Finding a feasible solution is the primary concern in power system dispatch. This paper studies the feasibility condition of power system dispatch under a multistage robust optimization framework considering the non-anticipativity of dispatch policy, which is difficult to be expressed via explicit constraints. The multistage robust feasible regions (MRFRs) are defined as the sets in the state space containing all points that can maintain the robust feasibility in the next period against renewable and demand uncertainties; we give a polyhedral projection condition to characterize exact MRFRs in a recursive manner, which can be regarded as an analog of Bellman’s optimality condition. However, because the multistage dispatch problem of a bulk power system has a high-dimensional state space, the computation of exact MRFRs suffers from the curse of dimensionality. We propose an inner approximation method that identifies the maximal polyhedra that are embraced by the unknown exact MRFRs; we devise a computationally efficient algorithm to retrieve the hyperplane representation of the inner approximator. Finally, we discuss how MRFRs can be used in combination with existing approaches, such as dynamic programming and rolling horizon optimization. Numerical simulations on a modified IEEE 118-bus system verify the effectiveness and advantages of the proposed methodNote to Practitioners—This paper is motivated by the problem of maintaining the feasibility in power system multistage dispatch under renewable generation uncertainty. The proposed method regards the multistage dispatch as a sequential decision-making process and recursively defines the MRFR using polyhedral projection technique, which contains all the state points in each period that can guarantee the robust feasibility in the next period. To release the curses of dimensionality, the large-scale MRFR is approximated by an inner hyper-rectangle in the state space, which can be decomposed into independent intervals of state variables, such as the generation power range of coal-fired unit and the state-of-charge range of battery storage unit. These decoupled intervals are convenient for practical use and desired in the real-world power system. At the current stage, the calculation of MRFR requires a linear model; in the future research, integers will be addressed so that more facilities such as non-ideal energy storage units and fast-startup generators can be involved.

In this article, distributed control methods are widely applied in the operation of distributed generators (DGs) in modern power grids. As distributed control, the control operation depends greatly on information exchange among neighboring distributed controllers, where harsh communication conditions (e.g., limited communication rates and accidental communication failures) may cause significant performance deterioration. Therefore, it is necessary to investigate distributed control of DGs under imperfect communication conditions in practical systems. This article proposes an event-based distributed DG frequency control strategy. By introducing an event-based update mechanism for real-time DG data measurements and the communication topology, the adaptability of the control strategy to low communication rates and communication failures is significantly enhanced. Besides, the above-mentioned nonideal communication conditions, the proposed control also shows high adaptability to communication delays. Furthermore, an optimal design method of the control parameters is developed, which ensures proper steady-state performance and optimizes the dynamic performance of the proposed control. Simulations based on MATLAB/Simulink and hardware experimental validations using dSPACE under various conditions verify the effectiveness of the proposed control.

Distributed control methods have been widely applied to the control and operation of microgrids due to their robustness and flexibility. Considering the distributed structure, the performance of distributed control depends greatly on the communication among DGs. It is necessary to study distributed control under weak communication conditions (e.g., low communication rates and frequent communication failures). This paper proposes a communication-resilient distributed frequency control strategy for microgrids. The proposed control contains an event-triggered update mechanism of the communication data among DGs and the communication topology, which ensures adaptability to limited communication rates and enhances the resiliency in face of communication failures. Moreover, the optimal design of the control parameters (i.e., the optimization of communication topologies and local controllers) is studied, which further improves the performance and practicability of the control strategy. The effectiveness and advantages of the proposed control are verified by simulation based on MATLAB/Simulink under various conditions.

Integration of heat and electricity supply improves the overall energy efficiency and system operational flexibility. The renewable powered heat-electricity energy system is a promising way to set up residential energy supply facilities in remote areas beyond the reach of power system infrastructures. However, the volatility of wind and solar energy brings about the risk of supply inadequacy. This article proposes a data-driven robust method to quantify two measures of such a risk in the stand-alone renewable powered heat-electricity energy system. The uncertainty of renewable generation is modeled through a family of ambiguous probability distributions around an empirical one based on the Wasserstein metric; then, the probability of heat and electricity load shedding during a short period and related penalty cost are discussed. Through a polyhedral characterization of renewable power feasible region, the load shedding probability under the Wasserstein ambiguity set comes down to a linear program. With a piecewise linear optimal value function of the penalty cost, its expectation under the worst case distribution in the Wasserstein ambiguity set also gives rise to a linear program. The proposed method requires moderate information on renewable generation and makes full use of available data, whereas sustains computational tractability. The evaluation result is robust against the inaccuracy of renewable power distributions. Case studies demonstrate the effectiveness of the proposed approach.

Policy iteration approximate dynamic programming (DP) is an important algorithm for solving optimal decision and control problems. In this paper, we focus on the problem associated with policy approximation in policy iteration approximate DP for discrete-time nonlinear systems using infinite-horizon undiscounted value functions. Taking policy approximation error into account, we demonstrate asymptotic stability of the control policy under our problem setting, show boundedness of the value function during each policy iteration step, and introduce a new sufficient condition for the value function to converge to a bounded neighborhood of the optimal value function. Aiming for practical implementation of an approximate policy, we consider using Volterra series, which has been extensively covered in controls literature for its good theoretical properties and for its success in practical applications. We illustrate the effectiveness of the main ideas developed in this paper using several examples including a practical problem of excitation control of a hydrogenerator.

Proactive preparedness to cope with extreme weather events is significantly helpful in reducing the restoration cost and enhancing the resilience of distribution systems. This paper is focused on the resource allocation problem in distribution systems ahead of a coming hurricane. Generation resources such as diesel oil and batteries are considered for allocation, which can be used to serve outage critical load in the post-hurricane restoration. Electric buses are also considered as a kind of resource. Considering the uncertainties of system faults, the allocation problem is formulated into a mixed-integer stochastic nonlinear program. A heuristic method is then proposed, which obtains the allocation plan by solving a mixed-integer linear program. Numerical simulations are performed on the IEEE 123-node feeder system under several scenarios to demonstrate the effectiveness of the proposed method. The impacts of resources transportation cost, initial distribution of electric buses, and hurricane severity on the allocation plan are discussed.

The emergence of smart grids has posed great challenges to traditional power system control given the multitude of new risk factors. This paper proposes an online supplementary learning controller (OSLC) design method to compensate the traditional power system controllers for coping with the dynamic power grid. The proposed OSLC is a supplementary controller based on approximate dynamic programming, which works alongside an existing power system controller. By introducing an action-dependent cost function as the optimization objective, the proposed OSLC is a nonidentifier-based method to provide an online optimal control adaptively as measurement data become available. The online learning of the OSLC enjoys the policy-search efficiency during policy iteration and the data efficiency of the least squares method. For the proposed OSLC, the stability of the controlled system during learning, the monotonic nature of the performance measure of the iterative supplementary controller, and the convergence of the iterative supplementary controller are proved. Furthermore, the efficacy of the proposed OSLC is demonstrated in a challenging power system frequency control problem in the presence of high penetration of wind generation.

Extensive approximate dynamic programming (ADP) algorithms have been developed based on policy iteration. For policy iteration based ADP of deterministic discrete-time nonlinear systems, existing literature has proved its convergence in the formulation of undiscounted value function under the assumption of exact approximation. Furthermore, the error bound of policy iteration based ADP has been analyzed in a discounted value function formulation with consideration of approximation errors. However, there has not been any error bound analysis of policy iteration based ADP in the undiscounted value function formulation with consideration of approximation errors. In this paper, we intend to fill this theoretical gap. We provide a sufficient condition on the approximation error, so that the iterative value function can be bounded in a neighbourhood of the optimal value function. To the best of the authors' knowledge, this is the first error bound result of the undiscounted policy iteration for deterministic discrete-time nonlinear systems considering approximation errors.

Dynamic reactive power control of doubly fed induction generators (DFIGs) plays a crucially important role in maintaining transient stability of power systems with high penetration of DFIG based wind generation. Based on approximate dynamic programming (ADP), this paper proposes an optimal adaptive supplementary reactive power controller for DFIGs. By augmenting a corrective regulation signal to the reactive power command of rotor-side converter (RSC) of a DFIG, the supplementary controller is designed to reduce voltage sag at the point of common connection (PCC) during a fault, and to mitigate output active power oscillation of the wind farm after a fault. As a result, the transient stability of both DFIG and the power grid is enhanced. An action dependent cost function is introduced to provide real-time online ADP learning control. Furthermore, a policy iteration algorithm using high-efficiency least square method is employed to train the supplementary controller in an online model-free manner. By using such techniques, the supplementary reactive power controller is endowed with capability of online optimization and adaptation. Simulations carried out on a benchmark power system integrating a large DFIG wind farm show that the ADP based supplementary reactive power controller can significantly improve the transient system stability in changing operation conditions.

Controller parameter tuning is an integral part of control engineering practice. Existing tuning methods usually start with an accurate mathematical model of the controlled system, which may pose some challenges for practicing engineers dealing with real systems. As such, parameter optimization and adaptation are treated as two independent steps during tuning. To address these issues, we propose a new, online parameterized controller tuning method for a general nonlinear dynamic system. This tuning method is based on direct heuristic dynamic programming (direct HDP), a model-free algorithm in the approximated dynamic programming (ADP) family. By using a Lyapunov stability approach, we provide uniformly ultimately bounded (UUB) results under some mild conditions for controller parameters, the critic neural network weights, and the action neural network weights. Simulation studies based on the benchmark cart-pole system demonstrate adaptability and optimization capabilities of the proposed controller parameter tuning method.

There is an extensive literature on value function approximation for approximate dynamic programming (ADP). Multilayer perceptrons (MLPs) and radial basis functions (RBFs), among others, are typical approximators for value functions in ADP. Similar approaches have been taken for policy approximation. In this paper, we propose a new Volterra series based structure for actor approximation in ADP. The Volterra approx-imator is linear in parameters with global optima attainable. Given the proposed approximator structures, we further develop a policy iteration framework under which a gradient descent training algorithm for obtaining the optimal Volterra kernels can be obtained. Associated with this ADP design, we provide a sufficient condition based on actor approximation error to guarantee convergence of the value function iterations. A finite bound of the final convergent value function is also given. Finally, by using a simulation example we illustrate the effectiveness of the proposed Volterra actor for optimal control of a nonlinear system.

Doubly fed induction generators (DFIGs) are widely used in wind power generation. For controlling DFIGs to maintain network frequency within a safety range, the proportional-derivative (PD) type virtual inertia controllers (VIC) are used in the active power control of DFIGs. However, as is well known, wind power generation conditions change directly with wind conditions in nature. Such changes create great challenge for the VIC design and actually force the control designs to go beyond the traditional problem formulation of using explicit objective functions associated with specific optimality. Controller parameter tuning thus necessarily becomes a part of the controller design. In this paper, we propose an approximate dynamic programming (ADP) structure for online tuning of the PD type virtual inertia controller parameters. The proposed ADP structure naturally takes into account the PD control into design objective and provides the PD controller with online parameter tuning capability through learning. Design and implementation details of the proposed methodology, including neural network weight initialization, design of the reinforcement signal, data preprocessing, and a bound on the online tuned parameters are discussed in this paper. Simulation studies carried out on the Power System Computer Aided Design/ Electro Magnetic Transient in DC System (PSCAD/EMTDC) software are used to demonstrate the effectiveness and efficiency of the proposed ADP-based online VIC parameter tuning methodology.

This paper addresses a design issue of an approximate dynamic programming structure and its respective convergence property. Specifically, we propose to impose a PID structure to the action and critic networks in the direct heuristic dynamic programming (direct HDP) online learning controller. We demonstrate that the direct HDP with such PID augmented states improves convergence speed and that it out performs the traditional PID even though the learning controller may be initialized to be like a PID. Also for the first time, by using a Lyapnov approach we show that the action and critic network weights retain the property of uniformly ultimate boundedness (UUB) under mild conditions.

Based on differential geometric control theory, this work proposes a novel zero dynamics design method for a class of nonlinear non-minimum phase systems, which using dynamic feedback to the controlled system to obtain stable zero dynamics through dimension extension. Nonlinear control law is then derived by means of the linear control design method. Furthermore, both the optimality of the control law and the closed-loop system's stability are mathematically and strictly proved using HJB equation and centre manifold theory respectively. A nonlinear optimal governor controller is also proposed on the foundation of ideal hydraulic turbine model. The simulation results show that the novel governor control strategy for hydraulic turbines could enhance transient stability of power systems more effectively than the conventional control law.