Frequency regulation with thermostatic load participation in power networks

We consider the problem of controlling thermostatic loads such that ancillary services are provided to the power network within the secondary frequency control timeframe. This problem has been widely studied in the literature, where stochastic control schemes have been proposed to avoid the possibility of load synchronization, which induces persistent frequency oscillations. However, stochastic schemes introduce delays in the response of thermostatic loads that may limit their ability to provide support at urgencies. In this paper, we present a deterministic control mechanism for thermostatic loads 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 propose appropriate conditions for the design of the frequency thresholds that bound the coupling between frequency and thermostatic load dynamics, so as to avoid synchronization phenomena. 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.ERC starting grant 67977

A distributed scheme for secondary frequency control with stability guarantees and optimal power allocation

We consider the problem of distributed secondary frequency regulation in power networks such that stability and an optimal power allocation are guaranteed. This is a problem that has been widely studied in the literature, where 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 incorporating additional information flow requirements which may limit its applicability, and with the existing literature on the latter relying on static models for generation and demand, which is restrictive. We propose a novel control scheme that aims to overcome these issues by making use of generation measurements in the control policy. In particular, our controller relies on practical measurements and allows distributed stability and optimality guarantees to be deduced for a broad range of linear generation dynamics, that can be of higher order. 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 various examples of turbine governor dynamics by using realistic numerical data. The practicality of our analysis is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system that verify that our proposed controller achieves convergence to the nominal frequency, an economically optimal power allocation, and improved performance compared to existing schemes used in the literature.ERC starting grant 67977

Stability and optimality of distributed schemes for secondary frequency regulation in power networks

© 2016 IEEE. We present a method for designing distributed generation and demand control schemes for secondary frequency regulation in power networks such that asymptotic 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. We also discuss how the dissipativity condition imposed can be easily verified for linear systems by solving an appropriate LMI. Our results are illustrated with simulations on the IEEE 68 bus system which demonstrate that the inclusion of controllable loads offer improved transient behavior and that an optimal power allocation among controllable loads is achieved

Secondary frequency regulation in power networks with on-off load side participation

© 2017 IEEE. We study the problem of secondary frequency regulation where ancillary services are provided via load-side participation. In particular, we consider on-off loads that switch when prescribed frequency thresholds are exceeded in order to assist existing secondary frequency control mechanisms. We show that system stability is not compromised despite the switching nature of the loads. However, such control policies are prone to Zeno-like behavior, which limits the practicality of these schemes. As a remedy to this problem, we propose a hysteresis on-off policy and provide stability guarantees in this setting. We provide numerical investigations of the results on a realistic power network.ERC starting grant 67977

Stability of Primary Frequency Control with on-Off Load Side Participation in Power Networks

We consider the problem of load side participation providing ancillary services to the power network within the primary frequency control timeframe. In particular, we consider on-off loads that switch when prescribed frequency thresholds are exceeded in order to assist existing primary frequency control mechanisms. However, such control policies are prone to chattering, which limits their practicality. To resolve this issue, we propose loads that follow a hysteretic on-off policy, and show that chattering behavior is not observed within such setting. Furthermore, we provide design conditions that ensure the existence of equilibria when such loads are implemented. However, as numerical simulations demonstrate, hysteretic loads may exhibit limit cycle behavior, which is undesirable. This is resolved by proposing a novel control scheme for hystertic loads. For the latter scheme, we provide asymptotic stability guarantees and show that no limit cycle or chattering will be exhibited. The practicality of our analytic results is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system.ER

Primary Frequency Regulation with Load-Side Participation-Part II: Beyond Passivity Approaches

We consider the problem of distributed generation and demand control for primary frequency regulation in power networks, such that stability and optimality of the power allocation can be guaranteed. It was shown in [1] that by imposing an input strict passivity condition on the net supply dynamics at each bus, combined with a decentralized condition on their steady state behaviour, convergence to optimality can be guaranteed for broad classes of generation and demand control dynamics in a general network. In this paper we show that by taking into account additional local information, the input strict passivity condition can be relaxed to less restrictive decentralized conditions. These conditions extend the classes of generation and load dynamics for which convergence to optimality can be guaranteed beyond the class of passive systems, thus allowing to reduce the conservatism in the analysis and feedback design.ER

Primary Frequency Regulation with Load-Side Participation-Part I: Stability and Optimality

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.ER

Frequency regulation with thermostatic load participation in power networks

We consider the problem of controlling thermostatic loads such that ancillary services are provided to the power network within the secondary frequency control timeframe. This problem has been widely studied in the literature, where stochastic control schemes have been proposed to avoid the possibility of load synchronization, which induces persistent frequency oscillations. However, stochastic schemes introduce delays in the response of thermostatic loads that may limit their ability to provide support at urgencies. In this paper, we present a deterministic control mechanism for thermostatic loads 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 propose appropriate conditions for the design of the frequency thresholds that bound the coupling between frequency and thermostatic load dynamics, so as to avoid synchronization phenomena. 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

Frequency Regulation With Thermostatically Controlled Loads: Aggregation of Dynamics and Synchronization

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

A novel distributed secondary frequency control scheme for power networks with high order turbine governor dynamics.

We consider the problem of distributed secondary frequency regulation such that stability and an economically optimal allocation are attained. We study an arbitrarily connected power network with general linear generation dynamics and use a swing equation to describe frequency dynamics. We propose a distributed averaging dynamic output control (DADOC) scheme that makes use of local frequency and generation measurements and provides stability and optimality guarantees when a broad class of high order turbine governor dynamical systems with quadratic cost functions are considered. The proposed controller includes a number of design parameters that affect the stability and optimality properties of the system. We choose these parameters 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. Moreover, to highlight the contribution of our work, we compare and explain the main advantages of DADOC schemes over existing schemes in the literature, in terms of required measurements for their implementation and allowable generation dynamics and cost functions such that stability and optimality are guaranteed. 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 nominal frequency and an economically optimal power allocation