Mathematical Problems in Engineering

Volume 2015, Article ID 142764, 9 pages

http://dx.doi.org/10.1155/2015/142764

## Efficiency Evaluation for Smart Grid Management Based on Stochastic Frontier Model and Data Envelope Analyses Model

North China Electric Power University, Beijing 102206, China

Received 29 July 2015; Accepted 28 September 2015

Academic Editor: Mohamed Djemai

Copyright © 2015 Yu Xiaobao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For the technical and allocative efficiency evaluation of smart grid, this paper has proposed two methods. One is based on Data Envelopment Analysis and another is based on Stochastic Frontier Model. Among them, the former considered the dynamics of smart grid development and development dynamics is the influence parameter. The latter analyzed self-duality between the Cobb-Douglas production function and cost function; then, it deduced the smart grid resources optimization allocative efficiency evaluation model which can avoid price information needs of input factor in conventional allocative efficiency evaluation. The validity and rationality of the two methods are verified by a case study.

#### 1. Introduction

In process of its construction, the advanced technology is the key factor for the development of the grid in the intelligent direction [1]. The impact of the assessment technology is significant for the smart grid. From the point of technological progress and technical efficiency, analysis of this effect is the main research idea at home and abroad [2]. In economic management science, the technical efficiency is the ability of maximum output under the fixed input factors of the production unit [3]. Technological progress indicates the contribution of technology to economic growth and is reflected as the effect of production units.

In network analysis of technical progress, people have proposed the intelligent technique evaluation method with Cobb-Douglas production function which reflects the level of intelligent power grid development through contribution degree of computing technology to economic benefits [4]. Data Envelopment Analysis (DEA) has been used to evaluate the technical efficiency and scale efficiency of the power network [5]. Some scholars also use DEA to evaluate the technical efficiency of the hydroelectric power enterprise or transmission and distribution system [6, 7].

One of the overall planning objectives for smart grid is to achieve a large range of resource optimization allocation [8]. As an important platform for optimizing the energy resources, the smart grid resource that optimizes allocation ability can be evaluated by allocative efficiency, which can also reflect the construction effect of optimizing asset. Allocative efficiency refers to the ability to rationally configure various factors of production when the input elements’ price information and technical level are fixed. However, in studies of evaluating the allocative efficiency, most scholars take the cost function as the theoretical basis and take the price information of the input elements as the precondition, which restricts the effective evaluation for allocative efficiency [9–11].

Although the smart grid is in the phase of overall construction, the price information of input element is often difficult to get in assessment of technical efficiency. Therefore, according to the analysis of self-dual characteristic between the Cobb-Douglas production function and cost function, this paper has proposed the smart grid efficiency evaluation method based on Data Envelopment Analysis and Stochastic Frontier Model, then compared the two models and verified their usefulness according to the calculation results.

#### 2. Efficiency Assessment Model

##### 2.1. Data Envelopment Evaluation Model

Data envelopment evaluation model is performed to evaluate the efficiency [12]. This model considers the development of smart grid in time continuity through its improvement. That is, the construction effect of smart grid at the end of the last time should be the initial condition of the next time, so the model of management efficiency assessment is dynamic. At the same time, it takes into account the relationships between different attributes, that is; the benefit of building an attribute can be construction investment of another attribute. The objective function of the data envelopment evaluation model is as follows:In this formula, is the value of input indicator under the attribute of decision element in years; is the value of output indicator under the attribute of decision element in years; is the slack variable of input indicator under the attribute of decision element in years; is the slack variable of output indicator under the attribute of decision element in years.

The constraints are shown below:In this formula, is correlation value of decision element from the attribute to attribute in time slot. is influence value of decision element in attribute from years to years.

Through the optimization of the model, the parameters are set as follows:From this, the efficiency of each decision element can be calculated as follows: Among them, the attribute efficiency values of decision-making unit DMU are as follows:

##### 2.2. Stochastic Frontier Analysis Model

In quantitative assessment of technological progress, the speed of technological progress and the contribution of technology can measure the technological development level of smart grid [13]. However, this evaluation method can only carry on the appraisal to the single grid enterprises in different time sections of smart grid technology development status. The evaluation results can only reflect their own intelligence level change with time, so it cannot cope with the horizontal comparison of a plurality of grid enterprises. In the evaluation of building smart grid technology in different power companies, the use of technical efficiency indicators can meet the requirement. The relationship between technological progress and technical efficiency can be reflected by Figure 1.