Electricity plan recommender system with electrical instruction-based recovery

Highlights

• Proposing an electricity plan recommender system (EPRS) with matrix recovery.

• Appliance classification avoids trivial changes in recovering appliance usages.

• Total electricity usages are set as a recovery instruction in recovering data.

• Novel matrix recovery could recover up to 38.15% more data.

• 93.56%–94.85% of users can obtain effective electricity plans with novel EPRS.

Abstract

Several electricity tariffs have emerged for Demand Side Management (DSM) and residential customers are faced with challenges to choose the plan satisfying their personal needs. Electricity Plan Recommender System (EPRS) can alleviate the problem. This paper proposes a novel EPRS model named EPRS with Electrical Instruction-based Recovery (EPRS-EI), which is a dual-stage model consisting of feature formulation stage and recommender stage. In the feature formulation stage, matrix recovery with electrical instructions is applied to recover appliance usages, and the recovered data is set as features representing customers’ living patterns. In the recommender stage, Collaborative Filtering Recommender System (CFRS) based on K-Nearest Neighbors (KNN) and adjusted similarity is applied to recommend personal electricity plans to customers based on the above features. Different from other EPRS models, EPRS-EI is the first model utilizing matrix recovery methods and similarity computation with electrical instructions. With these electrical instructions, the proposed model is able to utilize more explicit features and recommend more personalized plans. We then apply EPRS-EI to predict the testing customers’ preference for electricity plans. Simulation results on recovering electricity data and their applications in EPRS confirm the effectiveness of the proposed methods in comparison to state-of-the-art methods, with 93.56%–94.85% customers correctly recommended.

Introduction

An increasing number of factors including intermittent renewable power generation and load consumption have posed a threat to the stability of the power system. These factors cause the fluctuation of the power system and the growing peak value of electricity demand. To deal with the problems, Demand Side Management (DSM) [[1], [2], [3], [4], [5]] is used to regulate the demand of energy consumers. In DSM, with the purpose of shaving peak and filling valley, Pricing Based Demand Response (PBDR) [[6], [7], [8], [9]] is proposed to provide residential customers with various electricity plans, indirectly influencing their energy consumption patterns. For example, if a customer selects a plan with a lower charge in the morning, the customer may shift the use of some appliances from evening to morning.

In a matured electricity market, thousands of electricity plans are listed in the electricity plan interface, which brings challenges to residential customers for making choices among the great number of electricity plans. If a customer chooses an improper electricity plan, to compromise the electricity cost, the customer may have to change the living pattern and sacrifice the living comfort. Faced with this problem, a new technique named Electricity Plan Recommender System (EPRS) is introduced to help residential customers to choose proper electricity plans. In a project named Smart Grid Smart City (SGSC) [10], 200 residential customers are selected to make a comparison between choosing plans with and without EPRS. It shows that aggregated daily load profiles in the two scenarios are similar in shape but slightly different in the lowest and highest values. This project inspires some electricity market platforms, foster them to provide electricity plan recommender service, such as Energy Made Easy, iSelect and Power to Choose [[11], [12], [13]].

The current EPRS methods can be classified into the direct method and indirect method. The direct method is relatively easy to be realized, and the above EPRS models [[10], [11], [12], [13], [14]] belong to this class. These methods directly calculate the residential customers’ electricity charges through multiplying their total usages by the unit charge of electricity plans and recommend the electricity plans to make less charges to the residential customers. The main drawback of direct methods is that they lack consideration of the personal needs of customers, because two customers having the same electricity usages may have different living patterns.

In the last decade, the electricity meter can only count for the total appliance electricity usages of customers, so direct methods are the mainstream EPRS methods. Fortunately, with the development of the smart meter, the monitoring of household appliances has become an increasingly attractive research field. Unlike the traditional meters, smart meters and intelligent home devices [[14], [15], [16], [17], [18], [19], [20], [21], [22], [23]] can be utilized to monitor the living patterns of various residential customers, which give the possibility to extract key factors affecting personal living patterns. Based on this technology, indirect methods are introduced to recommend electricity plans based on such factors. Indirect methods are a dual-stage model, consisting of feature formulation stage and recommender stage. In the feature formulation stage, primary data and certain features are set as input and output respectively, and the outputted features are the key factors to represent the living patterns. In the recommender stage, the similarity [[24], [25], [26]] of customers is calculated and the testing personalized electricity plans can be obtained through the calculation based on similarity and training personal electricity plans. The dual-stage framework of EPRS is shown in Fig. 1 below.

Similar to the dual-stage of indirect methods, there are two stages as well in these methods. In the feature formulation stage, more explicit features will be obtained. In the recommender stage, personalization will be achieved. The creation will be firstly made in the recommender stage. Reference [27] proposed Cluster-based Recommender System (CB-RS), which set daily electricity usages of different hours as the features and used them to cluster customers. In CB-RS, customers in the same cluster shared the same series of recommended electricity plans. If a new testing feature is inputted into CB-RS, the recommended plans can be computed once the cluster is known. Compared to direct methods, CB-RS proposed clustering methods to recommend personal electricity plans to a new customer based on the cluster, but the disadvantage is that customers in the same cluster are allocated to the same range of electricity plans. The method Social Filtering EPRS (SF-EPRS) in Ref. [28] solved this problem by introducing Collaborative Filtering Recommender System (CFRS) [29] into the recommender stage. In SF-EPRS, the feature formulation stage was similar to that of CB-RS, but in recommender stage, a weighting function was used to compute the recommended electricity plans of a testing customer. With this weighting function, the recommended plans of all testing customers are possible to be different from each other, to satisfy the need for personalization in EPRS. The recommender methods of following papers [30,31] are all based on CFRS.

When the recommender stage is matured, researchers tend to utilize more explicit features in the feature formulation stage. In Ref. [30], Collaborative Filtering-based EPRS (CF-EPRS) was proposed. In this model, electricity usages of several selected appliances are transferred into operation duration in the feature formulation stage, and the operation duration is set as features used to compute similarity. Compared with the feature used in CF-EPRS [30], for example, the operation time of washing machine, the feature in CB-RS [27] and SF-EPRS [28], such as the average evening usage or average summer usage, is abstract and implicit. Further progress can be seen in Bayesian Hybrid Collaborative Filtering-based EPRS (BHCF-EPRS) [31]. To avoid the data incompletion, BHCF-EPRS additionally utilizes Bayesian Probabilistic Matrix Factorization (BPMF) [32] to recover the extracted operation time, which alleviates the sparse problem. Besides, BHCF-EPRS introduces a classification machine to compute the similarity, which makes customers with similar total electricity usages more possible to be set as nearest neighbors. To give the difference of typical indirect methods, Table 1 presents the two stages of these methods.

However, for BHCF-EPRS, although BPMF is an applicable way to recovery appliance usages, progress is possible to be made in improving the recovery precision, so we can extract more explicit features. According to Ref. [33], a sample matrix is an instinctively low-rank space, which means variables of a sample matrix only depend on a comparably smaller number of factors. The core of matrix recovery is to extract these factors and use them to reconstruct the corrupted data. For example, when predicting the rating of a movie, it is reasonable to assume that the rating may only be determined by a few preferences [34].

In matrix recovery, to exploit low-rank space, two methods are proposed, namely, Matrix Factorization (MF) [34] and Nuclear-Norm Minimization (NNM) [[35], [36], [37]]. The difference between these two methods is the treatment of the rank of the sample matrix. For MF, the rank of the sample matrix and the probability distribution of parameters are set before learning, for example, parameters in BPMF are set to follow Gaussian-Wishart distribution. Instead, NNM [[35], [36], [37]] does not set any prior information into low-rank space and they apply nuclear regularization [[38], [39], [40]] to regulate the sample matrix. A theorem in Ref. [35] shows that NNM can achieve global optimum if the sample matrix is relatively complete, while MF does not have similar convergence property.

In this paper, to get more explicit features, we introduce novel NNM methods to recover appliance usages. According to the difference of recovery principles, we reformulate two classic NNM methods into novel ones, and they are Robust Principal Component Analysis (RPCA) [35] and Low-Rank Representation (LRR) [36], which apply nuclear regularization to learn low-rank data matrix and low-rank representation matrix respectively. Different from the prototypes, the novel ones are combined with electrical recovery instructions, which makes novel methods specialize in recovering appliance usages. Therefore, the new methods are named RPCA with Electrical Instructions (PRCA-EI) and LRR with Electrical Instructions (LRR-EI), respectively, and the new EPRS model is named EPRS with Electrical Instruction-based Recovery (EPRS-EI).

The contributions of this paper are as follows:

• We propose EPRS-EI, which is a dual-stage model consisting of feature formulation stage and recommender stage. In feature formulation stage, appliance usages are recovered by PRCA-EI or LRR-EI and set as features, while in recommender stage, CFRS with K-Nearest Neighbors and adjusted similarity is applied to recommend personal electricity plans for customers.

• Different from the classical matrix recovery models, electrical recovery instructions are applied in PRCA-EI and LRR-EI, which makes matrix recovery models specialize in recovering appliance usages. The recovery instructions we use are appliance classification and total electricity usage. The appliance classification is utilized to keep the known appliance data unchanged, while the total electricity usage is used to make recovered data constrained.

• We also utilize a novel adjusted similarity evaluation in CRFS to computing the testing electricity plans. The total electricity usages are introduced into similarity evaluation for computing living pattern similarity among residential customers. In this case, residential customers with similar total electricity usages are more possible to be set as nearest neighbors.

• We provide algorithms to solve our proposed methods, together with the convergence behavior and computational complexity analysis. Finally, the results in a recovery simulation and application simulation of EPRS confirm the effectiveness of our proposed methods in comparison to the state-of-the-art methods.

The rest of the paper is organized as follows. Section 2 describes the proposed matrix recovery methods. In Section 3, the framework of the proposed EPRS is proposed. In Section 4, simulation results are conducted and discussed. Finally, the conclusion and future work are presented in Section 5.