View source for Black box model of power converter

The '''[[Black box|black box]] model of power converter''' also called behavior model, is a method of [[System identification|system identification]] to represent the characteristics of power converter, that is regarded as a black box. There are two types of black box model of power converter - when the model includes the load, it is called terminated model, otherwise un-terminated model. The type of black box model of power converter is chosen based on the goal of modeling. This [[Black box|black box]] model of power converter could be a tool for [[Filter design|filter design]] of a system integrated with power converters.
To successfully implement a black box model of a power converter, the equivalent circuit of the converter is assumed a-priori, with the assumption that this equivalent circuit remains constant under different operating conditions. The equivalent circuit of the black box model is built by measuring the stimulus/response of the power converter.

Different modeling methods of power converter could be applied in different circumstances. The [[Software:White box (software engineering)|white box]] model of power converters is suitable when all the inner components are known, which can be quite difficult due to the complex nature of the power converter. The [[Grey box model|grey box model]] combines some features from both, black box model and white box model, when parts of components are known or the relationship between physical elements and equivalent circuit is investigated.

== Assumption ==
Since the power converter consists of [[Engineering:Power semiconductor device|power semiconductor device]] switches, it is a [[Nonlinear system|nonlinear]] and [[Time-variant system|time-variant system]].<ref name="Banerjee-">{{cite book |last1=Banerjee |first1=Sounitro |title=Nonlinear phenomena in power electronics : attractors, bifurcations, chaos, and nonlinear control |date=2001 |publisher=John Wiley & Sons |isbn=978-0-780-35383-1 |pages=472}}</ref> One assumption of black box model of a power converter is that the system is regarded as [[Physics:Linear system|linear system]] when the filter is designed properly to avoid saturation and nonlinear effects. Another strong assumption related to the modeling procedure is that the equivalent circuit model is invariant under different operating conditions. Since in the modeling procedures circuit components are determined under different operating conditions.

== Equivalent circuit ==
The expression of a black box model of power converter is the assumed equivalent circuit model (in [[Frequency domain|frequency domain]]), which could be easily integrated in the circuit of a system in order to facilitate the process of filter design, [[Control system|control system]] design and [[Pulse-width modulation|pulse-width modulation]] design. In general, the equivalent circuit contains mainly two parts: active components like voltage/current sources, and passive components like impedance. The process of black box modeling is actually an approach to determine this equivalent circuit for the converter.

[[File:Equivalent circuit of black box model of power converter.png|thumb|upright=1.6|Six equivalent circuits types of power converter's black box model]]
=== Active components ===
The active components in equivalent circuit are voltage/current sources. They are usually at least two sources, which could be variety options depending on the analysis approach, such as two voltage sources, two current sources, and one voltage and one current source. 

=== Passive components=== 
The passive components containing [[Engineering:Resistor|resistor]]s, [[Engineering:Capacitor|capacitor]]s and [[Engineering:Inductor|inductor]]s can be expressed as combination of several [[Physics:Electrical impedance|impedances]] or [[Physics:Admittance|admittance]]s. Another expression method is to regard the passive components of the power converter as a [[Two-port network|two-port network]] and use a [[Admittance parameters|Y-matrix]] or [[Impedance parameters|Z-matrix]] to describe the characteristics of passive components.

== Modeling method ==
Different modeling methods can be utilized to define the equivalent circuit. It depends on the chosen equivalent circuit and the optional measurement techniques. However, many modeling methods need at least one or more assumption mentioned above in order to regard the systems as linear time-invariant system or periodically switched linear system.

=== One example of modeling method===
This method is based on the two assumptions mentioned in section Assumption, so the system is regarded as linear time-invariant system. Based on these assumptions, the equivalent circuit could be derived from several equations of different operating conditions. The equivalent circuit model is defined containing three impedances and two current sources, where five unknown parameters needs to be determined. Three sets of different operating conditions are built up by changing external impedance and the corresponding currents and voltages at the terminals of the power converter are measured or simulated as known parameters. In each condition, two equations containing five unknown  variables could be derived according to [[Kirchhoff's circuit laws]] and [[Engineering:Nodal analysis|nodal analysis]]. In total, six equations could be used to solve these five unknowns and the equivalent circuit could be determined in this way.

=== Other methods to determine passive elements===
There are many methods used to determine passive elements. The conventional method is to switch off the power converter and measure the impedance with an [[Physics:Impedance analyzer|impedance analyzer]], or measure the [[Scattering parameters|scattering parameters]] by a vector network analyzer and compute the impedance afterwards. These conventional methods assume that the impedances of power converter is the same in the operating condition and switched-off condition.

Many state-of-art methods are investigated to measure the impedance when the power converter is in operating condition. One method is to put two clamp-on current probes in the system, in which one is called receiving probe and another is injecting  probe.<ref name="Tarateeraseth-Jan-2010">{{cite journal |last1=Tarateeraseth |first1=V. |last2=Bo Hu |last3=Kye Yak See |last4=Canavero |first4=F.G. |title=Accurate Extraction of Noise Source Impedance of an SMPS Under Operating Conditions |journal=IEEE Transactions on Power Electronics |date=January 2010 |volume=25 |issue=1 |pages=111–117 |doi=10.1109/TPEL.2009.2024675|bibcode=2010ITPE...25..111T |hdl=10220/6219 |s2cid=26273089 |url=http://porto.polito.it/2362053/1/p_electr_SMPS_Impedance_2010.pdf }}</ref> The output of two probes are connected on a vector network analyzer, the impedance of power converter is measured after some calibration procedures in [[Physics:Common-mode signal|CM]] and [[Engineering:Differential signaling|DM]] measurement setups. This method is restricted with its delicate calibration procedure.

Another state-of-art method is to utilize a transformer and an impedance analyzer in two different setups in order to measure CM and DM impedance separately.<ref name="Mazzola-2019">{{cite journal |last1=Mazzola |first1=Enrico |last2=Grassi |first2=Flavia |last3=Amaducci |first3=Alessandro |title=Novel Measurement Procedure for Switched-Mode Power Supply Modal Impedances |journal=IEEE Transactions on Electromagnetic Compatibility |date=2019 |volume=62 |issue=4 |pages=1349–1357 |doi=10.1109/TEMC.2019.2941449|hdl=11311/1156827 |s2cid=208829058 |hdl-access=free }}</ref> The measurement range of this method is limited by the characteristics of the transformer.

== See also ==

*[[Black box|black box]]
*[[Grey box model|grey box model]]
*[[System identification|system identification]]
*[[Nonlinear system identification|nonlinear system identification]]
*[[Linear time-invariant system|linear time-invariant system]]
*[[Time-variant system|time-variant system]]
*[[Nonlinear system|nonlinear system]]

==References==
<references/>

[[Category:Electromagnetic compatibility]]
[[Category:Systems theory]]
[[Category:Dynamical systems]]

{{Sourceattribution|Black box model of power converter}}