# Robust Optimization for Household Load Scheduling with Uncertain Parameters
## 1 Introduction  
Residential customers are faced with diverse pricing schemes implemented by utilities to stimulate demand response [1; 2; 3], and are hence faced with the subsequent problem on how to operate the household appliances to minimize the electricity payment under the premise of human comfort. The growing integration of household generation, mainly intermittent renewable generation, makes this problem even more complex. By integrating advanced automatic control and information and communication technologies, home energy management systems (HEMS) make it possible for residential customers to optimally manage their household appliances, i.e., to shift and curtail household loads to properly respond to the various pricing schemes [4]. Under this background, HEMS have been attracting increasing attention in recent years. There are many studies that model the household load scheduling problem as a deterministic optimization problem [5; 6]. In [7], a detailed home energy management system structure is developed to determine the optimal day-ahead appliances scheduling under hourly pricing and peak power-limiting. In [8], in order to distinguish the energy consumption modes and corresponding status of different appliances, home appliances are assigned dynamic priorities, and a real-time household load priority scheduling algorithm, based on the allocated priority and renewable source availability prediction, is proposed to minimize the cost of energy consumption with customers' comfort constraints. Aiming at minimizing the electricity bill and customers' dissatisfaction at the same time, [PERSON] et al. [9] propose a multi-objective genetic algorithm to optimize the time allocation of domestic loads, and similar to the Non-dominated Sorting Genetic Algorithm II, some changes have been introduced in the proposed algorithm to adapt the physical characteristics of the load scheduling problem and improve the usability of results. However, in these studies, many parameters, such as the time-varying prices, ambient temperature, customer behaviors, etc., are assumed to be obtained through day/hour/minute-ahead forecasting, which contains inevitable uncertainties that will undermine the feasibility and optimality of the load schedules obtained. In order to tackle this issue, many researchers have conducted a large number of works and made very large achievements. In general, these works are divided into the following two methods. One method is to enhance the accuracy of forecast parameters by improving the forecasting methods. In [10], a new hybrid model that combines two well-known methods for short-term power forecasting of a grid-connected photovoltaic plant is introduced. And hourly forecasts of photovoltaic power output show a quite good accuracy and efficiency of the developed hybrid model. In [11], [PERSON] collects a variety of methods and ideas about electricity price forecasting. Although these methods have different strengths and weaknesses, it is proved that these methods have obtained varying degrees of success and forecasting precision. Another method is to make ultimate schedules to withstand the uncertainty through various kinds of uncertain optimizations. In [12], a stochastic scheduling technique is used to handle the uncertainties contained in the energy consumption and runtime of household appliances. In [13], typical uncertain parameters in the day-ahead temperature scheduling for air-conditioning are modeled by membership functions with fuzzy set theory. In [14], normally distributed random variables are used to describe the uncertain parameters, and a chance constrained optimization model is then formulated to accommodate the uncertainties. Although the aforementioned papers make great success to deal with these uncertain parameters in HEMS, there exists some limitations and shortcomings.