Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin
CRC Press, CRC Press LLC
ISBN: 0849398045   Pub Date: 11/01/98
  

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The remaining elements hij of matrix H can be determined in the same way. Transfer function H relates the input line currents of the converter with the output phase currents of the load. These currents are not available if the machine’s phases are delta connected. To solve this, a current transfer function is defined that relates input and output line currents by simple inspection of Figure 1. Each input line is connected to each of the three output lines, so to comply with Kirchhoff’s current law, the sum of the load’s line currents multiplied by the switches states must add up to the corresponding input line current. This can be stated as

where,

Hi = converter current transfer function, 3×3 matrix;
Iin = input line currents, 3×1 column vector;
Io = output line currents, 3×1 column vector.

Matrix Hi can also be expressed as a function of the converter’s switches, as shown in (16).

Equations (10) through (16) totally define the XDFC’s operation and provide a useful tool for modeling and controlling the converter due to the minimum processing requirements of the transfer function approach.

3. Space Vector Model of the DFC

Space vectors have proven to be an extremely useful modeling technique for static power converters. Since their introduction [7], they have been employed to modulate and control rectifiers, inverters, and DFCs [21][22]. The reason for their success is that they provide the engineer a better understanding of the converter operation.

Space vectors are obtained using a three-phase to two-phase matrix transformation. In this chapter, Park’s matrix is used (17).

Each electric state es of the DFC can be converted using (17) into a space vector sv as shown in (18).

where,

= space vector, 2×1 column vector;
P = Park’s transformation, 2×3 matrix;
es = converter electric state, 3×1 column vector.

Space vectors are bidimensional vectors, and thus can also be written in complex number notation, where element is the real part and element is the imaginary part.

Each converter electric state has two associated vectors, a voltage space vector toward the load side and a current space vector toward the input side. For voltage space vectors, es is defined by (19), and determined by (11) as a function of the input phase voltages and the converter’s transfer function H.

For current space vectors, es is defined by (20), and determined by (15) as a function of the output line currents and the converter’s current transfer function Hi.

Using complex number notation, space vectors can be written as

where its module and argument are defined by (22).

Table III shows the voltage and current space vectors for each of the 27 XDFC’s electric states. For the sake of simplicity, sinusoidal input voltages and sinusoidal output currents have been considered. These are shown in (23).

Figure 5 depicts voltage and current space vectors in the two-phase (α-β) plane. Space vectors 1 to 18 are stationary, i.e., they do not rotate; however, their phase changes in ±180° as their module varies sinusoidally in time as a function of time and the input frequency for voltage space vectors, and as a function of time and the output frequency for current space vectors. Space vectors 19 to 24 have a fixed module and a varying phase; consequently, they rotate as a function of time and the input frequency for voltage space vectors, and as a function of time and the output frequency for current space vectors. Space vectors 25, 26, and 27 are named null space vectors, as they produce zero output voltages and zero input currents.

Table III DFC Voltage and Current Space Vectors


Figure 5  Space vector representation of the DFC states.
a) Voltage space vectors and b) current space vectors at ωt = 0°.


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