Real-Time Pricing of Smart Grid Based on Piece-Wise Linear Functions
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Journal of Systems Science and Information  2019, Vol. 7 Issue (4): 295-316    DOI: 10.21078/JSSI-2019-295-22
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Real-Time Pricing of Smart Grid Based on Piece-Wise Linear Functions
Zhihong XU1,2, Liangyu GUO1, Yan GAO1, Muhammad HUSSAIN1, Panhong CHENG1
1. School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. Public Teaching Department, Rizhao Polytechnic, Rizhao 276826, China
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Abstract 

In a power grid system, utility is a measure of the satisfaction of users' electricity consumption; cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility, and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal; they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.

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Articles by authors
Zhihong XU
Liangyu GUO
Yan GAO
Muhammad HUSSAIN
Panhong CHENG
Key wordssmart grid   real-time pricing   piece-wise linear utility and cost functions   dual optimization method     
Received: 2019-03-04;
Fund:

Supported by the Natural Science Foundation of China (11171221)

Corresponding Authors: Yan GAO,E-mail:gaoyan@usst.edu.cn   
 E-mail: gaoyan@usst.edu.cn
About author: Zhihong XU,E-mail:rz-xzh@126.com;Liangyu GUO,E-mail:liang_workyu@163.com;Muhammad HUSSAIN,E-mail:mh.usst@yahoo.com;Panhong CHENG,E-mail:hollycheng@sina.cn
Cite this article:   
Zhihong XU,Liangyu GUO,Yan GAO et al. Real-Time Pricing of Smart Grid Based on Piece-Wise Linear Functions[J]. Journal of Systems Science and Information, 2019, 7(4): 295-316.
URL:  
http://123.57.41.99/Jwk_si/EN/10.21078/JSSI-2019-295-22     or     http://123.57.41.99/Jwk_si/EN/Y2019/V7/I4/295
 
[1] Li TAO, Yan GAO. Real-Time Pricing for Smart Grid with Multiple Companies and Multiple Users Using Two-Stage Optimization[J]. Journal of Systems Science and Information, 2018, 6(5): 435-446.
[2] Yeming DAI, Yan GAO. Real-Time Pricing Decision Based on Leader-Follower Game in Smart Grid[J]. Journal of Systems Science and Information, 2015, 3(4): 348-356.
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