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

Optimized Multi-input Single-output Energy Harvesting System

The energy harvesting sources has been introduced as a promising alternative for battery power. However, harvested energy is inherently sporadic, unstable, and unreliable. For this reason, a non-volatile processor has been previously proposed to bridge the intermittent executions in frequent power losses. Nonetheless, recurrent power failures reduce overall system performance which has forced researchers to look into multi-input energy harvesting systems. The purpose of this study is to investigate the possible solutions to improve the reliability and functionality of battery-less devices. This study has two major objectives: (1) implementing periodic checkpointing on WISP5, and (2) proposing optimized multi-input single-output energy harvesting system. The WISP5 was acquired from the Sensor Systems Laboratory, University of Washington, as a viable RFID energy harvesting system to implement software checkpointing techniques. We performed the periodic checkpointing every 50ms based on the RFID power fluctuation style. Then, we explored a number of possible maximum power point tracking techniques to extract maximum power from harvesters. As a result, we verified that the open circuit voltage control is the most cost effective and efficient technique for both thermoelectric (TEG) and photovoltaic (PV) . Also, we revealed that in low-level input voltages, following the fact that the maximum power extraction can be achieved at half of open circuit voltage does not result in maximum possible efficiency. Therefore, by adjusting the converter input voltage at about 66% of open circuit voltage, we improved power efficiency by about 18%.Electrical Engineerin

Ultimate bound analysis and optimisation with application to energy systems stability

Research Doctorate - Doctor of Philosophy (PhD)This thesis studies steady state behaviour of control systems subject to persistent perturbations. When non-vanishing perturbations act on an otherwise asymptotically stable system, convergence to the equilibrium point may not be achievable. Instead, it is desirable to have the system trajectories ultimately lie inside a tight ultimate bound set when starting within a region of attraction in the state space. This behaviour proves stability beyond local results and is considered as practical stability of systems under the effect of persistent perturbations. This study adopts ultimate bounds as the main instrument to analyse steady state behaviour of systems under persistent perturbations and makes contributions in two distinct directions. The first direction is the application of ultimate bounds to analyse regional (beyond linearised local) stability properties of frequency control systems in islanded microgrids of inverters which are inherently nonlinear and operate under the effect of persistent unknown load demand variations. The existing works on the frequency control problem have predominantly derived local results to address stability of the network in the vicinity of an equilibrium point. The second direction of the thesis is the minimisation of componentwise ultimate bounds by feedback control design in discrete-time linear systems under persistent perturbations with constant bounds, which serves as a certificate of improved practical stability of the perturbed system. Existing related work has studied the attenuation of disturbances by minimising state norms. A distinct contribution of the present thesis is its emphasis on state componentwise attenuation of persistent disturbances through ultimate boundedness. The analysis of ultimate boundedness in the framework of the frequency control problem in inverter-based microgrids with primary and secondary control loops led us to 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 attraction is guaranteed under a condition on the power mismatch between demand and generation at each inverter bus. This result departs from conventional studies which rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. By way of contrast, we derive an estimate of the region of attraction from which a quantifiable ultimate bound set for the state trajectories can be determined by recursive iterations of a nonlinear mapping, leading to closed-form expressions for some classes of microgrids. For the problem of feedback design to minimise state ultimate bounds in discrete-time linear systems subject to persistent bounded perturbations, we derive structural conditions on the system matrices to guarantee that a target eigenstructure, which is shown to achieve the lowest possible ultimate-bounds for one or more state components, can be assigned by state feedback. When the required structural conditions are satisfied, an eigenvector assignment procedure can be applied to simultaneously minimise multiple ultimate bounds in systems with multiple inputs, or one ultimate bound in systems with a single input. These results are applied to the voltage control problem under load variations in inverter based microgrids. The results on the minimisation of ultimate bounds are then extended to perturbed discrete-time switched linear systems to achieve closed-loop stability under arbitrary switching and minimum ultimate bounds for specific state components. Previous results derived an iterative algorithm that computes the required feedback matrices, and established conditions under which this procedure is possible. Based on these conditions, ultimate bound minimisation of some state components is achieved by exploiting available degrees of freedom in the iterative algorithm and assigning suitable eigenstructure to the subsystems

Computational Analysis of Impedance Transformations for Four-Wire Power Networks with Sparse Neutral Grounding

In low-voltage distribution networks, the integration of novel energy technologies can be accelerated through advanced optimization-based analytics such as network state estimation and network-constrained dispatch engines for distributed energy resources. The scalability of distribution network optimization models is challenging due to phase unbalance and neutral voltage rise effects necessitating the use of 4 times as many voltage variables per bus than in transmission systems. This paper proposes a novel technique to limit this to a factor 3, exploiting common physical features of low-voltage networks specifically, where neutral grounding is sparse, as it is in many parts of the world. We validate the proposed approach in OpenDSS, by translating a number of published test cases to the reduced form, and observe that the proposed "phase-to-neutral" transformation is highly accurate for the common single-grounded low-voltage network configuration, and provides a high-quality approximation for other configurations. We finally provide numerical results for unbalanced power flow optimization problems using PowerModelsDistribution.jl, to illustrate the computational speed benefits of a factor of about 1.42.Comment: 9 pages, ACM E-energy 202

An Open Optimal Power Flow Model for the Australian National Electricity Market

The Australian National Electricity Market (NEM) is a complex energy market that faces challenges due to the increasing number of distributed energy resources (DERs) and the transition to a net-zero emissions target. Power system modelling plays a crucial role in addressing these challenges by providing insights into different scenarios and informing decision-making. However, accessing power system data containing sensitive information can be a concern. Synthetic data offer a solution by allowing researchers to analyze and develop new methods while protecting confidential information. This paper utilizes an existing synthetic network model based on the NEM (`S-NEM2300'-bus system) to develop a benchmark for power system optimization studies. The model is derived and enhanced using PowerModels.jl and MATPOWER data models, and feasibility is ensured through power flow and optimal power flow studies. The resulting benchmark model, called `S-NEM2000'-bus system, is validated and enriched with additional parameters such a thermal limits, generation fuel categories and cost models. The `S-NEM2000'-bus system is an \emph{open} dataset which provides a valuable resource for optimization studies in the power system domain.Comment: 22 pages, 22 figures, 4 table

Ultimate bound minimisation by state feedback in discrete-time switched linear systems under arbitrary switching

We present a novel state feedback design method for perturbed discrete-time switched linear systems. The method aims at achieving (a) closed-loop stability under arbitrary switching and (b) minimisation of ultimate bounds for specific state components. Objective (a) is achieved by computing state feedback matrices so that the closed-loop subsystem evolution matrices generate a solvable Lie algebra (namely, they are all upper triangular in a common coordinate basis). Previous results derived an iterative algorithm that computes the required feedback matrices, and established conditions under which this procedure is possible. Based on these conditions, objective (b) is achieved by exploiting available degrees of freedom in the iterative algorithm.Fil: Heidari, Rahmat. Universidad de Newcastle; AustraliaFil: Braslavsky, Julio H.. Australian Commonwealth Scientific and Industrial Research Organisation; AustraliaFil: Seron, Maria Marta. Universidad de Newcastle; AustraliaFil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentin

On componentwise ultimate bound minimisation for switched linear systems via closed-loop lie-algebraic solvability

We present a novel state feedback design method for perturbed discrete-time switched linear systems. The method aims at achieving (a) closed-loop stability under arbitrary switching and (b) minimisation of ultimate bounds for specific state components. Objective (a) is achieved by computing state feedback matrices so that the closed-loop $A$ matrices generate a solvable Lie algebra (i.e. admit simultaneous triangularisation). Previous results derived an iterative algorithm that computes the required feedback matrices, and established conditions under which this procedure is possible. Based on these conditions, objective (b) is achieved by exploiting available degrees of freedom in the iterative algorithm