pwc-archive/papers-with-abstracts huggingface dataset:
On Finding the Leader's Strategy in Quadratic Aggregative Stackelberg Pricing Games
Authors: Marko Maljkovic, Gustav Nilsson, Nikolas Geroliminis
Date: 2023-04-23 00:00:00

This paper analyzes a class of Stackelberg games where different actors compete for shared resources and a central authority tries to balance the demand through a pricing mechanism. Situations like this can for instance occur when fleet owners of electric taxi services compete about charging spots. In this paper, we model the competition between the followers as an aggregative game, i.e., each player's decision only depends on the aggregate strategy of the others. While it has previously been shown that there exist dynamic pricing strategies to achieve the central authority's objective, we in this paper present a method to compute optimal static prices. Proof of convergence of the method is presented, together with a numerical study showcasing the benefits and the speed of convergence of the proposed method.
Robust Short-term Operation of AC Power Network with Injection Uncertainties
Authors: Anamika Tiwari, Abheejeet Mohapatra, Soumya Ranjan Sahoo
Date: 2023-04-23 00:00:00

With uncertain injections from Renewable Energy Sources (RESs) and loads, deterministic AC Optimal Power Flow (OPF) often fails to provide optimal setpoints of conventional generators. A computationally time-efficient, economical, and robust solution is essential for ACOPF with short-term injection uncertainties. Usually, applying Robust Optimization (RO) for conventional non-linear ACOPF results in computationally intractable Robust Counterpart (RC), which is undesirable as ACOPF is an operational problem. Hence, this paper proposes a single-stage non-integer non-recursive RC of ACOPF, using a dual transformation, for short-term injection uncertainties. The proposed RC is convex, tractable, and provides base-point active power generations and terminal voltage magnitudes (setpoints) of conventional generators that satisfy all constraints for all realizations of defined injection uncertainties. The non-linear impact of uncertainties on other variables is inherently modeled without using any affine policy. The proposed approach also includes the budget of uncertainty constraints for low conservatism of the obtained setpoints. Monte-Carlo Simulation (MCS) based participation factored AC power flows validate the robustness of the obtained setpoints on NESTA and case9241pegase systems for different injection uncertainties. Comparison with previous approaches indicates the efficacy of the proposed approach in terms of low operational cost and computation time.
A Wideband Reconfigurable Intelligent Surface for 5G Millimeter-Wave Applications
Authors: Ruiqi Wang, Yiming Yang, Behrooz Makki, Atif Shamim
Date: 2023-04-23 00:00:00

Despite the growing interest in reconfigurable intelligent surfaces (RISs) for millimeter-wave (mm-wave) bands, and the considerable theoretical work reported by the communication community, there is a limited number of published works demonstrating practical implementations and experimental results. To the authors' knowledge, no published literature has reported experimental results for RISs covering the n257 and n258 mm-wave bands. In this work, we propose a novel wideband RIS design that covers the entire mm-wave 5G n257 and n258 bands. In simulations, the unit cell can maintain a phase difference of 180{\deg} +- 20{\deg} and a reflection magnitude greater than -2.8 dB within 22.7 to 30.5 GHz (29.3% bandwidth) using one-bit PIN switches. The proposed unit cell design with four circular cutouts and long vias could realize wideband performance by exciting two adjacent high-order resonances (2.5f and 3.5f). The periodic unit cells can maintain an angular stability of 30{\deg}. Based on the proposed unit cell, a 20 by 20 RIS array is designed and fabricated with a size of 7.1{\lambda} by 7.1{\lambda}. The measurement results demonstrate that the proposed RIS could maintain a 3 dB peak gain variation bandwidth among various array configurations within 22.5 to 29.5 GHz (26.9%) and with a beam scanning capability of 50{\deg}, making this design a good candidate for 5G mm-wave applications.
Provable Reach-avoid Controllers Synthesis Based on Inner-approximating Controlled Reach-avoid Sets
Authors: Jianqiang Ding, Taoran Wu, Yuping Qian, Lijun Zhang, Bai Xue
Date: 2023-04-23 00:00:00

In this paper, we propose an approach for synthesizing provable reach-avoid controllers, which drive a deterministic system operating in an unknown environment to safely reach a desired target set. The approach falls within the reachability analysis framework and is based on the computation of inner-approximations of controlled reach-avoid sets(CRSs). Given a target set and a safe set, the controlled reach-avoid set is the set of states such that starting from each of them, there exists at least one controller to ensure that the system can enter the target set while staying inside the safe set before the target hitting time. Therefore, the boundary of the controlled reach-avoid set acts as a barrier, which separating states capable of achieving the reach-avoid objective from those that are not, and thus the computed inner-approximation provides a viable space for the system to achieve the reach-avoid objective. Our approach for synthesizing reach-avoid controllers mainly consists of three steps. We first learn a safe set of states in the unknown environment from sensor measurements based on a support vector machine approach. Then, based on the learned safe set and target set, we compute an inner-approximation of the CRS. Finally, we synthesize controllers online to ensure that the system will reach the target set by evolving inside the computed inner-approximation. The proposed method is demonstrated on a Dubin's car system.
Preliminary results on the herdability of complex multiagent systems via local information
Authors: Andrea Lama, Mario di Bernardo
Date: 2023-04-22 00:00:00

We present preliminary results on the problem of driving the dynamics of a group of agents, the herders, so as to steer the collective behaviour of another group of agents, the targets, interacting with them. We define this problem as the multiagent herding control problem and study the herdability of the target agents by relaxing some strong assumptions often made in the existing literature, namely that targets are cohesive in the absence of herders and that herders possess global information. We find that scaling laws exist linking crucial parameters such as the herders' sensing radius and the targets density with the herdability of the system. Our most surprising observation, supported by exhaustive numerical experiments, is that the crucial effect of limited sensing is that the minimum number of herders required to solve the problem significantly increases below a critical minimum density of the target agents.
AC Power Flow Feasibility Restoration via a State Estimation-Based Post-Processing Algorithm
Authors: Babak Taheri, Daniel K. Molzahn
Date: 2023-04-22 00:00:00
Tasks: State Estimation

This paper presents an algorithm for restoring AC power flow feasibility from solutions to simplified optimal power flow (OPF) problems, including convex relaxations, power flow approximations, and machine learning (ML) models. The proposed algorithm employs a state estimation-based post-processing technique in which voltage phasors, power injections, and line flows from solutions to relaxed, approximated, or ML-based OPF problems are treated similarly to noisy measurements in a state estimation algorithm. The algorithm leverages information from various quantities to obtain feasible voltage phasors and power injections that satisfy the AC power flow equations. Weight and bias parameters are computed offline using an adaptive stochastic gradient descent method. By automatically learning the trustworthiness of various outputs from simplified OPF problems, these parameters inform the online computations of the state estimation-based algorithm to both recover feasible solutions and characterize the performance of power flow approximations, relaxations, and ML models. Furthermore, the proposed algorithm can simultaneously utilize combined solutions from different relaxations, approximations, and ML models to enhance performance. Case studies demonstrate the effectiveness and scalability of the proposed algorithm, with solutions that are both AC power flow feasible and much closer to the true AC OPF solutions than alternative methods, often by several orders of magnitude in the squared two-norm loss function.
Transition System Representation of Boolean Control Networks
Authors: Daizhan Cheng, Xiao Zhang, Zhengping Ji
Date: 2023-04-22 00:00:00

First, the topological structure of a transition system is studied. Then, two types of transition system (TS) representations of Boolean networks (BNs) and Boolean control networks (BCNs) are investigated. The first kind of representation is state-based, which converts a BCN into a TS with either distinct control or non-distinct control. The second representation is output-based, which is also called the simulation of the original BCN. Some applications are also studied.
Optimal Vehicle Charging in Bilevel Power-Traffic Networks via Charging Demand Function
Authors: Yufan Zhang, Sujit Dey, Yuanyuan Shi
Date: 2023-04-22 00:00:00
Tasks: Decision Making

Electric vehicle (EV) charging couples the operation of power and traffic networks. Specifically, the power network determines the charging price at various locations, while EVs on the traffic network optimize the charging power given the price, acting as price-takers. We model such decision-making processes by a bilevel program, with the power network at the upper-level and the traffic network at the lower-level. However, since the two networks are managed by separate entities and the charging expense term, calculated as the product of charging price and charging demand, is nonlinear. Solving the bilevel program is nontrivial. To overcome these challenges, we derive the charging demand function using multiparametric programming theory. This function establishes a piecewise linear relationship between the charging price and the optimal charging power, enabling the power network operator to manage EV charging power independently while accounting for the coupling between the two networks. With the derived function, we are also able to replace the nonlinear charging expense term with a piecewise quadratic one, thus guaranteeing solution optimality. Our numerical studies demonstrate that different traffic demands can have an impact on charging patterns and the power network can effectively incentivize charging at low-price nodes through price setting.
Bilevel optimisation with embedded neural networks: Application to scheduling and control integration
Authors: Roberto X. Jiménez J
Date: 2023-04-21 00:00:00
Tasks: Scheduling

Scheduling problems requires to explicitly account for control considerations in their optimisation. The literature proposes two traditional ways to solve this integrated problem: hierarchical and monolithic. The monolithic approach ignores the control level's objective and incorporates it as a constraint into the upper level at the cost of suboptimality. The hierarchical approach requires solving a mathematically complex bilevel problem with the scheduling acting as the leader and control as the follower. The linking variables between both levels belong to a small subset of scheduling and control decision variables. For this subset of variables, data-driven surrogate models have been used to learn follower responses to different leader decisions. In this work, we propose to use ReLU neural networks for the control level. Consequently, the bilevel problem is collapsed into a single-level MILP that is still able to account for the control level's objective. This single-level MILP reformulation is compared with the monolithic approach and benchmarked against embedding a nonlinear expression of the neural networks into the optimisation. Moreover, a neural network is used to predict control level feasibility. The case studies involve batch reactor and sequential batch process scheduling problems. The proposed methodology finds optimal solutions while largely outperforming both approaches in terms of computational time. Additionally, due to well-developed MILP solvers, adding ReLU neural networks in a MILP form marginally impacts the computational time. The solution's error due to prediction accuracy is correlated with the neural network training error. Overall, we expose how - by using an existing big-M reformulation and being careful about integrating machine learning and optimisation pipelines - we can more efficiently solve the bilevel scheduling-control problem with high accuracy.
A Multi-Fidelity Bayesian Approach to Safe Controller Design
Authors: Ethan Lau, Vaibhav Srivastava, Shaunak D. Bopardikar
Date: 2023-04-21 00:00:00

Safely controlling unknown dynamical systems is one of the biggest challenges in the field of control. Oftentimes, an approximate model of a system's dynamics exists which provides beneficial information for the selection of controls. However, differences between the approximate and true systems present challenges as well as safety concerns. We propose an algorithm called SAFE-SLOPE to safely evaluate points from a Gaussian process model of a function when its Lipschitz constant is unknown. We establish theoretical guarantees for the performance of SAFE-SLOPE and quantify how multi-fidelity modeling improves the algorithm's performance. Finally, we demonstrate how SAFE-SLOPE achieves lower cumulative regret than a naive sampling method by applying it to find the control gains of a linear time-invariant system.
Real-Time Implementation of Dynamic State Estimation for Microgrid Load Bus Protection
Authors: Sarbajit Basu, Arthur K. Barnes, Adam Mate, Olga Lavrova
Date: 2023-04-21 00:00:00
Tasks: parameter estimation, State Estimation

Inverter-interfaced microgrids, owing to the lack of fault current, cannot be protected using traditional over-current protections, while admittance or differential relaying protection schemes are not practical to be implemented. Dynamic state estimation can track and predict power system transients and has been extensively investigated for setting-less protection. A novel real-time application of dynamic state estimation for protection is proposed in this paper, wherein parameter estimation and parallel processing is used to identify the state of the system. The implementation scheme has low process complexity and employs a data acquisition device and estimator that run on a general-purpose computer. This proposed implementation extends the state-of-the-art, under short-circuit conditions, to a real-time implementation with a lumped-load radial microgrid and a grid-forming inverter with current-limiting behavior.
Gradient-Based Distributed Controller Design Over Directed Networks
Authors: Yuto Watanabe, Kazunori Sakurama, Hyo-Sung Ahn
Date: 2023-04-21 00:00:00

In this study, we propose a design methodology of distributed controllers for multi-agent systems on a class of directed interaction networks by extending the gradient-flow method. Although the gradient-flow method is a common design tool for distributed controllers, it is inapplicable to directed networks. First, we demonstrate how to construct a distributed controller for systems over a class of time-invariant directed graphs. Subsequently, we establish better convergence properties and performance enhancement than the conventional gradient-flow method. To illustrate its application in time-varying networks, we address the dynamic matching problem of two distinct groups of agents with different sensing ranges. This problem is a novel coordination task that involves pairing agents from two distinct groups to achieve a convergence of the paired agents' states to the same value. Accordingly, we apply the proposed method to this problem and provide sufficient conditions for successful matching. Lastly, numerical examples for systems on both time-invariant and time-varying networks demonstrate the effectiveness of the proposed method.
Scalable Bilevel Optimization for Generating Maximally Representative OPF Datasets
Authors: Ignasi Ventura Nadal, Samuel Chevalier
Date: 2023-04-21 00:00:00
Tasks: Bilevel Optimization

New generations of power systems, containing high shares of renewable energy resources, require improved data-driven tools which can swiftly adapt to changes in system operation. Many of these tools, such as ones using machine learning, rely on high-quality training datasets to construct probabilistic models. Such models should be able to accurately represent the system when operating at its limits (i.e., operating with a high degree of ``active constraints"). However, generating training datasets that accurately represent the many possible combinations of these active constraints is a particularly challenging task, especially within the realm of nonlinear AC Optimal Power Flow (OPF), since most active constraints cannot be enforced explicitly. Using bilevel optimization, this paper introduces a data collection routine that sequentially solves for OPF solutions which are ``optimally far" from previously acquired voltage, power, and load profile data points. The routine, termed RAMBO, samples critical data close to a system's boundaries much more effectively than a random sampling benchmark. Simulated test results are collected on the 30-, 57-, and 118-bus PGLib test cases.
Protection Against Graph-Based False Data Injection Attacks on Power Systems
Authors: Gal Morgenstern, Jip Kim, James Anderson, Gil Zussman, Tirza Routtenberg
Date: 2023-04-21 00:00:00
Tasks: State Estimation

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. Recent research has focused on developing GSP-based methods for state estimation, attack detection, and topology identification using the representation of the power system voltages as smooth graph signals. Within this framework, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as non-smooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this paper, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation (TV) under practical constraints. We present the GFDI attack as the solution for a non-convex constrained optimization problem. The solution to the GFDI attack problem is obtained through approximating it using $\ell_1$ relaxation. A series of quadratic programming problems that are classified as convex optimization problems are solved to obtain the final solution. We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to a high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 and IEEE-118 bus test cases reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.
Enhancing Wind Power Forecast Precision via Multi-head Attention Transformer: An Investigation on Single-step and Multi-step Forecasting
Authors: Md Rasel Sarkar, Sreenatha G. Anavatti, Tanmoy Dam, Mahardhika Pratama, Berlian Al Kindhi
Date: 2023-04-21 00:00:00
Tasks: Time Series, Time Series Forecasting

The main objective of this study is to propose an enhanced wind power forecasting (EWPF) transformer model for handling power grid operations and boosting power market competition. It helps reliable large-scale integration of wind power relies in large part on accurate wind power forecasting (WPF). The proposed model is evaluated for single-step and multi-step WPF, and compared with gated recurrent unit (GRU) and long short-term memory (LSTM) models on a wind power dataset. The results of the study indicate that the proposed EWPF transformer model outperforms conventional recurrent neural network (RNN) models in terms of time-series forecasting accuracy. In particular, the results reveal a minimum performance improvement of 5% and a maximum of 20% compared to LSTM and GRU. These results indicate that the EWPF transformer model provides a promising alternative for wind power forecasting and has the potential to significantly improve the precision of WPF. The findings of this study have implications for energy producers and researchers in the field of WPF.
Conservative Sparse Neural Network Embedded Frequency-Constrained Unit Commitment With Distributed Energy Resources
Authors: Linwei Sang, Yinliang Xu, Zhongkai Yi, Lun Yang, Huan Long, Hongbin Sun
Date: 2023-04-21 00:00:00

The increasing penetration of distributed energy resources (DERs) will decrease the rotational inertia of the power system and further degrade the system frequency stability. To address the above issues, this paper leverages the advanced neural network (NN) to learn the frequency dynamics and incorporates NN to facilitate system reliable operation. This paper proposes the conservative sparse neural network (CSNN) embedded frequency-constrained unit commitment (FCUC) with converter-based DERs, including the learning and optimization stages. In the learning stage, it samples the inertia parameters, calculates the corresponding frequency, and characterizes the stability region of the sampled parameters using the convex hulls to ensure stability and avoid extrapolation. For conservativeness, the positive prediction error penalty is added to the loss function to prevent possible frequency requirement violation. For the sparsity, the NN topology pruning is employed to eliminate unnecessary connections for solving acceleration. In the optimization stage, the trained CSNN is transformed into mixed-integer linear constraints using the big-M method and then incorporated to establish the data-enhanced model. The case study verifies 1) the effectiveness of the proposed model in terms of high accuracy, fewer parameters, and significant solving acceleration; 2) the stable system operation against frequency violation under contingency.
Linear to multi-linear algebra and systems using tensors
Authors: Divyanshu Pandey, Adithya Venugopal, Harry Leib
Date: 2023-04-20 00:00:00
Tasks: tensor algebra, Tensor Networks

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product, known as the Einstein Product and its properties, many of the known concepts from Linear Algebra could be extended to a multi-linear setting. This enables to define the notions of multi-linear system theory where the input, output signals and the system are multi-domain in nature. This paper provides an overview of tensor algebra tools which can be seen as an extension of linear algebra, at the same time highlighting the difference and advantages that the multi-linear setting brings forth. In particular, the notion of tensor inversion, tensor singular value and tensor Eigenvalue decomposition using the Einstein product is explained. In addition, this paper also introduces the notion of contracted convolution in both discrete and continuous multi-linear system tensors. Tensor Networks representation of various tensor operations is also presented. Also, application of tensor tools in developing transceiver schemes for multi-domain communication systems, with an example of MIMO CDMA systems, is presented. Thus this paper acts as an entry point tutorial for graduate students whose research involves multi-domain or multi-modal signals and systems.