Simulation of Lake Winnipeg Water Level Regulation

Abstract

Lake Winnipeg is a large body of water located in western Canada. The construction of hydroelectric power plants on the Nelson River, which constitutes the only drain, has led to the consideration of the lake as a storage reservoir. The resulting regulation proposals can be evaluated by means of the model here developed. The model incorporates the multiple-basin structure of the lake, fluctuations in river inflows, and wind-set (the tilting of the lake surface under the action of a strong wind). The lake is represented by a first-order fluid model, containing two basins connected by a resistive channel. An analogous electrical model is derived from the fluid model, using current, voltage, capacitance, and resistance for (respectively) flow, water level, storage capacity, and flow resistance. A voltage source accounts for the wind-set function, whose coefficients are set to fit experimental data. The wind-set dynamics are modeled as first-order lags. The regulating element is the variable outflow resistance, which represents the control structure at the Nelson River. Several regulation schemes are examined by solving the model equations on a digital computer. The outflow resistance is a function of the water level as measured at some point in the lake. Solutions for various functions and measurement points are compared. The results show undesirably large level changes in the South Basin in spite of the good regulation achieved in the North Basin.