The approach to selecting engines and the level to operate each at a station with multiple engines is &scribed in this paper. The fuel usage versus horsepower curve is linearized into three straight line segments. Unitized variable arcs are generated for each segment. This is repeated for each of the engines. The generated horsepower distribution network problem is solved. The solution to the network problem is used to create a &creased area of linearization about the solution point for each engine. Another network problem is generated and solved. The procedure is repeated until the linear segment lengths have shrunk to within a preset tolerance of zero length. We have no proof of a global minimum fuel solution. The non-linear fuel consumption curves must be linearized because of the solution algorithm we use. Unitization variables enable the selection ofj ust one of the segments of linerarization. Regeneration of the problem amounts to a narrowing of the portion of the non-linear fuel curve for subsequent iterations. It is somewhat like a binary search procedure. CONDITIONS The objective for minimization is the sum of engine horsepower values times the cubic feet per horsepower hour at that horsepower. The variables have boundary values. Every engine has minimum and maximum practical operating ranges of horsepower as known by engineers and/or operators. This paper is written with the assumption that the horsepower boundaries are known. The total horsepower HT required by a station is determined from a polynomial generated from historical operating data. A network operating model converges to a set of suction and discharge pressures for each station on the system. Figure 1 is a way that the desired conditions for a station can be displayed. The coefficients a,b and c are determined with polynomial regression for each engine. Each engine's fuel consumption per horsepower per hour is a function of the horsepower produced by that engine; Fi = aHi + bHi + c as in figure 3. The fuel curve is then broken into three linear pieces so that SUM(hk) = Hi and, more specifically two of the hk = o and one of them equals Hi. Subsequent iterations accomplish the linearization narrowing by making the selected hj into three new hj by cutting them to a fraction of the previous values
Practical horsepower limits are known in an operating environment. We assume that an engine can operate at some range of horsepower from HLi to HHi. So then the maximum horsepower produced at a station could be SUM(HHi). Now, if the required horsepower to attain a specific flow at specified compression ratio is HT, we will select a group of engine horsepowers (HE 1, HE2 … HEN) so that HT= SUM(HEi). Figure 4 is a display of the fuel functions for four engines at a station.
