however, limit cycle behavior, which is undesirable. To address this, we propose an adapted hysteretic control scheme for which we provide convergence guarantees. Furthermore, we consider a mixed-integer optimization problem for power allocation and propose a suitable design of the control policy such that the cost incurred at equilibrium is within $\epsilon$ from the optimal cost, providing a non conservative value for $\epsilon$. The practicality of our analytic results is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system., Comment: 16 pages, 9 figures

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., Comment: 11 pages, 3 figures, 1 table

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.

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.

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.