# Electrical Engineering And Systems Science

Systems And Control

###### Featured Researches

## A Behavioral Input-Output Parametrization of Control Policies with Suboptimality Guarantees

Recent work in data-driven control has revived behavioral theory to perform a variety of complex control tasks, by directly plugging libraries of past input-output trajectories into optimal control problems. Despite recent advances, a key aspect remains unclear: how and to what extent do noise-corrupted data impact control performance? In this work, we provide a quantitative answer to this question. We formulate a Behavioral version of the Input-Output Parametrization (BIOP) for the optimal predictive control of unknown systems using output-feedback dynamic control policies. The main advantages of the proposed framework are that 1) the state-space parameters and the initial state need not be specified for controller synthesis, 2) it can be used in combination with state-of-the-art impulse response estimators, and 3) it allows to recover suboptimality results on learning the Linear Quadratic Gaussian (LQG) controller, therefore revealing, in a quantitative way, how the level of noise in the data affects the performance of behavioral methods. Specifically, it is shown that the performance degrades linearly with the prediction error of the behavioral model. We conclude the paper with numerical experiments to validate our results.

Read more## A Comparative Evaluation of Power Converter Circuits to Increase the Power Transfer Capability of High Voltage Transmission Lines

AC transmission lines with lengths greater than 80km cannot be used to their maximum capacity due to limits in voltage drops and transient stability. This inefficient way of using conductors in a transmission line can be overcome if the electrical frequency at which energy is transmitted is reduced. This is why this work focuses on the comparison of the Modular Multilevel Matrix Converter (MMMC) and the Back-to-Back Modular Multilevel Converter (BTB-MMC), topologies that have shown qualities as frequency converters. For comparison, an analytical model of each topology is used to relate design considerations to their operational variables. Among the aspects to be compared are, the requirements of the semiconductors, the required reactive components, operating losses and fault tolerance. Detailed design equations, EMTP simulations, and comparison table are presented.

Read more## A Comparative Study Between a Classical and Optimal Controller for a Quadrotor

This paper presents a simulation-based comparison between the two controllers, Proportional Integral Derivative (PID), a classical controller and Linear Quadratic Regulator (LQR), an optimal controller, for a linearized quadrotor model. To simplify an otherwise complicated dynamic model of a quadrotor, we derive a linear mathematical model using Newtonian and Euler's laws and applying basic principles of physics. This derivation gives the equations that govern the motion of a quadrotor, both concerning the body frame and the inertial frame. A state-space model is developed, which is then used to simulate the control algorithms for the quadrotor. Apart from the classic PID control algorithm, LQR is an optimal control regulator, and it is more robust for a quadrotor. Both the controllers are simulated in Simulink under the same initial conditions and show a satisfactory response.

Read more## A Comprehensive Multi-Period Optimal Power Flow Framework for Smart LV Networks

This paper presents an extensive multi-period optimal power flow framework, with new modelling elements, for smart LV distribution systems that rely on residential flexibility for combating operational issues. A detailed performance assessment of different setups is performed, including: ZIP flexible loads (FLs), varying degrees of controllability of conventional residential devices, such as electric vehicles (EVs) or photovoltaics (PVs), by the distribution system operator (DSO) (adhering to customer-dependent restrictions) and full exploitation of the capabilities offered by state-of-the-art inverter technologies. A comprehensive model-dependent impact assessment is performed, including phase imbalances, neutral and ground wires and load dependencies. The de-congestion potential of common residential devices is highlighted, analyzing capabilities such as active power redistribution, reactive power support and phase balancing. Said potential is explored on setups where the DSO can make only partial adjustments on customer profiles, rather than (as is common) deciding on the full profiles. The extensive analysis can be used by DSOs and researchers alike to make informed decisions on the required levels of modelling detail, the connected devices and the degrees of controlability. The formulation is computationally efficient, scaling well to medium-size systems, and can serve as an excellent basis for building more tractable or more targeted approaches.

Read more## A Continuation Method for Large-Scale Modeling and Control: from ODEs to PDE, a Round Trip

In this paper we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space- and time-varying systems. When applied to a large-scale network, the continuation provides a PDE describing evolution of continuous state approximation that respects the spatial structure of the original ODE. Our method is illustrated by multiple examples including transport equations, Kuramoto equations and heat diffusion equations. As a main example, we perform the continuation of a Newtonian system of interacting particles and obtain the Euler equations for compressible fluids, thereby providing an original alternative solution to Hilbert's 6th problem. Finally, we leverage our derivation of the Euler equations to control multiagent systems, designing a nonlinear control algorithm for robot formation based on its continuous approximation.

Read more## A Convex Optimization Approach to Learning Koopman Operators

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models. However, choosing appropriate models and bounding the approximation error is far from trivial. Motivated by these difficulties, in this paper we propose an optimization based approach to learning Koopman operators from data. Our results show that the Koopman operator, the associated Hilbert space of observables and a suitable dictionary can be obtained by solving two rank-constrained semi-definite programs (SDP). While in principle these problems are NP-hard, the use of standard relaxations of rank leads to convex SDPs. Further, these SDPs exhibit chordal sparsity leading to algorithms that scale linearly with the number of data points.

Read more## A Critical Look at Coulomb Counting Towards Improving the Kalman Filter Based State of Charge Tracking Algorithms in Rechargeable Batteries

In this paper, we consider the problem of state of charge estimation for rechargeable batteries. Coulomb counting is one of the traditional approaches to state of charge estimation and it is considered reliable as long as the battery capacity and initial state of charge are known. However, the Coulomb counting method is susceptible to errors from several sources and the extent of these errors are not studied in the literature. In this paper, we formally derive and quantify the state of charge estimation error during Coulomb counting due to the following four types of error sources: (i) current measurement error; (ii) current integration approximation error; (iii) battery capacity uncertainty; and (iv) the timing oscillator error/drift. It is shown that the resulting state of charge error can either be of the time-cumulative or of state-of-charge-proportional type. Time-cumulative errors increase with time and has the potential to completely invalidate the state of charge estimation in the long run. State-of-charge-proportional errors increase with the accumulated state of charge and reach its worst value within one charge/discharge cycle. Simulation analyses are presented to demonstrate the extent of these errors under several realistic scenarios and the paper discusses approaches to reduce the time-cumulative and state of charge-proportional errors.

Read more## A Data-Driven Energy Storage System-Based Algorithm for Monitoring the Small-Signal Stability of Power Grids with Volatile Wind Power

In this paper, we propose a data-driven energy storage system (ESS)-based method to enhance the online small-signal stability monitoring of power networks with high penetration of intermittent wind power. To accurately estimate inter-area modes that are closely related to the system's inherent stability characteristics, a novel algorithm that leverages on recent advances in wide-area measurement systems (WAMSs) and ESS technologies is developed. It is shown that the proposed approach can smooth the wind power fluctuations in near real-time using a small additional ESS capacity and thus significantly enhance the monitoring of small-signal stability. Dynamic Monte Carlo simulations on the IEEE 68-bus system are used to illustrate the effectiveness of the proposed algorithm in smoothing wind power and estimating the inter-area mode statistical properties.

Read more## A Data-Driven Modeling Framework of Time-Dependent Switched Dynamical Systems via Extreme Learning Machine

In this work, a data-driven modeling framework of switched dynamical systems under time-dependent switching is proposed. The learning technique utilized to model system dynamics is Extreme Learning Machine (ELM). First, a method is developed for the detection of the switching occurrence events in the training data extracted from system traces. The training data thus can be segmented by the detected switching instants. Then, ELM is used to learn the system dynamics of subsystems. The learning process includes segmented trace data merging and subsystem dynamics modeling. Due to the specific learning structure of ELM, the modeling process is formulated as an iterative Least-Squares (LS) optimization problem. Finally, the switching sequence can be reconstructed based on the switching detection and segmented trace merging results. An example of the data-driven modeling DC-DC converter is presented to show the effectiveness of the developed approach.

Read more## A Data-driven Nonlinear Recharge Controller for Energy Storage in Frequency Regulation

Battery energy storage boosts up the response speed of power system frequency regulation, but must be recharged carefully to minimize the distortion to the frequency regulation response. This paper proposes a nonlinear feedback controller to optimize the recharge for storage resources in frequency regulation. This controller is designed using a data-driven best-hindsight optimization framework, the resulting nonlinear recharge controller's gain depends on the storage state of charge as well as its power and energy rating. The developed controller is compared with two benchmark automatic generation control designs, one is a proportional-integral-based control from PJM Interconnection, the other one is based on linear-quadratic regulator. Simulation results using real area control error data from PJM Interconnection show the proposed controller achieves smaller deviations in both the area control error and the storage state of charge compared to the two benchmark controllers under various storage configurations.

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