Материал: Russian Journal of Building Construction and Architecture

Russian journal of building construction and architecture

node pressures and a selection (including the zero one); Т is a transportation property; the uppercase indices r and f correspond with actual and fictional network structures; the lower case index (d) belongs to the elements of a diagonal matrix.

From МВС we have a block with the lowercase index D with the size of a square matrix

(4)—(6) I I ID .

A unit matrix E f contains two unit elements with the opposite signs in each line, the number of columns is the same as that of fictional areas, the number of lines per unit is smaller due to the condition (3), i.e. its size is Jн 1 Jн .

The size of the combined square matrix (4) and (7) is I ID I Jн 1 .

and is specific, the number of areas with throttles precisely corresponds with the number without a unit of energy node outflows (Fig. 1).

For linearization of a nonlinear model (4)—(7) the Newton’s method can be employed. A corresponding linear model of a flow distribution is below:

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where

Gas Distribtion System

Fig. 1. Binary structural graph of an urban gas supply system of the medium (high) pressure stage: r, f are actual and fictional areas respectively

For the analysis of the mechanism of throttle characteristics, it is suggested that the results of a calculation experiment to model a flow distribution in the range of reverse analysis for a gas supply system of the medium pressure stage of a residential area are used (see Fig. 1) supplied with seven controlled throttles fitted on the branches of the energynode outflows. The prediction of the expense is made with eightpreviouslyspecified vlaues Qjfa with a considerable range of changes. Modelling was performed for two options for preliminary settings of the throttles with the total capacity of the system 3350 and 24985 m3/h at constant pressures in the energy nodes: Р1 = 0.5 МPа (power node) and Р16 = Р17 = Р18 = Р19 = Р20 = Р21 = Р22 = Р23 = 0.1 МPа (atmospheric pressure). The calculation experiment containing 17 specified options allowed 7 throttle characteristics to be synthesized (Fig. 2) in the relative coordinates

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Russian journal of building construction and architecture

with a dispersion not over 3,5 % where QDi(0), SDi(0) are initial properties corresponding with a zero iteration [2].

Fig. 2. Throttle characteristics of a gas supply system in the relative coordinates: 1, 2, 3 for the throttles in the areas 2—4, 2—3, 5—6 respectively;

4, 5, 6, 7 for the throttles in the areas 9—10, 12—13, 12—11, 14—15 respectively

The solution of the reverse analysis is obtained for the following restrictions if

of the throttle characteristics is not determined with error of the measuring devices but with a methodological (residual) error in the method of least squares. An important general result of the study is no variation of the throttle characteristics to the values of Qjfa specified by the user, preliminary settings of the throttles, pressure in the source, interaction of the throttles, etc.

The throttle characteristics of a system are fundamental to predicting the gas consumption by households and industries with a transition from EN-j to individual users connected to this energy nodes an be designed based on the principle of energy equivalence [2—6]. Large linearity of the objective function (3) poses a certain challenge that involves chnages in the number of iteration. The number of iterations during the experiment was within (0.5 – 50) × 103. Based on that, the algorithm of prelimiary and precise prediction can be set forth. Preliminarily it is performed using a range of changes Qjfa specified by the user and comprises modelling of flow distribution using the iteration solution of the system of equations (4)—(7), designing the throttle characteristics using the results of the calculations.

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A precise analysis implements all of the characteristics and involves specification of the variables SDj borrowed from the above characteristics and included in the flow distribution data base (4)—(6) and the direct analysis.

Conclusions

1.There are plans to develop energy nodes using gas distribution systems to improve throttle characteristics that are the only suitable data to control a system with N remotely controlled throttles.

2.Energy-powered valves with an optical and fibre connection, shutters with the interior (operating) characteristics that recreates the configuration of throttle characteristics of a system should be employed as throttles.

References

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