Turbine modeling for steady‐state analysis in hydropower plant networks with complex layouts using a modified global gradient algorithm

Abstract Turbines are generally oversimplified in conventional algorithms for steady‐state analysis of hydropower plant (HPP) networks. Moreover, conventional algorithms are hardly suitable for serial HPPs. In this paper, a modified global gradient algorithm (MGGA) is developed by extending turbine models and optimizing turbine interpolation. First, the nonlinear model of turbines is established with the proposed variable resistance factor and added to the global matrix. Then turbine unit quantity interpolation is proposed to compute the turbine operating parameters. Finally, turbine links and pipes can be iterated synchronously, and the global matrix is solved using the Newton–Raphson method. Characteristics of MGGA are evaluated by employing two test HPPs, including rapidity of convergence, computational stability of turbine, and applicability for serial HPPs. The results show that: (a) The iterative numbers of the MGGA are 0.72 and 4.98 times on average less than that of CA1 and CA2 for the accuracy of 10−6 in 400 operating conditions, even though MGGA has an obvious hysteretic nature; (b) Only MGGA can successfully calculate the extreme cases that large head losses in HPP networks; (c) Although fixed head nodes are not present between turbine links, such as serial HPPs, MGGA still works.