2 Calculation of the statistical stability of the electric power system

For a given scheme of the electric power system (Figure 3.1), calculate the dynamic stability for three-phase short-circuit and two-phase short-circuit on the ground on a given line in the presence of an ARE of proportional type on the generators. Catalog data of power system installations:

Table 2.1 - Catalog data of turbogenerator of power station 1

Type	Sn, VA	cosϕ	Q1, Mvar	Un, kV	х"d(н)	хd(н)	х2(н)	GD2, t·m2	Td0	n
ТGV-345	78	0,85	100	10.5	0.26	1.8	0.24	15	9	4

Table 2.2 - Catalog data of substation transformers 1

Type	n	Sn, MVA	UnHV, kV	UnLV, kV	uk, %	P	Pxx
	1	300	45	10.5	10.5

Table 2.3 - Catalog data of substation transformers 2

Type	n	Sn, MVA	UnHV, kV	UnLV, kV	uk, %	P	Pxx
	1	400	100	10.5	10.5

Table 2.4- Parameters of other elements

Power lines, n=2	System	Load
Ppl=150 MW	Uc=110 kV	Рload =350 МW
cosφ=0,85	Sc=234 MVA	cosφ=0.85
Un =15.75 кV	cos=0.85
ℓ=100 km	sin=0.341
х10=0,37 Оhm/km,
r10=0,132 Оhm/km

Figure 3.1 - Calculation scheme for option 23

The solution:

1. We compose substitution scheme and apply results of calculations to it.

2. Determine the parameters of the substitution circuit for this we specify basic values (voltage, power).

For the base voltage, we take the voltage on the buses of an equivalent system GS of infinite power (which has an infinite regulating effect of the load, which leads to a constant voltage on the buses of the equivalent system) U_b3 = 10.5 kV. The base power is assumed equal to S_b = 100 MVA.

We define the base voltages for the following steps:

Define the resistance of the elements:

- the equivalent generator G

- at substation 1 (T1):

- at substation 2 (T2):

- resistance of power lines:

We determine the total power of the load and the power flowing along the power lines to the buses of constant voltage:

We determine the voltage of the main stage in relative units:

We form the equivalent circuit on which is applied the obtained calculation values:

Figure 3.4 - The equivalent circuit

3. Calculation of the angular power characteristics for a normal mode

Determine the transient resistance x_d’’:

Determine the total reactance

Define the transient EMF:

Let us determine the transverse component of the transient EMF:

Define the transmitted power: