Blind Wideband Beamforming Algorithm Based on the Uncertainty Set

Without prior knowledge,the steering vector estimation error of the desired signal will deteriorate the beamforming performance to some extent.To solve this problem,a space-time blind wideband beamforming algorithm based on the uncertainty set is proposed.First of all,based on the space-time filtering model,the spherical constraint set is designed according to the uncertainty of the estimation error of the space-time steering vector.Then,the method of wideband beamforming under multiconstraints in the frequency domain is derived,and the calculation of parameters of steering vector estimation error and loading factor are given in detail.Finally,a blind broadband beamforming algorithm combined with the CAB algorithm is proposed.The improvement of the output signal-to-noise ratio is quantitatively analyzed by computer simulation to verify the correctness and robustness of the algorithm.

Data-driven Based Uncertainty Set Modeling Method for Microgrid Robust Optimization with Correlated Wind Power

Microgrid is considered an important part of the future zero carbon energy systems.However,the uncertainty caused by renewable energy source brings huge challenges to the scheduling of MG and restricts its ability of carbon emission reduction.In this paper,a novel improved multi-ellipsoidal uncertainty set modeling method is proposed to better depict the uncertainty of wind power and reduce the conservativeness of traditional robust optimization.Probabilistic information from historical data is utilized to capture the temporal correlation of forecast error of wind power,as well as the conditional correlation of forecast error with forecast value,making the uncertainty set more data-adaptive to variation of forecast results and more accurate for uncertainty description.A two-stage robust optimization model of a grid-connected microgrid is established based on the proposed uncertainty set and solved by column and constraint generation algorithm.Simulation results based on actual data illustrate the average unbalanced power of microgrid between day-ahead trading and real-time power exchange with utility grid is dropped by nearly 11.16%compared with a deterministic optimization method,11.86%with traditional box uncertainty set-based robust optimization method,and 2.89%with stochastic optimization method.

Optimal Dispatch for Flexible Uncertainty Sets in Multi-energy Systems: An IGDT Based Two-stage Decision Framework

The operational stability and economy of multi-energy systems(MES)are threatened by various uncertainties,such as variable renewable energy power,energy demands,and weather conditions.Most of the existing methods for the dispatch decisions of MES are based on the prescribed probability distribution or uncertainty sets of random variables,which have many disadvantages,such as potential infeasibility and over-conservatism.In this paper,we propose a novel dispatch model for MES that integrates dispatch decision making,uncertainty set selection,and operational cost control into a unified framework.First,the deterministic dispatch model of MES is introduced,in which the physical characteristics of district heating systems and buildings are fully considered.Then,a novel decision framework that combines the two-stage dispatch strategy and info-gap decision theory(IGDT)is proposed for MES,where the uncertainty set is flexible and can be optimized based on the operational cost budget.Finally,a revised algorithm,based on the column-and-constraint generation method,is proposed for the model.Case studies are performed on MES that includes a 33-bus distribution system and a heating network modified from a real 51-node network located in Jinlin Province,China.The results verify the effectiveness of the proposed method.

A Day-ahead Economic Dispatch Method Considering Extreme Scenarios Based on Wind Power Uncertainty

As the intermittency of wind power is a growing concern in the day-ahead economic dispatch,this paper proposes a day-ahead economic dispatch method considering extreme scenarios of wind power by using an uncertainty set.The uncertainty set inspired by robust optimization is used to describe wind power intermittency in this paper.Four extreme scenarios based on the uncertainty set are formulated to represent the worst cases of wind power fluctuation.An economic dispatch method considering the costs of both load shedding and wind curtailment is proposed.The economic dispatch model can be easily solved by a quadratic programming method owing to the introduction of four extreme scenarios and the uncertainty set of wind power.Simulation is done using the IEEE 30-bus system and the results verify the effectiveness of the proposed method.

Multi-stage Robust Scheduling for Community Microgrid with Energy Storage

Energy storage devices can effectively balance the uncertain load and significantly reduce electricity costs in the community microgrids(C-MGs) integrated with renewable energy sources. Scheduling of energy storage is a multi-stage decision problem in which the decisions must be guaranteed to be nonanticipative and multi-stage robust(all-scenario-feasible). To satisfy these two requirements, this paper proposes a method based on a necessary and sufficient feasibility condition of scheduling decisions under the polyhedral uncertainty set. Unlike the most popular affine decision rule(ADR) based multistage robust optimization(MSRO) method, the method proposed in this paper does not require the affine decision assumption, and the feasible regions(the set of all feasible solutions) are not reduced, nor is the solution quality affected. A simple illustrative example and real-scale scheduling cases demonstrate that the proposed method can find feasible solutions when the ADR-based MSRO fails, and that it finds better solutions when both methods succeed. Comprehensive case studies for a real system are performed and the results validate the effectiveness and efficiency of the proposed method.

Bernoulli particle flter with observer altitude for maritime radiation source tracking in the presence of measurement uncertainty

For maritime radiation source target tracking in particular electronic counter measures（ECM）environment,there exists two main problems which can deteriorate the tracking performance of traditional approaches.The frst problem is the poor observability of the radiation source.The second one is the measurement uncertainty which includes the uncertainty of the target appearing/disappearing and the detection uncertainty（false and missed detections）.A novel approach is proposed in this paper for tracking maritime radiation source in the presence of measurement uncertainty.To solve the poor observability of maritime radiation source target,using the radiation source motion restriction,the observer altitude information is incorporated into the bearings-only tracking（BOT）method to obtain the unique target localization.Then the two uncertainties in the ECM environment are modeled by the random fnite set（RFS）theory and the Bernoulli fltering method with the observer altitude is adopted to solve the tracking problem of maritime radiation source in such context.Simulation experiments verify the validity of the proposed approach for tracking maritime radiation source,and also demonstrate the superiority of the method compared with the traditional integrated probabilistic data association（IPDA）method.The tracking performance under different conditions,particularly those involving different duration of radiation source opening and switching-off,indicates that the method to solve our problem is robust and effective.

Robust Solutions to Uncertain Linear Complementarity Problems

In this paper, we adopt the robust optimization method to consider linear complementarity problems in which the data is not specified exactly or is uncertain, and it is only known to belong to a prescribed uncertainty set. We propose the notion of the p-robust counterpart and the p-robust solution of uncertain linear complementarity problems. We discuss uncertain linear complementarity problems with three different uncertainty sets, respectively, including an unknown-but-bounded uncertainty set, an ellipsoidal uncertainty set and an intersection-of-ellipsoids uncertainty set, and present some sufficient and necessary （or sufficient） conditions which p-robust solutions satisfy. Some special eases are investigated in this paper.

Optimal Design of Distributed Energy Resource Systems under Uncertainties Based on Two-Stage Robust Optimization

Distributed energy resource(DER)systems are widely used owing to their excellent economic and environmental performance.However,uncertainties in the system generate difficulties in the optimal design of DER systems.In practice,the distribution of uncertain parameters is generally unknown.In this work,a two-stage robust optimization(RO)model was proposed for the optimal design of DER systems considering uncertainties in renewable energy intensity,energy prices,and load demands.Three uncertainty sets(i.e.,the box,ellipsoid,and convex-hull uncertainty sets)were adopted to describe the distribution of uncertain parameters,and the proposed two-stage RO problem was solved using affine decision rules.A typical hospital in Lianyungang,Jiangsu Province,China,was selected as the case study object,and the effectiveness of the model was verified.The case study results showed that uncertainties in energy prices and load demands have a significant impact on system configuration and economic performance,and mainly affect the installed capacities of gas boilers,absorption chillers,and storages.Uncertainty set will affect the optimization results and an appropriate uncertainty set should be adopted to describe uncertainties precisely and increase accuracy of results.

A Two-stage Adaptive Robust Model for Residential Micro-CHP Expansion Planning

This paper addresses the planning problem of residential micro combined heat and power (micro-CHP) systems (including micro-generation units, auxiliary boilers, and thermal storage tanks) considering the associated technical and economic factors. Since the accurate values of the thermal and electrical loads of this system cannot be exactly predicted for the planning horizon, the thermal and electrical load uncertainties are modeled using a two-stage adaptive robust optimization method based on a polyhedral uncertainty set. A solution method, which is composed of column-and-constraint generation (C&CG) algorithm and block coordinate descent (BCD) method, is proposed to efficiently solve this adaptive robust optimization model. Numerical results from a practical case study show the effective performance of the proposed adaptive robust model for residential micro-CHP planning and its solution method.