Modelling of energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 38

Load node : Is consumption point giving the amount of gas flow F required, and
therefore operating pressure value p is what needs to be determined.

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The natural gas literature shows that steady-state calculations of load flows have
been described by many formulas but none of them have complete acceptance from
academia or industry. This is because the effects of friction are difficult to quantify
and this creates formula variations across the publications. Nevertheless, similar to
electric load flow studies, natural gas load flow studies are represented by a set of
non-linear equations which can be solved in a variety of ways. However, for sake of
uniformity, the nodal method approach based on KCL is developed in this work to
describe gas flow analysis.
All flow equations in pipes are derived from Bernoulli's equation and can be
defined for pipe connecting nodes k to m as:

w k w m

p k
ρg +

p m
ρg + 2 g +

ρgh k =

2 g +

ρgh m + hl f (3.33)

Each term from (3.33) represents a form of energy in terms of pressure p , veloc-
ity w and height h . Meanwhile, ρ is the density of the fluid and g is the gravitational
force, while hl f is the head loss due to friction.
The derivation of gas flow equations used in this work is based on Weymouth's
formulae, popular within the gas industry, and involves a number of simplifying
assumptions which include:

The fluid is non-viscous and incompressible;

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The temperature of the gas remains constant;

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Speed changes in the gas flow and height variations in the pipes are negligible;

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Natural gas density is constant throughout the network;

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Friction factor coefficient is constant along all pipe lengths.

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3.2.3 Nodal formulation and the incidence matrix
For a gas network the nodal formulation must satisfy the conservation law that
assures the sum of all pipe flows into a node must be equal to 0. The nodal flow
'mismatch' equation for node k can be formulated as:

F k = F Gk − F Dk − F Tk = F Rk − F Tk = 0 (3.34)

Similar to (3.1) in the electric load flow formulation, variables F Gk and F Dk
represent, respectively, source flow injections and flow demands. These variables are
usually known by the network operator and thus used as input data. This means the
gas load flow problem concentrates in determining all the transmitted pipe flows,
F Tk , that are linked to node k as functions of nodal pressures and pipeline friction
conditions.
In order to solve the gas load flow problem, an initial guess is made on the nodal
pressure values. This approximation is then successively corrected until a satisfying
solution is reached. During the solution process the pressures are just estimates of