Putting energy back in control

A control system design technique using the principle of energy balancing was analyzed. Passivity-based control (PBC) techniques were used to analyze complex systems by decomposing them into simpler sub systems, which upon interconnection and total energy addition were helpful in determining the overall system behavior. An attempt to identify physical obstacles that hampered the use of PBC in applications other than mechanical systems was carried out. The technique was applicable to systems which were stabilized with passive controllers

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

Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation

This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters

A Comprehensive Review on Constant Power Loads Compensation Techniques

Microgrid, because of its advantages over conventional utility grids, is a prudent approach to implement renewable resource-based electricity generation. Despite its advantages, microgrid has to operate with a significant proportion of constant power loads that exhibit negative incremental impedance and thus cause serious instability in the system. In this paper, a comprehensive review is presented on accomplished research work on stabilization of dc and ac microgrid. After reviewing these, microgrid system stabilization techniques are classified with required discussions. As found out in this paper, the stabilization techniques can basically be classified as compensation done: 1) at feeder side; 2) by adding intermediate circuitry; and 3) at load side. Finally, after analyzing the merits and drawbacks of each generalized technique, several infographics are presented to highlight the key findings of this paper

Energy Shaping of Underactuated Systems via Interconnection and Damping Assignment Passivity-Based Control with Applications to Planar Biped Robots

The sought goal of this thesis is to show that total energy shaping is an effective and versatile tool to control underactuated mechanical systems. The performance of several approaches, rooted in the port-Hamiltonian formalism, are analyzed while tackling distinct control problems: i) equilibrium stabilization; ii) gait generation; iii) gait robustication. Firstly, a constructive solution to deal with interconnection and damping assignment passivity-based control (IDA-PBC) for underactuated two-degree-of-freedom mechanical systems is proposed. This strategy does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending on generalized momenta are introduced by the controller. The methodology is applied to the stabilization of a translational oscillator with a rotational actuator system, as well as, to the gait generation for an underactuated compass-like biped robot (CBR). Then, the problem of gait generation is addressed using dissipative forces in the controller. In this sense, three distinct controllers are presented, namely simultaneous interconnection and damping assignment passivity-based control with dissipative forces, energy pumping-and-damping passivity-based control (EPD-PBC), and energy pumping-or-damping control. Finally, EPD-PBC is used to increase the robustness of the gait exhibited by the CBR over uncertainties on the initial conditions. The passivity of the system is exploited, as well as, its hybrid nature (using the hybrid zero dynamics method) to carry out the stability analysis. Besides, such an approach is applied to new gaits that are generated using IDA-PBC. Numerical case studies, comparisons, and critical discussions evaluate the performance of the proposed approaches