MATLAB: How are the L and R matrices derived from the parameters of the per unit synchronous machine in SimPowerSystems

Simscape Electrical

I am trying to understand how the L and R matrices derived from the parameters of the per unit synchronous machine in SimPowerSystems.

I went through the reference papers in order to understand how to get from the standard pu parameters to the matrices L and R.

Yet, the formulas I got (and verified with the books I have) from these papers would not lead to an unrealistic L matrix in case of Xl = 0.01 in my example.

Hence, I wonder which parameters does the SimPowerSystem algorithms compute realistic values and similar values to those I'd get with my simpler formulas from your references?

Best Answer

Here are the steps that we are using to calculate Xmd:

1. From Td’ and Td’’, the open-circuit time constant Tdo’ and Tdo’’ are estimated base on Ref.[1].

2. From Xd, Xd’, Xd’’, Xl, and Td’’, the d-axis damper time constant Tkd is estimated base on Ref.[2].

3. From Td’, Td’’, Tdo’, Tdo’’, Tkd, and Xd, Xmd is calculated based on Ref.[3].

References:

[1]. I. M. Canay, “Modelling of alternating-current machines having multiple rotor circuits”

[2]. Y. Takeda and B. Adkins, “Determination of Synchronous Machine Parameters Allowing for Unequal Mutual Inductances”

[3]. L. Salvatore, M. Savino, “Exact relationship between parameters and test data for models of synchronous machines”

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MATLAB: What algorithm is used to calculate the Transformation Ratio in the Synchronous machine block in SimPowerSystems

This change has been incorporated into the documentation in Release 2011a (R2011a). For previous releases, read below for any additional information:

The transformation ratio (TR) in the Synchronous machine block can be calculated employing the value of the nominal field current as follow:

        TR = (2/3)*(Inom_field/Ibase_stator) .............................(1)

where,

        'Inom_field' is the nominal field current (in the rotor field) 
        'Ibase_stator' is the stator base current.

The stator base current can be expressed as follows:

         Ibase_stator = sqrt(2/3)*(Pbase/Vbase)

where,

         'Pbase' is the base power
         'Vbase' is the base voltage

Please note that the transformation ratio calculated above is the same as given by the following equation:

          TR = (2/3)*(Nf/Ns).............................(2)

where,

         'Nf' is the number of field winding turns
         'Ns' is the number of stator winding turns

Although the latter expression (2) is more common in literature, the two expressions may be shown to be equal empirically.

MATLAB: How does using multiple SimPowerSystems Ideal Switch blocks in series with snubber impedances compare with reality in the power network in SimPowerSystems 4.3 (R2006b)

If you build a real circuit with two switches connected in series as in your example "Basic_network_topology.mdl", the voltage appearing across switches when both switches are opened will be dictated by the stray capacitance of each individual switch and by their capacitances to ground. We can assume that the resistive leakage current is negligible.

For a mechanical switch this stray capacitance can be evaluated based on the

switch geometry or it can be measured.

In your example, if you replace the resistive snubber by capacitive snubbers

by setting

 Rs=0 and Cs=10e-12

(assuming 10 pF stray capacitances), you will still obtain 50 V across each switch. See example model "Basic_network_topologyGS.mdl".

Now, if the capacitances are

 Cs1= 10 pF and Cs2=30 pF
 you get 
 Vsw1= 75 V  and Vsw2 = 25 V.

Naturally, if you use a Voltage sensor with given input impedance, the voltage sharing will be affected. For example, using a voltage sensor with 10-Megohm resistive input impedance to measure Vsw1 and Cs1=Cs2= 10 pF will give

 Vsw1| ~0  V Vsw2=100 V

If the voltage source is an AC source of 60 Hz and 100V peak voltage, you would get Vsw1 = 3.8 V peak and Vsw2 = 99.8 V .

In other words, the voltage sharing is highly dependant on the stray capacitances and voltage sensors input impedances as it would be in the real life.

Best Answer

Related Solutions

MATLAB: What algorithm is used to calculate the Transformation Ratio in the Synchronous machine block in SimPowerSystems

MATLAB: How does using multiple SimPowerSystems Ideal Switch blocks in series with snubber impedances compare with reality in the power network in SimPowerSystems 4.3 (R2006b)

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