Modelling of energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 35

Since the current values are not usually known in electrical networks, they have
to be calculated from the power equation. This implies that relationships between
nodal currents and voltages must be established. For a system conformed of n -th
nodes, the net nodal power injection at node k can be determined as:

V k ( I Tk ) ∗

S Tk = P Tk + jQ Tk = (3.23)

where ( I Tk ) ∗ is the complex conjugate of the current injected at node k .
Te r m s Y km , V k and I Tk can be expressed in rectangular form as:
Y km

= G km + jB km (3.24)

V k = e k + jf k (3.25)

n

I Tk = a Tk + jb Tk = ( G kn e n − B kn f n ) + j ( G kn f n + B kn e n ) (3.26)

m = 1

Henceforth, variables P Tk and Q Tk can be developed in rectangular form by
multiplying term (3.25) with the conjugate of (3.26); thus deducing:

P Tk = e k a Tk + f k b Tk (3.27)

Q Tk = f k a Tk − e k b Tk (3.28)

If we take (3.1) and (3.2) and substitute expressions (3.27) and (3.28), it is pos-
sible to rewrite the mismatch power equations as:

P k = P Gk − P Dk − ( e k a Tk + f k b Tk ) = 0 (3.29)

Q k = Q Gk − Q Dk − ( f k a Tk − e k b Tk ) = 0 (3.30)

A satisfactory answer in electrical load flow studies is found when the itera-
tive solver has reduced the power mismatch equations below a certain quantity or
tolerance value ( e.g. ) specified by the user, and defined for node k as:

| P k | ≤ P (3.31)

| Q k | ≤ Q (3.32)

3.2 Modelling natural gas networks

3.2.1 Fundamentals of natural gas systems
Natural gas systems consist of transporting the commodity through a large set of
highly integrated pipe networks operating over a wide range of pressures. This fos-
sil fuel is mainly obtained from gas wells in remote sites which are far from load
centres and fluid dynamic laws are applied in order to move the gas from one point
to another. Similar to power systems a hierarchical delivery system is employed.
Figure 3.3 shows a simplified natural gas flow path starting from the high-pressure
equipment and eventually leading to the low-pressure distribution networks for final
consumption.