Power Electronics – Introduction

Literature Review

  1. Power Electronic – Mohan
    1. Power Electronic Systems
      1. Introduction p 3
      2. Power Electronics Vs Linear Electronics
      3. Scope and applications
      4. Classification of Power Processors and Converters
      5. Matrix Converter
      6. Interdisciplinary nature of power electronics
  2. Libro Rashid – Power Electronic Handbook
    1. Power Electronic Defined p 1

Lunes 15 de noviembre, 11:08 am – Caracas, Quito, Guayaquil.


In broad terms, the task of power electronics is to process and control the flow of electric energy by supplying voltages and currents in a form that is optimally suited for user loads.

Figure 1-1 shows a power electronic system in a block diagram form. The power input to

this power processor is usually (but not always) from the electric utility at a line frequency

of 60 or 50 Hz, single phase or three phases. The phase angle between the input voltage

and the current depends on the topology and the control of the power processor. The

processed output (voltage, current, frequency, and the number of phases) is as desired by

the load. If the power processor’s output can be regarded as a voltage source, the output

current and the phase angle relationship between the output voltage and the current depend

on the load characteristic. Normally, a feedback controller compares the output of the

power processor unit with a desired (or a reference) value, and the error between the two

is minimized by the controller. The power flow through such systems may be reversible,

thus interchanging the roles of the input and the output.

In recent years, the field of power electronics has experienced a large growth due to

confluence of several factors. The controller in the block diagram of Fig. 1-1 consists of

linear integrated circuits and/or digital signal processors. Revolutionary advances in microelectronics methods have led to the development of such controllers. Moreover, these

advances in semiconductor fabrication technology have made it possible to significantly

improve the voltage- and current-handling capabilities and the switching speeds of power

semiconductor devices, which make up the power processor unit of Fig. 1-1. At the same

time, the market for power electronics has significantly expanded. Electric utilities in the

United States expect that by the year 2000 over 50% of the electrical load may be supplied

through power electronic systems such as in Fig. 1-1.

Power Electronics Defined

It has been said that people do not use electricity, but rather they use communication, light, mechanical work, entertainment, and all the tangible benefits of both energy and electronics. In this sense, electrical engineering is a discipline very much involved in energy conversion and information. In the general world of electronics engineering, the circuits engineers design and use are intended to convert information, with energy merely a secondary consideration in most cases. In radio frequency applications, energy and information are sometimes on a more equal footing, but the main function of any circuit is that of information transfer.

What about the conversion and control of electrical energy itself? Electrical energy sources are varied and of many types. It is natural, then, to consider how electronic circuits and systems can be applied to the challenges of energy conversion and management. This is the framework of power electronics, a discipline that is defined in terms of electrical energy conversion, applications, and electronic devices. More specifically,

DEFINITION: Power electronics involves the study of electronic circuits intended to control the flow of electrical energy. These circuits handle power flow at levels much higher than the individual device ratings.

Power Electronics Vs Linear Electronics

In any power conversion process such as that shown by the block diagram in Fig. 1- 1, a small power loss and hence a high energy efficiency is important because of two reasons: the cost of the wasted energy and the difficulty in removing the heat generated due to dissipated energy.

Other important considerations are reduction in size, weight, and cost. The above objectives in most systems cannot be met by linear electronics where the semiconductor devices are operated in their linear (active) region and a line-frequency transformer is used for electrical isolation. As an example, consider the direct current (dc) power supply of Fig. 1-2a to provide a regulated output voltage V, to a load.

The utility input may be typically at 120 or 240 V and the output voltage may be, for example, 5 V. The output is required to be electrically isolated from the utility input. In the linear power supply, a line-frequency transformer is used to provide electrical isolation and for stepping down the line voltage. The rectifier converts the alternating current (ac) output of the transformer low-voltage winding into dc. The filter capacitor reduces the ripple in the dc voltage vd. Figure 1-2b shows the vd waveform, which depends on the utility voltage magnitude (normally in a t 10% range around its nominal value).

The transformer turns ratio must be chosen such that the minimum of the input voltage v, is greater than the desired output V. For the range of the input voltage waveforms shown in Fig. 1-2b, the transistor is controlled to absorb the voltage difference between v and V, thus providing a regulated output. The transistor operates in its active region as an adjustable resistor, resulting in a low energy efficiency. The line-frequency transformer is relatively large and heavy.

In power electronics, the above voltage regulation and the electrical isolation are achieved, for example, by means of a circuit shown in Fig. 1-3a.

In this system, the utility input is rectified into a dc voltage vd, without a line-frequency transformer. By operating the transistor as a switch (in a switch mode, either fully on or fully 0ff) at some high switching frequency f, for example at 300 kHz, the dc voltage vd is converted into an ac voltage at the switching frequency. This allows a high-frequency transformer to be used for stepping down the voltage and for providing the electrical isolation.

In order to simplify this circuit for analysis, we will begin with the dc voltage vd as the dc input and omit the transformer, resulting in an equivalent circuit shown in Fig. 1-3b.

Suffice it to say at this stage (this circuit is fully discussed in Chapters 7 and 10) that the transistor diode combination can be represented by a hypothetical two-position switch shown in Fig. 1-4a (provided iL(t) > 0).

The switch is in position a during the interval t-on, when the transistor is on and in position b when the transistor is off during t-off. As a consequence, Voi equals Vd, and zero during t-on and t-off, respectively, as shown in Fig. 1-4b.

Let us define

where Voi is the average (dc) value of Voi-t, and the instantaneous ripple voltage V-ripple, which has a zero average value, is shown in Fig. 1-4c.

The L-C elements form a low-pass filter that reduces the ripple in the output voltage and passes the average of the input voltage, so that

where Vo, is the average output voltage. From the repetitive waveforms in Fig. 1-4b, it is easy to see that

As the input voltage Vd changes with time, Eq. 1-3 shows that it is possible to regulate Vo, at its desired value by controlling the ratio t-on/Ts which is called the duty ratio D of the transistor switch. Usually, Ts (= l/fs) is kept constant and t-on is adjusted.

There are several characteristics worth noting. Since the transistor operates as a switch, fully on or fully off, the power loss is minimized. Of course, there is an energy loss each time the transistor switches from one state to the other state through its active region (discussed in Chapter 2). Therefore, the power loss due to switchings is linearly proportional to the switching frequency. This switching power loss is usually much lower than the power loss in linear regulated power supplies.

At high switching frequencies, the transformer and the filter components are very small in weight and size compared with line-frequency components.

Scope and Applications of Power Electronics

The expanded market demand for power electronics has been due to several factors discussed below:

  1. Switch-mode (dc) power supplies and uninterruptible power supplies. Advances in microelectronics fabrication technology have led to the development of computers, communication equipment, and consumer electronics, all of which require regulated dc power supplies and often uninterruptible power supplies.
  2. Energy conservation. Increasing energy costs and the concern for the environment have combined to make energy conservation a priority. One such application of power electronics is in operating fluorescent lamps at high frequencies (e.g., above 20 kHz) for higher efficiency. Another opportunity for large energy conservation is in motor-driven pump and compressor systems. In a conventional pump system shown in Fig. 1-5a, the pump operates at essentially a constant speed, and the pump flow rate is controlled by adjusting the position of the throttling valve. This procedure results in significant power loss across the valve at reduced flow rates where the power drawn from the utility remains essentially the same as at the full flow rate. This power loss is eliminated in the system of Fig. 1-56, where an adjustable-speed motor drive adjusts the pump speed to a level appropriate to deliver the desired flow rate.

  1. Process control and factory automation. There is a growing demand for the enhanced performance offered by adjustable-speed-driven pumps and compressors in process control. Robots in automated factories are powered by electric servo (adjustable-speed and position) drives. It should be noted that the availability of process computers is a significant factor in making process control and factory automation feasible.
  2. Transportation. In many countries, electric trains have been in widespread use for a long time. Now, there is also a possibility of using electric vehicles in large metropolitan areas to reduce smog and pollution. Electric vehicles would also require battery chargers that utilize power electronics.
  3. Electro-technical applications. These include equipment for welding, electroplating, and induction heating.
  4. Utility-related applications. One such application is in transmission of power over high-voltage dc (HVDC) lines. At the sending end of the transmission line, line-frequency voltages and currents are converted into dc. This dc is converted back into the line-frequency ac at the receiving end of the line. Power electronics is also beginning to play a significant role as electric utilities attempt to utilize the existing transmission network to a higher capacity. Potentially, a large application is in the interconnection of photovoltaic and wind-electric systems to the utility grid.

Classification of Power Processors and Converters

For a systematic study of power electronics, it is useful to categorize the power processors, shown in the block diagram of Fig. 1-1, in terms of their input and output form or frequency.

In most power electronic systems, the input is from the electric utility source. Depending on the application, the output to the load may have any of the following forms:

  1. dc
    1. regulated (constant) magnitude
    2. adjustable magnitude
  2. ac
    1. constant frequency, adjustable magnitude
    2. adjustable frequency and adjustable magnitude

The utility and the ac load, independent of each other, may be single phase or three phase. The power flow is generally from the utility input to the output load.

The power processors of Fig. 1-1 usually consist of more than one power conversion stage (as shown in Fig. 1-6) where the operation of these stages is decoupled on an instantaneous basis by means of energy storage elements such as capacitors and inductors.

Therefore, the instantaneous power input does not have to equal the instantaneous power output. We will refer to each power conversion stage as a converter. Thus, a converter is a basic module (building block) of power electronic systems. It utilizes power semiconductor devices controlled by signal electronics (integrated circuits) and possibly energy storage elements such as inductors and capacitors. Based on the form (frequency) on the two sides, converters can be divided into the following broad categories:

  1. ac to dc
  2. dc to ac
  3. dc to dc
  4. ac to ac

We will use converter as a generic term to refer to a single power conversion stage that may perform any of the functions listed above. To be more specific, in ac-to-dc and dc-to-ac conversion, rectifier refers to a converter when the average power flow is from the ac to the dc side. Inverter refers to the converter when the average power flow is from the dc to the ac side.

Further insight can be gained by classifying converters according to how the devices within the converter are switched. There are three possibilities:

  1. Line frequency (naturally cornmutated) converters, where the utility line voltages present at one side of the converter facilitate the turn-off of the power semiconductor devices. Similarly, the devices are turned on, phase locked to the line voltage waveform. Therefore, the devices switch on and off at the line frequency of 50 or 60 Hz.
  2. Switching (forced-commutated) converters, where the controllable switches in the converter are turned on and off at frequencies that are high compared to the line frequency.
  3. Resonant and quasi-resonant converters, where the controllable switches turn on and/or turn off at zero voltage and/or zero current.

Matrix Converter as a Power Processors

Theoretically, it is possible to replace the multiple conversion stages and the intermediate energy storage element by a single power conversion stage called the matrix converter. Such a converter uses a matrix of semiconductor bidirectional switches, with a switch connected between each input terminal to each output terminal, as shown in Fig. 1-9a for an arbitrary number of input and output phases:

With this general arrangement of switches, the power flow through the converter can reverse. Because of the absence of any energy storage element, the instantaneous power input must be equal to the power output, assuming idealized zero-loss switches. However, the phase angle between the voltages and currents at the input can be controlled and does not have to be the same as at the output (i.e., the reactive power input does not have toequal the reactive power output). Also, the form and the frequency at the two sides are independent, for example, the input may be three-phase ac and the output dc, or both maybe dc, or both may be ac.

In spite of numerous laboratory prototypes reported in research publications, the matrix converters so far have failed to show any significant advantage over conventional converters and hence have not found applications in practice

Interdisciplinary Nature of Power Electronics

The discussion in this introductory chapter shows that the study of power electronics encompasses many fields within electrical engineering, as illustrated by Fig. 1- 10.

Combining the knowledge of these diverse fields makes the study of power electronics challenging as well as interesting. There are many potential advances in all these fields that will improve the prospects for applying power electronics to new applications.


Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Ecuador (Quito, Guayaquil, Cuenca)

WhatsApp: 00593984950376

email: dademuchconnection@gmail.com




Actividad – Literature Review
Martes 03 octubre, 11:05 am


  1. Introduccion-al-analisis-de-circuitos-robert-l-boylestad
    1. Capacitores 375 (387)
  2. Análisis de Redes – Van Valkenburg, 1999 – Network Analysis – Universidad de Illinois.
    1. El Parámetro Capacitancia p 20 (23)
  3. Análisis de Sistemas Lineales – Prof. Ebert Brea
    1. Análisis de Sistemas en el Dominio Continuo pp 29 – (58)



Por tanto se concluye que la intensidad del campo eléctrico en cualquier punto a una distancia r de una carga puntual de Q coulombs, será directamente proporcional a la magnitud de la carga e inversamente proporcional al cuadrado de la distancia a la carga.


Al instante en que el interruptor se cierra, se extraen los electrones de la placa superior y se depositan sobre la placa inferior debido a la batería, dando por resultado una carga neta positiva sobre la placa superior del capacitor y una carga negativa sobre la placa inferior…Cuando el voltaje en el capacitor es igual al de la batería, cesa la transferencia de electrones y la placa tendrá una carga neta Q=CV=CE

En este punto el capacitor asumirá las características de un circuito abierto: una caída de voltaje en las placas sin flujo de carga entre las placas.

El voltaje en un capacitor no puede cambiar de forma instantánea.

De hecho, la capacitancia en una red es también una medida de cuanto se opondrá ésta a un cambio en el voltaje de la red. Mientras mayor sea la capacitancia, mayor será la constante de tiempo y mayor el tiempo que le tomará cargar hasta su valor final

Ejemplo 2.2 (Fuente:3) La Figura 2.3 muestra un sistema compuesto por una resistencia y un capacitor, y cuyos valores son representados respectivamente por R y C. Además, la figura muestra que el sistema eléctrico es excitado por una señal x(t) = u(t) y su respuesta es medida a través de la tensión sobre el capacitor, donde u(t) representa la función escalón unitario:

El modelo matemático asociado al sistema representado por la Figura 2.3 puede obtenerse empleando elementales ecuación de redes eléctricas:

Entonces, al comparar el modelo matemático definido por la Ecuación (2.12) con el modelo obtenido, se tiene que el coeficiente a0 y la señal de excitación son:


Al aplicar la solución expresada por medio de la Ecuación (2.21), se puede afirmar que:

Al operar la Ecuación (2.26) se tiene que la respuesta del sistema es dada por:

Note que:

por cuanto el elemento de memoria representado por el capacitor no permite cambios bruscos y por tal motivo y(0-) = y(0) = y(0+). Además, para buscar una respuesta a la pregunta debe tomarse en cuenta que la excitación tiene un valor de cero y ella ha permanecido en cero desde mucho tiempo atrás, es decir, desde menos infinito, obviamente y(0) = 0.

Literature Review by: Larry Francis Obando – Technical Specialist

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, Caracas.

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contact: Ecuador (Quito, Guayaquil, Cuenca)

WhatsApp: 00593984950376

email: dademuchconnection@gmail.com

Copywriting, Content Marketing, Tesis, Monografías, Paper Académicos, White Papers (Español – Inglés)

Flujos de Potencia – Análisis y Simulación.

White Paper – Objetivos.

  • Analizar las características generales de los sistemas de transmisión de potencia, en especial de las líneas de transmisión.
  • Describir el modelo matemático de los parámetros relevantes que determinan la calidad del flujo de potencia en las líneas de transmisión.
  • Formular el modelo matemático del flujo de potencia en líneas de transmisión.
  • Simular la operación de las líneas de transmisión mediante el software Matlab, utilizando el modelo matemático formulado.



Los cálculos de flujo de potencia son tareas muy amplias y comunes en las etapas de planificación del sistema de potencia.Tradicionalmente, las redes de transmisión se diseñaban e implementaban basándose en la experiencia e intuición del ingeniero eléctrico. Hoy en día, la planificación de un Sistema Eléctrico de Potencia (SEP), cuenta con numerosos métodos de análisis que utilizan modelos matemáticos o heurísticos que minimizan o maximizan una función objetivo sujeta a un conjunto de restricciones.

Así lo afirma Nuques Ochoa (2009), quien desarrolló un modelo matemático para optimizar la expansión del sistema nacional de transmisión ecuatoriano desde su etapa de planificación. Este autor plantea que el principal problema en la formulación del modelo fue la intervención de un conjunto de variables entre las que se encuentran los flujos de potencia por las líneas de transmisión, la cual es una variable continua; el número de circuitos a ser implementados, la cual es una variable entera, así como una serie de restricciones lineales y no lineales, conformando por tanto un fenómeno de naturaleza no lineal entera mixta. Así, a medida que se expande la red eléctrica, se multiplica el número de variables y por ende sucede un aumento exponencial de posibles combinaciones que conducen a numerosas y distintas soluciones. Para enfrentar esta complejidad, Ochoa propone el uso de la técnica denominada Algoritmo Evolutivo de Rebotes Simulados con el fin de obtener planes de expansión más económicos y eficientes.

En épocas recientes han evolucionado los métodos para analizar los flujos de potencia en los sistemas eléctricos, tales como la matriz de impedancia y el método Newton-Raphson. Sin embargo, el método de flujo de potencia desacoplado de Newton, el cual utiliza la técnica de eliminación de matriz dispersa, ha sido reconocido como el más eficiente para hallar soluciones en el análisis del flujo de potencia de sistemas eléctricos de gran escala (Zhang, Rehtanz, & Pal, 2012).

Fernández y Fuentes (2011) diseñaron un programa capaz de solucionar el problema de flujo de carga para el análisis de cualquier sistema eléctrico de potencia, específicamente para resolver el problema de flujo óptimo de potencia en dichos sistemas. El requisito fundamental para realizar este tipo de herramientas que permiten el análisis computarizado de los sistemas de potencia, es el conocimiento detallado de los componentes, primera tarea que ejecutan en su investigación, derivando de este análisis las ecuaciones que representan cada componente para luego crear un sistema de ecuaciones que represente la dinámica del sistema en su totalidad. El estudio del flujo de carga se realiza utilizando el método Newton-Raphson para resolver ecuaciones algebraicas no lineales, con lo cual en realidad se busca la solución en régimen permanente de la red del sistema. El programa informático fue desarrollado en lenguaje Python.

Guzmán (2012) realizó un estudio sobre el uso del programa PSAT (Power System Analysis Toolbox), soportado por la plataforma de Matlab, para el análisis y simulación de sistemas eléctricos de potencia. El autor afirma que, debido a la complejidad y la gran cantidad de datos que se manejan, las herramientas de la computación son imprescindibles para aportar capacidades suficientes al ingeniero eléctrico a la hora de analizar o diseñar los sistemas de potencia, los cuáles pueden ser divididos en etapas o silos, lo que facilita la manipulación y estudio de todos los factores que determinan la calidad de dichos sistemas.

Guzmán (2014) parte de un modelo matemático de cada uno de los componentes del Sistema Eléctrico Nacional Interconectado (SNI) del Ecuador, para desarrollar una aplicación en Matlab que permita determinar el Flujo de Potencia Óptimo o OPF (Optimal Power Flow) y minimizar las pérdidas de potencia activa, utilizando el método de puntos interiores Primal-Dual. Los resultados de las pruebas en esta investigación verifican que mientras más controles se apliquen en la ejecución de un OPF, se logra mayor reducción de pérdidas en MW (Mega Watts).

En contingencias del sistema eléctrico, se pueden producir bajas de tensión en las barras y sobrecargas en otros elementos de la red. Aguas (2014) desarrolló una aplicación en Matlab para el esquema de alivio de cargas óptimo por bajo voltaje para el SIN ecuatoriano, para lo cual primero desarrolló un modelo matemático de todos los componentes del sistema.

La eficiencia, la confiabilidad y la economía son factores fundamentales que determinan la calidad de los sistemas de potencia, por lo que requieren de una planificación científica, la cual sólo es posible mediante el modelado matemático de los componentes de dicho sistema. Cuando un sistema de potencia está trabajando bajo condiciones específicas de generación, carga y topología de red, la solución de dicho sistema se denomina  flujo de potencia. Las ecuaciones de flujo de potencia que arroja un modelo matemático del sistema, permiten calcular los diferentes parámetros para mantener la operatividad dentro de sus rangos normales y, primordialmente, minimizar las pérdidas de potencia activa en las líneas de transmisión.

En el Ecuador, las constantes caídas de tensión en las líneas de transmisión largas causadas por resistencias, inductancias, capacitancias y conductancias afectan mayormente a grandes clientes en el sector industrial. Debido a esta situación, el ARCONEL (Agencia de Regulación y Control de Electricidad) penaliza a las distribuidoras eléctricas que no cumplan con la Regulación sobre la Calidad del Transporte de Electricidad y del Servicio de Transmisión y Conexión en el Sistema Nacional Interconectado, el cual indica que Las distorsiones o variaciones de voltajes por sobre los límites de calidad en las barras y líneas  del sistema de transmisión que sean causados por las distribuidoras eléctricas, serán solucionados por éste”. La sanción corresponderá a 30 SBU (Salario Básico Unificado) y la reincidencia será sancionada con el máximo de 40 SBU,


Ocho (8) hábitos mentales esenciales para el éxito en la elaboración de material escrito.

El “Council of writing program administrators”, el “National council of teahcers of English”, y el “National writing project”, han identificado estos 8 hábitos como esenciales para el éxito como escritor:

  • Curiosity: the desire o know more about the world;
  • Opennes: the willingness to consider new ways of being and thinking in the world;
  • Engagement: a sense of invesment and involvement in learning;
  •  Creativity: the ability to use novel approaches for generating, investigating, and representing ideas;
  • Persistence: the ability to sustain interest in and attention to short – and long – term projects;
  • Responsability: the ability to take ownership of one´s action and understand the consequences of those actions for oneself and others;
  • Flexibility: the ability to adapt to situations, expectations, or demands;
  • Metacognition: the ability to reflect on one´s own thinking as well as the individual and cultural processes used to structure knowledge.

El documento siguiente provee de una explicación completa sobre cada hábito: