Demand　response　enables　numerous　small-scale　consumers　to　minimize　their　costs　as　independent　decision-makers.　Consequently,　the　power　system　operation　is　dominated　by　the　equilibrium　of　multiple　end-users.　This　paper　proposes　the　concept　of　user　equilibrium　of　DR　in　the　smart　grid　representing　a　state　that　no　end-users　can　profit　more　by　adjusting　their　own　consumption.　Then　the　user　equilibrium　is　reformulated　as　the　solution　of　a　convex　programming　problem,　named　as　the　user　equilibrium　problem.　The　corresponding　proof　is　also　provided.　An　efficient　solution　algorithm　is　proposed　to　obtain　the　equilibrium　among　numerous　end-users　based　on　the　branch-and-price　method.　Compared　with　the　existing　works,　the　operating　constraints　of　flexible　loads　are　modelled　in　details　and　can　be　considered.　Numerical　examples　are　presented　to　validate　the　proposed　concept　and　method.　©　2020　IEEE.