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Register a new userReal-time Dispatchable Region of Active Distribution Networks Based on a Tight Convex Relaxation Model
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The uncertainty in distributed renewable generation poses security threats to the real-time operation of distribution systems. The real-time dispatchable region (RTDR) can be used to assess the ability of power systems to accommodate renewable generation at a given base point. DC and linearized AC power flow models are typically used for bulk power systems, but they are not suitable for low-voltage distribution networks with large r/x ratios. To balance accuracy and computational efficiency, this paper proposes an RTDR model of AC distribution networks using tight convex relaxation. Convex hull relaxation is adopted to reformulate the AC power flow equations, and the convex hull is approximated by a polyhedron without much loss of accuracy. Furthermore, an efficient adaptive constraint generation algorithm is employed to construct an approximate RTDR to meet the requirements of real-time dispatch. Case studies on the modified IEEE 33-bus distribution system validate the computational efficiency and accuracy of the proposed method.
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After disasters, distribution networks have to be restored by repair, reconfiguration, and power dispatch. During the restoration process, changes can occur in real time that deviate from the situations considered in pre-designed planning strategies. That may result in the pre-designed plan to become far from optimal or even unimplementable. This paper proposes a centralized-distributed bi-level optimization method to solve the real-time restoration planning problem. The first level determines integer variables related to routing of the crews and the status of the switches using a genetic algorithm (GA), while the second level determines the dispatch of active/reactive power by using distributed model predictive control (DMPC). A novel Aitken- DMPC solver is proposed to accelerate convergence and to make the method suitable for real-time decision making. A case study based on the IEEE 123-bus system is considered, and the acceleration performance of the proposed Aitken-DMPC solver is evaluated and compared with the standard DMPC method.
The rapidly growing use of lithium-ion batteries across various industries highlights the pressing issue of optimal charging control, as charging plays a crucial role in the health, safety and life of batteries. The literature increasingly adopts model predictive control (MPC) to address this issue, taking advantage of its capability of performing optimization under constraints. However, the computationally complex online constrained optimization intrinsic to MPC often hinders real-time implementation. This paper is thus proposed to develop a framework for real-time charging control based on explicit MPC (eMPC), exploiting its advantage in characterizing an explicit solution to an MPC problem, to enable real-time charging control. The study begins with the formulation of MPC charging based on a nonlinear equivalent circuit model. Then, multi-segment linearization is conducted to the original model, and applying the eMPC design to the obtained linear models leads to a charging control algorithm. The proposed algorithm shifts the constrained optimization to offline by precomputing explicit solutions to the charging problem and expressing the charging law as piecewise affine functions. This drastically reduces not only the online computational costs in the control run but also the difficulty of coding. Extensive numerical simulation and experimental results verify the effectiveness of the proposed eMPC charging control framework and algorithm. The research results can potentially meet the needs for real-time battery management running on embedded hardware.
This paper outlines reduced-order models for grid-forming virtual-oscillator-controlled inverters with nested current- and voltage-control loops, and current-limiting action for over-current protection. While a variety of model-reduction methods have been proposed to tame complexity in inverter models, previous efforts have not included the impact of current-reference limiting. In addition to acknowledging the current-limiting action, the reduced-order models we outline are tailored to networks with resistive and inductive interconnecting lines. Our analytical approach is centered on a smooth function approximation for the current-reference limiter, participation factor analysis to identify slow- and fast-varying states, and singular perturbation to systematically eliminate the fast states. Computational benefits and accuracy of the reduced-order models are benchmarked via numerical simulations that compare them to higher-order averaged and switched models.
This paper presents a method for the optimal siting and sizing of energy storage systems (ESSs) in active distribution networks (ADNs) to achieve their dispatchability. The problem formulation accounts for the uncertainty inherent to the stochastic nature of distributed energy sources and loads. Thanks to the operation of ESSs, the main optimization objective is to minimize the dispatch error, which accounts for the mismatch between the realization and prediction of the power profile at the ADN connecting point to the upper layer grid, while respecting the grid voltages and ampacity constraints. The proposed formulation relies on the so-called Augmented Relaxed Optimal Power Flow (AR-OPF) method: it expresses a convex full AC optimal power flow, which is proven to provide a global optimal and exact solution in the case of radial power grids. The AR-OPF is coupled with the proposed dispatching control resulting in a two-level optimization problem. In the first block, the site and size of the ESSs are decided along with the level of dispatchability that the ADN can achieve. Then, in the second block, the adequacy of the ESS allocations and the feasibility of the grid operating points are verified over operating scenarios using the Benders decomposition technique. Consequently, the optimal size and site of the ESSs are adjusted. To validate the proposed method, simulations are conducted on a real Swiss ADN hosting a large amount of stochastic Photovoltaic (PV) generation.
Optimal power flow (OPF) is the fundamental mathematical model in power system operations. Improving the solution quality of OPF provide huge economic and engineering benefits. The convex reformulation of the original nonconvex alternating current OPF (ACOPF) model gives an efficient way to find the global optimal solution of ACOPF but suffers from the relaxation gaps. The existence of relaxation gaps hinders the practical application of convex OPF due to the AC-infeasibility problem. We evaluate and improve the tightness of the convex ACOPF model in this paper. Various power networks and nodal loads are considered in the evaluation. A unified evaluation framework is implemented in Julia programming language. This evaluation shows the sensitivity of the relaxation gap and helps to benchmark the proposed tightness reinforcement approach (TRA). The proposed TRA is based on the penalty function method which penalizes the power loss relaxation in the objective function of the convex ACOPF model. A heuristic penalty algorithm is proposed to find the proper penalty parameter of the TRA. Numerical results show relaxation gaps exist in test cases especially for large-scale power networks under low nodal power loads. TRA is effective to reduce the relaxation gap of the convex ACOPF model.
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