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.

December 20, 2024

Blog #48 - The Branch-Current Method of Solution

December 20, 2024/ Graham VanBrunt

As part of my problem series in this video, I will be solving the Problem Using the Branch-Current Method of Solution.

Once I am finished with this series of problems I will be posting them in my Stan store, at this web address…https://stan.store/GVB

In this problem we are to calculate the current through each of the resistors in this DC circuit using the branch-current method of solution. The branch-current method makes use of the… Superposition Theorem, which states…”In a linear circuit with several sources, the current though and voltage drop, for any element in the circuit, is the sum of the currents and voltages produced by each source acting independently.”

To start…I am going to label all the nodes…There are four nodes in this circuit, as indicated by the letters Node A, Node B, Node C and, Node D.

Nodes are junctions where two or more current paths come together…

A branch is a portion of a circuit consisting of one or more elements in series. This circuit contains 2 sources and 3 branches, each branch of which is a current path in the network.

Branch ABC consists of the power supply E1 and R1 in series, branch ADC consists of the power supply E2 and R2 in series, and branch CA consists of R3 only. I am assigning a distinct current of arbitrary direction to each branch of the network.

I1, I2 & I3 these currents create voltage drops across each resistor. The polarities of which is determined by the assumed direction of current and the passive sign convention.

The polarity of the power-supply terminals is fixed and is therefore not dependent on the assumed direction of current.

Notice the words arbitrary and assumed direction… after the calculations are made if the assumed current is minus then the current will be flowing in the other direction to the assumed direction.

A closed loop is any continuous connection of branches, that allows us to trace a path, which leaves a point in one direction and returns to that same starting point…from another direction without leaving the network.

Now we apply Kerchof's Voltage Law around each closed loop…for loop ABCA or loop 1…remember Kerchof's Voltage Law tells us that…the algebraic sum of changes in potential around any closed circuit path or loop, must be zero…starting at node A voltage source E1 raises the potential to 8 volts therefore plus 8 and the resistors voltage change is - 2I1 for resistor R1 and - 4I3 for resistor R3. These voltage changes when added together must equal zero (KVL) so we write that in the form of an equation,… as you see here…the currents are the unknowns.

For loop ADCA…plus 24 for E2 and the resistors drop the voltage by - I2 for resistor R2 and - 4I3 for resistor R3. These voltage changes when added together must equal zero… we write that in the form of an equation plus 24 - I2 - 4I3 = 0. Kerchof's Current Law at node C tells us that I1 + I2 = I3.

The three equations now can be solved by the elimination method. Firstly, by rearranging the last equation, we can clearly see that we can express I3 in terms of I1 & I2.

➜ Now using the above two equations I'm going to substitute for I3 which is equal to I1 + I2.

We now have 2 equations with 2 unknowns…I1 & I2 The unknowns being the two loop currents…We could've gone immediately to these two equations to solve this problem however we introduced a 3rd equation and a 3rd unknown by using Kirchhoff current law…which as you recall generated…the KCL (bottom) equation this points out the fact that there are more than one way to solve or analyze a mesh equation…Solving for I1 & I2 will also give us I3 which is all just mathematics and I’ll leave that to you to solve as a mathematical exercise.

If you have made it this far and are indeed finished calculating the equations, coming up with the answers for the three current in this problem…you have demonstrated your interest in electrical systems. One of the systems that are out there in today's world is home automation. You can use your newly acquired knowledge to possibly proceed with automating your home.

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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…https://bit.ly/47YB3vh...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.