Low computational complexity model reduction of power systems with preservation of physical characteristics

A data-driven algorithm recently proposed to solve the problem of model reduction by moment matching is extended to multi-input, multi-output systems. The algorithm is exploited for the model reduction of large-scale interconnected power systems and it offers, simultaneously, a low computational complexity approximation of the moments and the possibility to easily enforce constraints on the reduced order model. This advantage is used to preserve selected slow and poorly damped modes. The preservation of these modes has been shown to be important from a physical point of view and in obtaining an overall good approximation. The problem of the choice of the socalled tangential directions is also analyzed. The algorithm and the resulting reduced order model are validated with the study of the dynamic response of the NETS-NYPS benchmark system (68-Bus, 16-Machine, 5-Area) to multiple fault scenarios

ADAPTIVE NONLINEAR MODEL REDUCTION FOR FAST POWER SYSTEM SIMULATION

The dissertation proposes a new adaptive approach to power system model reduction for fast and accurate time-domain simulation. This new approach is a compromise between linear model reduction for faster simulation and nonlinear model reduction for better accuracy. During the simulation period, the approach adaptively switches among detailed and linearly or nonlinearly reduced models based on variations of the system state: it employs unreduced models for the fault-on period, uses weighted column norms of the admittance matrix to decide which functions are to be linearized in power system differential-algebraic equations for large changes of the state, and adopts a linearly reduced model for small changes of the state.Two versions of the adaptive model reduction approach are introduced. The first version uses traditional power system partitioning where the model reduction is applied to a defined large external area in a power system and the other area that is defined as the study area keeps full detailed models. The second version applies the adaptive model reduction to the whole system.Speed improvement techniques using parallelization are investigated. The first technique uses parallelism in space; it further divides the study area into subareas that can be simulated in parallel. The second technique uses parallelism in time; it integrates the adaptive model reduction into the coarse solver of the Parareal method.In addition, the dissertation proposes integration of tensor decomposition into the adaptive model reduction approach to further improve the speed and accuracy of simulation.All proposed approaches are validated by comprehensive case studies on the 140-bus 48-machine Northeast Power Coordinating Council system, 2383-bus 327-machine Polish system, and 5617-machine 70285-bus Eastern Interconnection system using different dynamic models

Approximation, analysis and control of large-scale systems - Theory and Applications

This work presents some contributions to the fields of approximation, analysis and control of large-scale systems. Consequently the Thesis consists of three parts. The first part covers approximation topics and includes several contributions to the area of model reduction. Firstly, model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays, is considered. Secondly, a theoretical framework and a collection of techniques to obtain reduced order models by moment matching from input/output data for linear (time-delay) systems and nonlinear (time-delay) systems is presented. The theory developed is then validated with the introduction and use of a low complexity algorithm for the fast estimation of the moments of the NETS-NYPS benchmark interconnected power system. Then, the model reduction problem is solved when the class of input signals generated by a linear exogenous system which does not have an implicit (differential) form is considered. The work regarding the topic of approximation is concluded with a chapter covering the problem of model reduction for linear singular systems. The second part of the Thesis, which concerns the area of analysis, consists of two very different contributions. The first proposes a new "discontinuous phasor transform" which allows to analyze in closed-form the steady-state behavior of discontinuous power electronic devices. The second presents in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance principle for the study of "liminf" convergence properties of solutions of dynamical systems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control with input constraints is studied and a methodology to compute approximate solutions of the resulting partial differential equation is proposed.Open Acces

Control and stability enhancement of grid-interactive voltage source inverters under grid abnormalities

Doctor of PhilosophyDepartment of Electrical and Computer EngineeringBehrooz MirafzalVoltage source inverters (VSIs) are an essential interface for grid integration of renewable energy resources. Grid-tied VSIs are employed in power grids to integrate distributed generation units, e.g. photovoltaic arrays, wind turbines and energy storage units, to the utility and extract the maximum energy from the DG units in an efficient manner. However, the stability of VSIs and by extension the entire DG system can be degraded under abnormal grid conditions. In this dissertation, new control and switching techniques for stability and power quality improvement of grid-tied VSIs under abnormal grid conditions are presented. For grids with a low inertia and a low short-circuit ratio, commonly referred to as weak grids, grid connection may make VSIs susceptible to voltage distortion and instability. In this dissertation, through root locus analysis of a detailed state-space model, the design of several circuit and control parameters of the grid-tied VSI are evaluated for improving stability in weak grids. It is shown that grid-side filter inductances can be increased for stable operation of VSIs in weak grids. Accordingly, a virtual inductance emulating the effect of an increased inductance in the grid-side filter is developed in this dissertation, which enables stable operation of VSIs in weak grids without the tradeoffs, i.e. additional voltage drop, increased cost and larger size, associated with a larger inductor. The virtual inductance scheme is realized through the injection of a feedforward current element in the VSI controller through a gain component. The measured grid currents, which are sensed for regular VSI controller operation, are employed as the feedforward component eliminating the need for any additional sensors for the utilization of this control scheme. Furthermore, a direct model reference adaptive control (MRAC) scheme is employed in this dissertation to tune the virtual inductance gain block according to a stable reference model for varying grid conditions. The use of direct MRAC scheme allows tuning of the virtual inductance block without the need for a plant parameter estimation stage. The virtual inductance scheme enables stable operation of VSIs in weak grids without system parameter redesign, thereby maintaining the steady-state performance of the system. The efficacy of the virtual inductance feedforward scheme is verified through hardware tests carried out on a three-phase grid-tied experimental setup. Along with extracting energy from the DG sources, grid-tied VSIs are capable of providing various ancillary services to the utility under abnormal conditions. However, providing ancillary services could drive the inverter voltages beyond the linear modulation region resulting in grid current distortions, which could violate the requirements for grid integration of DGs. An atypical pulse width modulation (PWM) technique is proposed in this dissertation, which maximizes the dc-bus utilization of VSIs, which in turn enables the VSIs to supply the maximum extracted power from the DG units to the grid when providing ancillary services while operating in the linear modulation region. The switching scheme is realized by injecting common mode components in the PWM references, computed based on instantaneous reference magnitudes. The proposed scheme is suitable when providing both symmetrical and asymmetrical ancillary services. In this dissertation, negative-sequence compensation and harmonic compensation are employed as instances of symmetrical and asymmetrical ancillary services. The proposed scheme can be integrated with any control scheme and carrier-based PWM combinations. The efficacy of the proposed atypical PWM scheme is verified through both simulation and hardware tests