To reduce the uncertain influence of wind power and solar photovoltaic power on virtual power 11 plant (VPP) operation, robust optimization theory (ROT) is introduced to build a stochastic scheduling 12 model for VPP considering the uncertainty, price-based demand response (PBDR) and incentive-based 13 demand response (IBDR). First, the VPP components are described including the wind power plant (WPP), 14 photovoltaic generators (PV), convention gas turbine (CGT), energy storage systems (ESSs) and demand 15 resource providers (DRPs). Then, a scenario generation and reduction frame is proposed for analyzing and 16 simulating output stochastics based on the interval method and the Kantorovich distance. Second, a 17 bi-level robust scheduling model is proposed with a double robust coefficient for WPP and PV. In the 18 upper layer model, the maximum VPP operation income is taken as the optimization objective for building 19 the scheduling model with the day-ahead prediction output of WPP and PV. In the lower layer model, the 20 day-ahead scheduling scheme is revised with the actual output of the WPP and PV under the objectives of 21 the minimum system net load and the minimum system operation cost. Finally, the independent micro-grid 22 in a coastal island in eastern China is used for the simulation analysis. The results illustrate that the model 23 can overcome the influence of uncertainty on VPP operations and reduce the system power shortage cost 24 by connecting the day-ahead scheduling with the real-time scheduling. ROT could provide a flexible 25 decision tool for decision makers, effectively addressing system uncertainties. ESSs could replace CGT to 26 provide backup service for the WPP and PV, to smooth the VPP output curve and to improve the WPP and 27 © 2016. This manuscript version is made available under the Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/ PV grid connection by its charging-discharging characteristics. Meanwhile, IBDR and PBDR could 28 smooth the load curve to the maximum extent, link the generation side with the demand side to minimize 29 abandoned power value and reach the optimum benefit of VPP operation. 30 1 Introduction 32 Since energy and environmental problems become very serious, distributed energy resources (DERs), 33 especially wind power and solar photovoltaic power, are playing increasingly important roles in the energy 34 structure. However, constraints of small installed capacity, intermittence, uncertainty and other 35 characteristics, make entrance and operation of the power market difficult for DERs[1]. Thus, the virtual 36 power plant (VPP) was proposed as a new technology for DERs in the power market [2]. Without changing 37 the DERs grid connection method, VPP integrates different types of DERs, such as distributed power 38 sources, energy storage systems and controllable loads, by using advanced control, calculation and 39 communication technology [3]. In recent years, smart grid technology has gained significant attention. The 40 government...

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We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary, which has not been solved before because the Green's function technique and the Laplacian matrix approach are invalid in this case. Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network. In this paper, we give a general resistance formula that is composed of a single summation by using the recursion-transform method. Meanwhile, several interesting results are derived by the general formula. Further, the current distribution is given explicitly as a byproduct of the method.

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In this paper, we made a new breakthrough, which proposes a new Recursion–Transform (RT) method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.