Types of Electrical Grid

The power station of the grid is located near the fuel source which reduces the transportation cost of the system. But it is located far away from the populated areas. The power which is generated at high voltage is stepped down by the help of step down transformer in the substation and then supply to the consumers. The electrical grid is mainly classified into two types. They are

1. Regional Grid – The Regional grid is formed by interconnecting the different transmission systems of a particular area through the transmission line.
2. National Grid-It is formed by interconnecting the different regional grid.

Reason for an Interconnection

The interconnection of the grid provides the best use of power resources and ensures great security to supply. It makes the system economical and reliable. The generating stations are interconnected for reducing the reserve generation capacity in each area.

If there is a sudden increase in load or loss of generation in a zone, then it borrows from the adjacent interconnected area. But for the interconnections of the network, a certain amount of generating capacity known as the spinning reserve is required. The spinning reserve consists of a generator running at a normal speed and ready to supply power instantaneously.

Types of an Interconnections

The interconnection between the network is mainly classified into two types, i.e., the HVAC link and the HVDC link.

HVAC (High Voltage Alternating Current) Interconnection

In HVAC link the two AC systems are interconnected by an AC link. For interconnecting the AC system, it is necessary that there should be sufficiently close frequency control on each of the two systems.

For the 50Hz system, the frequency should lie between 48.5 Hz and 51.5 Hz. Such interconnection is known as synchronous interconnection or synchronous tie. The AC link provides a rigid connection between two AC systems to be interconnected. But the AC interconnection has certain limitations.

The interconnection of an AC system has suffered from the following problems.

1. The interconnection of the two AC networks is the synchronous tie. The frequency disturbances in one system are transferred to the other system.
2. The power swings in one system affect the other system. Large power swing in one system may result in frequent tripping due to which major fault occurs in the system. This fault causes complete failure of the whole interconnected system.
3. There is an increase in the fault level if an existing AC system is connected with the other AC system with an AC tie line. This is because the additional parallel line reduces the equivalent reactance of the interconnected system. If the two AC system is connected to the fault line, then the fault level of an each AC system remains unchanged.

HVDC (High Voltage Direct Current) Interconnection

The DC interconnection or DC tie provides a loose coupling between the two AC systems to be interconnected. The DC tie between two AC systems is non-synchronous (Asynchronous). The DC interconnection has certain advantages. They are as follows.

1. The DC interconnection system is asynchronous thus the system which is to be interconnected is either of the same frequency or at the difference frequency. The DC link thus provides the advantages of the interconnection of two AC network at different frequencies. It also enables the system to operate independently and to maintain its frequency standards.
2. The HVDC links provide fast and reliable control of the magnitude and direction of power flow by controlling the firing angle of converters. The rapid control of power flow increases the limit of transient stability.
3. The power swings in the interconnected AC networks can be damped rapidly by modulating the power flow through the DC tie. Thus, the stability of the system is increased.
4. Nowadays, the customary grids are replaced by smart grids. The smart grid uses the smart meter and appliances which improves the efficiency of the system.

It can also be called a three-point starter. Its structure is shown in Figure. To start the motor, the handle is moved from off position to the first contact position. The total obstacle is in the armature circuit, the field connection is connected directly to the supply through a volt coil. Comes in as soon as the speed of the motor increases in the same way as the archete back emf emits and decreases in the value of current Now the handle is moved to the second step. Again this type of function will be done eventually at the last step of the handle. This time the armature will connect directly to the supply and this time the handle does not come with a no-volt coil. The magnet will hold the handle in the Walt coil, and the motor will not need to hold the handle to continue and the motor will rotate at full speed.

Mechanism of 3 points Starter is done so that if the magnetism of the nvc coil is exhausted for any reason, and the handle will be re-off position through the spring, then the supply will not be supplied directly to the motor, with the handle again All the process has to be done, the overloaded relay in the starter is also fitted. It also protects from overload. In the mechanism of which the motor is overloaded.

There is a 3-point Starter equipped with such safety systems

Hiring an electrical wiring contractor is often an expensive proposition. Yet, without proper expertise, trying to install or repair your own electrical wiring project can be a dangerous undertaking. Severe electrical shock, burns, and lethal electrocution can be the dire consequences of ill-advised bravado. Improper wiring installations can also lead to the bigger problems of appliance failures and circuit shorts. In some cases, electrical fires can spark and destroy your beautiful home. While shady electrical wiring contractors exist, there’s also a reason these contractors are expensive.

Safety First

Before you begin to tamper with any wiring or electrical switches, you need to make sure your home and appliances have grounding. Simply put, grounding is a way of ensuring any unintentional current that escapes from its normal path gets channeled into the Earth and not a human body. Many electrical codes now require grounding electrodes or grounding plates to create this safety feature, but older homes may not have this feature. You should make sure your home is fitted with this grounding whether you’re considering taking on a wiring project or not.

The other crucial electrical safety feature for your home is a ground-fault circuit interrupter (GFCI). In the effect that an unintentional ground is created this safety device detects the current drain and shuts off your electrical power. These devices are different than circuit breakers which protect wires from overheating and sparking. A circuit breaker doesn’t protect you from electrocution and a GFCI doesn’t protect your wiring. Again, most electrical codes now require a GFCI device for newer homes, but an older home may not have one. If you don’t know if your home has a GFCI or grounding for your appliances, you should find out before dealing with any electrical wiring project.

Common Home Wiring Projects

While these safety features usually protect you from most electrical dangers, things can still go wrong. Here are some common electrical wiring projects and some things to consider for each one.

Phone Wiring

With computer modems and fax machines going in so many homes, cable and phone wiring have become the most popular home wiring project. Many phone companies used to take care of both interior and exterior wiring. This is no longer the case. The phone company will still take care of the interior wiring but they’ll charge you a hefty price for it. Typical phone wiring is run in one of two main ways. You can run an individual wire from your outside phone box to a new phone jack or you can run wiring from an existing phone jack. Most people elect to use an existing phone jack as the jumping off point to reduce the amount of wiring you need, but if you run wiring from the outside phone box it will be easier to troubleshoot any future wiring problems.

Thermostat Wiring

If something goes wrong with your heating or cooling system, you may begin to suspect the problem lies with your thermostat wiring. You should feel free to take your thermostat off the wall to visually inspect the wiring, but you should never mess with thermostat wiring unless you know exactly what you’re doing. The wiring may look harmless but if you start messing around and change any of the connections, you can easily destroy your heating and cooling systems. Thermostat wiring is mostly control wiring, but amongst this wiring can sometimes be high voltage wiring that can instantly burn and/or kill you. Your best bet is to leave the wiring alone, eliminate other reasonable possibilities that might be causing your heating or cooling malfunction, and then call an electrician.

Ceiling Fan Wiring

With the proper safety precautions, ceiling fan wiring is a viable DIY project. Contacting the manufacturer or some basic research should give you the necessary information for the proper electrical wiring colors and functions. There are standard colors but also many exceptions to the rule. One thing you don’t want to do is let your ceiling fan motor run on a dimmer switch designed for a light fixture. This will cause the motor to hum. An electrical wiring contractor can replace your original electrical wiring to accommodate additional ceiling fan options. For example, an electrician can give you an extra wall switch so you can control the fan and the light separately.

Hot Tub Wiring

Too many people try to install their own hot tub wiring. Among the more complicated wiring projects, it’s probably best to leave this project to a professional unless you really know what you’re doing. Some states require that hot tub wiring is done by a certified electrician.

So what formulas do you need to have memorized for the SAT math section before the day of the test? In this complete guide, I’ll cover every critical formula you MUST know before you sit down for the test. I’ll also explain them in case you need to jog your memory about how a formula works. If you understand every formula in this list, you’ll save yourself valuable time on the test and probably get a few extra questions correct.

Formulas Given on the SAT, Explained

This is exactly what you’ll see at the beginning of both math sections (the calculator and no calculator section). It can be easy to look right past it, so familiarize yourself with the formulas now to avoid wasting time on test day.

You are given 12 formulas on the test itself and three geometry laws. It can be helpful and save you time and effort to memorize the given formulas, but it is ultimately unnecessary, as they are given on every SAT math section.

You are only given geometry formulas, so prioritize memorizing your algebra and trigonometry formulas before the test day (we’ll cover these in the next section). You should focus most of your study effort on algebra anyways because geometry has been de-emphasized on the new SAT and now makes up just 10% (or less) of the questions on each test.

Nonetheless, you do need to know what the given geometry formulas mean. The explanations of those formulas are as follows:

Area of a Circle

A=πr²

> π is a constant that can, for the purposes of the SAT, be written as 3.14 (or 3.14159)

> r is the radius of the circle (any line drawn from the center point straight to the edge of the circle)

Circumference of a Circle

C=2πr (or C=πd)

> d is the diameter of the circle. It is a line that bisects the circle through the midpoint and touches two ends of the circle on opposite sides. It is twice the radius.

Area of a Rectangle

A=lw

> l is the length of the rectangle

> w is the width of the rectangle

Area of a Triangle

> b is the length of the base of the triangle (the edge of one side)

> h is the height of the triangle

i.  In a right triangle, the height is the same as a side of the 90-degree angle. For non-right triangles, the height will drop down through the interior of the triangle, as shown above.

The Pythagorean Theorem

a²+b²+c²

> In a right triangle, the two smaller sides (a and b) are each square. Their sum is equal to the square of the hypotenuse (c, the longest side of the triangle).

Properties of Special Right Triangle: Isosceles Triangle

> An isosceles triangle has two sides that are equal in length and two equal angles opposite those sides.

> An isosceles right triangle always has a 90-degree angle and two 45 degree angles.

> The side lengths are determined by the formula: x, x, x√2, with the hypotenuse (the side opposite 90 degrees) having a length of one of the smaller sides *√2.

i. E.g., An isosceles right triangle may have side lengths of 12, 12, and 12√2.

Properties of Special Right Triangle: 30, 60, 90 Degree Triangle

> A 30, 60, 90 triangle describes the degree measures of the triangle’s three angles.

> The side lengths are determined by the formula: x, x√3, and 2x

i. The side opposite 30 degrees is the smallest, with a measurement of x.

ii. The side opposite 60 degrees is the middle length, with a measurement of x√3.

iii. The side opposite 90 degree is the hypotenuse (longest side), with a length of 2x.

iv. For example, a 30-60-90 triangle may have side lengths of 5, 5√3, and 10.

Volume of a Rectangular Solid

V=lwh

> l is the length of one of the sides.

> h is the height of the figure.

> w is the width of one of the sides.

Volume of a Cylinder

V=πr²h

> r is the radius of the circular side of the cylinder.

> h is the height of the cylinder.

Volume of a Sphere

> r is the radius of the sphere.

Volume of a Cone

> r is the radius of the circular side of the cone.

> h is the height of the pointed part of the cone (as measured from the center of the circular part of the cone).

Volume of a Pyramid

> l is the length of one of the edges of the rectangular part of the pyramid.

> h is the height of the figure at its peak (as measured from the center of the rectangular part of the pyramid).

> w is the width of one of the edges of the rectangular part of the pyramid.

Law: the number of degrees in a circle is 360

Law: the number of radians in a circle is 2π

Law: the number of degrees in a triangle is 180

Gear up that brain because here come the formulas you have to memorize.

Formulas Not Given on the Test

For most of the formulas on this list, you’ll simply need to buckle down and memorize them (sorry). Some of them, however, can be useful to know but are ultimately unnecessary to memorize, as their results can be calculated via other means. (It’s still useful to know these, though, so treat them seriously).

We’ve broken the list into “Need to Know” and “Good to Know,” depending on if you are a formula-loving test taker or a fewer-formulas-the-better kind of test taker.

Slopes and Graphs

How to write the equation of a line

> The equation of a line is written as:y=mx+b

i. If you get an equation that is NOT in this form (ex. mx−y=b), then re-write it into this format! It is very common for the SAT to give you an equation in a different form and then ask you about whether the slope and intercept are positive or negative. If you don’t re-write the equation into y=mx+b, and incorrectly interpret what the slope or intercept is, you will get this question wrong.

> m is the slope of the line.

> b is the y-intercept (the point where the line hits the y-axis).

> If the line passes through the origin (0,0), the line is written as y=mx.

Good to Know

> Midpoint formula

i. Given two points, A(x₁,y₁), B(x₂,y₂), find the midpoint of the line that connects them:

> Distance formula

i. Given two points, A(x1,y1),B(x2,y2), find the distance between them:

You don’t need this formula, as you can simply graph your points and then create a right triangle from them. The distance will be the hypotenuse, which you can find via the Pythagorean Theorem.

Circles

Good to Know

> Length of an arc

i. Given a radius and a degree measure of an arc from the center, find the length of the arc

ii. Use the formula for the circumference multiplied by the angle of the arc divided by the total angle measure of the circle (360)

Area of an arc sector

> Given a radius and a degree measure of an arc from the center, find the area of the arc sector

i. Use the formula for the area multiplied by the angle of the arc divided by the total angle measure of the circle

Averages

Need to Know

> The average is the same thing as the mean

> Find the average/mean of a set of numbers/terms

Probabilities

Need to Know

> Probability is a representation of the odds of something happening.

Good to Know

> A probability of 1 is guaranteed to happen. A probability of 0 will never happen.

Percentages

Need to Know

Trigonometry

Trigonometry is a new addition to the new 2016 SAT math section. Though it makes up less than 5% of math questions, you won’t be able to answer the trigonometry questions without knowing the following formulas.

Difference of Squares

What you see below is a double bar chart. Take a close look at it and study it, so you can become familiar with its features

After you have examined the double bar chart above, here are a few good observations you can make from the graph:

The scale is on the left of the graph and it is 10 units.

The title is “Scores on a Fractions Test with or without Preparation”

Preparation helped students to score higher

The lowest score without preparation is 45 and the highest score is 85

The lowest score with preparation is 55 and the highest score is 100.

The students who made the most improvement are Darline, Carla, and John. Their score improved by 15.

The student who made the least improvement is Peter. Although Jetser’s score is still slow, he improved by 10 points while Peter’s improved only by 5 points

How to construct a double bar graph:

1. Decide what title you will give the graph
2. Decide if you want horizontal or vertical bars
3. Choose a scale
4. Put the label on the axes
5. Draw the bars

Example
Use the table below to construct a double bar chart. We will follow all steps outlined above to construct this graph

1. The title can be clearly seen from the table.
2. We will choose vertical bars
3. Since the scores differ from one another mostly by 5, 10, 15, or 20, it makes sense to chose a scale of 10

If the variation between scores were like 1, 2, 3, 4, or 5, it would have been better to choose a scale of 1 or 2

4. We put names on the x-axis and scores on the y-axis. If we had decided to make horizontal bars, we would have put names on the y-axis and scores on the x-axis

5. Finally, we drawbars. The double bar graph is shown below:

Also Read   Making Line Graphs

The title is ” Scores on a basic math test”

The scale is at the left of the graph. The distance between each square is 10, so the scale is 10

It shows scores for a student over a period of time or after taking 10 basic math test.

A wealth of information can be deducted from the graph

The lowest score is 40 and the highest score is 100

The greatest increase or improvement happened between test #2 and test #3. As you can see the student went from a score of 40 to a score of 70.

The lowest decrease or happened between test #6 and test #7. The student went from a score of 90 to a score of 60

Looking at the graphs, it looks like although the score dropped a couple of times, over time the student made consistent progress.

Example:

Use the following data to make a line graph

We get:

The graph has an upward trend and shows that over time, gas prices kept increasing.

Looking at the graph, you can see that the line is steeper between 2007 and 2008.

This means that the highest increase was experienced between 2007 and 2008. Gas prices went up by a dollar

Also Read  Double Bar Graphs

Example #1:

Add 2x² + 3x + 4 and 3x² + x + 1

Step #1:

Model both polynomials with tiles

Step #2:

Combine all tiles that are alike or the same and count them

You got a total of 5 light blue square tiles, so 5x²

You got a total of 4 green rectangle tiles, so 4x

You got a total of 5 blue small square tiles, so 5

Putting it all together, we get 5x² + 4x + 5

I hope from the above modeling, it is clear that we can only combine tiles of the same type

For example, you could not add light blue square tiles to green rectangle tiles just like it would not make sense to add 5 potatoes to 5 apples

Try adding 5 potatoes to 5 apples and tell me if you got 10 apples or 10 potatoes. It just does not make sense

Keep this important fact in mind when adding polynomials

We call tiles that are alike or are the same type “like terms”, so this means again that you can only add like terms

Basically, likes terms are terms with the same variable and the same exponent

For example, 2x² and 5x² are like terms because they have the same variable which is x and the same exponent which is 2.

To add like the term, just add the coefficients, or the numbers attached to the term, or the number on the left side of the term

2x² + 5x² = (2 + 5)x² = 7x²

Example #2:

Add 6x² + 2x + 4 to 10x² + 5x + 6

Combine all like terms. You could use parentheses to keep things organized

(6x² + 10x²) + ( 2x + 5x) + (4 + 6)

Add the coefficient

(6 + 10)x² + (2 + 5)x + 4 + 6

We get 16x² + 7x + 10

Example #1: Done by combining like terms and adding the coefficients

Add 2x² + 3x + 4 to 3x² + x + 1

Combine all like terms. You could use parentheses to keep things organized

(2x² + 3x²) + ( 3x + x) + (4 + 1)

Add the coefficient

(2 + 3)x² + (3 + 1)x + 4 + 1

We get 5x² + 4x + 5

Notice that if the term is x, you can rewrite it as 1x, so your coefficient is 1

• Isolate the absolute value on one side of the equation.
• Is the number on the other side of the equation negative? If you answered yes, then the equation has no solution. If you answered no, then go on to step 3.
• Write two equations without absolute values. The first equation will set the quantity inside the bars equal to the number on the other side of the equal sign; the second equation will set the quantity inside the bars equal to the opposite of the number on the other side.
• Solve the two equations.

Follow these steps to solve an absolute value equality which contains two absolute values (one on each side of the equation):

• Write two equations without absolute values.  The first equation will set the quantity inside the bars on the left side equal to the quantity inside the bars on the right side.  The second equation will set the quantity inside the bars on the left side equal to the opposite of the quantity inside the bars on the right side.
• Solve the two equations.

Let’s look at some examples.

Example 1: Solve |2x – 1| + 3 = 6

Step 1: Isolate the absolute value

|2x – 1| + 3 = 6

|2x – 1| = 3

Step 2: Is the number on the other side of the equation negative?

No, it’s a positive number, 3, so continue on to step 3

Step 3: Write two equations without absolute value bars

2x – 1 = 3

2x – 1 = -3

Step 4: Solve both equations

2x – 1 = 3         :     2x – 1 = -3

2x = 4               :        2x = -2

x = 2                 :        x = -1

Example 2: Solve |3x – 6| – 9 = -3

Step 1: Isolate the absolute value

|3x – 6| – 9 = -3

|3x – 6| = 6

Step 2: Is the number on the other side of the equation negative?

No, it’s a positive number, 6, so continue on to step 3

Step 3: Write two equations without absolute value bars

3x – 6 = 6

3x – 6 = -6

Step 4: Solve both equations

3x – 6 = 6        :     3x – 6 = -6

3x = 12            :         3x = 0

x = 4                :           x = 0

Example 3: Solve |5x + 4| + 10 = 2

Step 1: Isolate the absolute value

|5x + 4| + 10 = 2

|5x + 4| = -8

Step 2: Is the number on the other side of the equation negative?

Yes, it’s a negative number, -8. There is no solution to this problem.

Example 4:  Solve |x – 7| = |2x – 2|

Step 1: Write two equations without absolute value bars

x – 7 = 2x – 2

x – 7 = -(2x – 2)

Step 4: Solve both equations

x – 7 = 2x – 2         :            x – 7 = -2x + 2

-x – 7 = -2              :              3x – 7= 2

-x = 5                     :                   3x = 9

x = -5                     :                      x = 3

Example 5:  Solve |x – 3| = |x + 2|

Step 1: Write two equations without absolute value bars

x – 3 = x + 2

x – 3 = -(x + 2)

Step 4: Solve both equations

x – 3 = x + 2                                            :           x – 3 = -x – 2

– 3 = -2                                                    :           2x – 3= -2

false statement                                        :            2x = 1

No solution from this equation                 :             x = 1/2

So the only solution to this problem is x = 1/2

Example 6:  Solve |x – 3| = |3 – x|

Step 1: Write two equations without absolute value bars

x – 3 = 3 – x

x – 3 = -(3 – x)

Step 4: Solve both equations

x – 3 = 3 – x                :       x – 3 = -(3 – x)

2x – 3 = 3                   :      x – 3= -3 + x

2x = 6                         :      -3 = -3

x = 3                           :      All real numbers are solutions to this equation

Since 3 is included in the set of real numbers, we will just say that the solution to this equation is All Real Numbers

It provides an easier way to write numbers and make multiplication and division of very large or very small numbers a lot easier.

A number is in this format if we can write it as:

a × 10ⁿ

with 1 ≤ a < 10 and n is an integer.

1 ≤ a < 10 means that a is a number between 1 and 10

Thus, a can be 1,2,3,4,5,6,7,8, and 9

Let’s start with something simple.Write 500 in this useful notation:

500 = 5 × 100 = 5 × 10²

You can also claim as we saw before that there is a decimal point after 0 and write 500.0

Then, move the decimal point 2 places to the left between 5 and 0 to get 5.000, which is the same as 5.

Since you moved it two places to the left, you know that your exponent is 2.

Your base is always 10

Thus, 500 = 5 × 10²

More examples of scientific notation:

1) 75000

75000 = 75000.0

Move the decimal point 4 places to the left between 7 and 5.

We get 7.5000, which is the same as 7.5

Since we moved it 4 places to the left, your exponent is 4 and your base is still 10.

Thus, 75000 = 7.5 × 10⁴

Sometimes, instead of moving your decimal point to the left, you have to move it to the right as the following example demonstrates:

When you move your decimal point to the right, your exponent is negative.

2) 0.002

Move your decimal point 3 places to the right after the 2 to get 0002. and 0002. is the same as 2. or 2

Since you had to move it 3 places to the right, your exponent is -3 and the base is still 10

Thus, 0.002 = 2 × 10^-3

3) 0.000065

Move the decimal point 5 places to the right

The answer is 6.5 × 10^-5

4) 650000

Move the decimal point 5 places to the left

The answer is 6.5 × 10⁵