Voltage collapse is a type of blackout-inducing dynamic instability that occurs when power demand exceeds the maximum power that can be transferred through a network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficient use of network resources and does not account for unforeseen events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization, i.e., the design of load controllers aimed at stabilizing the point of voltage collapse. We formulate the problem of voltage stability for a star direct current network as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We introduce a voltage collapse stabilization controller and show that the high-voltage equilibrium is stabilized. More importantly, we are able to achieve proportional load shedding under extreme loading conditions. We further highlight the key features of our controller using numerical illustrations.
One of the major challenges of voltage stabilization in converter-based DC microgrids are the multiple interacting units displaying intermittent supply behavior. In this paper, we address this by a decentralized scalable, plug-and-play voltage controller for voltage-source converters (VSCs) at primary level. In contrast to existing approaches, we follow a systematic and constructive design based on port-Hamiltonian systems (PHSs) which does neither require the heuristic proposition of a Lyapunov function nor the computation of auxilliary variables such as time-derivatives. By employing the Ham…
Voltage stabilization in DC microgrids: an approach based on line-independent plug-and-play controllers
Università degli Studi di Pavia（帕维亚大学）；United Technologies Research Center Ireland（联合技术研究院爱尔兰）；Automatic Control Laboratory, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院自动控制实验室）
Voltage instability is one of the main causes of power system blackouts. Emerging technologies such as renewable energy integration, distributed energy resources and demand responses may introduce significant uncertainties in analyzing of system-wide voltage stability. This paper starts with summarizing different known voltage instability mechanisms, and then focuses on a class of voltage instability which is induced by the singular surface of the algebraic manifold. We argue and demonstrate that this class can include both dynamic and static voltage instabilities. To determine the minimum dis…
This paper presents an investigation into load dynamics that potentially cause voltage instability or collapse in distribution networks. Through phasor-based, time domain simulations of a dynamic load (DL) model from the literature, we show that the load dynamics alone do not cause voltage instability or collapse. By comparing the DL model to a benchmark model, we identify an important limitation with the DL model. We characterise this limitation and recommend that future work use load models with physical state variables. By investigating when and how load dynamics cause voltage instability, …
This paper addresses the problem of real-time monitoring of long-term voltage instability (LTVI) by using local field measurements. Existing local measurement-based methods use Thevenin equivalent parameter estimation that is sensitive to the noise in measurements. For solving this issue, we avoid the Thevenin approach by projecting the power flow equations as circles to develop local static-voltage stability indicator (LS-VSI) that is robust to measurement noises. The proposed method is an attractive option for practical implementation because of its decentralized nature, robustness to noise,…
The renewable energy is connected to the power grid through power electronic converters, which are lack of make the inertia of synchronous generator/machine (SM) be lost. The increasing penetration of renewable energy in power system weakens the frequency and voltage stability. The Grid-Forming Converters (GFCs) simulate the function of synchronous motor through control method in order to improve the stability of power grid by providing inertia and stability regulation mechanism. This kind of converter control methods include virtual synchronous machine, schedulable virtual oscillator control …
The impasse surface is an important concept in the differential-algebraic equation (DAE) model of power systems, which is associated with short-term voltage collapse. This paper establishes a necessary condition for a system trajectory hitting the impasse surface. The condition is in terms of admittance matrices regarding the power network, generators and loads, which specifies the pattern of interaction between those system components that can induce voltage collapse. It applies to generic DAE models featuring high-order synchronous generators, static loads, induction motor loads and lossy po…
A standard operational requirement in power systems is that the voltage magnitudes lie within prespecified bounds. Conventional engineering wisdom suggests that such a tightly-regulated profile, imposed for system design purposes and good operation of the network, should also guarantee a secure system, operating far from static bifurcation instabilities such as voltage collapse. In general however, these two objectives are distinct and must be separately enforced. We formulate an optimization problem which maximizes the distance to voltage collapse through injections of reactive power, subject…
With the gradual transformation of power generation towards renewables, distributed energy resources are becoming more and more relevant for grid stabilization. In order to involve all participants in the joint solution of this challenging task, we propose a distributed, model-based and unifying controller for frequency and voltage regulation in AC microgrids, based on steady-state optimal control. It not only unifies frequency and voltage control, but also incorporates the classic hierarchy of primary, secondary and tertiary control layers with each closed-loop equilibrium being a minimizer o…
This paper proposes a network decoupling method based on Holomorphic Embedding (HE) for voltage stability analysis. Using the proposed HE method with a physical load scaling factor s, it develops a set of decoupled two-bus circuit channels between a target bus and the swing bus. Accordingly, a complex-valued virtual index, named σ(s), is introduced in each channel to assess the voltage stability of prospective operating conditions with ensured accuracy. Then the stability margin at each bus can be analyzed by visualizing its respective σ(s) index on the σ plane with a unified boundary of volta…
This paper explores whether graph embedding methods can be used as a tool for analysing the robustness of power-grids within the framework of network science. The paper focuses on the strain elevation tension spring embedding (SETSe) algorithm and compares it to node2vec and Deep Graph Infomax, and the measures mean edge capacity and line load. These five methods are tested on how well they can predict the collapse point of the giant component of a network under random attack. The analysis uses seven power-grid networks, ranging from 14 to 2000 nodes. In total, 3456 load profiles are created f…
Fast-acting smart inverters that utilize preset operating conditions to determine real and reactive power injection/consumption can create voltage instabilities (over-voltage, voltage oscillations and more) in an electrical distribution network if set-points are not properly configured. In this work, linear distribution power flow equations and droop-based Volt-Var and Volt-Watt control curves are used to analytically derive a stability criterion using \lyapnouv analysis that includes the network operating condition. The methodology is generally applicable for control curves that can be repres…
Standard power system models are parameter dependent differential-algebraic equation (DAE) type. Following a transient event, voltage collapse can occur as a bifurcation of the transient load flow solutions which is marked by the system trajectory reaching a singular surface in state space where the voltage causality is lost. If a fault is expected to cause voltage collapse, preventive control decisions such as changes in AVR settings need to be taken in order to get enhance the system stability. In this regard, the knowledge of sensitivity of critical clearing time (CCT) to controllable syste…
Solvability of Power Flow Equations Through Existence and Uniqueness of Complex Fixed Point
Energy Systems Division, Argonne National Laboratory（阿贡国家实验室能源系统部）；School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院工业与系统工程学院）
We formulate a Stackelberg game between an attacker and a defender of a power system. The attacker attempts to alter the load setpoints of the power system covertly and intelligently, so that the voltage stability margin of the grid is reduced, driving the entire system towards a voltage collapse. The defender, or the system operator, aims to compensate for this reduction by retuning the reactive power injection to the grid by switching on control devices, such as a bank of shunt capacitors. A modified Backward Induction method is proposed to find a cost-based Stackelberg equilibrium (CBSE) of…
