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David J. Hill

Publications and source records attributed to David J. Hill.

At least 19 recordsLinked to original sources

Power Grid Topology Control

Power grids are facing major challenges from growing renewable integration and worsening climate impacts. While flexibility on both the demand and generation sides has been widely explored to address these challenges, network-side flexibility, especially in network topology, remains highly underutilized. Advances in communication, power electronics, and circuit breakers have made network topology increasingly controllable. However, leveraging this topological flexibility poses substantial challenges, primarily due to the inherent non-convexity and hybrid dynamics in associated optimization and control problems. This monograph surveys the development of power grid topology control in both early and recent years. It begins by discussing the fundamental topological constraints involved in topology control problems. Subsequently, it introduces steady-state topology control for transmission and distribution networks separately, covering fundamentals, a state-of-the-art review, and representative recent advances. Additionally, the network topology transition problem, which addresses the implementation of optimal topology solutions and has garnered increasing attention in recent years, is further modeled and analyzed. Beyond utilizing the flexibility of steady-state network topology, controlling network topology during transients can also contribute to system stabilization. Traditional approaches, such as intentional controlled islanding for transmission networks, as well as recently developed topology control methods for microgrid stabilization, exemplify this concept. Finally, a summary of this monograph is provided.

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On Directed Graphs With Real Laplacian Spectra

It is reported that dynamical systems over digraphs have superior performance in terms of system damping and tolerance to time delays if the underlying graph Laplacian has a purely real spectrum. This paper investigates the topological conditions under which digraphs possess real or complex Laplacian spectra. We derive sufficient conditions for digraphs, which possibly contain self-loops and negative-weighted edges, to have real Laplacian spectra. The established conditions generally imply that a real Laplacian spectrum is linked to the absence of the so-called digon sign-asymmetric interactions and non-strong connectivity in any subgraph of the digraph. Then, two classes of digraphs with complex Laplacian spectra are identified, which imply that the occurrence of directed cycles is a major factor to cause complex Laplacian eigenvalues. Moreover, we extend our analysis to multilayer digraphs, where strategies for preserving real/complex spectra from graph interconnection are proposed. Numerical experiments demonstrate that the obtained results can effectively guide the redesign of digraph topologies for a better performance.

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The Role of Electric Grid Research in Addressing Climate Change

Addressing the urgency of climate change necessitates a coordinated and inclusive effort from all relevant stakeholders. Critical to this effort is the modeling, analysis, control, and integration of technological innovations within the electric energy system, which plays a crucial role in scaling up climate change solutions. This perspective article presents a set of research challenges and opportunities in the area of electric power systems that would be crucial in accelerating Gigaton-level decarbonization. Furthermore, it highlights institutional challenges associated with developing market mechanisms and regulatory architectures, ensuring that incentives are aligned for stakeholders to effectively implement the technological solutions on a large scale.

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Chance Constrained Economic Dispatch Considering the Capability of Network Flexibility Against Renewable Uncertainties

This paper incorporates a continuous-type network flexibility into chance constrained economic dispatch (CCED). In the proposed model, both power generations and line susceptances are continuous variables to minimize the expected generation cost and guarantee a low probability of constraint violation in terms of generations and line flows under renewable uncertainties. From the analytical form of CCED, we figure out the mechanism of network flexibility against uncertainties -- while renewable uncertainties shrink the usable line capacities and aggravate transmission congestion, network flexibility mitigates congestion by re-routing the base-case line flows and reducing the line capacity shrinkage caused by uncertainties. Further, we propose an alternate iteration solver for this problem. By duality theory, we set up a master problem in the form of second-order cone programming to optimize generation dispatch scheme and a subproblem in the form of linear programming to optimize line susceptances. A satisfactory solution can be obtained efficiently by alternately solving these two problems. The proposed method applies to both Gaussian uncertainty and non-Gaussian uncertainty by means of Gaussian mixture model. The case studies on the IEEE 14-bus system and IEEE 118-bus system suggest that network flexibility can significantly improve operational economy while ensuring security under uncertainties.

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Distributed Multi-Time Slot Power Balancing Control of Power Systems with Energy Storage Devices

This paper studies a crucial problem in power system balancing control, i.e., the multi-time slot economic dispatch (MTSED) problem, for power grids with substantial renewables, synchronous generators (SGs), and energy storage devices (ESDs). The target of MTSED is to optimally coordinate active/reactive power outputs of all controllable units to meet a forecast net demand profile over multiple time slots within a receding finite time horizon. Firstly, the MTSED is formulated as an optimization problem with operational constraints, including the limits on the output of each controllable unit, ramping rates of SGss, energy levels of ESDs, and bus voltages. Then, a novel projection-based algorithm is developed to solve the problem in a distributed way. In particular, the distributed algorithm is not limited to solving the MTSED problem but also applies to more general optimization problems with both generic convex objective functions and hard feasibility constraints. Finally, case studies verify the effectiveness of the proposed method.

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Optimal Transmission Switching with Uncertainties from both Renewable Energy and N-k Contingencies

This paper focuses on the N-k security-constrained optimal transmission switching (OTS) problem for variable renewable energy (VRE) penetrated power grids. A new three-stage stochastic and distributionally robust OTS model is proposed. The first stage has the primary purpose to schedule the power generation and network topology based on the forecast of VRE. The second stage controls the power generation and voltage magnitudes of voltage-controlled buses in response to VRE uncertainty, and the third stage reacts to N-k contingencies additionally by line switching and load shedding. The VRE and N-k contingencies, considering different availability of their probability distributions, are tackled by stochastic and distributionally robust optimization, respectively. By adopting stage-wise realization of uncertainties in VRE and contingencies, the associated corrective controls with different mechanisms can be handled separately and properly, which makes the proposed OTS model more realistic than existing two-stage ones. For solving the proposed OTS model, its tractable reformulation is derived, and a solution approach that combines the nested column-and-constraint generation algorithm and Dantzig-Wolfe procedure is developed. Finally, case studies include a simple IEEE network for illustrative purposes and then real system networks to demonstrate the efficacy of the proposed approach.

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Impasse Surface of Differential-Algebraic Power System Models: An Interpretation Based on Admittance Matrices

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 power networks. We also identify a class of static load parameters that prevent power systems from hitting the impasse surface; this proves a conjecture made by Hiskens that has been unsolved for decades. Moreover, the obtained results lead to an early indicator of voltage collapse and a novel viewpoint that inductive compensation to the power network has a positive effect on preventing short-term voltage collapse, which are verified via numerical simulations.

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Bumpless Topology Transition

The topology transition problem of transmission networks is becoming increasingly crucial with topological flexibility more widely leveraged to promote high renewable penetration. This paper proposes a novel methodology to address this problem. Aiming at achieving a bumpless topology transition regarding both static and dynamic performance, this methodology utilizes various eligible control resources in transmission networks to cooperate with the optimization of line-switching sequence. Mathematically, a composite formulation is developed to efficiently yield bumpless transition schemes with AC feasibility and stability both ensured. With linearization of all non-convexities involved and tractable bumpiness metrics, a convex mixed-integer program firstly optimizes the line-switching sequence and partial control resources. Then, two nonlinear programs recover AC feasibility, and optimize the remaining control resources by minimizing the $\mathcal{H}_2$-norm of associated linearized systems, respectively. The final transition scheme is selected by accurate evaluation including stability verification using time-domain simulations. Finally, numerical studies demonstrate the effectiveness and superiority of the proposed methodology to achieve bumpless topology transition.

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Optimal Topology Transition

Network topology has significant impacts on operational performance of power systems. While extensive research efforts have been devoted to optimization of network topology for improving various system performances, the problem of how to transition from the initial topology to the desired optimal topology requires study. To address this problem, we propose the concept of optimal topology transition (OTT). This aims to find the topology transition trajectory from an initial topology to a desired terminal topology, which optimizes certain transition performance and satisfies operational constraints. The OTT problem is further formulated as a mixed-integer program under certain assumptions. Next, we propose the formulation of transition-embedded topology optimization that is capable of optimizing network topology and its transition trajectory simultaneously. Considering the time complexity of directly solving the mixed-integer programs, an efficient problem-specific solution algorithm is developed. Finally, numerical studies demonstrate the effectiveness of the proposed OTT and transition-embedded topology optimization models, as well as the superiority of the obtained optimal transition trajectories compared to ad hoc transition trajectories.

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Consensus-based Frequency and Voltage Regulation for Fully Inverter-based Islanded Microgrids

This paper proposes a new distributed consensus-based control method for voltage and frequency control of fully inverter-based islanded microgrids (MGs). The proposed method includes the active power sharing in voltage control to improve the reactive power sharing accuracy and thus generalizes some existing secondary frequency and voltage control methods. Firstly, frequency is regulated by distributed secondary frequency control. Secondly, voltage is regulated by distributed average voltage control and decentralized individual voltage control. It offers a tunable trade-off between voltage regulation, active, and reactive power sharing accuracy. Therefore, it avoids the abuse of sacrificing reactive power sharing accuracy for exact voltage regulation which is a common issue of existing methods. The proposed method is implemented in a distributed way that does not require a prior knowledge of the MG network structure and loads and hence can ensure scalability. Simulation results shows that the proposed controller achieves different compromise between the above three targets under different modes of operation.

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Convex Relaxation of AC Optimal Power Flow with Flexible Transmission Line Impedances

Flexible transmission line impedances on one hand are a promising control resource for facilitating grid flexibility, but on the other hand add much complexity to the concerned optimization problems. This paper develops a convexification method for the AC optimal power flow with flexible line impedances. First, it is discovered that a flexible-impedance line is equivalent to a constant-impedance line linking a pair of transformers with correlated and continuously adjustable tap ratios. Then, with this circuit equivalent, the original optimization problem is reformulated into a semi-definite program under the existing convex relaxation framework, which improves the solution tractability and optimality in an easy-to-implement manner. The proposed method is verified by numerical tests on the IEEE 118-bus system.

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Formulating Connectedness in Security-Constrained Optimal Transmission Switching Problems

This paper focuses on the issue of network connectedness (NC) in security-constrained optimal transmission switching problems, which is complicated by branch contingencies and corrective line switching. Two criteria are firstly proposed with the principle of preserving NC as much as possible within reasonable limits. By extending the electrical flow based NC constraints, a proposition is derived to associate different cases of NC with the optimum of a linear program, yielding the mathematical formulation of the NC criteria. By Karush-Kuhn-Tucker conditions, this formulation is further transformed into a tractable version which can be incorporated with existing SCOTS models without affecting the applicability of original solution approaches. Finally, case studies on various networks and SCOTS models demonstrate the efficacy of the proposed approach.

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Augmented Synchronization of Power Systems

Power system transient stability has been translated into a Lyapunov stability problem of the post-disturbance equilibrium for decades. Despite substantial results, conventional theories suffer from the stringent requirement of knowing the post-disturbance equilibrium a priori. In contrast, the wisdom from practice, which certificates stability by only the observation of converging frequencies and voltages, seems to provide an equilibrium-independent approach. Here, we formulate the empirical wisdom by the concept of augmented synchronization and aim to bridge such a theory-practice gap. First, we derive conditions under which the convergence to augmented synchronization implies the convergence to the equilibrium set, laying the first theoretical foundation for the empirical wisdom. Then, we reveal from what initial values the power system can achieve augmented synchronization. Our results open the possibility of an equilibrium-independent power system stability analytic that re-defines the nominal motion as augmented synchronization rather than certain equilibrium. Single-machine examples and the IEEE 9-bus system well verify our results and illustrate promising implications.

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Dispatch of Virtual Inertia and Damping: Numerical Method with SDP and ADMM

Power grids are evolving toward 100% renewable energy interfaced by inverters. Virtual inertia and damping provided by inverters are essential to synchronism and frequency stability of future power grids. This paper numerically addresses the problem of dispatch of virtual inertia and damping (DID) among inverters in the transmission network. The DID problem is first formulated as a nonlinear program (NLP) by the Radua collocation method which is flexible to handle various types of disturbances and bounds constraints. Since the NLP of DID is highly non-convex, semi-definite programming (SDP) relaxation for the NLP is further derived to tackle the non-convexity, followed by its sparsity being exploited hierarchically based on chordality of graphs to seek enhancement of computational efficiency. Considering high dimension and inexactness of the SDP relaxation, a feasibility-embedded distributed approach is finally proposed under the framework of alternating direction method of multipliers (ADMM), which achieves parallel computing and solution feasibility regarding the original NLP. Numerical simulations carried out for five test power systems demonstrate the proposed method and necessity of DID.

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Ensuring Network Connectedness in Optimal Transmission Switching Problems

Network connectedness is indispensable for the normal operation of transmission networks. However, there still remains a lack of efficient constraints that can be directly added to the problem formulation of optimal transmission switching (OTS) to ensure network connectedness strictly. To fill this gap, this paper proposes a set of linear connectedness constraints by leveraging the equivalence between network connectedness and feasibility of the vertex potential equation of an electrical flow network. The proposed constraints are compatible with any existing OTS models to ensure topology connectedness. Furthermore, we develop a reduction version for the proposed connectedness constraints, seeking for improvement of computational efficiency. Finally, numerical studies with a DC OTS model show the deficiency of OTS formulations without full consideration of network connectedness and demonstrate the effectiveness of the proposed constraints. The computational burden caused by the connectedness constraints is moderate and can be remarkably relieved by using the reduced version.

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Chance-Constrained OPF in Droop-Controlled Microgrids with Power Flow Routers

High penetration of renewable generation poses great challenge to power system operation due to its uncertain nature. In droop-controlled microgrids, the voltage volatility induced by renewable uncertainties is aggravated by the high droop gains. This paper proposes a chance-constrained optimal power flow (CC-OPF) problem with power flow routers (PFRs) to better regulate the voltage profile in microgrids. PFR refer to a general type of network-side controller that brings more flexibility to the power network. Comparing with the normal CC-OPF that relies on power injection flexibility only, the proposed model introduces a new dimension of control from power network to enhance system performance under renewable uncertainties. Since the inclusion of PFRs complicates the problem and makes common solvers no longer apply directly, we design an iterative solution algorithm. For the subproblem in each iteration, chance constraints are transformed into equivalent deterministic ones via sensitivity analysis, so that the subproblem can be efficiently solved by the convex relaxation method. The proposed method is verified on the modified IEEE 33-bus system and the results show that PFRs make a significant contribution to mitigating the voltage volatility and make the system operate in a more economic and secure way.

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Event-triggered controllers based on the supremum norm of sampling-induced error

The paper proposes a novel event-triggered control scheme for nonlinear systems based on the input-delay method. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the derivative of the continuous-time input function, while the auxiliary input is defined as the input disturbance caused by the sampling or equivalently the integral of the auxiliary output over the sampling period. As a result, a cyclic mapping forms from the input to the output via the system dynamics and back from the output to the input via the integral. The event-triggering law is constructed to make the mapping contractive such that the stabilization is achieved and an easy-to-check Zeno-free condition is provided. With this idea, we develop a theorem for the event-triggered control of interconnected nonlinear systems which is employed to solve the event-triggered control for lower-triangular systems with dynamic uncertainties.

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A Hierarchical Framework for Ambient Signals based Load Modeling with Exploring the Hidden Quasi-convexity

Load modeling is an important issue in modeling a power system. The approach of ambient signals-based load modeling (ASLM) was recently proposed to better track the time-varying changes of load models. To improve computation efficiency and model structure complexity, a hierarchical framework for ASLM is proposed in this paper. Through this framework, the hidden quasi-convexity of load modeling problem is explored for the first time, and more complicated static load model structures can be applied. In the upper stage, the identification of dynamic load parameters is regarded as an optimization problem. In the lower stage, the optimal static load parameters are obtained through linear regression for a given group of dynamic load parameters. Afterwards, the regression residuals are regarded as the objective function (OF) of the upper stage optimization problem. The proposed method is validated by the case study results in Guangdong Power Grid. The results have shown that the OF is mostly quasi-convex after the transformation of induction motor model, which provides the basis for the application of gradient-based optimization algorithm. The case study results also validate that the proposed approach has better computation efficiency and model structure complexity compared with the previous ASLM approach.

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