Whether you are new to the industry or are well seasoned and want to review some of the basic information that you learned in the past, these courses and lessons will clearly outline what you are looking for. “Power Systems Electric” is On-Line training that bridges the gaps between textbook theories and practical power systems experience. As a retired electrical engineer who has gone through the experience of developing a career in electrical power systems, I know how frustrating it can be to try and find the answers, so I put together these courses that I feel would have been a major help to me in my development. I have also taken suggestions from students of what they would like to see in addition to these courses which I have given live in person.

Basic Electrical Learning

For those new to the industry, there is a beginner’s group of courses that cover the “Fundamentals of Electricity ” including DC and AC Circuit Analysis. These lessons examine such basics as Ohm’s Law, Series, and Parallel Circuits. The first, and perhaps most important, relationship between current, voltage, and impedance, “Ohm’s Law”, and its relevance to Series and Parallel Circuits. Subsequently, this will lead to the development of Kirchhoff’s Laws as they help to further analyze Network Analysis & Metering Circuits.

Conductors and Insulators are investigated along with their connected components, Capacitors, Inductors, and how they are influenced by Electromagnetism.

Alternating Current (AC – an electric current that periodically reverses direction) is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans, and electric lamps into a wall socket.

The abbreviations AC and DC are often used to mean simply alternating and direct, as they are applied to current or voltage.

These AC courses deal specifically with sinusoidal waveforms and will provide the student with the basic understanding of working with circuits involving Alternating Current, which includes sinusoidal waveforms, vectors & phasors, reactance & impedance of R,L,C circuits, as they relate to the basic laws and theorems of electricity. This includes working with AC Power, Power Factor, Resonance, Complex Numbers, Reactance, and Impedance

Advanced Electrical Learning

These Courses involve subjects such as “Short Circuit Analysis for HV Three-Phase Systems ” which introduces the student to the basic concepts of fault studies on a high voltage three-phase system. System modeling is then used in order to aid in this process, with the ability to move between asymmetrical and symmetrical systems. With hey Searle and extensive study of “Per Phase” & “Per Unit” methodologies system faults are analyzed with the use of symmetrical components.

“A Per-Unit System ” is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified because quantities expressed as per unit do not change when they are referred from one side of a transformer to the other.

In these courses, you will learn exactly what Per Unit Analysis is, the main advantages of using it, how manufacturers of equipment use and rate their products, and the technique of converting to and from the Per Unit system.

Several examples of working with Per Unit are demonstrated in this crisp clear presentation. When you finish you will have a though understanding of this subject.

It is important for all power engineers and technicians to be familiar with the concept of Per Unit as it is being used and referred to every day in power flow, short circuit evaluation, and motor starting studies.

The method of “Symmetrical Components ” is used to simplify asymmetrical three-phase voltages and current analysis by converting the unbalanced system into two sets of balanced phasors and a set of single-phase phasors, or symmetrical components. These sets of phasors are called the positive, negative, and zero sequence components.

An understanding of this method is essential for the understanding of fault analysis and modern-day protection schemes. These courses will provide you with the knowledge to comprehend the concept and how it is applied.

Supplemental Electrical Lessons

In all power electrical analyses, the student will encounter special Trigonometric and Mathematical identities and equations. This site contains special supplemental lessons that zero in on those identities and equations. For example, there are lessons that take you from the “Fundamentals of Trigonometry ” to the more sophisticated requirements in electrical engineering. As you work and study in electrical engineering you are going to run into proofs and equations that are based on trigonometry. A good example of this is when studying AC current, voltage, and impedance calculations, phasors or vectors are used and combined mathematically. Further adventures into complex power will also require a knowledge of trig functions and identities. As a student of this course, you will be introduced to these or at least re-introduced to these that may have been long since forgotten.
In mathematics, “The Derivative of a Function ” of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object’s velocity: this measures how quickly the position of the object changes when time advances.

Specialized Electrical Lessons

Specialized lessons include the “Protection & Control(P & C)” principles of high voltage stations. HV Bus Differential Protection is studied along with restrictions due to CT saturation & mismatch and its solution, “Restraint Differential Protection”.

High Voltage Circuit Breakers are examined as to the various Types (Oil, Vacuum, Air Blast, SF6), their Controls as well as the introduction of potential transformers & current transformers, and their use in conjunction with the relevant instruments such as ammeters, voltmeters, watt meters, and energy meters.

Other lessons include the study of “Transformers ” including core construction along with losses, cooling, and mitigation techniques. Three-phase transformer configurations are studied along with harmonic distortion, CT saturation, and on-load tap-changer problems and how these problems are dealt with. Over-current and restraint differential transformer protection is developed along with a look at some examples of ” Old School relays” as well as modern IDE (intelligent Electrical Devices) relays.

Transformer Connections: (Y – Y; Delta – Delta; Y – Delta; Delta – Y & Y – Zag Zig) are examined along with Transformer Clock System Vector Nomenclature.

Lastly, there is a special section dedicated to “Single and Three-Phase Metering “, including old analog and new digital kilowatt-hour meters.

Conclusion

Regardless of whether or not you are new to the industrial power system, you’ll find what you’re looking for on this site in the way of training. In order to review or select any of these courses, left-click on any of the blue highlighted hyperlinked words of this posting or on “14 Courses Available” from the top menu of the landing page. All of the courses have a free introduction

As a bonus and in the way of a thank you, for your interest in PSPT’s WEB (and Blog) page, I’m making available my 50-page “Electrical Power” crib sheets. These were prepared for use with my courses that are available on this site. There is one section associated with each course and is extremely valuable while viewing the course, as well as a recall of the pertinent formulas and information after the fact. The contained information is also useful during any technical career as a quick reference from time to time. Simply click here or on the picture to the right to be taken to where you can download this item.

November 16, 2024

Blog #31 - Loop or Mesh Analysis - analyzing a two loop circuit with multiple resistors and 2 power supplies.

November 16, 2024/ Graham VanBrunt

As part of my problem series in this blog, I will be analyzing a two loop circuit with multiple resistors and 2 power supplies.

Once I am finished with this series of problems I will be posting them in my Stan store, at the WEB address shown.

Before proceeding I want to explain the three WEB addresses that you will be directed to using. You have already seen the first…https://stan.store/GVB…this is the web address of my Stan Store which will give you direct access to all of my electrical courses.

On the last page, you'll find an address that will direct you to obtain the 50-page crib sheets and notes that will not only be handy when you're taking any of the courses in my Stan Store but also for reference during any time during your career. Here, you will also be asked for your email address which will not be shared or distributed anyway but it will allow me to keep in touch and let you know of any additions or updates to my courses and blogs.

Near the end of this blog, I will be introducing you to a supplier of electrical products which in my estimation are a value worthy of paying attention to.

Looking at the same circuit, this time we are going to calculate the current through each of the resistors in this DC circuit using mesh or loop current analysis.

The term mesh is used because of the similarity in appearance between the closed loops of the network and a wire mesh fence. One can view the circuit as a “window frame” and the meshes as the “windows.” A mesh is a closed pathway with no other closed pathway within it. A loop is also a closed pathway, but a loop may have other closed pathways within it. Therefore, all meshes are loops, but all loops are not meshes. For example, the loop made by the closed path BCDAB is not a mesh because it contains two closed paths: BCAB and CDAC.

Step #1 Draw in the loop currents…Loop currents I1 and I2 are drawn in the clockwise direction in each window. The loop current or mesh current is a fictitious current that enables us to obtain the actual branch currents more easily. The number of loop currents required is always equal to the number of windows of the network. This assures that the resulting equations are all independent. Loop currents may be drawn in any direction, but assigning a clockwise direction to all of them simplifies the process of writing equations…It leads to less confusion and similar to the previous solution, if loop currents turn out to be negative then the assumed the direction of that current is opposite to that of our original assumption.

In Step #2 we indicate the Polarities of each voltage drop within Each Loop.

Identify polarities to agree with the assumed direction of the loop currents.

Starting with Loop #1 at R2…then R3 and ending with E1. Notice that the voltage drops across the resistors are positive w.r.t. the current flow and the voltage drop across the power supply is negative because it is not dropping the voltage in the direction of the current but doing just the opposite providing a voltage rise.

Writing the KVL around each mesh in any direction…it is convenient to follow the same direction as the loop current therefore…

Loop #2…Notice that the polarities across R3 are the opposite for each loop current and the polarities of E1 and E2 are unaffected by the direction of the loop currents passing through them. Also with the assumed current flow of I2…E2 provides a voltage drop and therefore considered positive in the loop equation.

Step #3 Write KVL around Each Mesh following the same direction as the loop current:

for the I1 Loop ☞ we get -8 + 2I1 + 4(I1 - I2) = 0

for the I2 Loop ☞ we get +24 + 4(I2 - I1) + I2 = 0

We can now use these two equations to solve for I1 and I2

Let's rewrite these two equations removing the brackets.

We can now collect the like terms and end up with these two equations.

The first equation can be simplified by dividing both the left-hand side and the right hand side by a factor of 2 and rewriting both equations gives us these two equations. We would now like to reduce the two equations to one by multiplying the first equation by 5…which gives us 15I1 - 10I2 = 20 and the second equation by 2…which gives us 8I1 - 10I2 = 48.

We can now reduce the two equations to one with one unknown by subtracting the second from the first. This removes I2. And leaves us with…

7I1 = -28 This allows us to solve for I1…

I1 = -4

We now will solve for I2…by using this equation…3I1 - 2I2 = 4 and replacing I1 with -4 to give us this equation which simplifies to - 2I2 = 16 and allows us to solve for I2 = -8 Amps.

The minus signs for I1 & I2 indicate that the two loop currents flow in a direction opposite to that assumed; that is, they both flow counterclockwise. Loop current I1 is therefore 4 Amps in a counter clockwise direction and loop current I2 is 8 Amps also in a counter clockwise direction…The true direction of loop current I2 through resistor R3 is from C to A. The true direction of loop current I1 through resistor R3 is from A to C. Therefore, in reality, the current through R3 is (I2 - I1) or 8 - 4 = 4 A in the direction of CA.

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Remember, this video has been brought to you by PSPT, where you will find electrical train training videos when you go to this web address, which will also give you a free copy of my 50 page crib sheets that you can use while viewing any of the courses or just keep handy during your every day work.