A new approach to the mathematic modelling of hydropower governing systems

Norway´s power supply is entirely hydroelectric. Most of the plants are of high head type excavated in rock with long, often complicated, tunnel systems. Because the power lines are occasionally broken by icing during heavy winter storms, all the main power plants have been designed for isolated operation on resistive load. The combination of isolated operation, long transmission lines and long and complex tunnel systems require a thorough stability analysis of the speed control of the units in the systems. Resonance in the conduits is the main obstacle to maintaining stability. The structure matrix method presented has been developed into a very useful and reliable tool for the mathematical modelling of hydropower governing systems especially when the hydraulic part of the system is very complex. As a general method, it can also be used to study the stability or hydraulic resonance of pumping schemes and piping networks. The method can be developed further by including the electric grid so that a complete hydroelectric power network involving various power plants can be modelled