Abstract-We consider a price signal with two settings: offpeak tariff and on-peak tariff. Some loads are connected to specific electricity meters which allow the consumption of power only in off-peak periods. Historically, off-peak periods were located during the night and on-peak periods during the day. Changing the assignment of off-peak periods is an easy method for distribution system operators to access to the flexibility of small consumers. This solution can be implemented quickly as the infrastructure needed already exists in some countries.We propose a mixed-integer linear model to assign optimally the off-peak hours so as to minimize a societal cost. This cost gathers together the cost of electricity, the financial losses due to energy curtailments of photovoltaic installations and the loads' wellbeing. Our model considers automatic tripping of inverters and constraints of the electrical distribution networks. Simulation results show that the new disposition of off-peak hours could reduce significantly the photovoltaic energy curtailed in the summer.Index Terms-Mathematical programming, Optimization, Smart grids, Sustainable development. NOMENCLATUREThis section defines the main symbols used in this paper.T \ {0} S nodes S h nodes to which houses are connected K flexible loads G distinct groups g(k) group g ∈ G to which load k belongs K(i) flexible loads connected to node i D days of the time horizon Parameters'pr' is a period. If the chosen timestep is 1 h, pr = h.C ij,t capacity of link (i, j) in period t α t price for 1 kW pr in period t π c consumer's money gain having produced 1 kW pr λ cost for a loss of 1 kW pr on the consumer side η i,t maximum power injected at node i in period t ρ i,t curtailable power production at node i in period t ζ i,t static load power consumption at node i in period t β k,t amount of off-peak periods added tonumber of off-peak periods for group g during day d µ daily maximum number of rate switchings Variables l ij,t power going from node i to node j in period t n i,t power balance at node i in period t r i,t curtailed quantity at node i in period t s k,t state of load k at the end of period t ≥ 0 x k,t fraction of period during which load k consumes power in period t u g,t equals 1 if consumer group g is off-peak in period t, 0 otherwise w k,t auxiliary variable needed in order to define x k,t p i,t variable power consumed at node i in period t z g,t equals 1 if there is a rate switching between periods t − 1 and t
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