Hydropower - Formula

MIKE HYDRO calculates the hydroelectric power produced from the following formula:

(A.2.1)   Appendix_A00007.jpg

Where P is the power generated, Appendix_A00010.jpg is the effective head (difference) [L], Q is the discharge/release through turbine(s) [L3/T], Appendix_A00013.jpg is the machine (power) efficiency [-], g is the gravitational constant [L/T2] and Appendix_A00016.jpg is the density of water [M/L3]. Machine (power) efficiency Appendix_A00019.jpg may also be specified as a func­tion of Q, in which case Appendix_A00022.jpg is replaced by Appendix_A00025.jpg in equation (A.2.1).

The effective head difference is:

(A.2.2)   Appendix_A00028.jpg

The hydropower formula is non-linear because of the dependencies of head difference on discharge and machine efficiency. Tailwater levels are generally a function of discharge, and so are additional conveyance head losses in the channel (both increase with discharge). In addition the tailwater can also become governed by backwater from the reservoir downstream rather than discharge of the supplying reservoir. In the simulations, the applicable tailwa­ter level for use in equation (A.2.2) is found from

(A.2.3)   Appendix_A00031.jpg

In MIKE HYDRO, the following inter-dependencies between variables can be assumed constant or insignificant by leaving out the respective detailed spec­ifications:

Appendix_A00034.jpg (leaving out the tail water table)

Appendix_A00037.jpg (leaving out the conveyance head loss table)

Appendix_A00040.jpg (leaving out the power efficiency table)

Water demand for power generation is calculated by solving the power for­mula, equation (A.2.1), for Q (the solution must be found iteratively). When the effective head difference is small, turbines are however shut off, both because they are inefficient and because the required discharge would grows very large. Accordingly, a minimum head for operation can also be specified. If the head is less than the minimum head, Q is set to zero, i.e., no water is routed through the turbines, regardless of demand.