Abstract This paper presents a robust framework for handling a conic multiobjective linear optimization problem, where the objective and constraint functions are involving affinely parameterized data uncertainties. More precisely, we examine optimality conditions and calculate efficient solutions of the conic robust multiobjective linear problem. We provide necessary and sufficient linear conic criteria for efficiency of the underlying conic robust multiobjective linear program. It is shown that such optimality conditions can be expressed in terms of linear matrix inequalities and second-order conic conditions for a multiobjective semidefinite program and a multiobjective second order conic program, respectively. We show how efficient solutions of the conic robust multiobjective linear problem can be found via its conic programming reformulation problems including semidefinite programming and second-order cone programming problems. Numerical examples are also provided to illustrate that the proposed conic programming reformulation schemes can be employed to find efficient solutions for concrete problems including those arisen from practical applications.

This work addresses the challenge of accurately forecasting electricity prices within the volatile Australian market, especially during extreme conditions. It leverages advanced generative pre-trained Large Language Models (LLMs) to analyze the content of electricity market notices with the goal of identifying the drivers behind extreme price fluctuations. Additionally, this approach employs LLMs for an in-depth time-series analysis of electricity prices, providing Australian electricity company traders with insights to refine their trading strategies. To enhance forecasting accuracy this study adopts the QLoRA method for fine-tuning open access LLMs, enabling the analysis of market notices to generate a time series event dataset. A CNN-LSTM network architecture is designed to process both electricity price data and market notice information, thereby improving forecast precision in periods of extreme price volatility. The proposed decision support framework undergoes simulation and evaluation using data from the Australian electricity market, demonstrating its potential to significantly benefit traders in navigating the complexities of the energy sector.

Abstract In this paper, we consider a polynomial problem with equilibrium constraints in which the constraint functions and the equilibrium constraints involve data uncertainties. Employing a robust optimization approach, we examine the uncertain equilibrium constrained polynomial optimization problem by establishing lower bound approximations and asymptotic convergences of bounded degree diagonally dominant sum-of-squares (DSOS), scaled diagonally dominant sum-of-squares (SDSOS) and sum-of-squares (SOS) polynomial relaxations for the robust equilibrium constrained polynomial optimization problem. We also provide numerical examples to illustrate how the optimal value of a robust equilibrium constrained problem can be calculated by solving associated relaxation problems. Furthermore, an application to electric vehicle charging scheduling problems under uncertain discharging supplies shows that for the lower relaxation degrees, the DSOS, SDSOS and SOS relaxations obtain reasonable charging costs and for the higher relaxation degrees, the SDSOS relaxation scheme has the best performance, making it desirable for practical applications.

Electric vehicles (EVs) often consume large amounts of energy, and uncoordinated charging of many EVs may lead to grid overload, adversely impacting other customers. Electricity distributors require full visibility on the EV distribution to better manage operation planning of their distribution grid. However, they often have incomplete knowledge of EV presence in their network. Identifying EV customers (charging at home) using smart meter data is a nontrivial task for the grid network and energy scheduling. The difficulties include recognizing charging patterns, balancing the number of EV and non-EV customers during modeling, and building an efficient classification model. In this article, we propose a periodic pattern recognition method to extract useful EV charging patterns. Real world smart meter datasets are unbalanced with few EVs and majority of energy customers are those without EVs. We improve Kmedoids evaluated by dynamic time warping to obtain the representative non-EV training samples so that balanced samples over EV and non-EV customers can be obtained. We develop an ensemble classification model (ECM) by taking advantages of multiple classifiers, in which the optimization consists of obtaining the optimal subset of periodic patterns and the optimal parameters in each classifier and the optimal weights for combining classifiers. The superiority of the proposed ECM is demonstrated in comparison to several baseline models.

In this study, a new learning control scheme is designed to investigate the stability of a multilayer supply chain network (SCN) and to further improve the convergence speed of the nodes’ states of such a multilayer SCN. Specifically, a multilayer SCN model with three layers is first established and some practical constraints on the states of the proposed SCN model are involved and discussed. By taking the quantities of goods transmitted between different nodes as control inputs, a new kind of learning control scheme is subsequently proposed to discuss the stability of the nodes’ states within the SCN. It is further shown that the convergence speed of nodes’ states with this scheme is faster than that yielded by using some traditional schemes. The contributions of our scheme are twofold: 1) it can save the limited control resource and 2) it can improve the convergence speeds of the states of all nodes. Numerical simulations are finally given to illustrate the effectiveness and advantages of the designed learning scheme.

In this study, the stability of a hierarchical network with delayed output is discussed by applying a kind of optimal periodic control. To reduce the number of the nodes of the original hierarchical network, an aggregation algorithm is first presented to take some nodes with the same information as an aggregated node. Furthermore, the stability of the original hierarchical network can be guaranteed by the optimal periodic control of the aggregated hierarchical network. Then, an optimal control scheme is proposed to reduce the bandwidth waste in information transmission. In the control scheme, the time sequence is separated into two parts: the deterministic segment and the dynamic segment. With the optimal control scheme, two targets are achieved: 1) the outputs of the original and aggregated hierarchical system are both asymptotically stable and 2) the nodes with slow convergent rate can catch up with the convergence speeds of other nodes.

An increasing number of electric vehicles (EVs) make transition energy request from gasoline to electricity possible. As a result, the EVs play a new major role in the smart grid system. Along with the rapid development of energy storage technology, the battery stations constructued for EVs can also provide power to many other applications at lower cost, compared with the power generator, in peak load hours. To achieve such a goal, an efficient collaboration among EVs and battery stations is a new challenge. In this paper, the features of EV charging and battery charging/discharging problems are formulated using a bilevel programming model. The objective is to minimize the EV charging cost, with the maximal battery station operation revenue. The simulation shows the rescheduled charging activities can shift to avoid peak load while the peak load can be shaved by battery discharging.

Demand response (DR) can provide a cost-effect approach for reducing peak loads while renewable energy sources (RES) can result in an environmental-friendly solution for solving the problem of power shortage. The increasingly integration of DR and renewable energy bring challenging issues for energy policy makers, and electricity market regulators in the main power grid. In this paper, a new two-stage stochastic game model is introduced to operate the electricity market, where Stochastic Stackelberg-Cournot-Nash (SSCN) equilibrium is applied to characterize the optimal energy bidding strategy of the forward market and the optimal energy trading strategy of the spot market. To obtain a SSCN equilibrium, sampling average approximation (SAA) technique is harnessed to address the stochastic game model in a distributed way. By this game model, the participation ratio of demand response can be significantly increased while the unreliability of power system caused by renewable energy resources can be considerably reduced. The effectiveness of proposed model is illustrated by extensive simulations.

There has been a desirable trend in recent years towards Electric Vehicles (EVs) contributing less air pollution and noise pollution than internal combustion engine vehicle. EV charging/discharging problem brings a new challenge to the power operation and control. In this paper, the charging/discharging problem is modelled by noncooperative game theory, the payoff function of this model not only maximizes the revenue of discharging activity, but also minimizes overall generation cost by decreasing electricity price on peak hours. The result of simulation illustrates that charging behaviors can shift the charging demand from peak hours to off-peak hours, while discharging behaviors can shave the peak loads in the parking periods.

It has been estimated that the cumulative sales of Electric Vehicles (EVs) will be up to 5.9 million and the stock of EVs will be up to 20 million by 2020 [1]. As the number of EVs is expanding, there is a growing need for widely distributed, publicly accessible, EV charging facilities. The public EV Chargers (EVCs) are expected to be found and will be needed where there is on-street parking, at taxi stands, in parking lots at places of employment, hotels, airports, shopping centres, convenience shops, fast food restaurants, and coffee houses, etc. In this work, we aim to optimize the distribution of public EVCs across the city such that (i) the overall revenue generated by the EVCs is maximized, subject to (ii) the overall driver discomfort (e.g., queueing time) for EV charging is minimized. This is the first study on EVC distribution where EVCs are assumed to be installed in almost all regions across a city. The problem is formulated using a bilevel optimization model. We propose an alternating framework to solve it and have proved that a local minima is achievable. Moreover, this work introduces novel methods to extract information to understand the discomfort of petroleum car drivers, EV charging demands, parking time and parking fees across the city. The source data explored include the trajectories of taxis, the distribution of petroleum stations and various local features. The empirical study uses the real data sets from Shenzhen City, one of the largest cities in China. The extensive tests verify the superiority of the proposed bilevel optimization model in all aspects.