**2. Static power converters**

Static power converters can take numerous topologies which enable AC-AC, AC-DC, DC-AC, and DC-DC conversion. AC-AC converters vary in complexity from the crude chopping of the AC waveform in order to regulate the delivered average power like in light dimmers and electric stove burners to varying the produced frequency like in Variable Speed Drives (VSD) for AC motors. AC-DC converters usually utilize the simple rectifier bridge configuration. They are popular in windmill applications as a front stage before converting to AC for interface with the utility grid. This last stage employs the DC-AC converter which is also popular in applications like solar panels interface with the utility grid. In addition to the AC-DC converter, most household and commercial electronic equipment use DC-DC converters. These converters produce the multiple DC voltage levels necessary for the operation of the equipment. DC-DC converters are also critical for battery powered portable electronic devices where power density is high and efficiency of converters is critical to the charging cycle of the device.

### **2.1. AC-AC converter**

134 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

more intensive analysis and design schemes.

**2. Static power converters** 

and theoretical development are provided for completeness.

exists between two magnetic coils with the proper turns-ratio. Mutual induction is possible due to the rate at which the magnetic lines cut the wires of the transformer coils and the produced electromotive force that is capable of producing current in closed electric loops. This fundamental concept is not applicable to DC voltage and current due to the absence of the alternating nature of the produced magnetic fields. Therefore, changing DC voltage from one level to another must be achieved using different methodologies. One possible methodology is to modulate DC voltages by switching them on and off at proper rates and durations such that the average produced voltage is controlled. The key concept here is to store energy then release it at the proper time with the proper rate needed for the desired load. Energy storage elements like inductors and capacitors facilitate this methodology. Therefore, a combination of energy storage elements and switching schemes provide the basic ingredients for the design of DC-DC conversion devices. Such devices are referred to as power electronic DC-DC converters. The modes of operation of these devices are dependent on the shape of the produced voltage waveform which is manipulated by the switching scheme and the size of the energy storage elements. Compared to AC transformers which usually exhibit linear characteristics for its most modes of operation, DC transformers (DC-DC converters) possess highly non-linear characteristics which require

Optimization of power electronics systems' design and operation is important to accommodate the growing need for energy efficiency in portable electronic devices to extend their battery life and respond to their increasing functionality and features. These features demand more electric power while the devices must reduce in size and weight; i.e. increased energy density. DC-DC converters are embedded in numerous electronic equipment and they have become an integral part of many commercial and industrial products. These converters are employed to lower (buck) or raise (boost) DC voltage levels as needed by the application. Buck and boost converters are emphasized in this chapter for their different topologies and modes of operation. The presented methodologies facilitate analysis, characterization, and design of efficient DC-DC converters. Sufficient background

Static power converters can take numerous topologies which enable AC-AC, AC-DC, DC-AC, and DC-DC conversion. AC-AC converters vary in complexity from the crude chopping of the AC waveform in order to regulate the delivered average power like in light dimmers and electric stove burners to varying the produced frequency like in Variable Speed Drives (VSD) for AC motors. AC-DC converters usually utilize the simple rectifier bridge configuration. They are popular in windmill applications as a front stage before converting to AC for interface with the utility grid. This last stage employs the DC-AC converter which is also popular in applications like solar panels interface with the utility grid. In addition to the AC-DC converter, most household and commercial electronic equipment use DC-DC Converting AC at the same frequency is most effectively achieved using induction transformers. This is particularly true for high frequency/low-power applications where the magnetic core is relatively small. Applications that require converting to different frequencies, however, can be achieved in several configurations. One configuration may utilize an intermediate stage of AC-DC back-to-back with DC-AC as is the case for wind energy conversion for example; assuming that the wind turbine is coupled to an AC electric generator. Cycloconverters (Rashid, 2004) on the other hand, don't require an intermediate stage as they utilize chopping techniques to shape the waveform directly. Conversion from three-phase to either single-phase or three-phase is usually possible with the proper control scheme. One crude application to regulate power at the same frequency using waveform chopping is that of the light-dimmer (Paul, 2001); used here to illustrate some of the basic concepts. Although light dimmers usually regulate power consumption without altering the fundamental frequency of the source, they provide a more economical solution compared to tap-changing induction type transformers.

Fig. 1 depicts the circuit configuration for a simple light dimmer where the primary power control device is the Triac whose gate firing device is the Diac (Skvarenina, 2002). The Diac is a fixed break-over voltage device compared to the Triac that permits a variable firing angle through its gate terminal. Compared to the Silicon Controlled rectifier (SCR) which is also gate controlled, the Triac permits device firing on the positive and negative half-cycles of the AC waveform. The SCR has a similar characteristic to that of a rectifier (unidirectional) but with an adjustable conduction angle (Rashid, 2004). Both devices are self-commutated, i.e. they turn off naturally at the zero crossings of the waveform. The triggering circuit for the Triac is comprised of R1, R2, and C where the potentiometer R2 represents the adjustable resistor which is usually operated by the dial (or slide switch) on the operating plate of the light dimmer. The value of R2 controls the conduction phase of the Triac. As the capacitor charges to a voltage higher than the break-over voltage of the Diac, a pulse is produced at the gate of the Triac to turn it on. In the conduction mode, the internal resistance of the Triac becomes small causing the flow of current through the light bulb. A higher value of R2 elongates the charging time of C (longer time constant τ=C(R1+R2)), causing a delayed triggering pulse and a shorter conduction period for the Triac. The average power transmitted to the light bulb becomes less, resulting in a dimmer light. The same logic works for both halves of the source's waveform cycle. This application will be analyzed using Matlab in Section 4 to demonstrate some of the capabilities of the SimPower and Simulink tool boxes.

**Figure 1.** Light Dimmer Circuit

Several practical notes relative to the circuit in Fig. 1 are due,

