Category Archives: University Maths

Harmonics Introduction

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Harmonics Analysis are the processes of solving a periodic, non-sinusoidal quantity into small sinusoidal parts. [Ref.19, ch.34]

Any periodic function can be show as the formula below [5].

 

[5]

Where an and bn are the Fourier coefficients and n is a positive integer and the period of f(x) is 2pi  therefore,

[6]

[7]

bn Fourier coefficient[8]

 

In Static Var Compensators, some of the harmonics are generated by the current through the Thyristor Controlled Reactor.

Some of those can be reduced between the transformer and between a 12-pulse operation of the compensator.

Here are some of the problems caused by the harmonics:

 

  • Nuisance tripping of circuit breakers or fuses blowing.
  • Erroneous operation of control system equipment.
  • Excessive heating and failure of transformers, motors, capacitors, switchgear lighting, cables, etc.
  • Electronic communication interference.
  • Excessive neutral current.

 

 

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Introduction Static Var Compensators

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Most of the industrial installations with loads require compensations to be able to correct or balance these existent fluctuations and uses Static Var Compensators.

As was mentioned in 1.1 one of the systems, which allows to compensate the power, is between the use of Static Var Compensators.

These are being used increasingly due to the technical advantages, which they offer between transmission systems. Advantages such as: [Ref.12, pp.2]

 

  • Compensation for the change in reactive power produced by a change in the transmitted power.
  • In the event of line switching caused by faults or changing network configuration, there is compensation for a change in reactive power.
  • Reduction and limitation of power frequency over voltages produced by the load.
  • Improvement of the system in a long distance transmission.

 

Figure 1.4 shows a simple schematic of a Static Var Compensators. It is comprised of the following features:

  • Transformer
  • Thyristor Controlled Reactor (TCR)
  • Thyristor Switched Capacitor (TSC)
  • Capacitors Bank

The transformer is not part of the of the Static Var Copensators.

Thyristor Controlled Reactor is part of the Static Var Copensators and is based on a couple of thyristors and impedance in series as shown in Figure 1.4. TCR will produce the sufficient inductive reactance to compensate the network.

 

Transmission capacitive reactance is part of the Static Var Copensators, as the delay angle () increases, less vars from the network are going to be absorbed and the current through the TCR can be varied triggering the thyristors at different angles. As the delay angle () is higher as the load phase angle () then the fundamental component of the thyristors current is reduced. It is shown in detail in chapter 4 section 4.1.2.

 

Figure 1.4

 

Thyristor Switched capacitors are part of the Static Var Copensators and are also based on a couple of thyristors, which will turn on and turn off the capacitor in the shortest time possible. The TSC is switched on and off, thus providing discreet step variation of the Static Var Compensator (SVC) capacitive current. In this way, transients are minimized.

The main advantage of the thyristor switched capacitors is that losses can be minimized when they are used in combination with Thyristor Controlled Reactor.

We have seen a quick introduction to the Static Var Compensators and we hope this will be sueful to understand the next concepts.

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You can correct or balance existent fluctuations with Static Var Compensators (SVC info)

Power Factor Compensation

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Power Factor  [4] is the existing relation between the true power (P) or real average power and the apparent power (S) or the complex power [Ref.3, ch.3].

 

[4]

 

As the power factor drops the system becomes less efficient. A drop from 1.0 to 0.9 results in 15% more current being required for the same load.

A power factor of 0.7 requires approximately 43% more current; and a power factor of 0.5 requires approximately 100% more current.

The objective, therefore, should be to reduce the reactive power drawn from the supply by improving the power factor.

If an AC motor were 100% efficient, it would consume only active power but, since most
motors are only 75% to 80% efficient, they operate at a low power factor. This means poor energy and cost efficiency because the Electricity Companies charge you at penalty rates for poor power factor.

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Power factor definition (We hope you find this useful!)

 

 

 

 

 

 

 

 

 

Reactive Power

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In this section we are going to see different aspects related with the reactive Power.

The loads on an electrical distribution system are classified into the following three groups: resistive, inductive or capacitive.

In a general plant, the most common is likely to be inductive due to the lighting, transformers, relays and AC induction motors. All inductive loads require two kinds of power to operate:

 

  • Reactive power “ used to energize the magnetic field Reactive Power. It is a result of Reactance in an AC circuit.

  • The amount of Reactive Power is equal to the square root of the Apparent Power (voltage multiplied by amps) squared minus the True power (Watts) squared.

  • The reactive power is expressed in VARs or Volt Amps Reactive. [1]

 

  • Active power – used to produce the motive force. It is the Power consumed, used or dissipated. Referred to as the True Power. In other words, Watts of a circuit that can be found by multiplying the Resistance in Ohms by the Current I in amps squared, or by multiplying the Voltage by the Current or by dividing the square of the Voltage by the Resistance. [2]

 

The operating power from the distribution system is composed of both, the active power and the reactive power. The reactive power only provides the magnetic field whereas the active power does useful work in driving the motor.

The figure 2.1 shows a phasor diagram. Therefore, reactive power is the vector sum of the current and the voltage.

(Var) [1]

 

(W) [2]

 

 

Figure 1.2

 

The apparent power is expressed by volt-amperes (VA) as shows below [3].

(VA)  [3]

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Reactive Power definition (We hope you find this useful!)

Background and Proposal – active power

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The proposal of this project is to analyse the problem of the unnecessary consumption of the active power for an electrical industrial installation.

Creating a scale prototype that could be used for laboratory demonstrations on power factor control proposes.

Loads, transformers, lines, motors, etc absorb power that is actually more reactive. Consequently, more harmonics are generated.

Consumers of electricity have to be aware of this fact and to know that this causes higher voltage drops and conductive power losses.

A bad electrical industrial installation for the consumer will use more active power than reactive. Therefore, the power factor (cos O) will be smaller than one. For this reason the consumer A,  is probably paying for and consuming more electricity than consumer B  whose power factor (cos O) is around one. (Optimal power factor) [Ref.3, ch.3]

Different technologies can be used to achieve this:

  • The insertion of capacitor banks which will generate a reactive power proportional to the voltage and the capacity.
  • The use of Static Var Compensators where they are connected or disconnected from the network using thyristors acting as electronic switches. The voltage is in phase with the network voltage and the reactive generation is controlled by regulating the amplitude of the source.
  • The use of AC Static Switches, which will activate or deactivate capacitors depending on the inductance load. This means between a regulator that will try to maintain (cosO= 1). (See Figure 1.1) using Static Var Compensators.

Thus, a technique to generate the reactive power has been found.

Figure 1.1

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