Shahab Mehraeen

Decentralized Dynamic Surface Control of Large-Scale Interconnected Systems in Strict-Feedback Form Using Neural Networks With Asymptotic Stabilization

A novel neural network (NN)-based nonlinear decentralized adaptive controller is proposed for a class of large-scale, uncertain, interconnected nonlinear systems in strict-feedback form by using the dynamic surface control (DSC) principle, thus, the “explosion of complexity” problem which is observed in the conventional backstepping approach is relaxed in both state and output feedback control designs. The matching condition is not assumed when considering the interconnection terms. Then, NNs are utilized to approximate the uncertainties in both subsystem and interconnected terms. By using novel NN weight update laws with quadratic error terms as well as proposed control inputs, it is demonstrated using Lyapunov stability that the system states errors converge to zero asymptotically with both state and output feedback controllers, even in the presence of NN approximation errors in contrast with the uniform ultimate boundedness result, which is common in the literature with NN-based DSC and backstepping schemes. Simulation results show the effectiveness of the approach.

Power System Stabilization Using Adaptive Neural Network-Based Dynamic Surface Control

In this paper, the power system with an excitation controller is represented as a class of large-scale, uncertain, interconnected nonlinear continuous-time system in strict-feedback form. Subsequently, dynamic surface control (DSC)-based adaptive neural network (NN) controller is designed to overcome the repeated differentiation of the control input that is observed in the conventional backstepping approach. The NNs are utilized to approximate the unknown subsystem and the interconnection dynamics. By using novel online NN weight update laws with quadratic error terms, the closed-loop signals are shown to be locally asymptotically stable via Lyapunov stability analysis, even in the presence of NN approximation errors in contrast with other NN techniques where a bounded stability is normally assured. Simulation results on the IEEE 14-bus power system with generator excitation control are provided to show the effectiveness of the approach in damping oscillations that occur after disturbances are removed. The end result is a nonlinear decentralized adaptive state-feedback excitation controller for damping power systems oscillations in the presence of uncertain interconnection terms.

Zero-Sum Two-Player Game Theoretic Formulation of Affine Nonlinear Discrete-Time Systems Using Neural Networks

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control input and disturbance for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle-point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. Numerical example is provided illustrating the effectiveness of the approach.

Decentralized Optimal Control of a Class of Interconnected Nonlinear Discrete-Time Systems by Using Online Hamilton-Jacobi-Bellman Formulation

In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton-Jacobi-Bellman equation forward-in-time for the decentralized near optimal regulation of a class of nonlinear interconnected discrete-time systems with unknown internal subsystem and interconnection dynamics, while the input gain matrix is considered known. Even though the unknown interconnection terms are considered weak and functions of the entire state vector, the decentralized control is attempted under the assumption that only the local state vector is measurable. The decentralized nearly optimal controller design for each subsystem consists of two neural networks (NNs), an action NN that is aimed to provide a nearly optimal control signal, and a critic NN which evaluates the performance of the overall system. All NN parameters are tuned online for both the NNs. By using Lyapunov techniques it is shown that all subsystems signals are uniformly ultimately bounded and that the synthesized subsystems inputs approach their corresponding nearly optimal control inputs with bounded error. Simulation results are included to show the effectiveness of the approach.

Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control input and disturbance for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle-point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. Numerical example is provided illustrating the effectiveness of the approach.

Modeling and Nonlinear Optimal Control of Weak/Islanded Grids Using FACTS Device in a Game Theoretic Approach

A nonlinear discrete-time model along with an optimal stabilizing controller using a unified power quality conditioner (UPQC) is proposed for weak/islanded grids in this paper. An advanced stabilizing controller greatly benefits islanded medium-sized grid and microgrid due to their relatively small stored energy levels, which adversely affect their stability, as opposed to larger grids. In addition, a discrete-time grid model and controller are preferred for digital implementation. Here, the discrete-time Hamilton-Jacobi-Isaacs optimal control method is employed to design an optimal grid stabilizer. While UPQC is conventionally utilized for power quality improvement in distribution systems in the presence of renewable energy, here, the stabilizing control is added and applied to the UPQC series voltage in order to mitigate the grids oscillations besides UPQCs power conditioning tasks. Consequently, the UPQC can be employed to stabilize a grid-tie inverter (GTI) or a synchronous generator (SG) with minimum control effort. When controlling the GTI associated with renewable energy sources, a reduced UPQC structure is proposed that only employs the series compensator. Next, a successive approximation method along with neural networks is utilized to approximate a cost function of the grid dynamical states, the UPQC control parameters, and disturbance, in a two-player zero-sum game with the players being UPQC control and grid disturbances. Subsequently, the cost function is used to obtain the nonlinear optimal controller that is applied to the UPQC. Simulation results show effective damping behavior of the proposed nonlinear controller in controlling both GTI and SG in weak and islanded grids.

Novel Decentralized Control of Power Systems With Penetration of Renewable Energy Sources in Small-Scale Power Systems

In this paper, the power grid with penetration of renewable energy sources is modeled as a multigenerator interconnected power network. The power grid includes distributed energy resources including conventional synchronous generators and renewable energy sources; here called renewable generators that are connected to the grid via grid-tie inverters (GTIs). With the proposed modeling, the GTI resembles a synchronous generator with excitation control. The modeling takes into account the dc-link capacitor stored energy as a dynamical state, in contrast with the available methods, and through an appropriate controller assures the stability of the dc link and the entire grid without needing an abundant-energy dc link. Next, the power grid comprising the synchronous and renewable generators is converted to decentralized control form with subsystems in Brunovsky canonical form whose interactions with the rest of the grid are unknown. A decentralized adaptive neural network (NN) feedback controller is proposed with quadratic update law to stabilize the rotor speed and dc-link voltage oscillations in asymptotic fashion in the presence of grid disturbances. The proposed controller is then simplified. Though the solar power interacting with conventional synchronous generators is considered in this paper, the proposed modeling and controller design can be applied to many other renewable energy systems. Simulation results on the IEEE 14-bus power system with penetration of solar power are provided to show the effectiveness of the approach in damping oscillations that occur after disturbances.

Decentralized Discrete-Time Adaptive Neural Network Control of Interconnected DC Distribution System

In this paper, the interconnected dc distribution system is represented as a class of interconnected, nonlinear discrete-time systems with unknown dynamics. The dc distribution system comprises several dc sources, here called subsystems, along with resistive and constant-power loads (CPLs.) Each subsystem includes a dc-dc converter (DDC) and exploits distributed energy resources (DERs) such as photovoltaic, wind, etc. Due to the power system frequent disturbances this system is prone to instability in the presence of the DDC dynamical components. On the other hand, designing a centralized controller may not be viable due to the distance between the subsystems (dc sources.) Therefore, in this paper the stability of the interconnected dc distribution system is enhanced through decentralized adaptive nonlinear controller design that employs neural networks (NNs) to mitigate voltage and power oscillations after disturbances have occurred. The adaptive NN-based controller is introduced to overcome the unknown dynamics of each subsystems converter and stabilize the entire grid, assuming that only the local measurements are available to each converter. Simulation results are provided to show the effectiveness of the approach in damping oscillations that occur in the presence of disturbances.

Stability of the Small-Scale Interconnected DC Grids via Output-Feedback Control

A decentralized nonlinear model and controller is proposed to stabilize the interconnected small-scale islanded dc grids in the presence of renewable energy sources with proven stability in this paper. The dc interconnected network comprises dc sources along with resistive and constant-power loads (CPLs). Though the dc sources are photovoltaic (PV) in this paper, the proposed controller can be applied to other types of low-inertia intermittent sources as well. All sources and/or CPL loads are connected to the grid through simple dc–dc converters (DDCs) to avoid power electronic complexities. The negative-resistance CPLs can destabilize the grid in the presence of the DDC dynamical components. The decentralized nonlinear output-feedback controller mitigates rapid voltage and power oscillations caused by the disturbances and measurement noises, and stabilizes the grid. Since the proposed output-feedback controller needs only partial knowledge of the local converter states, the number of measure points reduces leading to a simple implementation. Simulation results on a small-scale dc grid are provided to show the performance of the proposed controller.

GA-based optimal power flow for microgrids with DC distribution network

Microgrids comprise a variety of distributed energy resources, energy storage devices, and loads. The majority of sources are not suitable for direct connection to the electrical network due to the characteristics of the energy produced, such as low voltage DC power from fuel cells and PV arrays or high frequency AC power from microturbines. Therefore, voltage source converters (VSCs) are required to interface them with the network. In microgrids with the DC distribution network, the DC voltage reference setting for the VSCs operating in the voltage regulator mode, and the optimal power reference settings of the remaining VSCs working in the power dispatcher mode must be pre-determined to maintain the DC voltage within desired margins. In this paper, the problem has been formulated as an optimization problem with VSCs switching and conduction losses selected as the objective function. Computational intelligence techniques, including genetic algorithm (GA) and simulated annealing (SA) based optimization methods, have been employed to solve the optimization problem. The results of the optimal power flow have been compared with a conventional power flow.