Modelling of energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 43

Table 3.2 SI base units for thermal and electric power

Variable Natural gas system Electrical system

kg/ms 2 m 2 kg/s 3 A Potential

m 3 /s

Flux A

kg/ms 2 × m 3 /s m 2 kg/s 3 A × A

Potential × Flux

Power m 2 kg/s 3 m 2 kg/s 3

Although there are some key analogies between electric and natural gas systems,
there also exist some important differences; some of these are [66]:

Natural gas flows at 60-100 km/h, while electric energy moves much faster;

●

The ability to store power in natural gas systems to meet peak demand has been
tackled and is a mature technology. Meanwhile, electrical systems have not been
able to develop significant storage capacities at a reasonable cost;

●

Since electricity is not a storable commodity, economies of scale are larger for
electrical systems than for natural gas systems. Hence, it is expensive to retrofit
a power line, while on the contrary, it is not capital intensive to change operating
pressures in pipes to increase capacity;

●

Faults which lead to outages do not occur as fast in natural gas systems (monitored
periodically) as they do in electrical systems (monitored in real time).

●

3.3.2 The Newton-Raphson algorithm
As seen in sections 3.1.3 and 3.2.3, the nodal formulations for steady-state load flow
studies in electrical and natural gas systems require iterative procedures to solve the
particular characteristics each problem represents. Whichever solvers used should
run until the mismatch functions (3.1), (3.2) and (3.34) are satisfied. Although var-
ious techniques are well known in the literature, evidence has shown that methods
which efficiently reduce both computation time and data storage have an impor-
tant advantage. Due to this reason, the Newton-Raphson approach is preferred
against others, such as the Gauss-Seidl and Hardy Cross methods. Furthermore,
Newton's algorithm features strong convergence characteristics by finding better suc-
cessive approximations of the functions roots; this condition is especially true if the
iteration begins near the solution.
The Newton-Raphson method is derived from a Taylor's expansion , wisely
employing the sparsity of the connectivity matrix to obtain a straightforward
formulation and solution independent of the network size that is to be analysed.
A two-dimensional problem is used as an example to briefly describe the tech-
nique, and in which term x 0 represents the set of unknown state variables:

f ( x 0 ) x 2
2

f ( x 0 ) x

f ( x 0 + x ) = f ( x 0 ) + + +···= 0 (3.54)

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