Calculation of power grid modes¶
This example shows how to use the Grid Calculation application on the example of the power system shown in the figure:
To enter the scheme into the application and calculate the mode, a number of sequential actions are required.
1. Drawing up the substitution diagram¶
In order to correctly specify the circuit in the application, it is necessary to first make a substitution diagram with numbering of all nodes. Loads and generators are defined by power injection, overhead lines are modelled according to the Π-substitution diagram, autotransformers (AT) are represented according to the star diagram with an intermediate node and three branches, two of which have transformation ratios, static capacitor banks (SCB) are replaced by a shunt.
2. Calculation of substitution scheme parameters¶
Formulas for calculation of parameters of substitution diagrams of power system elements.
Overhead line:
Active resistance:
$R_л=r_0·L/n_ц$
Inductive resistance:
$X_л=x_0·L/n_ц$
Capacitive conductivity to ground:
$B_л=b_0·L·n_ц$
The calculations are summarised in the table:
|Параметр\ВЛ|1-2|5-6|6-7|7-8|5-8|
|:---|:---|:---|:---|:---|:---|
||AC 400/51|AC 240/32|AC 240/32|AC 240/32|AC 240/32|AC 240/32|
|$U_{ном}, кВ$|220|110|110|110|110|110|110|
|$r_0, Ом/км$|0.0730|0.118|0.118|0.118|0.118|
|$x_0, Ом/км$|0.42|0.405|0.405|0.405|0.405|0.405|
|$b_0, мкСм/км$|2.701|2.808|2.808|2.808|2.808|2.808|
|$L, км$|300|40|50|30|60|
|$n_ц$|2|1|1|1|1|1|
|$R_л, Ом$|10.95|4.72|5.9|3.54|7.08|
|$X_л, Ом$|63|16.2|20.25|12.15|24.3|
|$B_л, мкСм$|1620.6|112.32|140.4|84.24|168.48|
AT:
Active resistances are calculated taking into account winding powers B:C:H = 100%:100%:50%:
$R_{в}=R_{с}=\frac{ΔP_{кв-с}}{2·S_{ном}}·\frac{U_н^{2}}{S_{ном}}·\frac{1}{n_т}=\frac{0.430}{2·200}·\frac{230^{2}}{200}·\frac{1}{2}=0.142 Ом$
$R_{н}=2·R_{в}=0.284 Ом$
Recalculation of short-circuit voltages:
$u_{кв}=0.5(u_{кв-с}+u_{кв-н}-u_{кс-н})=0.5(11+32-20)=11.5 \%$
$u_{кс}=0.5(u_{кв-с}-u_{кв-н}+u_{кс-н})=0.5(11-32+20)=-0.5 \%$
$u_{кн}=0.5(-u_{кв-с}+u_{кв-н}+u_{кс-н})=0.5(-11+32+20)=20.5 \%$
Since $u_{кс}$ physically cannot be negative, we take it to be zero.
Inductive resistances:
$X_{в}=\frac{u_{кв}}{100}·\frac{U_н^{2}}{S_{ном}}·\frac{1}{n_т}=\frac{11.5}{100}·\frac{230^{2}}{200}·\frac{1}{2}=15.208 Ом$
$X_{с}=\frac{0}{100}·\frac{230^{2}}{200}·\frac{1}{2}=0 Ом$
$X_{н}=\frac{u_{кн}}{100}·\frac{U_н^{2}}{S_{ном}}·\frac{1}{n_т}=\frac{20.5}{100}·\frac{230^{2}}{200}·\frac{1}{2}=27.111 Ом$
Active and inductive conductances of the AT magnetising branch:
$G_{х}=\frac{P_х}{U_н^{2}}·n_т=\frac{0.125}{230^{2}}·2=4.725 мкСм$
$B_{х}=\frac{Q_х}{U_н^{2}}·n_т=\frac{1}{230^{2}}·2=37.807 мкСм$
Transformation coefficients:
$k_{тв-н}=\frac{U_н}{U_в}=\frac{11}{230}=0.0478$
$k_{тв-с}=\frac{U_с}{U_в}=\frac{121}{230}=0.526$
BSC:
$B_{БСК}=\frac{Q_{БСК}}{U_{ном}^{2}}=\frac{7.2}{110^{2}}=595.041 мкСм$
3. Scheme assignment in the appendix¶
To open the application go to the Engee workspace and in the upper left corner under Applications select Calculation of power grid modes.
Three tabs with tables are used to work with the application: Nodes, Branches, Generators. When opening the application, they will be empty. In all three tables there is a column of row number N, it must be filled in when adding each row.
Nodes¶
Let's start with node assignment. To add a node, select the Nodes tab and click the Add Row button.
Node 1 is a basic node, for it it is necessary to set the rated voltage, type and add a generator to this node on the Generators tab. The columns of the node number Nnode = 1 and the set voltage Vzd = 230 kV are set for the generator.
Node number 2 is a load node, it is necessary to set the type, nominal voltage and conductivity of the shunt of the autotransformer cross branch. Active and capacitive conductivities of the shunt are set with plus sign, and inductive conductivity with minus sign. By default, there are no columns for shunt conductance on the Nodes tab. To add columns, click the Customise visible columns -> Node columns -> Gsh, Bsh button.
After adding the columns enter the values of conductivities, it should turn out as in the figure:
Node #3 is also a load node, enter the type and nominal voltage.
Node #4 - for it we set the load, type "generator" and nominal voltage 10 kV. Load power is set in columns Pn = 80 MW and Qn = 40 Mvar. At the generator the columns of node number Nnode = 4, active power Pr = 150 MW, set voltage Vzd = 10.5 kV and reactive power control limits Qmax = 100 Mvar and Qmin = -100 Mvar are set.
Nodes 5-8 are load nodes, in node 7 it is necessary to set BSC in the form of shunt.
The result should be the following tables Nodes and Generators:
Branches¶
Let's move on to the branch assignment. Branches are of two types: line and transformer. The branch type is determined by the value of the transformation ratio: if Kt = 1, it is a line; if Kt ≠ 1, it is a transformer. To add the first branch, go to the Branches tab and add a line. Branches connect nodes, so for all branches you need to specify a start and end node.
Branch 1-2 is an overhead line, for it it is necessary to set resistances and conductivity.
Branch 2-3 is one of the AT branches, which does not contain a transformer - therefore it is set similarly to overhead line, without taking into account capacitive conductivity.
Branch 3-4 is a transformer branch, it is necessary to set the transformer coefficient.
Branch 3-5 is a transformer branch with zero inductive resistance.
Other branches are overhead lines, they are set by analogy with branch 1-2. The result should be the following table of branches:
This completes the data entry step.
4. Calculation of the mode¶
To calculate the mode it is necessary to press the Start Calculation button. If everything is set correctly, Solution found will appear in the upper left corner and the calculated voltages and powers will appear in the tables.
The calculation results can be saved using the Save file with mode button.
The directory with the saved mode file will appear in the Engee file browser:
To verify the correctness of the data setting and mode calculation, let's compare the results with the RastrWin programme. Results of mode calculation in RastrWin:
Note that in the application the positive power direction is set from bus to line, while in RastrWin it is set from end to beginning. As a result, the power signs of the branches may be different.
Conclusions¶
In this example it was shown how to calculate parameters of power system elements and perform steady-state calculations using the RastrWin application. The results obtained confirm the correctness of the application and its compliance with the calculations performed in the RastrWin programme.