arXiv subjects

Chin-Yao Chang

Publications and source records attributed to Chin-Yao Chang.

17 recordsLinked to original sources

arXiv2024

Adaptive Online Model Update Algorithm for Predictive Control in Networked Systems

In this article, we introduce an adaptive online model update algorithm designed for predictive control applications in networked systems, particularly focusing on power distribution systems. Unlike traditional methods that depend on historical data for offline model identification, our approach utilizes real-time data for continuous model updates. This method integrates seamlessly with existing online control and optimization algorithms and provides timely updates in response to real-time changes. This methodology offers significant advantages, including a reduction in the communication network bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt after disturbances. Furthermore, our algorithm is tailored for non-linear convex models, enhancing its applicability to practical scenarios. The efficacy of the proposed method is validated through a numerical study, demonstrating improved control performance using a synthetic IEEE test case.

eess.SY↗

arXiv2023

A Privacy Preserving Distributed Model Identification Algorithm for Power Distribution Systems

Distributed control/optimization is a promising approach for network systems due to its advantages over centralized schemes, such as robustness, cost-effectiveness, and improved privacy. However, distributed methods can have drawbacks, such as slower convergence rates due to limited knowledge of the overall network model. Additionally, ensuring privacy in the communication of sensitive information can pose implementation challenges. To address this issue, we propose a distributed model identification algorithm that enables each agent to identify the sub-model that characterizes the relationship between its local control and the overall system outputs. The proposed algorithm maintains the privacy of local agents by only communicating through dummy variables. We demonstrate the efficacy of our algorithm in the context of power distribution systems by applying it to the voltage regulation of a modified IEEE distribution system. The proposed algorithm is well-suited to the needs of power distribution controls and offers an effective solution to the challenges of distributed model identification in network systems.

eess.SY↗

arXiv2023

Robust Data-Driven Control for Systems with Noisy Data

This paper presents a robust data-driven controller design based on the noisy input-output data without assumptions on the statistical properties of the noises. We start with the direct data-representation of system models that take elements from behavioral system theory, followed by analyses of the upper bound of the "modeling" error with the data representation with presence of noises. Some pre-conditioning methods are put into the context based on how the derived bound is structured. We lastly leverage the upper bound to develop robust controllers that ride through the data noises.

math.OC↗

arXiv2022

Zero-Knowledge Proof-Based Approach for Verifying the Computational Integrity of Power Grid Controls

The control of future power grids is migrating from a centralized to a distributed/decentralized scheme to enable a massive penetration of distributed energy resources and bring extreme enhancements of autonomous operations in terms of grid resilience, security, and reliability. Most effort has been on the design of distributed/decentralized controllers; however, the guarantees of the proper execution of the controls are also essential but relatively less emphasized. A common assumption is that local controllers would fully follow the designated controller dynamics based on the data received from communication channels. Such an assumption could be risky because proper execution of the controller dynamics is then built on trust in secure communication and computation. On the other hand, it is impractical for a verifier to repeat all the computations involved in the controls to verify the computational integrity. In this work, we leverage a type of cryptography technology, known as zero-knowledge scalable transparent arguments of knowledge to verify the computational integrity of control algorithms, such that verifiers can check the computational integrity with much less computational burden. The method presented here converts the challenge of data integrity into a subset of computational integrity. In this proof-of-concept paper, our focus will be on projected linear dynamics that are commonly seen in distributed/decentralized power system controllers. In particular, we have derived polynomial conditions in the context of zk-STARKs for the projected linear dynamics.

math.OC↗

arXiv2022

On Hybrid Quantum and Classical Computing Algorithms for Mixed-Integer Programming

Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to solve unconstrained binary programming problems, while mixed-integer linear programming is of most interest in practice. We attempt to bridge the gap between the capability of quantum computing and real-world applications by developing a new approach for mixed-integer programming. The approach applies Benders decomposition to decompose the mixed-integer programming into binary programming and linear programming sub-problems, which are solved by a noisy intermediate-scale quantum processor and conventional processor, respectively. The algorithm is provably able to reach the optimal solution of the original mixed-integer programming problem. The algorithm is tested on a D-Wave 2000Q quantum processing unit and is shown to be effective for small-scaled test cases. We also test the algorithm on a mixed-integer programming inspired by power system applications. Many insights are drawn from the numerical results for both the capabilities and limitations of the proposed algorithm.

math.OC↗

arXiv2021

Enabling DER Participation in Frequency Regulation Markets

Distributed energy resources (DERs) are playing an increasing role in ancillary services for the bulk grid, particularly in frequency regulation. In this paper, we propose a framework for collections of DERs, combined to form microgrids and controlled by aggregators, to participate in frequency regulation markets. Our approach covers both the identification of bids for the market clearing stage and the mechanisms for the real-time allocation of the regulation signal. The proposed framework is hierarchical, consisting of a top layer and a bottom layer. The top layer consists of the aggregators communicating in a distributed fashion to optimally disaggregate the regulation signal requested by the system operator. The bottom layer consists of the DERs inside each microgrid whose power levels are adjusted so that the tie line power matches the output of the corresponding aggregator in the top layer. The coordination at the top layer requires the knowledge of cost functions, ramp rates and capacity bounds of the aggregators. We develop meaningful abstractions for these quantities respecting the power flow constraints and taking into account the load uncertainties, and propose a provably correct distributed algorithm for optimal disaggregation of regulation signal amongst the microgrids.

eess.SY↗

arXiv2020

Economic Dispatch With Distributed Energy Resources: Co-Optimization of Transmission and Distribution Systems

The increasing penetration of distributed energy resources (DERs) in the distribution networks has turned the conventionally passive load buses into active buses that can provide grid services for the transmission system. To take advantage of the DERs in the distribution networks, this letter formulates a transmission-and-distribution (T&D) systems co-optimization problem that achieves economic dispatch at the transmission level and optimal voltage regulation at the distribution level by leveraging large generators and DERs. A primal-dual gradient algorithm is proposed to solve this optimization problem jointly for T&D systems, and a distributed market-based equivalent of the gradient algorithm is used for practical implementation. The results are corroborated by numerical examples with the IEEE 39-Bus system connected with 7 different distribution networks.

math.OC↗

arXiv2020

Online Data-Enabled Predictive Control

We develop an online data-enabled predictive (ODeePC) control method for optimal control of unknown systems, building on the recently proposed DeePC [1]. Our proposed ODeePC method leverages a primal-dual algorithm with real-time measurement feedback to iteratively compute the corresponding real-time optimal control policy as system conditions change. The proposed ODeePC conceptual-wise resembles standard adaptive system identification and model predictive control (MPC), but it provides a new alternative for the standard methods. ODeePC is enabled by computationally efficient methods that exploit the special structure of the Hankel matrices in the context of DeePC with Fast Fourier Transform (FFT) and primal-dual algorithm. We provide theoretical guarantees regarding the asymptotic behavior of ODeePC, and we demonstrate its performance through numerical examples.

math.OC↗

arXiv2020

On the Computational Viability of Quantum Optimization for PMU Placement

Using optimal phasor measurement unit placement as a prototypical problem, we assess the computational viability of the current generation D-Wave Systems 2000Q quantum annealer for power systems design problems. We reformulate minimum dominating set for the annealer hardware, solve the reformulation for a standard set of IEEE test systems, and benchmark solution quality and time to solution against the CPLEX Optimizer and simulated annealing. For some problem instances the 2000Q outpaces CPLEX. For instances where the 2000Q underperforms with respect to CPLEX and simulated annealing, we suggest hardware improvements for the next generation of quantum annealers.

quant-ph↗

arXiv2019

Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel Distributed-Approx Newton algorithms that approximate the standard Newton optimization method. We first develop the notion of an optimal edge weighting for the communication graph over which agents implement the second-order algorithm, and propose a convex approximation for the nonconvex weight design problem. We next build on the optimal weight design to develop a discrete Distributed Approx-Newton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full box-constrained problem, we develop a continuous Distributed Approx-Newton algorithm which is inspired by first-order saddle-point methods and rigorously prove its convergence to the primal and dual optimizers. A main property of each of these distributed algorithms is that they only require agents to exchange constant-size communication messages, which lends itself to scalable implementations. Simulations demonstrate that the Distributed Approx-Newton algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods.

math.OC↗

arXiv2018

Virtual-Voltage Partition-Based Approach to Optimal Transmission Switching

This paper deals with optimal transmission switching (OTS) problems involving discrete binary decisions about network topology and non-convex power flow constraints. We adopt a semidefinite programming formulation for the OPF problem which, however, remains nonconvex due to the presence of discrete variables and bilinear products between the decision variables. To tackle the latter, we introduce a novel physically-inspired, virtual-voltage approximation that leads to provable lower and upper bounds on the solution of the original problem. To deal with the exponential complexity caused by the discrete variables, we introduce a graph partition-based algorithm which breaks the problem into several parallel mixed-integer subproblems of smaller size. Simulations demonstrate the high degree of accuracy and affordable computational requirements of our approach.

math.OC↗

arXiv2018

Low Complexity Distributed SDP Approach for General OPF Problems with Reactive Power Cost

Optimal power flow (OPF) problem is a class of large-scale and non-convex optimization problem. Various algorithms are proposed to solve the challenging OPF problem. Recent studies show that semidefinite programming (SDP) can either provide an exact or near global optima for many existing OPF problems. However, SDP-based approaches usually have the complexity growing exponentially with respect to the network size, which may not be suitable for large-scale OPF problem. In this paper, we rewrite the OPF problem as a combination of several non-convex subproblems. We then consider SDP convex relaxation on the subproblems instead of the relaxation on the centralized formulation commonly found in the literature. The formulation leads to new conditions of exact SDP convex relaxation that generalize some existing results. Based on the distributed formulation, we also develop algorithms to find a near global optimum for general OPF problems. A bound on the difference between the near global solution and the optimum is also established. An important feature of the proposed SDP algorithms is that the complexity only grows approximately linearly with respect to the network size. Numerical studies further demonstrate that the computational time of the proposed algorithms need noticeable shorter time than the existing SDP-based OPF solvers.

math.OC↗

arXiv2017

Maximizing Algebraic Connectivity of Constrained Graphs in Adversarial Environments

This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design problem of adding edges to an initial graph, which introduces a nonconvex binary decision variable, in addition to subjugation to general convex constraints on the feasible edge set. Unlike previous methods, our method is justifiably not greedy and capable of accommodating these additional constraints. We also study a scenario in which a coordinator must selectively protect edges of the network from a chance of failure due to a physical disturbance or adversarial attack. The coordinator needs to strategically respond to the adversary's action without presupposed knowledge of the adversary's feasible attack actions. We propose three heuristic algorithms for the coordinator to accomplish the objective and identify worst-case preventive solutions. Each algorithm is shown to be effective in simulation and we provide some discussion on their compared performance.

math.OC↗

arXiv2017

Scheduled-Asynchronous Distributed Algorithm for Optimal Power Flow

Optimal power flow (OPF) problems are non-convex and large-scale optimization problems with important applications in power networks. This paper proposes the scheduled-asynchronous algorithm to solve a distributed semidefinite programming (SDP) formulation of the OPF problem. In this formulation, every agent seeks to solve a local optimization with its own cost function, physical constraints on its nodal power injection, voltage, and power flow of the lines it is connected to, and decision constraints on variables shared with neighbors to ensure consistency of the obtained solution. In the scheduled-asynchronous algorithm, every pair of connected nodes in the electrical network update their local variables in an alternating fashion. This strategy is asynchronous, in the sense that no clock synchronization is required, and relies on an orientation of the electrical network that prescribes the precise ordering of node updates. We establish the asymptotic convergence properties to the primal-dual optimizer when the orientation is acyclic. Given the dependence of the convergence rate on the network orientation, we also develop a distributed graph coloring algorithm that finds an orientation with diameter at most five for electrical networks with geometric degree distribution. Simulations illustrate our results on various IEEE bus test cases.

math.OC↗

arXiv2017

Weight Design of Distributed Approximate Newton Algorithms for Constrained Optimization

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a novel Distributed Approx-Newton algorithm that approximates the standard Newton optimization method. A main property of this distributed algorithm is that it only requires agents to exchange constant-size communication messages. The convergence of this algorithm is discussed and rigorously analyzed. In addition, we aim to address the problem of designing communication topologies and weightings that are optimal for second-order methods. To this end, we propose an effective approximation which is loosely based on completing the square to address the NP-hard bilinear optimization involved in the design. Simulations demonstrate that our proposed weight design applied to the Distributed Approx-Newton algorithm has a superior convergence property compared to existing weighted and distributed first-order gradient descent methods.

math.NA↗

arXiv2016

On Resilience Analysis and Quantification for Wide-Area Control of Power Systems

Wide-area control is an effective mean to reduce inter-area oscillations of large power systems. Its dependence on communication of remote measurement signals makes the closed-loop system vulnerable to cyber attacks. This paper develops a framework to analyze and quantify resilience of a given wide-area controller under disruptive attacks on certain communication links. Resilience of a given controller is measured in terms of closed-loop eigenvalues under the worst possible attack strategy. The computation of such a resilience index is challenging especially for large-scale power systems due to the discrete nature of the attack strategies. To address the challenge, we propose an optimization-based formulation and a convex relaxation approach to facilitate the computation. Conditions under which the relaxation is exact are derived and an efficient algorithm with guaranteed convergence is also developed. The proposed framework and the algorithm allow us to quantify resilience for given wide-area controllers and also provide sufficient conditions to guarantee closed-loop stability under all possible communication attacks. Simulations are performed on the IEEE 39-bus system to illustrate the proposed resilience analysis and computation framework.

math.OC↗

arXiv2015

Distributed Control of Inverter-Based Lossy Microgrids for Power Sharing and Frequency Regulation Under Voltage Constraints

This paper presents a new distributed control framework to coordinate inverter-interfaced distributed energy resources (DERs) in island microgrids. We show that under bounded load uncertainties, the proposed control method can steer the microgrid to a desired steady state with synchronized inverter frequency across the network and proportional sharing of both active and reactive powers among the inverters. We also show that such convergence can be achieved while respecting constraints on voltage magnitude and branch angle differences. The controller is robust under various contingency scenarios, including loss of communication links and failures of DERs. The proposed controller is applicable to lossy mesh microgrids with heterogeneous R/X distribution lines and reasonable parameter variations. Simulations based on various microgrid operation scenarios are also provided to show the effectiveness of the proposed control method.

math.OC↗