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Efficient and robust modeling systems include a computation module, or hydraulic solver, which is the core driving engine for modeling packages. Conventional hydraulic models can be used to analyze operational scenarios for a variable-speed pump (VSP) delivering target hydraulic characteristics of either the fixed hydraulic head or the desired pump flow. However, modelers must repeatedly adjust relative speed factors for achieving the target hydraulic performance, which can be a time-consuming task. This article presents an enhanced variable-speed pump (VSP) solution method to automatically calculate the relative pump-speed coefficient for attaining the prescribed hydraulic head or pumping the preferred amount of flow. Engineers can use this method to model not only a single VSP but also multiple VSPs with rule-based logic controls. This allows the target control head to be specified at any location or for the target flow to be specified for VSPs of different capacities. The extended method provides a flexible, robust modeling approach for engineers to analyze a variety of VSP configurations in water and wastewater collection systems. Includes 9 references, tables, figures.