Power2sys (Power System Blockset)

Analyze an electric circuit built with the Power System Blockset

Syntax

POWER2SYS('simwin');
[A,B,C,D,x0,state_var,inputs,outputs,uss,xss,yss,freqyss,Hlin]= 
POWER2SYS('simwin');
[A,B,C,D,x0,state_var,inputs,outputs,uss,xss,yss,freqyss,Hlin]= 
POWER2SYS('simwin','n');

Description

The Power2sys block is used to computes the equivalent state-space model of an electrical network built with the Power System Blockset. power2sys extracts the linear part of the simwin system and builds the corresponding state-space model. State variables are the inductor currents and capacitor voltages. Nonlinear elements are simulated by current sources (state-space model inputs) driven by the voltages (state-space model outputs) across the nonlinear elements.

[A,B,C,D,x0,state_var,inputs,outputs,uss,xss,yss,freqyss, Hlin]=POWER2SYS('simwin') computes the equivalent state-space model of the Simulink window named simwin. A,B,C,D are the standard matrices of the state-space system described by the equations

x0 is a vector containing the initial conditions of the state variables listed in state_var.

state_var is a string matrix containing names of the state variables (x vector). Each line of state_var begins with a prefix Uc_ for capacitor voltages or Il_ for inductor currents, followed by the name of the block in which the element (C or L) is found. Inductor current direction and capacitor voltages polarities are defined by the input and output of the block. The following conventions are used:

Current flowing in the arrow direction is positive.
voltage = Vinput-Voutput.

A suffix is added to the line for blocks containing more than two inductances or capacitors: for example, the three winding Linear Transformer block will produce three state_var lines, one for each leakage inductance, with the suffix coil:x where x is the winding number of the transformer.

inputs is a string matrix containing names of the inputs of the system (vector u). Each line of inputs begins with a prefix U_ for voltage sources or I_ for current sources, followed by the name of the source block.

The following conventions are used for inputs:

Source current flowing in the arrow direction is positive.
Positive source voltage is indicated by a + sign on the icon.

A suffix may be added to the input for blocks containing more than one source. For example, the Simplified Alternator block produces two current inputs with suffixes AB and BC.

outputs is a string matrix containing names of the outputs of the state-space system (vector y). Each line of outputs begins with a prefix U_ for voltage outputs or I_ for current outputs, followed by the name of the block which produces the output. Sign conventions are indicated by the polarities of the voltage measurement and current measurement blocks.

uss, xss, and yss are complex matrices containing the steady-state values (phasors) of inputs, states and outputs. If voltage and current sources all generate the same frequency, these are column vectors. If sources with different frequencies are used, each column of the matrices corresponds to a frequency contained in the freqyss vector.

freqyss is a column vector containing the n_freq input source frequencies ordered by increasing values.

Hlin is the complex transfer impedance three-dimension array (n_output by n_input by n_freq) of the linear system corresponding to the frequencies contained in the freqyss vector. For a particular frequency, Hlin is defined by

yss(:,ifreq) = Hlin(:,:,ifreq) x uss(:,ifreq)

Netlist. When called with a second argument 'n', powers2sys generates a netlist stored in a file, simwin.net. This file contains the node numbers automatically generated by power2sys, as well as parameter values of all linear elements. See formats in the circ2ss reference section.

Example

Obtain the state-space matrices and steady-state voltages and currents for the following circuit.

First open the psbnetsim2.mdl example then execute power2sys:

psbnetsim2
[A,B,C,D,x0,states,inputs,outputs,uss,xss,yss,freqyss,
Hlin]=power2sys('psbnetsim2')

A =
    1.0e+04 *
          0      6.2500
   -0.0083      -1.4250

B =
    1.0e+04 *
          0     -6.2500
    0.0083       1.000
C =
     1    120
     0      0

D =
     0   -120
     0    1

Initial values of states:

x0 =
 -513.1443
    2.9190

states =
Uc_120 Ohms 16 uF                                
Il_51 Ohms  12 mH                                

inputs =
U_1000V 60Hz                          
I_Breaker  Ron=0.01 Lon=10e-6         

outputs =
U_Breaker  Ron=0.01 Lon=10e-6         
I_Current Measurement

Steady-state phasor values of input sources, states, and outputs

uss =
        1000
              0

xss =
   1.0e+02 *
   4.8392 - 5.1314i
   0.0310 + 0.0292i

yss =
   1.0e+02 *
   8.5535 - 1.6287i
            0

The system contains only one source frequency:

freqyss =
    60

Transfer function matrix:

Hlin =
   0.8553 - 0.1629i -44.3596 + 4.4368i
        0             1.0000

There are two state variables in this circuit. Note that the breaker block is a nonlinear element, which is represented by a current source (second input) driven by the voltage across the breaker (first output).