power_analyze - Analyze electric circuit

Syntax

sps = power_analyze('sys','structure')
sps = power_analyze('sys','sort')
sps = power_analyze('sys','ss')
[A,B,C,D,x0,states,inputs,outputs,uss,xss,yss,freqyss,Hlin]= 
power_analyze(`sys');
power_analyze('sys','net')

Description

The power_analyze command computes the equivalent state-space model of the specified electrical model built with SimPowerSystems software. It evaluates the A, B, C, D standard matrices of the state-space system described by the equations

where the state vector x represents the inductor currents and capacitor voltages, the input vector u represents the voltage and current sources, and the output vector y represents the voltage and current measurements of the model.

Nonlinear elements, such as the switch devices, motors and machines, are simulated by current sources driven by the voltages across the nonlinear element terminals. The nonlinear elements produces additional current source inputs to the u vector, and additional voltage measurements outputs to the y vector.

The Simulink blocks of the model, as well as internal Simulink models of the SimPowerSystems nonlinear elements are not represented in the state-space matrices.

State-Space Matrices

The A, B, C, D matrices are computed for the particular circuit topology where all the switch devices, if any, are considered to be open status (that is, with infinite impedance).

power_analyze also computes the Aswitch, Bswitch, Cswitch, and Dswitch matrices for the circuit topology that take into account the initial state (open/closed) of the Breaker and Ideal Switch blocks present in the model. The initial state of power electronic devices (Diodes, Thyristors, and so on) is considered to be open, unless a nonzero initial current value is specified in the mask of the device when Lon parameter is different from zero.

For a circuit that contains no switches, the Aswitch, Bswitch, Cswitch, and Dswitch matrices have exactly the same values as the A, B, C, D matrices.

States

In SimPowerSystems software, each state variable name 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.

A string is added to this prefix for blocks containing more than one inductance or capacitor. For example, the Linear Transformer block is represented with four state variables, one for each of the three leakage inductances, defined with the prefixes Il_winding_x:, where x is the winding number of the transformer, and one state for the magnetization inductance defined with the prefix Il_Lm:.

Inputs

Each input state variable name begins with a prefix U_ for voltage sources or I_ for current sources, followed by the name of the source block. A string can be added to the prefix for blocks containing more than one source. For example, the Synchronous Machine block produces two current inputs with prefixes I_A: and I_B: (phase A and phase B machine currents).

Outputs

Each output state variable name begins with a prefix U_ for voltage outputs or I_ for current outputs, followed by the name of the block that produces the output. A string can be added to the prefix for blocks containing more than one output. For example, the Synchronous Machine block produces two voltage outputs with prefixes U_AB: and U_BC: (two machine phase-to-phase voltages).

Sign Conventions

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.

The sign conventions used for voltages and currents of state variables and measurement outputs are described in Measuring Voltages and Currents. See also Sign Conventions for Voltages and Currents for current directions and voltage polarities.

Output Arguments: Structure

sps = power_analyze('sys','structure') creates a structure array sps with fields and values describing the model sys.

The fields of the structure array are defined in the following order.

Field	Description
`circuit`	Name of the model
`states`	`char` array of state variable names
`inputs`	`char` array of system input names
`outputs`	`char` array of system output names
`A`	`nstates`-by-`nstates` state-space A matrix
`B`	`nstates`-by-`ninput` state-space B matrix
`C`	`noutput`-by-`nstates` state-space C matrix
`D`	`noutput`-by-`ninput` state-space D matrix
`x0`	`nstates`-by-1 vector of initial conditions of the state variables listed in states
`xss`	`nstates`-by-`nfreq` steady-state values of `states`. A set of values is computed for every frequency specified in the `frequencies` vector.
`uss`	`ninput`-by-`nfreq` steady-state values of `inputs`. A set of values is computed for every frequency specified in the `frequencies` vector.
`yss`	`noutput`-by-`nfreq` steady-state values of `outputs`. A set of values is computed for every frequency specified in the `frequencies` vector.
`frequencies`	1-by-`nfreq` vector of input source frequencies ordered by increasing values
`DependentStates`	`char` array of dependent state variable names. The dependent states are not included in the state-space equations.
`x0DependentStates`	Vector of initial conditions of dependent states
`xssDependentStates`	`nstates`-by-`nfreq` steady-state values of dependent states
`Adiscrete`	Discrete state-space A matrix. Returns an empty value when the Powergui is in continuous or in phasor mode.
`Bdiscrete`	Discrete state-space B matrix. Returns an empty value when the Powergui is in continuous or in phasor mode.
`Cdiscrete`	Discrete state-space C matrix. Returns an empty value when the Powergui is in continuous or in phasor mode.
`Ddiscrete`	Discrete state-space D matrix. Returns an empty value when the Powergui is in continuous or in phasor mode.
`x0discrete`	Vector of discrete initial conditions. Returns an empty value when the Powergui is in continuous or in phasor mode.
`SampleTime`	Sample time value used to compute discrete state-space matrices
`Aswitch`	A matrix taking into account the initial status of switch devices
`Bswitch`	B matrix taking into account the initial status of switch devices
`Cswitch`	C matrix taking into account the initial status of switch devices
`Dswitch`	D matrix taking into account the initial status of switch devices
`x0switch`	Vector of initial values of switch currents
`Hlin`	`nfreq`-by-`noutput`-by-`ninput` complex transfer function of impedances of the linear system corresponding to the frequencies contained in the frequencies vector. For a particular frequency, `Hlin` is defined by `yss(:,i) = Hlin(i,:,:) * uss(:,i)`
`OscillatoryModes`	Display the oscillatory modes of the state-space system

The table uses the following conventions:

nstates is the number of states.
ninput is the number of inputs.
noutput is the number of outputs.
nfreq is the number of input source frequencies.

[A,B,C,D,x0,states,inputs,outputs,uss,xss,yss,frequencies,Hlin] = power_analyze('sys') returns the state-space calculations in separate variables.

Output Arguments: Sort

sps = power_analyze('sys','sort') returns a structure array sps with the following fields related to the interconnection of SimPowerSystems blocks in a model. The fields are defined in the following order.

Field	Description
`circuit`	Name of the model
`SampleTime`	Sample time for discrete systems
`RlcBranch`	`rlc` matrix in the `power_statespace` format
`RlcBranchNames`	List of blocks containing the state variable
`SourceBranch`	Source matrix in the `power_statespace` format
`SourceBranchNames`	Names of the blocks defined as sources
`InputNames`	Names of the inputs of the system
`OutputNames`	Names of the outputs of the system
`OutputExpressions`	Output expression in the `power_statespace` format
`OutputMatrix`	Output expression in matrix format (internal)
`MeasurementBlocks`	Names of the voltage and current measurement blocks

Output Arguments: ss

sps = power_analyze('sys','ss') creates a continuous state-space model of the model sys with matrices A, B, C, D. You must have Control System Toolbox software installed for this option. The output is a state-space object.

Output Arguments: Net

power_analyze('sys','net') generates a netlist stored in a file, sys.net. The file contains the node numbers automatically generated by power_analyze, as well as parameter values of all linear elements. See the formats described in the power_statespace reference page.

Example

Obtain the state-space matrices and steady-state voltages and currents for the power_netsim2 circuit.

The command

sps = power_analyze('power_netsim2','structure');

returns the state-space model in the sps structure variable.

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

sps.uss =
	0
	1000

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

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

sps.inputs = 
	I_Breaker
	U_Source

sps.outputs =
	U_Breaker
	I_Current Measurement

The inductor current of the 51-ohm, 12-mH block and the capacitor voltage of the 120-ohm, 16-µF block are the two state variables in this circuit. The Breaker block is a nonlinear element that is represented by a current source (the first input) driven by the voltage across its terminals (the first output).