Heuristic algorithm for coordinating smart houses in MicroGrid

Abstract

This work presents a framework for eciently managing the energy needs of a set of houses connected in a micro-grid conguration. The micro-grid consists of houses and local renewable plants, each seen as independent agents with their specic goals. In particular houses have the option to buy energy from the national grid or from the local renewable plants. We discuss a practical heuristic that leads to energy allocation schedules that are cost-eective for the individual houses and protable for the local plants. We present experiments describing the benets of our proposal. The results illustrate that houses and micro plants can make considerable saving when they work in micro grid compared with working alone.

Easy knapsacks and the complexity of energy allocation problems in the smart grid

“…Also, if the system has no renewable power generator then, again, the allocation is easy as we can simply allocate everything at a time for which λ(t) is minimal. Conversely, if the number of appliances is large the problem is NP-hard, even for τ = 2 [1,3]. Here we strengthen such result.…”

“…. , n. The model presented in [3] is quite general but to simplify our presentation we restrict ourselves mainly to so called uniphase interruptible appliances: at each time step t each unit i is either "OFF" or it is "ON" and if it is "ON" it uses an amount of power equal to α i . Each appliance's state can be changed freely at any time.…”

“…Note that if the number of appliances is fixed the set of feasible solutions for instances of P1 can be enumerated in time polynomial in τ . In fact this is true also if we required each appliance to be used an arbitrary, but fixed, number of times, or if the appliances had any of the more complex energy usage patterns defined in [3] ( Fig. 1 gives an example of the energy requirements for a multiphase non-interruptible appliance.)…”

“…Here we strengthen such result. Arikiez et al [3] evaluate the performances of an exact algorithm for P1 and observe that they degrade rapidly if n or τ become large. However it is not clear whether a so called pseudo-polynomial [12,Chapter 4] algorithm may exist that allow P1 to be solved in time polynomial in the magnitude of the numbers involved in the problem instance (this has proved to be beneficial in practical contexts [2]).…”

“…The authors showed that if power demands can be served preemptively then the allocation problem can be solved effectively, and if that is not the case then the problem is NP-hard. Arikiez et al [3] studied a Micro-Grid scenario that generalizes Koutsopoulos et al's model. A set of houses and a set of (renewable) energy generators is given, fully connected to each other and connected to a national electricity generator (NEG).…”