A Versatile Probability Model of Photovoltaic Generation Using Pair Copula Construction


Photovoltaic (PV) generation is increasingly popular in power systems. The nonlinear dependence associated with a large number of distributed PV sources adds the complexity to construct an accurate probability model and negatively affects confidence levels and reliability, thereby resulting in a more challenging operation of the systems. Most probability models have many restrictions when constructing multiple PV sources with complex dependence. This paper proposes a versatile probability model of PV generation on the basis of pair copula construction. In order to tackle the computational burden required to construct pair copula in high-dimensional cases, a systematic simplification technique is utilized that can significantly reduce the computational effort while preserving satisfactory precision. The proposed method can simplify the modeling procedure and provide a flexible and optimal probability model for the PV generation with complex dependence. The proposed model is tested using a set of historical data from colocated PV sites. It is then applied to the probabilistic load flow (PLF) study of the IEEE 118-bus system. The results demonstrate the effectiveness and accuracy of the proposed model.


Electrical and Computer Engineering


National Natural Science Foundation of China
Ministry of Science and Technology of the People's Republic of China. 863 Program
Key Laboratory of Control of Power Transmission and Transformation, Ministry of Education
State Energy Smart Grid R&D Center


This work was supported in part by the National Natural Science Foundation of China under Grant 51307107 and Grant 51477098, in part by the National High-Tech R&D Program of China 863 program under Grant 2014AA052003, in part by SRFDP under Grant 20130073120034, and in part by the Key Laboratory of Control of Power Transmission and Transformation, Ministry of Education, and State Energy Smart Grid R&D Center, Shanghai, China.

Keywords and Phrases

Electric load flow; Photovoltaic cells; Computational burden; Computational effort; IEEE 118-bus system; Modeling procedure; Nonlinear dependence; Probability modeling; Probability; Multiple dependence; Pair copula; Photovoltaic (PV) generation; Probabilistic load flow (PLF); Simplification

International Standard Serial Number (ISSN)

1949-3029; 1949-3037

Document Type

Article - Journal

Document Version


File Type





© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Oct 2015