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In this section, for the modulation of the field current, the implementation of the suggested ANN-based model is demonstrated with the integration of MATLAB/Simulink, ANSYS Maxwell, and ANSYS Simplorer. In the simulated system, the FEM model of SG, which is created in ANSYS Maxwell, and the circuit of the six-pulse uncontrolled rectifier load are simulated in the ANSYS Simplorer environment (see Figure 11). Additionally, the modulation of the field current is optimally determined according to the ANN-based model provided in the MATLAB/Simulink environment (see Figure 12). Figure 11. Test system created in ANSYS Simplorer.

Figure 11 In this section, for the modulation of the field current, the implementation of the suggested ANN-based model is demonstrated with the integration of MATLAB/Simulink, ANSYS Maxwell, and ANSYS Simplorer. In the simulated system, the FEM model of SG, which is created in ANSYS Maxwell, and the circuit of the six-pulse uncontrolled rectifier load are simulated in the ANSYS Simplorer environment (see Figure 11). Additionally, the modulation of the field current is optimally determined according to the ANN-based model provided in the MATLAB/Simulink environment (see Figure 12). Figure 11. Test system created in ANSYS Simplorer.

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Table 1. Parameters of the studied machine.
Table 1. Parameters of the studied machine.
Figure 2. (a) Two-dimensional FE model of synchronous generator. (b) Coupling SG and load models within Maxwell Circuit Editor. To reduce the simulation time, simulation results are obtained for 1/6 of the model geometry given in Figure 2a. Note that for proper analysis sensitivity, the number of meshes is automatically determined as 1428 by ANSYS Maxwell. The load model is coupled with the 2D FE model of the SG through the Maxwell Circuit Editor (see Figure 2b). The PC used for the simulations has a 12-core Ryzen 9 3900x processor and 32 GB of RAM. Using this PC hardware, each simulation is run in 21.5 min.
Figure 2. (a) Two-dimensional FE model of synchronous generator. (b) Coupling SG and load models within Maxwell Circuit Editor. To reduce the simulation time, simulation results are obtained for 1/6 of the model geometry given in Figure 2a. Note that for proper analysis sensitivity, the number of meshes is automatically determined as 1428 by ANSYS Maxwell. The load model is coupled with the 2D FE model of the SG through the Maxwell Circuit Editor (see Figure 2b). The PC used for the simulations has a 12-core Ryzen 9 3900x processor and 32 GB of RAM. Using this PC hardware, each simulation is run in 21.5 min.
Figure 3. Terminal voltage harmonic spectrum of the SG under the no-loading condition.
Figure 3. Terminal voltage harmonic spectrum of the SG under the no-loading condition.
Figure 4. Terminal voltage and phase current harmonic spectrum of the SG under the rated loading condition.
Figure 4. Terminal voltage and phase current harmonic spectrum of the SG under the rated loading condition.
Figure 5. Lowest THDy values obtained for the tested excitation currents. Thus, for the pure DC excitation and the various excitation currents modulated as an AC harmonic current superimposed on that of the DC, the terminal voltages are simulated. In the simulations, for the modulated excitation currents, the magnitude and angle of the harmonic component are varied. Then, the minimum THDy values are determined for each modulated field current case. Accordingly, under low (25%), medium (50%), and full (100%) loading levels, the THDy value for the pure DC excitation current and the minimum THDy values for the modulated field current cases are presented in Figure 5. It can be observed from Figure 5 that for all three loading levels, the minimum THDy values are achieved by modulating the 6th harmonic current (300 Hz) and the DC current. Under 25%, 50%, and 100% loading ratios for the conventional pure DC field current,
Figure 5. Lowest THDy values obtained for the tested excitation currents. Thus, for the pure DC excitation and the various excitation currents modulated as an AC harmonic current superimposed on that of the DC, the terminal voltages are simulated. In the simulations, for the modulated excitation currents, the magnitude and angle of the harmonic component are varied. Then, the minimum THDy values are determined for each modulated field current case. Accordingly, under low (25%), medium (50%), and full (100%) loading levels, the THDy value for the pure DC excitation current and the minimum THDy values for the modulated field current cases are presented in Figure 5. It can be observed from Figure 5 that for all three loading levels, the minimum THDy values are achieved by modulating the 6th harmonic current (300 Hz) and the DC current. Under 25%, 50%, and 100% loading ratios for the conventional pure DC field current,
Figure 6. Surface plots of THDy values in terms of magnitudes and phase angles of AC component with 300 Hz frequency (6th harmonic) under (a) 100%, (b) 50%, and (c) 25% loading conditions. Here, to detail the behavior of the terminal voltages’ distortion for the field current modulation with the 6th harmonic current (300 Hz) and DC components, the THDy varia- tions are plotted in terms of the magnitude and phase angle of the harmonic component under the considered loading levels (see Figure 6). Figure 6 clearly shows that for the achieved minimum THDy values under three loading levels, such as 100%, 50% and 25%, he optimal values of the harmonic current’s phase angle are 180°, 255°, and 315°, respec- tively. Accordingly, it can be posited that for the considered non-linear load, the optimal phase angle of the harmonic current added to DC field current varies between 180° and 360° with the decrement of the loading level. For the same objective, under the respective oading levels, the optimal magnitudes of the harmonic component are 20%, 15%, and 10% of the DC component. This means that there is a direct proportional relation between the optimal magnitude of the harmonic current and the loading level.
Figure 6. Surface plots of THDy values in terms of magnitudes and phase angles of AC component with 300 Hz frequency (6th harmonic) under (a) 100%, (b) 50%, and (c) 25% loading conditions. Here, to detail the behavior of the terminal voltages’ distortion for the field current modulation with the 6th harmonic current (300 Hz) and DC components, the THDy varia- tions are plotted in terms of the magnitude and phase angle of the harmonic component under the considered loading levels (see Figure 6). Figure 6 clearly shows that for the achieved minimum THDy values under three loading levels, such as 100%, 50% and 25%, he optimal values of the harmonic current’s phase angle are 180°, 255°, and 315°, respec- tively. Accordingly, it can be posited that for the considered non-linear load, the optimal phase angle of the harmonic current added to DC field current varies between 180° and 360° with the decrement of the loading level. For the same objective, under the respective oading levels, the optimal magnitudes of the harmonic component are 20%, 15%, and 10% of the DC component. This means that there is a direct proportional relation between the optimal magnitude of the harmonic current and the loading level.
Figure 7. Structure of the used ANN. The structure of the ANN used for the study is given in Figure 7. It has three main parts: input, hidden, and output layers. The input parameters of the first layer are defined as the effective value (I7,) and phase angle (a;) of the 6th harmonic component superimposed on the DC field current and the loading ratio (Ir) of the SG. In the third layer, the magnitudes and phase angles of the terminal harmonic phase voltages are defined as output parameters or targets.
Figure 7. Structure of the used ANN. The structure of the ANN used for the study is given in Figure 7. It has three main parts: input, hidden, and output layers. The input parameters of the first layer are defined as the effective value (I7,) and phase angle (a;) of the 6th harmonic component superimposed on the DC field current and the loading ratio (Ir) of the SG. In the third layer, the magnitudes and phase angles of the terminal harmonic phase voltages are defined as output parameters or targets.
Table 2. MSE values of the ANN.
Table 2. MSE values of the ANN.
In Equations (7) and (8), iw is the weight matrix between the input and the hidden lay- ers, and Iw is the weight matrix between the hidden and the output layers. Additionally, M and S are the numbers of neurons in the input and hidden layers, Vj, ann is the magnitude of the hth harmonic phase voltage, ;, ann is the phase angle of the hth harmonic phase voltage, and b, and b are the bias of the hidden and output layers, respectively. Note that each of the harmonic components has been trained separately. ~ The ANN structure detailed here is developed in the MATLAB/Simulink environment. According to the structure shown in Figure 7, the relationship between the outputs and the input parameters can be written as in Equations (7) and (8).
In Equations (7) and (8), iw is the weight matrix between the input and the hidden lay- ers, and Iw is the weight matrix between the hidden and the output layers. Additionally, M and S are the numbers of neurons in the input and hidden layers, Vj, ann is the magnitude of the hth harmonic phase voltage, ;, ann is the phase angle of the hth harmonic phase voltage, and b, and b are the bias of the hidden and output layers, respectively. Note that each of the harmonic components has been trained separately. ~ The ANN structure detailed here is developed in the MATLAB/Simulink environment. According to the structure shown in Figure 7, the relationship between the outputs and the input parameters can be written as in Equations (7) and (8).
Figure 8. Magnitudes of the non-fundamental harmonic phase voltages simulated by FE and pre. dicted by the developed ANN model.
Figure 8. Magnitudes of the non-fundamental harmonic phase voltages simulated by FE and pre. dicted by the developed ANN model.
Figure 9. Phase angles of the non-fundamental harmonic phase voltages simulated by FE and predicted by the developed ANN model.
Figure 9. Phase angles of the non-fundamental harmonic phase voltages simulated by FE and predicted by the developed ANN model.
Figure 10. Magnitudes and phase angles of the fundamental harmonic phase voltages simulated by FE and predicted by the developed ANN model.
Figure 10. Magnitudes and phase angles of the fundamental harmonic phase voltages simulated by FE and predicted by the developed ANN model.
Figure 12. Implementation blocks of the proposed model in MATLAB/Simulink environment.
Figure 12. Implementation blocks of the proposed model in MATLAB/Simulink environment.
Figure 13. Individual and total harmonic distortions of the terminal line voltages obtained via the proposed (ANN) and FE model under (a) low (20%), (b) semi (50%), (c) full (100%) and (d) over (120%) loading levels for optimally modulated excitation current cases.
Figure 13. Individual and total harmonic distortions of the terminal line voltages obtained via the proposed (ANN) and FE model under (a) low (20%), (b) semi (50%), (c) full (100%) and (d) over (120%) loading levels for optimally modulated excitation current cases.
Related topics:
EngineeringTotal Harmonic Distortion
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