Optimal Operation of Integrated Heat and Electricity Systems:A Tightening McCormick Approach

Combined heat and electricity operation with variable mass flow rates promotes flexibility,economy,and sustainability through synergies between electric power systems(EPSs)and district heating systems(DHSs).Such combined operation presents a highly nonlinear and nonconvex optimization problem,mainly due to the bilinear terms in the heat flow model—that is,the product of the mass flow rate and the nodal temperature.Existing methods,such as nonlinear optimization,generalized Benders decomposition,and convex relaxation,still present challenges in achieving a satisfactory performance in terms of solution quality and computational efficiency.To resolve this problem,we herein first reformulate the district heating network model through an equivalent transformation and variable substitution.The reformulated model has only one set of nonconvex constraints with reduced bilinear terms,and the remaining constraints are linear.Such a reformulation not only ensures optimality,but also accelerates the solving process.To relax the remaining bilinear constraints,we then apply McCormick envelopes and obtain an objective lower bound of the reformulated model.To improve the quality of the McCormick relaxation,we employ a piecewise McCormick technique that partitions the domain of one of the variables of the bilinear terms into several disjoint regions in order to derive strengthened lower and upper bounds of the partitioned variables.We propose a heuristic tightening method to further constrict the strengthened bounds derived from the piecewise McCormick technique and recover a nearby feasible solution.Case studies show that,compared with the interior point method and the method implemented in a global bilinear solver,the proposed tightening McCormick method quickly solves the heat–electricity operation problem with an acceptable feasibility check and optimality.

Video Recognition for Analyzing the Characteristics of Vehicle–Bicycle Conflict

Vehicle–bicycle conflict incurs a higher risk of traffic accidents,particularly as it frequently takes place at intersections.Mastering the traffic characteristics of vehicle–bicycle conflict and optimizing the design of intersections can effectively reduce such conflict.In this paper,the conflict between right-turning motor vehicles and straight-riding bicycles was taken as the research object,and T-Analyst video recognition technology was used to obtain data on riding(driving)behavior and vehicle–bicycle conflict at seven intersections in Changsha,China.Herein,eight typical traffic characteristics of vehicle–bicycle conflict are summarized,the causes of vehicle–bicycle conflict are analyzed using 18 factors in three dimensions,the internal relationship between intersection design factors and traffic conflicts is explored,and the guiding of design optimization based on the width of bicycle lanes and the soft separation between vehicles and bicycles is discussed.The results showed that colored paved bicycle lanes were better,performing better at a width of 2.5 m compared to 1.5 m.However,the colored pavement was not suitable for the entire road and had to be set at the position,at which the trajectories of a bicycle and motor vehicle overlapped.Thus,a 2.5-m-wide bicycle lane provides good safety.However,there are still defects in the existing safety indicators,so it is necessary to develop new indicators to reflect real vehicle–bicycle conflict situations more comprehensively.

Energy Management of Price-maker Community Energy Storage by Stochastic Dynamic Programming

In this paper,we propose an analytical stochastic dynamic programming(SDP)algorithm to address the optimal management problem of price-maker community energy storage.As a price-maker,energy storage smooths price differences,thus decreasing energy arbitrage value.However,this price-smoothing effect can result in significant external welfare changes by reduc-ing consumer costs and producer revenues,which is not negligible for the community with energy storage systems.As such,we formulate community storage management as an SDP that aims to maximize both energy arbitrage and community welfare.To incorporate market interaction into the SDP format,we propose a framework that derives partial but sufficient market information to approximate impact of storage operations on market prices.Then we present an analytical SDP algorithm that does not require state discretization.Apart from computational efficiency,another advantage of the analytical algorithm is to guide energy storage to charge/discharge by directly comparing its current marginal value with expected future marginal value.Case studies indicate community-owned energy storage that maximizes both arbitrage and welfare value gains more benefits than storage that maximizes only arbitrage.The proposed algorithm ensures optimality and largely reduces the computational complexity of the standard SDP.Index Terms-Analytical stochastic dynamic programming,energy management,energy storage,price-maker,social welfare.