The recent rise of electricity generation based on renewable energy sources increases the demand for transmission capacity. Capacity expansion via the upgrade of transmission line capacity, e.g., by conversion to a high-voltage direct current (HVDC) line, is an attractive option. In this paper, it is shown that if the upgrade to HVDC is applied systematically to selected transmission lines across the grid, a hybrid architecture is obtained that enables an efficient and globally optimal solution of the optimal power flow (OPF) problem. More precisely, for conventional meshed AC transmission grids the OPF problem is nonconvex and in general NP-hard, rendering it hard to solve. We prove that after the upgrade to the proposed hybrid architecture, the same mesh topology facilitates an exact convex relaxation of the OPF problem, enabling its globally optimal solution with efficient polynomial time algorithms. This OPF method is then employed in simulations, which demonstrate that the hybrid architecture can increase the effective transmission capacity and substantially reduce the generation costs, even compared to the AC grid with optimal transmission switching.
This paper explores the stability of nonsynchronous hybrid ac/dc power grids under the grid-forming hybrid angle control strategy. We formulate dynamical models for the ac grids and transmission lines, interlinking converters, and dc generations and interconnections. Next, we establish the existence and uniqueness of the closed-loop equilibria for the overall system. Subsequently, we demonstrate global attractivity of the equilibria, local asymptotic stability of the desired equilibrium point, and instability and zero-Lebesgue-measure region of attraction for other equilibria. The theoretic re…
Recently, we proposed a capacity expansion approach for transmission grids that combines the upgrade of transmission capacity with a transition in system structure to improve grid operation. The key to this concept is a particular hybrid AC/DC transmission grid architecture, which is obtained by uprating selected AC lines via a conversion to HVDC. We have shown that this system structure improves optimal power flow (OPF) solvability and that it can reduce the total generation costs. In this work, we study the benefits of this hybrid architecture in the context of a deregulated electricity mark…
In this work, we analyze the effect of transmission line dynamics on grid-forming control for inverter-based AC power systems. In particular, we investigate a dispatchable virtual oscillator control (dVOC) strategy that was recently proposed in the literature. When the dynamics of the transmission lines are neglected, i.e., if an algebraic model of the transmission network is used, dVOC ensures almost global asymptotic stability of a network of AC power inverters with respect to a pre-specified solution of the AC power-flow equations. While this approximation is typically justified for convent…
Network segmentation of a power grid's communication system is one way to make the grid more resilient to cyber attacks. We develop a novel trilevel programming model to optimally segment a grid communication system, taking into account the actions of an information technology (IT) administrator, attacker, and grid operator. The IT administrator is given an allowance to segment existing networks, and the attacker is given a fixed budget to attack the segmented communication system in an attempt to inflict damage on the grid. Finally, the grid operator is allowed to redispatch the grid after th…
The day-ahead energy and reserve management with transmission restrictions and voltage security limits is a challenging task for large-scale power systems in the presence of real-time variations caused by the uncertain demand and the fluctuating power output of renewable energy sources (RESs). The proposed formulation in this work supports joint scheduling of energy and reserve to promote an economic and reliable operation. To improve its scalability, a two-stage iterative optimization algorithm is proposed based on Bender's decomposition framework. Therewith, the optimal schedule is computed …
This paper investigates the implementation and application of the multi-variable grid-forming hybrid angle control (HAC) for high-power converters in transmission grids. We explore the system-level performance and robustness of the HAC concept in contrast to other grid-forming schemes i.e., power-frequency droop and matching controls. Our findings suggest that similar to the ac-based droop control, \ac{hac} enhances the small-signal frequency stability in low-inertia power grids, and akin to the dc-based matching control, HAC exhibits robustness when accounting for the practical limits of the …
In this work, we investigate grid-forming (GFM) control for dc/ac power converters in emerging power systems that contain ac and dc networks, renewable generation, and conventional generation. We propose a novel power-balancing GFM control strategy that simultaneously forms the converter ac and dc voltage (i.e., dual-port GFM), unifies standard grid-following (GFL) and GFM functions, and is backwards compatible with conventional machine-based generation. Notably, in contrast to state-of-the-art control architectures that use a mix of grid-forming and grid-following control, dual-port GFM contr…
This paper presents a decentralized controller for sharing primary AC frequency control reserves through a multi-terminal HVDC grid. By using Lyapunov arguments, the proposed controller is shown to stabilize the equilibrium of the closed-loop system consisting of the interconnected AC and HVDC grids, given any positive controller gains. The static control errors resulting from the proportional controller are quantified and bounded by analyzing the equilibrium of the closed-loop system. The proposed controller is applied to a test grid consisting of three asynchronous AC areas interconnected by…
Many countries are currently challenged with the extensive integration of renewable energy sources, which necessitates vast capacity expansion measures. These measures in turn require comprehensive power flow studies, which are often computationally highly demanding. In this work a reduction strategy for large-scale grid models is introduced which not only reduces the model complexity but also preserves the structure and designated grid features. The objective is to ensure that areas crucial to the behavior and the relation of all elements to their physical counterparts remain unchanged. This …
The energy transition will lead to an imbalance in electric power generation and demand along the north-south axis of Germany. To manage this imbalance, the transmission system operators proposed a network development plan that requires several thousand kilometers of new lines, which received extensive opposition. In our recent work, we proposed a landscape-preserving network development approach, i.e., the hybrid architecture, which relies on the conversion of some existing AC lines and transformers to HVDC operation. In this work, we show that this approach can meet the projected capacity an…
In this paper we propose a distributed dynamic controller for sharing frequency control reserves of asynchronous AC systems connected through a multi-terminal HVDC (MTDC) grid. We derive sufficient stability conditions, which guarantee that the frequencies of the AC systems converge to the nominal frequency. Simultaneously, the global quadratic cost of power generation is minimized, resulting in an optimal distribution of generation control reserves. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from …
In this paper, we present distributed controllers for sharing primary and secondary frequency control reserves for asynchronous AC transmission systems, which are connected through a multi-terminal HVDC grid. By using Lyapunov arguments, the equilibria of the closed-loop system are shown to be globally asymptotically stable. We quantify the static errors of the voltages and frequencies, and give upper bounds for these errors. It is also shown that the controllers have the property of power sharing, i.e., primary and secondary frequency control reserves are shared fairly amongst the AC systems.…
This paper introduces a new grid-forming control for power converters, termed hybrid angle control (HAC) that ensures the almost global closed-loop stability. HAC combines the recently proposed matching control with a novel nonlinear angle feedback reminiscent of (though not identical to) classic droop and dispatchable virtual oscillator controls. The synthesis of HAC is inspired by the complementary benefits of the dc-based matching and ac-based grid-forming controls as well as ideas from direct angle control and nonlinear damping assignment. The proposed HAC is applied to a high-fidelity non…
As renewable sources increasingly replace existing conventional generation, the dynamics of the grid drastically changes, posing new challenges for transmission system operations, but also arising new opportunities as converter-based generation is highly controllable in faster timescales. This paper investigates grid stability under the massive integration of grid-forming converters. We utilize detailed converter and synchronous machine models and describe frequency behavior under different penetration levels. First, we show that the transition from 0% to 100% can be achieved from a frequency …
The coordinated alternating current optimal power flow (ACOPF) for coupled transmission-distribution grids has become crucial to handle problems related to high penetration of renewable energy sources (RESs). However, obtaining all system details and solving ACOPF centrally is not feasible because of privacy concerns. Intermittent RESs and uncontrollable loads can swiftly change the operating condition of the power grid. Existing decentralized optimization methods can seldom track the optimal solutions of time-varying ACOPFs. Here, we propose an online decentralized optimization method to trac…
Real-world network systems, for example, power grids, are critical to modern economies. Due to the increasing system scale and complex dependencies inside of these networks, system failures can widely spread and cause severe damage. We have experienced massive cascading failures in power grids, such as major U.S. western grid failures in 1996 and the great Northeast blackout of 2003. Therefore, analyzing cascading failures and defense strategies, in response to system catastrophic breakdown, is crucial. Although many efforts have been performed to prevent failure propagation throughout systems…
Resilient Transmission Grid Design: AC Relaxation vs. DC approximation
Center for Nonlinear Studies, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室非线性研究中心）；Department of Industrial Operations Engineering, University of Michigan（密歇根大学工业运营工程系）
