Online Optimization in Power Systems With High Penetration of Renewable Generation:Advances and Prospects

Traditionally,offline optimization of power systems is acceptable due to the largely predictable loads and reliable generation.The increasing penetration of fluctuating renewable generation and internet-of-things devices allowing for fine-grained controllability of loads have led to the diminishing applicability of offline optimization in the power systems domain,and have redirected attention to online optimization methods.However,online optimization is a broad topic that can be applied in and motivated by different settings,operated on different time scales,and built on different theoretical foundations.This paper reviews the various types of online optimization techniques used in the power systems domain and aims to make clear the distinction between the most common techniques used.In particular,we introduce and compare four distinct techniques used covering the breadth of online optimization techniques used in the power systems domain,i.e.,optimization-guided dynamic control,feedback optimization for single-period problems,Lyapunov-based optimization,and online convex optimization techniques for multi-period problems.Lastly,we recommend some potential future directions for online optimization in the power systems domain.

Trajectory online optimization for unmanned combat aerial vehicle using combined strategy

This paper presents a combined strategy to solve the trajectory online optimization problem for unmanned combat aerial vehicle (UCAV). Firstly, as trajectory directly optimizing is quite time costing, an online trajectory functional representation method is proposed. Considering the practical requirement of online trajectory, the 4-order polynomial function is used to represent the trajectory, and which can be determined by two independent parameters with the trajectory terminal conditions; thus, the trajectory online optimization problem is converted into the optimization of the two parameters, which largely lowers the complexity of the optimization problem. Furthermore, the scopes of the two parameters have been assessed into small ranges using the golden section ratio method. Secondly, a multi-population rotation strategy differential evolution approach (MPRDE) is designed to optimize the two parameters; in which, 'current-to-best/1/bin', 'current-to-rand/1/bin' and 'rand/2/bin' strategies with fixed parameter settings are designed, these strategies are rotationally used by three subpopulations. Thirdly, the rolling optimization method is applied to model the online trajectory optimization process. Finally, simulation results demonstrate the efficiency and real-time calculation capability of the designed combined strategy for UCAV trajectory online optimizing under dynamic and complicated environments.

A Scheme Library-Based Ant Colony Optimization with 2-Opt Local Search for Dynamic Traveling Salesman Problem

The dynamic traveling salesman problem(DTSP)is significant in logistics distribution in real-world applications in smart cities,but it is uncertain and difficult to solve.This paper proposes a scheme library-based ant colony optimization(ACO)with a two-optimization(2-opt)strategy to solve the DTSP efficiently.The work is novel and contributes to three aspects:problemmodel,optimization framework,and algorithmdesign.Firstly,in the problem model,traditional DTSP models often consider the change of travel distance between two nodes over time,while this paper focuses on a special DTSP model in that the node locations change dynamically over time.Secondly,in the optimization framework,the ACO algorithm is carried out in an offline optimization and online application framework to efficiently reuse the historical information to help fast respond to the dynamic environment.The framework of offline optimization and online application is proposed due to the fact that the environmental change inDTSPis caused by the change of node location,and therefore the newenvironment is somehowsimilar to certain previous environments.This way,in the offline optimization,the solutions for possible environmental changes are optimized in advance,and are stored in a mode scheme library.In the online application,when an environmental change is detected,the candidate solutions stored in the mode scheme library are reused via ACO to improve search efficiency and reduce computational complexity.Thirdly,in the algorithm design,the ACO cooperates with the 2-opt strategy to enhance search efficiency.To evaluate the performance of ACO with 2-opt,we design two challenging DTSP cases with up to 200 and 1379 nodes and compare them with other ACO and genetic algorithms.The experimental results show that ACO with 2-opt can solve the DTSPs effectively.

Digital Twin Technology of Human-Machine Integration in Cross-Belt Sorting System

The Chinese express delivery industry processes nearly 110 billion items in 2022,averaging an annual growth rate of 200%.Among the various types of sorting systems used for handling express items,cross-belt sorting systems stand out as the most crucial.However,despite their high degree of automation,the workload for operators has intensified owing to the surging volume of express items.In the era of Industry 5.0,it is imperative to adopt new technologies that not only enhance worker welfare but also improve the efficiency of cross-belt systems.Striking a balance between efficiency in handling express items and operator well-being is challenging.Digital twin technology offers a promising solution in this respect.A realization method of a human-machine integrated digital twin is proposed in this study,enabling the interaction of biological human bodies,virtual human bodies,virtual equipment,and logistics equipment in a closed loop,thus setting an operating framework.Key technologies in the proposed framework include a collection of heterogeneous data from multiple sources,construction of the relationship between operator fatigue and operation efficiency based on physiological measurements,virtual model construction,and an online optimization module based on real-time simulation.The feasibility of the proposed method was verified in an express distribution center.

Online distributed optimization with stochastic gradients:high probability bound of regrets

In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a network.To handle this problem,an online distributed stochastic mirror descent algorithm is proposed.Existing works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the regrets.Different from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's inverse.Under mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time horizon.Finally,a simulation is provided to demonstrate the effectiveness of our theoretical results.

Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions

This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.

Zeroth-Order Methods for Online Distributed Optimization with Strongly Pseudoconvex Cost Functions

This paper studies an online distributed optimization problem over multi-agent systems.In this problem,the goal of agents is to cooperatively minimize the sum of locally dynamic cost functions.Different from most existing works on distributed optimization,here we consider the case where the cost function is strongly pseudoconvex and real gradients of objective functions are not available.To handle this problem,an online zeroth-order stochastic optimization algorithm involving the single-point gradient estimator is proposed.Under the algorithm,each agent only has access to the information associated with its own cost function and the estimate of the gradient,and exchange local state information with its immediate neighbors via a time-varying digraph.The performance of the algorithm is measured by the expectation of dynamic regret.Under mild assumptions on graphs,we prove that if the cumulative deviation of minimizer sequence grows within a certain rate,then the expectation of dynamic regret grows sublinearly.Finally,a simulation example is given to illustrate the validity of our results.

Mechanism and optimization of fuel injection parameters on combustion noise of DI diesel engine

Combustion noise takes large proportion in diesel engine noise and the studies of its influence factors play an important role in noise reduction. Engine noise and cylinder pressure measurement experiments were carried out. And the improved attenuation curves were obtained, by which the engine noise was predicted. The effect of fuel injection parameters in combustion noise was investigated during the combustion process. At last, the method combining single variable optimization and multivariate combination was introduced to online optimize the combustion noise. The results show that injection parameters can affect the cylinder pressure rise rate and heat release rate, and consequently affect the cylinder pressure load and pressure oscillation to influence the combustion noise. Among these parameters, main injection advance angle has the greatest influence on the combustion noise, while the pilot injection interval time takes the second place, and the pilot injection quantity is of minimal impact. After the optimal design of the combustion noise, the average sound pressure level of the engine is distinctly reduced by 1.0 d B(A) generally. Meanwhile, the power, emission and economy performances are ensured.

Privacy Preserving Distributed Bandit Residual Feedback Online Optimization Over Time-Varying Unbalanced Graphs

This paper considers the distributed online optimization(DOO) problem over time-varying unbalanced networks, where gradient information is explicitly unknown. To address this issue, a privacy-preserving distributed online one-point residual feedback(OPRF) optimization algorithm is proposed. This algorithm updates decision variables by leveraging one-point residual feedback to estimate the true gradient information. It can achieve the same performance as the two-point feedback scheme while only requiring a single function value query per iteration. Additionally, it effectively eliminates the effect of time-varying unbalanced graphs by dynamically constructing row stochastic matrices. Furthermore, compared to other distributed optimization algorithms that only consider explicitly unknown cost functions, this paper also addresses the issue of privacy information leakage of nodes. Theoretical analysis demonstrate that the method attains sublinear regret while protecting the privacy information of agents. Finally, numerical experiments on distributed collaborative localization problem and federated learning confirm the effectiveness of the algorithm.

Online optimization for optical readout of a single electron spin in diamond

The nitrogen-vacancy(NV)center in diamond has been developed as a promising platform for quantum sensing,especially for magnetic field measurements in the nano-tesla range with a nano-meter resolution.Optical spin readout performance has a direct effect on the signal-to-noise ratio(SNR)of experiments.In this work,we introduce an online optimization method to customize the laser waveform for readout.Both simulations and experiments reveal that our new scheme optimizes the optically detected magnetic resonance in NV center.The SNR of optical spin readout has been witnessed a 44.1%increase in experiments.In addition,we applied the scheme to the Rabi oscillation experiment,which shows an improvement of 46.0%in contrast and a reduction of 12.1%in mean deviation compared to traditional constant laser power SNR optimization.This scheme is promising to improve sensitivities for a wide range of NV-based applications in the future.

Distributed regularized online optimization using forward-backward splitting

This paper considers the problem of distributed online regularized optimization over a network that consists of multiple interacting nodes.Each node is endowed with a sequence of loss functions that are time-varying and a regularization function that is fixed over time.A distributed forward-backward splitting algorithm is proposed for solving this problem and both fixed and adaptive learning rates are adopted.For both cases,we show that the regret upper bounds scale as O(VT),where T is the time horizon.In particular,those rates match the centralized counterpart.Finally,we show the effectiveness of the proposed algorithms over an online distributed regularized linear regression problem.

Boosting for Distributed Online Convex Optimization

Decentralized Online Learning(DOL)extends online learning to the domain of distributed networks.However,limitations of local data in decentralized settings lead to a decrease in the accuracy of decisions or models compared to centralized methods.Considering the increasing requirement to achieve a high-precision model or decision with distributed data resources in a network,applying ensemble methods is attempted to achieve a superior model or decision with only transferring gradients or models.A new boosting method,namely Boosting for Distributed Online Convex Optimization(BD-OCO),is designed to realize the application of boosting in distributed scenarios.BD-OCO achieves the regret upper bound O(M+N/MNT)where M measures the size of the distributed network and N is the number of Weak Learners(WLs)in each node.The core idea of BD-OCO is to apply the local model to train a strong global one.BD-OCO is evaluated on the basis of eight different real-world datasets.Numerical results show that BD-OCO achieves excellent performance in accuracy and convergence,and is robust to the size of the distributed network.

A new two-axis solar tracker based on the online optimization method:Experimental investigation and neural network modeling

This article presents a new two-axis solar tracker based on an online optimization algorithm so as to track the position of the sun without using its movement model.In this research,four well-known optimization algorithms are employed to find the two unknown parameters named azimuth and zenith angles,which determine the position of the sun.The magnitude of the sunray is considered as the cost function of all algorithms.Then,several experiments are carried out to find the best optimization algorithm with optimal population size,number of iterations,and also the best initialization method.Uniform initialization leads to faster convergence compared to random initialization.The results clearly show that the particle swarm optimization algorithm with a population size of 15 and 7 iterations using uniform initialization method has better performance than the other algorithms,with a convergence time of less than 40 s.The average fitness value or voltage received by the tracker is 2.4 Volts in this method,which is higher than other methods.TLBO also performs well with a population size of 15 and 7 iterations.Afterward,the artificial neural network with one hidden layer and 20 neurons is employed to predict these two parameters in each day and moment in a year in Shiraz city according to the experimental data extracted from PSO.Number of the day from January and the time are inputs and zenith and azimuth angles are considered the output of neural network modeling.The performance of the proposed ANN model is evaluated using regression plots,demonstrating a strong correlation between predicted and target outputs.Finally,the outcomes reveal the feasibility of using online optimization algorithms and neural network modeling in an effort to bypass the complex mathematical model of mechatronic systems and predict the movement of the sun automatically.

Experimental Tests of Autonomous Ground Vehicles with Preview

This paper describes the design and experimental tests of a path planning and reference tracking algorithm for autonomous ground vehicles. The ground vehicles under consideration are equipped with forward looking sensors that provide a preview capability over a certain horizon. A two-level control framework is proposed for real-time implementation of the model predictive control （MPC） algorithm, where the high-level performs on-line optimization to generate the best possible local reference respect to various constraints and the low-level commands the vehicle to follow realistic trajectories generated by the high-level controller. The proposed control scheme is implemented on an indoor testbed through networks with satisfactory performance.

Online optimal control of nonlinear discrete-time systems using approximate dynamic programming

In this paper,the optimal control of a class of general affine nonlinear discrete-time(DT) systems is undertaken by solving the Hamilton Jacobi-Bellman(HJB) equation online and forward in time.The proposed approach,referred normally as adaptive or approximate dynamic programming(ADP),uses online approximators(OLAs) to solve the infinite horizon optimal regulation and tracking control problems for affine nonlinear DT systems in the presence of unknown internal dynamics.Both the regulation and tracking controllers are designed using OLAs to obtain the optimal feedback control signal and its associated cost function.Additionally,the tracking controller design entails a feedforward portion that is derived and approximated using an additional OLA for steady state conditions.Novel update laws for tuning the unknown parameters of the OLAs online are derived.Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signals approach the optimal control inputs with small bounded error.In the absence of OLA reconstruction errors,an optimal control is demonstrated.Simulation results verify that all OLA parameter estimates remain bounded,and the proposed OLA-based optimal control scheme tunes itself to reduce the cost HJB equation.

Online calibration of combustion phase in a diesel engine

In this work, an online calibration mechanism is proposed for the combustion phase in a diesel engine. In particular, a simplified event-based engine model, of which the output predicts the optimum combustion phase, is used to aid the calibration, and the model is updated online along with the engine operation to keep the integrity high so as to improve the quality of optimum combustion phase prediction. It is found this mechanism can be applied to develop an online automated calibration process when the engine system shifts to a new operating point. of the proposed mechanism. Engine test results are included to demonstrate the effectiveness

Online distributed tracking of generalized Nash equilibrium on physical networks——Closing the Loop via Measurement Feedback

In generalized Nash equilibrium(GNE)seeking problems over physical networks such as power grids,the enforcement of network constraints and time-varying environment may bring high computational costs.Developing online algorithms is recognized as a promising method to cope with this challenge,where the task of computing system states is replaced by directly using measured values from the physical network.In this paper,we propose an online distributed algorithm via measurement feedback to track the GNE in a time-varying networked resource sharing market.Regarding that some system states are not measurable and measurement noise always exists,a dynamic state estimator is incorporated based on a Kalman filter,rendering a closed-loop dynamics of measurement-feedback driven online algorithm.We prove that,with a fixed step size,this online algorithm converges to a neighborhood of the GNE in expectation.Numerical simulations validate the theoretical results.

Follow the perturbed approximate leader for solving semi-bandit combinatorial optimization

Combinatorial optimization in the face of uncertainty is a challenge in both operational research and machine learning.In this paper,we consider a special and important class called the adversarial online combinatorial optimization with semi-bandit feedback,in which a player makes combinatorial decisions and gets the corresponding feedback repeatedly.While existing algorithms focus on the regret guarantee or assume there exists an efficient offline oracle,it is still a challenge to solve this problem efficiently if the offline counterpart is NP-hard.In this paper,we propose a variant of the Follow-the-Perturbed-Leader(FPL)algorithm to solve this problem.Unlike the existing FPL approach,our method employs an approximation algorithm as an offline oracle and perturbs the collected data by adding nonnegative random variables.Our ap-proach is simple and computationally efficient.Moreover,it can guarantee a sublinear(1+ε)-scaled regret of order O(T^(2/3))for any smallε>0 for an important class of combinatorial optimization problems that admit an FPTAS(fully polynomial time approximation scheme),in which T is the number of rounds of the learning process.In addition to the theoretical analysis,we also conduct a series of experiments to demonstrate the performance of our algorithm.

Efficient online portfolio simulation using dynamic moving average model and benchmark index

Online portfolio selection and simulation are some of the most important problems in several research communities,including finance,engineering,statistics,artificial intelligence,machine learning,etc.The primary aim of online portfolio selection is to determine portfolio weights in every investment period(i.e.,daily,weekly,monthly,etc.)to maximize the investor’s final wealth after the end of investment period(e.g.,1 year or longer).In this paper,we present an efficient online portfolio selection strategy that makes use of market indices and benchmark indices to take advantage of the mean reversal phenomena at minimal risks.Based on empirical studies conducted on recent historical datasets for the period 2000 to 2015 on four different stock markets(i.e.,NYSE,S&P500,DJIA,and TSX),the proposed strategy has been shown to outperform both Anticor and OLMAR—the two most prominent portfolio selection strategies in contemporary literature.