Topic 03: Linear Loads Found in Past Residential Electrical Environments

The most common type of linear resistive load found in past residential environments is the incandescent lamp. These lamps used in these environments ranged from a few watts to as high as 200 watts. The second most common type are resistive linear loads with resistive heating elements: stove eyes, oven elements, toaster elements, electric blankets, heating pads and stack heaters.

The third most common type of linear load in past residential environments is inductive loads. Every refrigerator, freezer, washing machine, clothes dryer, blender, mixer, hair dryer, dishwasher, vacuum cleaner, and fan has an electric motor.

Electric furnaces also contain heating elements (for electric heat) and one or more blower fan (squirrel cage). Gas furnaces also have one or more blower fans / ventilation fans. Window air conditioners had compressors and a blower fan. Central air conditioning units also had compressors and blower fans.

A few common household loads—the clothes dryer and the hair dryer had electric motors and resistive heating elements. No residential loads were capacitive loads. Capacitive loads were found in industrial electrical environments. 

No residential loads were capacitive loads. Capacitive loads were found in industrial electrical environments.

Basic Electrical Components & Symbols for the Three Common Types of Linear Loads

There are three linear electrical elements—resistors, inductors and capacitors that make up all linear loads. They determine how the linear load will behave when it receives a voltage signal.  They also determine how the voltage, and its current response will behave as they travel through the load before the desired output is reached. It is important to understand the fundamental characteristics of these elements before starting to learn about power quality. Understanding the fundamental characteristics of these elements will help the power quality engineer to understand, identify, solve and prevent (UISP) power quality problems. The fundamental characteristics of these elements determines how desirable voltage and current signals behave as well as how undesirable signals behave. In power quality, the power quality engineer may need to make adjustments to one or more of these elements to change the behavior of a voltage or current signal to solve and prevent a power quality problem. If the engineer doesn’t fully understand how the fundamental characteristics of these elements affect voltage and current signals, he/she will have a difficult time solving and preventing power quality problems.

Symbols

Each element performs a specific function on the voltage applied across it or the current injected through it. In other words, each element will reduce the current flowing through or speed it up. Remember, voltage is the stimulus, and current is the response. Let’s look at what each element specifically does to the current during this beginning course.

Figure 3 – Left: Electrical Symbol for a Resistor, Middle: Electrical Symbol for an Inductor, Right: Electrical Symbol for a Capacitor

Resistors

Resistors – Resistors are simple electrical elements that limit or reduce the flow of current. Reduced current flow means fewer amps (i.e., electrons) are flowing through the resistor (and circuit that it is in), but the electrons flowing through the resistor never completely stop. Resistors are measured by a parameter called resistance. The unit of measure for resistors is ohms, designated by the Greek symbol, omega, or Ω. The three equations—Ohm’s Law for resistance that link the voltage applied across it and the current through it are shown below.

V = I x R                          Equation 1

I = V/R                            Equation 2

R = V/I                            Equation 3

The simple equations above describe how changing the resistance affects the current trying to flow through it. In Equation 2, if the resistance is increased, the current will be reduced. However, the voltage dropped across the resistor will increase. If the resistance is decreased, the current will increase; but the voltage dropped across the resistor will decrease. The resistance is just a constant (of proportionality) between the voltage and current. Resistance only affects the magnitude of the voltage and current, not the timing relationship. Because resistance does not impact the timing between the voltage and current, the phasing between the voltage and current is not affected either.

Figure 4 illustrates the relationship between the voltage (stimulus) and the current (response) through a resistor. One can see they both start, cross the zero axis and stop at the same points during one cycle. (A cycle is defined as the point where a waveform starts to where it ends and then repeats.) Resistors don’t cause a timing delay (or phase shift) of the current. The current flows in time with the voltage. An incandescent lamp, the most common linear load, is a resistive load where the current is in phase with the voltage. When the start, zero-crossing point and stop points all line up, the voltage and current are said to be in phase with each other. 

There are some other interesting aspects of resistors that are very important to the stability of the voltage applied across it and the current flowing through it. Voltage and current must be stable if they are to be controlled within a system. The stability of voltages and currents is important if loads are to operate reliably and predictably. This is true regardless of if the loads are linear or non-linear.

In fact, the resistance can be changed as often and as quickly as necessary to achieve the desirable effects on the voltage and current. The resistance can be ramped up or down, and the voltage will follow without a problem.

But resistors alone cannot provide the voltage and current control needed to make technologies possible. For example, resistors cannot store energy, but they can dissipate energy. Resistors can reduce current flow, but they have no ability to stop current flow. Resistors cannot perform switching (i.e., ON and OFF functions), but they are used in circuits that include switching devices. 

Inductors

·     Inductors – Inductors (can also be called coils) are simple electrical elements that increase or decrease the voltage across them based on the flow of current through them. However, they don’t do it in the same way that resistors do. Resistors simply act on the current in a consistent way regardless of the nature of the current—whether it’s an AC (alternating current) or DC (direct current) current. (When we say regardless of whether it’s AC, we are also referring to regardless of what the frequency of the current is. The frequency can be zero (0) hertz or 100 MHz (megahertz) or any value between or above these values.) Inductors can store energy whereas resistors cannot. If the current flowing through an inductor is doubled, the energy store in it is increased by the square of the current. In an inductor, the frequency of the current partly determines the voltage developed across it. If the frequency of the current increases, the voltage across the inductor will also increase.

These two equations describe how the voltage and current behave in an inductor. Equation 4 describes how the current flowing through an inductor causes a voltage to develop across it. This looks like a complicated equation, but it’s really very simple. This equation says that if there’s a change in current over time, then there’ll be a voltage developed across the inductor. If there’s no change in the current flowing through the inductor, then there’s no voltage across it. Another way to look at it is if the current on one end of an inductor is the same as it is on the other end, there’ll be no voltage across it.

So, there are four quantities that, if increased, will increase the voltage across the inductor. These can be seen by examining Equation 4.

• 1) The change in current through it (The larger the change, the higher the voltage.).
• 2) The faster the change in current occurs, the higher the voltage.
• 3) The higher the frequency of the current flowing through the inductor, the higher the voltage.
• 4) The large the inductance, L, of the inductor, the higher the voltage.

Equation 5 describes the relationship between the voltage and current when the voltage is known. It is the opposite of Equation 4. Equation 5 says that the area under the curve of the voltage from t = 0 to t = t plus the initial condition, C (The initial condition is the amount of current that was flowing through the inductor when the voltage changed.) is equal to the total current flowing through the inductor. This equation is a little more difficult to understand than Equation 4. Equation 5 is provided here because it is the inverse of Equation 4. 

Equation 4 is the most important when it comes to understanding power quality. We will learn more about why in a later course (or lesson). It tells us one reason why so many power quality problems occur in BESs when electronic non-linear loads are powered by today’s BESs. Equation 4 is the electrical phenomenon we as power quality engineers are trying to combat. But Equation 4 is part of the Laws of Physics and explains one reason why transformers and motors work. Equation 4 is here to stay. We, as power quality engineers, have to make adjustments to how we power buildings, how we operate BESs, how we design loads (linear and non-linear), so the three—power, buildings and equipment are all compatible with each other.

Figure 5 illustrates the relationship between the voltage (stimulus) and the current (response) through an inductor. One can see they do not start, cross the zero axis and stop at the same points during one cycle. The voltage and current in an inductor (or inductive circuit) are not in phase with each other.  The best way to remember if the voltage or current are delayed in an inductive circuit is memorize the phrase, “ELI the ICE man”. “ELI” refers to the relationship between the voltage and current in an inductive (L) circuit. “E” used to be the electrical variable that represented voltage. However, nowadays it is “V”. In “ELI”, the “E” comes before the “I”, or one can say the “I” comes after the “E”. Thus, the voltage “V” appears first, then the current “I”. Therefore, the current “I” lags (or is delayed) the voltage “V”. Thus, the inductor causes the current “I” to be shifted late by -90°.

Resistors don’t cause a timing delay (or phase shift) of the current. The current flows in time with the voltage. An incandescent lamp, the most common linear load, is a resistive load where the current is in phase with the voltage. When the start, zero-crossing point and stop points all line up, the voltage and current are said to be in phase with each other. 

Capacitors

• Capacitors – Capacitors are also very simple electrical elements that increase or decrease the current flowing through them based on the voltage applied across them. They are the electrical opposites of inductors. Capacitors can store energy like inductors. If the voltage applied across a capacitor is doubled, the energy store in it is increased by the square of the voltage. In a capacitor, the frequency of the voltage across it partly determines the current that flows through it. If the frequency of the voltage increases, the current flowing through the capacitor will also increase.

These two equations describe how the voltage and current behave in a capacitor. Equation 6 describes how the voltage applied across a capacitor causes a current to flow through it. This looks like a complicated equation, but it’s really very simple. This equation says that if there’s a change in voltage over time, then there’ll be a current flow through the capacitor. If there’s no change in the voltage across the capacitor, then there’s no current flowing through it. Another way to look at it is if the voltage on one end of a capacitor is the same as it is on the other end, there’ll be no current flowing through it.

So, there are four quantities that, if increased, will increase the current through the capacitor. These can be seen by examining Equation 6.

• 1) The change in voltage across it (The larger the change, the higher the current.).
• 2) The faster the change in voltage occurs, the higher the current.
• 3) The higher the frequency of the voltage across the inductor, the higher the current.
• 4) The large the capacitance, C, of the capacitor, the higher the current.

Equation 7 describes the relationship between the voltage and current when the current is known. It is the opposite of Equation 6. Equation 7 says that the area under the curve of the current from t = 0 to t = t plus the initial condition, C (The initial condition is the amount of voltage that was across the capacitor when the current changed.) is equal to the total voltage across the capacitor. This equation is a little more difficult to understand than Equation 6. Equation 7 is provided here because it is the inverse of Equation 6.

Equation 6 is also important when it comes to understanding power quality. We will learn more about why in a later course (or lesson). It tells us one reason why so many power quality problems occur in BESs when electronic non-linear loads are powered by today’s BESs. Equation 6 is another electrical phenomenon we as power quality engineers are trying to combat. But Equation 6 is part of the Laws of Physics. Equation 6 is here to stay. We, as power quality engineers, have to make adjustments to how we power buildings, how we operate BESs, how we design loads (linear and non-linear), so the three—power, buildings and equipment are all compatible with each other.

Figure 6 illustrates the relationship between the voltage (stimulus) and the current (response) through a capacitor. One can see they also do not start, cross the zero axis and stop at the same points during one cycle. The voltage and current in a capacitor (or capacitive circuit) are also not in phase with each other. The best way to remember if the voltage or current are delayed in a capacitive circuit is memorize the phrase, “ELI the ICE man”. “ICE” refers to the relationship between the voltage and current in a capacitive (C) circuit. “E” used to be the electrical variable that represented voltage. However, nowadays it is “V”. In “ICE”, the “E” comes after the “I”, or one can say the “I” comes before the “E”. Thus, the current “I” appears first, then the voltage “V”. Therefore, the current “I” leads (or is advanced) ahead of the voltage “V”. Thus, the capacitor causes the current “I” to be shifted ahead by +90°.