# power_analyze

Analyze electric circuit

## Syntax

```sps = power_analyze('sys','structure') [A,B,C,D,x0,states,inputs,outputs,uss,xss,yss,frequencies,Hlin] =... power_analyze('sys') sps = power_analyze('sys','sort') sps = power_analyze('sys','ss') power_analyze('sys','net') SW = power_analyze('sys','getSwitchStatus') sps = power_analyze('sys','setSwitchStatus',SW) ```

## Description

The `power_analyze` command computes the equivalent state-space model of the specified electrical model built with Simscape™ Electrical™ Specialized Power Systems software. It evaluates the A, B, C, D standard matrices of the state-space system described by the equations

`$\begin{array}{l}\stackrel{˙}{x}=Ax+Bu\\ y=Cx+Du\end{array}$`

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 motors or machines, are simulated either by current sources driven by the voltages across the nonlinear element terminals, or by voltage sources driven by the currents through the nonlinear element terminals. The nonlinear elements produce additional current and voltage source inputs to the u vector, and additional voltage and current measurements outputs to the y vector.

For the switching devices elements, such as the breakers, diodes, and thyristors, the state-space calculations include only the resistance and capacitance elements of the snubber devices.

The Simulink® blocks of the model, as well as the internal Simulink models of the Simscape Electrical Specialized Power Systems 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 Simscape Electrical Specialized Power Systems 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 character vector 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. Text 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. Text 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.

## 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`

`noutput`-by-`ninput`-by-`nfreq` 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 Simscape Electrical Specialized Power Systems 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.

## Output Arguments: getSwitchStatus

`SW = power_analyze('sys','getSwitchStatus')` returns a structure array with switch names and their initial status. You can use the `SW` structure to specify switch statuses for a particular circuit topology and to compute the corresponding state-space matrices using the command `sps = power_analyze('sys','setSwitchStatus',SW)`. The `SW` structure contains the following fields.

Field

Description

`SwitchNames`

Names of the switches of the system

`SwitchStatus`

Vector of initial states of switches

## Output Arguments: setSwitchStatus

`sps = power_analyze('sys','setSwitchStatus',SW)` creates a structure array `sps` with fields and values describing the state-space matrices of model `sys` for the switch status defined in `SW`. Use the command ``` SW = power_analyze('sys','getSwitchStatus')``` to obtain the `SW` structure array.

Field

Description

`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

## Examples

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).