CXVI. Some general theorems for non-linear systems possessing resistance

Limitations of demand- and pressure-driven modeling for large deficient networks

“…Here W defines the total energy lost in the system and P h the total power taken from the fixed potential nodes. Millar (1951) extends the theoretical framework for nonlinear systems by dividing the energy loss into two components called the content G and co-content J . The sum of content and co-content is equal to the total energy lost in the system.…”

“…Based on the works of Cherry (1951) and Millar (1951) for electrical systems, Collins et al (1978) introduced a primal and dual formulation of the hydraulic problem based in mathematical optimization theory. These formulations are also known as the Content and Co-Content models.…”

Modeling the Behavior of Flow Regulating Devices in Water Distribution Systems Using Constrained Nonlinear Programming

“…Co-Content for water distribution systems may be specified in an analogous way to which Millar (1951) proposed definitions for electrical networks. First, define the function  as the Co-Content for both the pipes and unknown head nodes in the network as (Birkhoff 1963):…”

“…These principles can be applied to solving the pipe network equations. Based on the work of Cherry (1951) and Millar (1951) for the calculation of electrical networks, Collins et al (1978) …”

On Kirchhoff's equations and variational approaches to electrical network analysis

“…Similar methods have been reported in the literature at various times, and typically involve one set of Kirchhoff equations being derived from the other with the help of a functional. [5][6][7][8][9]22 In this note, we first discuss the energy conservation principle for lumped electrical networks and demonstrate how it can be utilized to directly derive one set of Kirchhoff equations from the other. This is followed by a variational extension of the same principle to generate a functional that is stationary at the actual operating point of the network (i.e., when the currents and voltages are at their values consistent with the KCL, KVL, and the component behavior equations).…”