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The variation of the voltage across the dipole is governed by equation 6. The RC parallel dipole is modelled by the scheme illustrated in figure 3. In a L in series with RC parallel dipole, the variation of the current through the inductance is governed by equation 7 and the variation of the voltage across the capacity is governed by equation 8.

The L in series with RC parallel dipole is modelled by the scheme illustrated in figure 4. Model of a RC parallel dipole. Model of a L in series with RC parallel dipole. The input generator is a DC voltage source and the output generator is also a DC voltage source. The output voltage is always smoothed by a capacitor. Only the non-isolated DC-DC converters are studied in this paragraph.

The switches are assumed ideal, as well as passive elements L, C. The buck converter circuit is illustrated in figure 5 a. The most common strategy for controlling the power transmitted to the load is the intersective Pulse Width Modulation PWM. A control voltage v m is compared to a triangular voltage v t.

The triangular voltage v t determines the switching frequency f t. The switch T is controlled according to the difference v m — v t figure 5b. Three operating phases are counted figure 5c :. Buck converter. The variation of the current through the capacitor C is governed by equation The variation of the voltage across the capacity is governed by equation Equation 12 describes the variation of the voltage across the inductance which depends on the operating phase.

F is a logical variable equal to one if v m is greater than or equal to v t , F equal to zero if v m is less than v t. Sign i L is also a logical variable which is equal to one if i L is positive, sign i L equal to zero if i L is zero. Simulink model of the open-loop buck converter is shown in figure 6 a. The Buck block is illustrated in figure 6 c. Equation 12 is modelled by blocks addition, multiplication and logic.

The structure of the converter requires a current i L necessarily positive or zero. Also, the inductance current is modelled by an integrator block that limits the minimum value of i L to zero. The PWM control block is illustrated in figure 6 b. Buck converter described in Simulink. A closed-loop buck converter circuit is illustrated in figure 7 a. The measurement of the output voltage is realized by 2 resistances R 1 and R 2.

The regulation is achieved by a PID controller. Simulink model of the closed loop converter is shown in figure 7 b. Simulink PID control block is illustrated in figure 7 c. The voltage reference was fixed to 2. The simulation of the closed-loop buck converter is illustrated in figure 7 d.

The list of configuration parameters used for is:. From figure 7a, we deduce the theoretical value of V o :. Simulation is in good agreement with theoretical value. From figure 7d, we deduce that the transient state last roughly 0. The boost converter circuit is illustrated in figure 8 a.

The principle of the switch control is described in figure 5b Three operating phases are counted figure 8c :. The variation of the voltage across the inductance L equation 14 and the current through the capacity equation 15 depend on the operating phase. Simulink model of a open-loop boost converter is shown in figure 9 a. The Boost block is illustrated in figure 9 b. Equation 14 , 15 and 16 are modeled by addition blocks, multiplication blocks and logic blocks. Also, the inductance current is modeled by an integrator block that limits the minimum value of i L to zero.

The simulation of the open-loop boost converter is illustrated in figure 9 c. The list of configuration parameters used is:. In steady-state, we deduce theoretical value of V o :. From figure 9c, we deduce that the transient state last roughly 2. Boost converter.

Boost converter described in Simulink. An inverter is a DC — AC power converter. This converter obtains AC voltage from DC voltage. The applications are numerous: power backup for the computer systems, variable speed drive motor, induction heating In most cases, the dead times introduced into the control of the switches do not change the waveform of the inverter. This paragraph is dedicated to the simulation of a three-phase inverter without taking into account the dead times introduced into the control of the switches.

A variable speed drive for AC motor is shown in figure It consists on a continuous voltage source and a three-phase inverter feeding an AC motor. In order to simplify the modelling, the electrical equivalent circuit of the AC motor is described by an inductance L M in series with a resistance R M. The motor runs with delta connection of the stator.

Electrical circuit. There are many strategies for controlling the switches. The most common control strategy is the intersective PWM. Its principle is reminded in figure Three phase PWM control. Knowing the conduction intervals of the switches, it is then possible to determine the waveform of different voltages and currents.

The line to neutral voltage v 10 , v 20 et v 30 are dependent on the state of the switches. The input current i i is deduced from the current of switches K 1 , K 3 and K 5 :. Simulink model of the three-phase inverter is shown in figure 12 a.

The control block is illustrated in figure 12 b. It models a three phases PWM control. The inverter block is illustrated in figure 12 c. The simulation of the open-loop three-phase inverter is illustrated in figure The relation between the amplitude of the sinusoidal voltage and the triangular voltage determines the maximum value of the fundamental line-line voltage of the inverter:. Neglecting the current harmonics, the maximum value of the line current is deduced from equation 22 :.

Three phase inverter. Simulation example of a three-phase inverter with PWM control. Three-phase AC to DC converters are widely used in many industrial power converters in order to obtain continuous voltage using a classical three-phase AC-line.

These converters, when they are used alone or associated for specific applications, can present problems due to their non-linear behaviour. It is then important to be able to model accurately the behaviour of these converters in order to study their influence on the input currents waveforms and their interactions with the loads classically inverters and AC-motors.

Several studies have shown the importance to have tools to simulate the behaviour of complex power electronics systems Ladoux et al. Although constant topology methods have been developed Araujo et al. In this chapter, an original and simple method is developed to model and simulate AC-DC converters taking into account overlap phenomenon with continuous and discontinuous conduction modes using Matlab-Simulink.

An example is presented in figure Basic model of a single-phase rectifier. In this chapter, the proposed approach is completely different from the approach based on commutation functions. The overlap phenomenon and the unbalance of line impedances can be taken into account by modifying the commutation functions to correspond to the real behaviour of the rectifiers in these conditions.

Indeed, the commutations are not instantaneous. Several contributions have already been proposed in scientific literature to refine the modelling of rectifiers. Some methods have been developed in order to model and simulate power factor corrected single-phase AC-DC converters Pandey et al. The six-pulse AC-DC converter is illustrated in figure 15 a. Inductances L i characterize the line inductances and L o characterizes the output inductance.

The AC-DC converter modelling is based on the variable topology approach. The diodes are modelled by an ideal model which traduces the state of the switch:. All the diodes are state-off figure 15b. Six-pulse diode rectifier. Naturally, the method is equivalent under unbalanced conditions but the mathematical expressions of the different variables are more complex. To shift from phase P 0 diodes state-off to phase P 1 D 1 D 5 state-on , the voltage across diodes D 1 and D 5 have to be equal to zero.

In this case, all diodes are opened. Equation 24 describes this mode. From the figure 15c, we can write equations 25 , 26 and 27 :. For example, for conduction mode P 2 : D 1 and D 6 are state-on. The indexes s and t are permuted as presented below:. From the figure 15c, we can write equations 30 and 31 :. Equations have been detailed in Batard et al. For example, for overlap mode O 2 : D 1 , D 2 and D 6 are state-on.

The simulink model of the six-pulse diode rectifier is illustrated in figure 16 a. The resistive load is modelled as a gain. The internal structure of the diodes rectifier block is presented in figure 16 b. Four different blocks can be seen on this scheme. The first one called MF1 is a Matlab function which computes each diode voltage. The inputs of this block are the initial phase and the three-phase network voltages. Its computing algorithm is shown in figure 16 d.

The new operating phase depends on the initial phase, the diode voltages and currents. The Current block computes each diode current which permits to obtain the DC current and the line currents. Diode rectifier model. The internal structure of the Current block is shown in figure 16 c.

We use then six integrator blocks one for each diode. The integrator blocks are set to limit their minimal output value to zero lower saturation limit , this feature permits to avoid the problem of accurate determination of the instant when diodes currents reach to zero. Simulations and experimental waveforms related to figure 15 are shown in figure The simulation parameters are adjusted as follows:. It can be seen that the simulated waveforms are very close to the experimental ones.

The overlap interval 1 is equivalent for simulation and experimental results 1 0. Comparison of Simulation and Experimental Waveforms in a six-pulse diode rectifier. This model has also been tested with a load constituted of an inverter and an induction machine. The results of this test have validated operations for discontinuous conduction mode.

For the same configuration parameters, the simulation time was 5 s. The Simulink model of the controlled rectifier is very close to the Simulink model of the diode rectifier. Only the condition to turn the thyristor on is different to the condition to turn the diode on. Explore examples that illustrate modeling, control, and simulation of electrical systems. A starting point for creation of a new electrical model. The model also opens an Electrical Starter Palette that shows how you can create your own customized library that also provides links to Foundation Library components.

A model of a shunt motor. In a shunt motor, the field and armature windings are connected in parallel. The rotor inertia J is 2. The parameters values are set to match the 1. The model uses these parameters to verify manufacturer-quoted no-load speed, no-load current, and stall torque. For the defining equations and their validation, see Jackey, R. Simulate a battery pack consisting of multiple series-connected cells in an efficient manner.

It also shows how a fault can be introduced into one of the cells to see the impact on battery performance and cell temperatures. For efficiency, identical series-connected cells are not just simply modeled by connecting cell models in series. Instead a single cell is used, and the terminal voltage scaled up by the number of cells.

The fault is represented by changing the parameters for the Cell 10 Fault subsystem, reducing both capacity and open-circuit voltage, and increasing the resistance values. Simulate a battery pack that consists of multiple series-connected cells. It also shows how you can introduce a fault into one of the cells to see the impact on battery performance and cell temperatures.

You can represent the fault by defining different parameters for the faulty cell. For the defining equations and their validation, see T. Huria, M. Ceraolo, J. Gazzarri, R. Model a thermal runaway in a lithium-ion battery pack. The model measures the cell heat generation, the cell-to- cell heat cascade, and the subsequent temperature rise in the cells, based on the design.

The cell thermal runaway abuse heat is calculated using calorimeter data. Simulation is run to evaluate the number of cells that go into runaway mode, when just one cell is abused. To delay or cancel the cell-to-cell thermal cascading, this example models a thermal barrier between the cells. An implementation of a nonlinear bipolar transistor based on the Ebers-Moll equivalent circuit. The 1uF decoupling capacitors have been chosen to present negligible impedance at 1KHz.

The model is configured for linearization so that a frequency response can be generated. The use of a small-signal equivalent transistor model to assess performance of a common-emitter amplifier. The 47K resistor is the bias resistor required to set nominal operating point, and the Ohm resistor is the load resistor. Parameters set are typical for a BC Group B transistor. How higher fidelity or more detailed component models can be built from the Foundation library blocks.

The model implements a band-limited op-amp. It includes a first-order dynamic from inputs to outputs, and gives much faster simulation than if using a device-level equivalent circuit, which would normally include multiple transistors. This model also includes the effects of input and output impedance Rin and Rout in the circuit , but does not include nonlinear effects such as slew-rate limiting. The Op-Amp block in the Foundation library models the ideal case whereby the gain is infinite, input impedance infinite, and output impedance zero.

The Finite Gain Op-Amp block in this example has an open-loop gain of 1e5, input resistance of K ohms and output resistance of 10 ohms. As a result, the gain for this amplifier circuit is slightly lower than the gain that can be analytically calculated if the op-amp gain is assumed to be infinite.

A differentiator, such as might be used as part of a PID controller. It also illustrates how numerical simulation issues can arise in some idealized circuits. The model runs with the capacitor series parasitic resistance set to its default value of 1e-6 Ohms.

Setting it to zero results in a warning and a very slow simulation. See the User's Guide for further information. A standard inverting op-amp circuit. As the Op-Amp block implements an ideal i. A noninverting op-amp circuit. An implementation of a nonlinear inductor where the inductance depends on the current. For best numerical efficiency, the underlying behavior is defined in terms of a current-dependent flux.

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Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation. Search MathWorks. Open Mobile Search. Off-Canvas Navigation Menu Toggle. Main Content. Consider the following two-input, two-output control system. Note u and y are shorthand notations for the InputName and OutputName properties, respectively.

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