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Dimension reduction method for optimal operation of large-scale hydropower plants
with Karhunen-Loève theory and dispatching features

SHEN Jianjian ，ZHANG Bo ，CHENG Chuntian ，
1
1
1
2 2 2
LI Xiufeng ，JIANG Yan ，ZHAO Zhenyu
（1. Dalian University of Technology，Dalian 116024，China；
2. Yunnan Electric Power Dispatch and Communication Center，Kunming 650011，China）
Abstract：The computing efficiency of the optimal operation of large-scale hydropower plants is one of the
toughest problems in the operation of hydropower and power systems， which is a theoretical and technical
barrier to solve the complex system with more than 100 hydropower plants. This study presents a dimension
reduction method for optimal operation of large-scale hydropower plants with Karhunen-Loève （KL） theory
and dispatching features. Based on a long series of historical operation records， the principal component
analysis is used to identify characteristic value of water level change in the front of the dam and corre⁃
sponding characteristic function. The KL expansion method is then introduced to represent random variables
of the water level at any period as a linear function of characteristic terms of reservoir level change. Thus，
the operation decision of a specified reservoir inflow process can be determined by a combination of ran⁃
dom coefficients of all characteristic terms. A framework of iterative optimization is constructed，where a so⁃
lution procedure for searching random coefficients of characteristic terms is given to efficiently solve optimal
operations of large-scale hydropower plants. The presented method is verified by long-term operations of a
provincial hydropower system with more than 100 plants in Yunnan. The validity，efficiency，and sensitivity
of this method are respectively demonstrated by several case studies. A comparison with conventional dynam⁃
ic programming and its modifications shows that the method contributes a substantial improvement of compu⁃
tational efficiency while ensuring basically the same solution accuracy.
Keywords：KL theory；dispatching features；dimension reduction；hydropower plants；optimal operation
（责任编辑：王冰伟）

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