Permanent Magnet Synchronous Motors are Globally Asymptotically Stabilizable with PI Current Control

This note shows that the industry standard desired equilibrium for permanent magnet synchronous motors (i.e., maximum torque per Ampere) can be globally asymptotically stabilized with a PI control around the current errors, provided some viscous friction (possibly small) is present in the rotor dynamics and the proportional gain of the PI is suitably chosen. Instrumental to establish this surprising result is the proof that the map from voltages to currents of the incremental model of the motor satisfies some passivity properties. The analysis relies on basic Lyapunov theory making the result available to a wide audience

Geometric characterization on the solvability of regulator equations

The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained

On some dynamic properties of electrical power systems : sobre algunas propiedades dinámicas de los sistemas eléctricos de potencia

This thesis treats some dynamic properties of power system models. An extension of the classical concept of dissipativity is formulated to deal with these systems described by differential-algebraic equations on phasor variables. A class of models of these systems the same that is known to admit an energy function is shown to be dissipative in the sense mentioned above, to later be extended to include realistic models of synchronous machines and other devices. The small signal models are shown to satisfy a convex constraint in the frequency domain that is later articulated with Integral Quadratic Constraints, a well-known stability analysis tool. Specific features of realistic power system models, as the effect of voltage regulation and damping injection, are precisely captured and incorporated into the analysis. It is shown that a trade-off between the mentioned control actions and the voltage sensitivity is a sufficient condition to establish the robustness of the electromechanical modes. This result and others mentioned above are validated through several examples.Esta tesis trata algunas propiedades dinámicas de los sistemas eléctricos de potencia. Se formula una extensión del concepto clásico de disipatividad compatible con estos sistemas, descritos por ecuaciones algebraico-diferenciales sobre variables fasoriales. Se muestra que una clase de modelos de estos sistemas satisface este concepto de disipatividad y se muestra que también lo hacen modelos detallados de máquinas síncronas y otros dispositivos de potencia. Se demuestra que los modelos en pequeña señal satisfacen una restricción convexa en el dominio de la frecuencia, capaz de ser articulada con herramientas bien conocidas de análisis de estabilidad. Características específicas de los sistemas eléctricos reales, tales como la acción de la regulación de tensión y las señales estabilizadoras, son precisamente definidas e incorporadas al análisis. Se demuestra que un adecuado balance entre las acciones de control mencionadas y la sensibilidad a variaciones de tensión es una condición suficiente para la robustez de los modos electromecánicos del sistema. Este resultado y otros mencionados anteriormente son validados mediante el análisis de varios ejemplos

Energy Shaping Control for Stabilization of Interconnected Voltage Source Converters in Weakly-Connected AC Microgrid Systems

With the ubiquitous installations of renewable energy resources such as solar and wind, for decentralized power applications across the United States, microgrids are being viewed as an avenue for achieving this goal. Various independent system operators and regional transmission operators such as Southwest Power Pool (SPP), Midcontinent System Operator (MISO), PJM Interconnection and Electric Reliability Council of Texas (ERCOT) manage the transmission and generation systems that host the distributed energy resources (DERs). Voltage source converters typically interconnect the DERs to the utility system and used in High voltage dc (HVDC) systems for transmitting power throughout the United States. A microgrid configuration is built at the 13.8kV 4.75MVA National Center for Reliable Energy Transmission (NCREPT) testing facility for performing grid-connected and islanded operation of interconnected voltage source converters. The interconnected voltage source converters consist of a variable voltage variable frequency (VVVF) drive, which powers a regenerative (REGEN) load bench acting as a distributed energy resource emulator. Due to the weak-grid interface in islanded mode testing, a voltage instability occurs on the VVVF dc link voltage causing the system to collapse. This dissertation presents a new stability theorem for stabilizing interconnected voltage source converters in microgrid systems with weak-grid interfaces. The new stability theorem is derived using the concepts of Dirac composition in Port-Hamiltonian systems, passivity in physical systems, eigenvalue analysis and robust analysis based on the edge theorem for parametric uncertainty. The novel stability theorem aims to prove that all members of the classes of voltage source converter-based microgrid systems can be stabilized using an energy-shaping control methodology. The proposed theorems and stability analysis justifies the development of the Modified Interconnection and Damping Assignment Passivity-Based Control (Modified IDA-PBC) method to be utilized in stabilizing the microgrid configuration at NCREPT for mitigating system instabilities. The system is simulated in MATLAB/SimulinkTM using the Simpower toolbox to observe the system’s performance of the designed controller in comparison to the decoupled proportional intergral controller. The simulation results verify that the Modified-IDA-PBC is a viable option for dc bus voltage control of interconnected voltage source converters in microgrid systems

Improving transient stability of power systems by using passivity-bassed nonlinear STATCOM controller

This report presents a novel nonlinear control scheme for designing Static Synchronous Compensators (STATCOM). A passivity-based approach is proposed for designing robust nonlinear STATCOM controller. The mathematical model of STATCOM will be represented by a Euler-Lagrange (EL) system corresponding to a set of EL parameters. The STATCOM modeled in the a–b–c reference frame are first shown to be EL systems whose EL parameters are explicitly identified. The energy-dissipative properties of this model are fully retained under the d-q axis transformation. By employing the Park’s transformation, the differential geometry approach is used to investigate the power system dynamics with considering STATCOM under the synchronous d-q frame. Based on the transformed d-q EL model, passivity-based controllers are then synthesized using the technique of damping injection. Two possible passivity-based feedback designs are discussed, leading to a feasible dynamic current-loop controller. Motivated from the usual power electronics control schemes, the internal dc-bus voltage dynamics are regulated via an outer loop proportional plus integral (PI) controller cascaded to the d-axis current loop. The STATCOM controller based on passivity is obtained with a feedback control law from linear system models. The STATCOM controlled by the proposed passivity-based current control scheme with outer loop PI compensation has the features of enhanced robustness under model uncertainties, decoupled current-loop dynamics, guaranteed zero steady-state error, and asymptotic rejection of constant load disturbance. Digital computer simulation for a large operation point variations have been studied the STATCOM controller design. For analysis of the system performance, the PSCAD/EMTDC programme was applied. Simulation results show that the proposed STATCOM controller can effectively enhance transient stability of the power system even in the presence of large operation point variations