arXiv subjects

Changhong Zhao

Publications and source records attributed to Changhong Zhao.

At least 19 recordsLinked to original sources

arXiv2025

Robust Distribution Network Reconfiguration Using Mapping-based Column-and-Constraint Generation

The integration of intermittent renewable energy sources into distribution networks introduces significant uncertainties and fluctuations, challenging their operational security, stability, and efficiency. This paper considers robust distribution network reconfiguration (RDNR) with renewable generator resizing, modeled as a two-stage robust optimization (RO) problem with decision-dependent uncertainty (DDU). Our model optimizes resizing decisions as the upper bounds of renewable generator outputs, while also optimizing the network topology. We design a mapping-based column-and-constraint generation (C&CG) algorithm to address the computational challenges raised by DDU. Sensitivity analyses further explore the impact of uncertainty set parameters on optimal solutions. Case studies demonstrate the effectiveness of the proposed algorithm in reducing computational complexity while ensuring solution optimality.

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arXiv2025

Approximating Dispatchable Regions in Three-Phase Radial Networks with Conditions for Exact SDP Relaxation

The concept of dispatchable region plays a pivotal role in quantifying the capacity of power systems to accommodate renewable generation. In this paper, we extend the previous approximations of the dispatchable regions on direct current (DC), linearized, and nonlinear single-phase alternating current (AC) models to unbalanced three-phase radial (tree) networks and provide improved outer and inner approximations of dispatchable regions. Based on the nonlinear bus injection model (BIM), we relax the non-convex problem that defines the dispatchable region to a solvable semidefinite program (SDP) and derive its strong dual problem (which is also an SDP). Utilizing the special mathematical structure of the dual problem, an SDP-based projection algorithm is developed to construct a convex polytopic outer approximation to the SDP-relaxed dispatchable region. Moreover, we provide sufficient conditions to guarantee the exact SDP relaxation by adding the power loss as a penalty term, thereby providing a theoretical guarantee for determining an inner approximation of the dispatchable region. Through numerical simulations, we validate the accuracy of our approximation of the dispatchable region and verify the conditions for exact SDP relaxation.

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arXiv2025

A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedback

The increasing penetration of distributed energy resources (DERs) adds variability as well as fast control capabilities to power networks. Dispatching the DERs based on local information to provide real-time optimal network operation is the desideratum. In this paper, we propose a data-driven real-time algorithm that uses only the local measurements to solve time-varying AC optimal power flow (OPF). Specifically, we design a learnable function that takes the local feedback as input in the algorithm. The learnable function, under certain conditions, will result in a unique stationary point of the algorithm, which in turn transfers the OPF problems to be optimized over the parameters of the function. We then develop a stochastic primal-dual update to solve the variant of the OPF problems based on a deep neural network (DNN) parametrization of the learnable function, which is referred to as the training stage. We also design a gradient-free alternative to bypass the cumbersome gradient calculation of the nonlinear power flow model. The OPF solution-tracking error bound is established in the sense of universal approximation of DNN. Numerical results on the IEEE 37-bus test feeder show that the proposed method can track the time-varying OPF solutions with higher accuracy and faster computation compared to benchmark methods.

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arXiv2024

Achieving Social Optimum and Budget Balance via a Joint Electricity-Carbon Pricing Mechanism

Decarbonizing electric grids is a crucial global endeavor in the pursuit of carbon neutrality. Taking carbon emissions from generation into account when pricing electricity usage is an essential way to achieve this goal. However, such pricing is not trivial due to the requirements of an effective electricity market, such as maintaining budget balance, providing incentives to motivate participants to follow the dispatch schedule, and minimizing the impact on affected parties compared to when they were in the traditional electricity market. Although existing joint electricity-carbon pricing mechanisms have shown promising performance in reducing emissions in power networks, they can hardly meet all the requirements. This paper proposes a novel joint electricity-carbon pricing mechanism based on primal-dual optimality condition-enabled transformation. An algorithm for determining the critical market parameter is developed. The proposed pricing mechanism is proven to possess all the desired properties, including budget balance, individual rationality, dispatch-following incentive compatibility, and truthful-bidding incentive compatibility. These properties ensure the proposed mechanism can incentivize market participants to achieve carbon-aware social optimum in a self-organized and sustainable way. Numerical experiments show the advantages of the proposed pricing mechanism compared to the existing marginal-based and carbon emission flow-based pricing mechanisms.

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arXiv2024

Hierarchical Game for Coupled Power System with Energy Sharing and Transportation System

The wide deployment of distributed renewable energy sources and electric vehicles can help mitigate climate crisis. This necessitates new business models in the power sector to hedge against uncertainties while imposing a strong coupling between the connected power and transportation networks. To address these challenges, this paper first proposes an energy sharing mechanism considering AC power network constraints to encourage local energy exchange in the power system. Under the proposed mechanism, all prosumers play a generalized Nash game. We prove that the energy sharing equilibrium exists and is socially optimal. Furthermore, a hierarchical game is built to characterize the interactions both inside and between the power and transportation systems. Externally, the two systems are engaged in a generalized Nash game because traffic flows serve as electric demands by charging behaviors, and each driver pays the energy sharing price for charging. The hierarchical game is then converted into a mixed-integer linear program (MILP) with the help of optimality conditions and linearization techniques. Numerical experiments validate the theoretical results and show the mutual impact between the two systems.

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arXiv2024

Reinforcement Learning for Distributed Transient Frequency Control with Stability and Safety Guarantees

This paper proposes a reinforcement learning-based approach for optimal transient frequency control in power systems with stability and safety guarantees. Building on Lyapunov stability theory and safety-critical control, we derive sufficient conditions on the distributed controller design that ensure the stability and transient frequency safety of the closed-loop system. Our idea of distributed dynamic budget assignment makes these conditions less conservative than those in recent literature, so that they can impose less stringent restrictions on the search space of control policies. We construct neural network controllers that parameterize such control policies and use reinforcement learning to train an optimal one. Simulations on the IEEE 39-bus network illustrate the guaranteed stability and safety properties of the controller along with its significantly improved optimality.

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arXiv2023

DeepOPF-U: A Unified Deep Neural Network to Solve AC Optimal Power Flow in Multiple Networks

The traditional machine learning models to solve optimal power flow (OPF) are mostly trained for a given power network and lack generalizability to today's power networks with varying topologies and growing plug-and-play distributed energy resources (DERs). In this paper, we propose DeepOPF-U, which uses one unified deep neural network (DNN) to solve alternating-current (AC) OPF problems in different power networks, including a set of power networks that is successively expanding. Specifically, we design elastic input and output layers for the vectors of given loads and OPF solutions with varying lengths in different networks. The proposed method, using a single unified DNN, can deal with different and growing numbers of buses, lines, loads, and DERs. Simulations of IEEE 57/118/300-bus test systems and a network growing from 73 to 118 buses verify the improved performance of DeepOPF-U compared to existing DNN-based solution methods.

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arXiv2023

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to the solutions at which the power networks may be exposed to the risk of voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on a three-phase unbalanced nonlinear distribution power flow model to mitigate the errors arising from model linearization. The resultant gradients feature a blocked structure that enables us to further develop an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE $123$-bus test feeder and a $4,518$-node test feeder show that the proposed method can enhance the overall voltage safety while achieving comparable computational efficiency with the linearized algorithm.

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arXiv2023

Differentially Private Stochastic Convex Optimization in (Non)-Euclidean Space Revisited

In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) in Euclidean and general $\ell_p^d$ spaces. Specifically, we focus on three settings that are still far from well understood: (1) DP-SCO over a constrained and bounded (convex) set in Euclidean space; (2) unconstrained DP-SCO in $\ell_p^d$ space; (3) DP-SCO with heavy-tailed data over a constrained and bounded set in $\ell_p^d$ space. For problem (1), for both convex and strongly convex loss functions, we propose methods whose outputs could achieve (expected) excess population risks that are only dependent on the Gaussian width of the constraint set rather than the dimension of the space. Moreover, we also show the bound for strongly convex functions is optimal up to a logarithmic factor. For problems (2) and (3), we propose several novel algorithms and provide the first theoretical results for both cases when $1<p<2$ and $2\leq p\leq \infty$.

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arXiv2023

Hierarchical Optimal Power Flow with Improved Gradient Evaluation

Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which rested on primal-dual gradients evaluated in a linearized distribution power flow model. Specifically, we identify a risk of voltage violation arising from the model linearization, and propose a more accurate gradient evaluation method to eliminate that risk. We further develop a hierarchical primal-dual algorithm to solve OPF based on the proposed gradient evaluation method. Numerical results on IEEE networks show that our algorithm can enhance voltage safety with satisfactory computational efficiency.

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arXiv2022

An Online Joint Optimization-Estimation Architecture for Distribution Networks

In this paper, we propose an optimal control-estimation architecture for distribution networks, which jointly solves the optimal power flow (OPF) problem and static state estimation (SE) problem through an online gradient-based feedback algorithm. The main objective is to enable a fast and timely interaction between the optimal controllers and state estimators with limited sensor measurements. First, convergence and optimality of the proposed algorithm are analytically established. Then, the proposed gradient-based algorithm is modified by introducing statistical information of the inherent estimation and linearization errors for an improved and robust performance of the online control decisions. Overall, the proposed method eliminates the traditional separation of control and operation, where control and estimation usually operate at distinct layers and different time-scales. Hence, it enables a computationally affordable, efficient and robust online operational framework for distribution networks under time-varying settings.

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arXiv2022

Deep-Learning-Aided Voltage-Stability-Enhancing Stochastic Distribution Network Reconfiguration

Power distribution networks are approaching their voltage stability boundaries due to the severe voltage violations and the inadequate reactive power reserves caused by the increasing renewable generations and dynamic loads. In the broad endeavor to resolve this concern, we focus on enhancing voltage stability through stochastic distribution network reconfiguration (SDNR), which optimizes the (radial) topology of a distribution network under uncertain generations and loads. We propose a deep learning method to solve this computationally challenging problem. Specifically, we build a convolutional neural network model to predict the relevant voltage stability index from the SDNR decisions. Then we integrate this prediction model into successive branch reduction algorithms to reconfigure a radial network with optimized performance in terms of power loss reduction and voltage stability enhancement. Numerical results on two IEEE network models verify the significance of enhancing voltage stability through SDNR and the computational efficiency of the proposed method.

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arXiv2022

An Energy Sharing Mechanism Considering Network Constraints and Market Power Limitation

As the number of prosumers with distributed energy resources (DERs) grows, the conventional centralized operation scheme may suffer from conflicting interests, privacy concerns, and incentive inadequacy. In this paper, we propose an energy sharing mechanism to address the above challenges. It takes into account network constraints and fairness among prosumers. In the proposed energy sharing market, all prosumers play a generalized Nash game. The market equilibrium is proved to have nice features in a large market or when it is a variational equilibrium. To deal with the possible market failure, inefficiency, or instability in general cases, we introduce a price regulation policy to avoid market power exploitation. The improved energy sharing mechanism with price regulation can guarantee existence and uniqueness of a socially near-optimal market equilibrium. Some advantageous properties are proved, such as prosumer's individual rationality, a sharing price structure similar to the locational marginal price, and the tendency towards social optimum with an increasing number of prosumers. For implementation, a practical bidding algorithm is developed with convergence condition. Experimental results validate the theoretical outcomes and show the practicability of our model and method.

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arXiv2022

Improved Successive Branch Reduction for Stochastic Distribution Network Reconfiguration

We propose an improved successive branch reduction (SBR) method to solve stochastic distribution network reconfiguration (SDNR), a mixed-integer program that is known to be computationally challenging. First, for a special distribution network with a single redundant branch, we propose an improved design for a one-stage SBR algorithm in the literature to incorporate uncertain renewable generations and loads. Based on solving stochastic optimal power flow, the improved algorithm identifies and searches through a small set of candidate branches, from which it determines the optimal branch to open and obtains a radial network with the minimum expected operational cost. Then, for a general network with multiple redundant branches, we design a heuristic two-stage SBR algorithm based on a close-and-open procedure that iteratively runs the proposed one-stage SBR algorithm. Numerical results on the IEEE 33-bus and 123-bus distribution network models verify the proposed method in terms of optimality and computational efficiency.

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arXiv2022

Optimal Power Flow with State Estimation In the Loop for Distribution Networks

We propose a framework for integrating optimal power flow (OPF) with state estimation (SE) in the loop for distribution networks. Our approach combines a primal-dual gradient-based OPF solver with a SE feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on a few appropriate online state measurements and noisy "pseudo-measurements". We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least squares (WLS) estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudo measurement variability and inherent sensor measurement noise.

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arXiv2022

Improved Approximation of Dispatchable Region in Radial Distribution Networks via Dual SOCP

The concept of dispatchable region is useful in quantifying how much renewable generation power the system can handle. In this paper, we aim to provide an improved dispatchable region approximation method in distribution networks. First, based on the nonlinear Dist-Flow model, an optimization problem that minimizes the sum of slack variables is formulated to describe the dispatchable region. The nonconvexity caused by alternating-current (AC) power flow constraints makes it intractable. To deal with this issue, the problem is relaxed to a second-order cone program (SOCP) whose strong dual problem is derived. Then, an SOCP-based projection algorithm is developed to construct a convex polytopic approximation. We prove that the proposed algorithm can generate the accurate SOCP-relaxed dispatchable region under certain conditions. Furthermore, a heuristic method is proposed to approximately remove the regions that make the SOCP relaxation inexact. The final region obtained is the difference of several convex sets and can be nonconvex. Thus, the proposed approach may provide a better approximation of the actually nonconvex dispatchable region than previous work that could construct convex sets only. Numerical results demonstrate that the proposed method can achieve a high accuracy of approximation with simple computation.

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arXiv2022

AC-Feasible Power Transfer Regions of Virtual Power Plants: Characterization and Application

Distributed energy resources (DERs) in distribution networks can be aggregated as a virtual power plant (VPP) for transmission-level operations. A critical challenge for such coordination is the complexity of the AC-feasible power transfer region between a VPP and the transmission system at their point of common coupling. To overcome this challenge, this paper develops a characterization method for such regions. The proposed method constructs linear constraints to inner-approximate the AC-feasible power transfer regions. To guarantee AC-feasibility, the parameters in these constraints are determined by applying the Brouwer fixed point theorem to the second-order Taylor expansion of the nonlinear Dist-Flow equations. Based on the power transfer regions characterized with our method, a transmission-level operation problem with VPP participation is formulated and solved through big-M linearization. The proposed methods are verified by numerical experiments in the IEEE 33-bus and IEEE 136-bus test systems.

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arXiv2021

Cost Functions over Feasible Power Transfer Regions of Virtual Power Plants

A virtual power plant (VPP) facilitates the integration of distributed energy resources (DERs) for the transmission-level operation. A challenge in operating a VPP is to characterize the cost function over its feasible power transfer region under DERs' uncertainties. To address this challenge, a characterization method is presented in this paper for the intraday operation of a VPP based on the concepts of nonanticipativity and robustness to DERs' uncertainties. The characterization stems from designing a second-order cone programming (SOCP) problem, based on which a feasible power transfer region across all time periods is constructed by exploring boundary points at each time period and establishing time coupling constraints. Furthermore, a cost function over the feasible power transfer region is formulated as a convex piecewise surface whose breakpoints are obtained by solving SOCP problems, together with a constant compensation cost from a linear programming problem. Finally, to alleviate the heavy computational burden brought by numerous DERs, an approximation method is presented by identifying the critical DERs whose uncertainties have dominant impacts. The effectiveness of the presented methods is verified by the numerical experiments in a 3-bus system and the IEEE 136-bus system.

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