Ece 476 Power System Analysis

ECE 476 POWER SYSTEM ANALYSIS

Lecture 9 Transformers, Per Unit

Professor Tom Overbye Department of Electrical and Computer Engineering Announcements

Be reading Chapter 3 HW 3 is 4.32, 4.41, 5.1, 5.14. Due September 22 in class.

1 Transformer Equivalent Circuit

Using the previous relationships, we can derive an equivalent circuit model for the real transformer

This model is further simplified by referring all impedances to the primary side '2 ' r22ar re r 12 r '2 ' xaxxxx22e 12 2 Simplified Equivalent Circuit

3 Calculation of Model Parameters

The parameters of the model are determined based upon – nameplate data: gives the rated voltages and power – open circuit test: rated voltage is applied to primary with secondary open; measure the primary current and losses (the test may also be done applying the voltage to the secondary, calculating the values, then referring the values back to the primary side). – short circuit test: with secondary shorted, apply voltage to primary to get rated current to flow; measure voltage and losses.

4 Transformer Example

Example: A single phase, 100 MVA, 200/80 kV transformer has the following test data: open circuit: 20 amps, with 10 kW losses short circuit: 30 kV, with 500 kW losses Determine the model parameters.

5 Transformer Example, cont’d

From the short circuit test 100MVA 30 kV I 500AjX , R 60 sc 200kV e e 500 A 2 Psc RIesc 500 kW Re 2 , 22 Hence Xe 60 2 60 From the open circuit test 200 kV 2 RM4 c 10 kW 200 kV R jX jX 10,000 X 10,000 e em20 A m

6 Residential Distribution Transformers

Single phase transformers are commonly used in residential distribution systems. Most distribution systems are 4 wire, with a multi-grounded, common neutral.

7 Per Unit Calculations

A key problem in analyzing power systems is the large number of transformers. – It would be very difficult to continually have to refer impedances to the different sides of the transformers This problem is avoided by a normalization of all variables. This normalization is known as per unit analysis.

actual quantity quantity in per unit base value of quantity

8 Per Unit Conversion Procedure, 1

1. Pick a 1 VA base for the entire system, SB 2. Pick a voltage base for each different voltage level,

VB. Voltage bases are related by transformer turns ratios. Voltages are line to neutral. 2 3. Calculate the impedance base, ZB= (VB) /SB

4. Calculate the current base, IB = VB/ZB 5. Convert actual values to per unit Note, per unit conversion on affects magnitudes, not the angles. Also, per unit quantities no longer have units (i.e., a voltage is 1.0 p.u., not 1 p.u. volts)

9 Per Unit Solution Procedure

1. Convert to per unit (p.u.) (many problems are already in per unit) 2. Solve 3. Convert back to actual as necessary

10 Per Unit Example

Solve for the current, load voltage and load power in the circuit shown below using per unit analysis with an SB of 100 MVA, and voltage bases of 8 kV, 80 kV and 16 kV.

Original Circuit

11 Per Unit Example, cont’d

8kV 2 Z Left 0.64 B 100MVA 80kV 2 Z Middle 64 B 100MVA 16kV 2 Z Right 2.56 B 100MVA

Same circuit, with values expressed in per unit.

12 Per Unit Example, cont’d

1.0 0 I 0.22 30.8 p.u. (not amps) 3.91 j 2.327

VL 1.0 0 0.22 30.8 p.u. V 2 SVI* L 0.189 p.u. LLLZ

SG 1.0 0 0.22 30.8 30.8 p.u. 13 Per Unit Example, cont’d

To convert back to actual values just multiply the per unit values by their per unit base

V Actual 0.859 30.8 16 kV 13.7 30.8 kV L Actual SL 0.189 0 100 MVA 18.9 0 MVA Actual SG 0.22 30.8 100 MVA 22.0 30.8 MVA 100 MVA IMiddle 1250 Amps B 80 kV Actual I0.2230.8Middle Amps27530.8

14 Three Phase Per Unit

Procedure is very similar to 1 except we use a 3 VA base, and use line to line voltage bases 3 1. Pick a 3 VA base for the entire system, SB 2. Pick a voltage base for each different voltage

level, VB. Voltages are line to line. 3. Calculate the impedance base 2 22 VVVBLL,,,(3 BLN ) BLN ZB 311 SSSBBB3 Exactly the same impedance bases as with single phase!

15 Three Phase Per Unit, cont'd

4. Calculate the current base, IB

311 31SSSBBB3 IIBB 3VBLL, 33VVBLN,, BLN Exactly the same current bases as with single phase!

5. Convert actual values to per unit

16 Three Phase Per Unit Example

Solve for the current, load voltage and load power in the previous circuit, assuming a 3 power base of 300 MVA, and line to line voltage bases of 13.8 kV, 138 kV and 27.6 kV (square root of 3 larger than the 1 example voltages). Also assume the generator is Y-connected so its line to line voltage is 13.8 kV. Convert to per unit as before. Note the system is exactly the same!

17 3 Per Unit Example, cont'd

1.0 0 I 0.22 30.8 p.u. (not amps) 3.91 j 2.327

VL 1.0 0 0.22 30.8 p.u. V 2 SVI* L 0.189 p.u. LLLZ

SG 1.0 0 0.22 30.8 30.8 p.u.

Again, analysis is exactly the same!

18 3 Per Unit Example, cont'd

Differences appear when we convert back to actual values V Actual 0.859 30.8 27.6 kV 23.8 30.8 kV L Actual SL 0.189 0 300 MVA 56.7 0 MVA Actual SG 0.22 30.8 300 MVA 66.0 30.8 MVA 300 MVA IMiddle 1250 Amps (same current!) B 3138 kV Actual I0.2230.Middle 8 Amps 275 30.8

19 3 Per Unit Example 2

Assume a 3 load of 100+j50 MVA with VLL of 69 kV is connected to a source through the below network:

What is the supply current and complex power?

Answer: I=467 amps, S = 103.3 + j76.0 MVA 20

Per Unit Change of MVA Base

Parameters for equipment are often given using power rating of equipment as the MVA base To analyze a system all per unit data must be on a common power base OriginalBase NewBase ZZZpu actual pu VV22 OriginalBase base base NewBase Hence Z pu OriginalBase/ NewBase Z pu SBase SBase NewBase OriginalBase SBase NewBase Z pu OriginalBase Z pu SBase 21 Per Unit Change of Base Example

A 54 MVA transformer has a leakage reactance or 3.69%. What is the reactance on a 100 MVA base? 100 X 0.0369 0.0683 p.u. e 54

22 Transformer Reactance

Transformer reactance is often specified as a percentage, say 10%. This is a per unit value (divide by 100) on the power base of the transformer. Example: A 350 MVA, 230/20 kV transformer has leakage reactance of 10%. What is p.u. value on 100 MVA base? What is value in ohms (230 kV)? 100 X 0.10 0.0286 p.u. e 350 2302 0.0286 15.1

100 23 Three Phase Transformers

There are 4 different ways to connect 3 transformers Y-Y -

Usually 3 transformers are constructed so all windings share a common core 24 3 Transformer Interconnections

-Y Y-

25 Y-Y Connection

Magnetic coupling with An/an, Bn/bn & Cn/cn VVI1 Anaa,, AB A VVIaan ab a

26 Y-Y Connection: 3 Detailed Model

27 Y-Y Connection: Per Phase Model

Per phase analysis of Y-Y connections is exactly the same as analysis of a single phase transformer. Y-Y connections are common in transmission systems. Key advantages are the ability to ground each side and there is no phase shift is introduced. 28 - Connection

Magnetic coupling with AB/ab, BC/bb & CA/ca VI11 I ABa,, AB A VIaIaab ab a

29 - Connection: 3 Detailed Model

To use the per phase equivalent we need to use the delta-wye load transformation 30 - Connection: Per Phase Model

Per phase analysis similar to Y-Y except impedances are decreased by a factor of 3. Key disadvantage is - connections can not be grounded; not commonly used.

31 -Y Connection

Magnetic coupling with AB/an, BC/bn & CA/cn

32 -Y Connection V/I Relationships

VVAB AB aVVV,an ab 3 an 30 Vaan VV30 30 Hence VV 3AB and 3 An ab aaan For current we get

I AB 1 IaIaAB Iaab 1 II3 30 I I30 AAB AB3 A 1 aI 30 aA3 33 -Y Connection: Per Phase Model

Note: Connection introduces a 30 degree phase shift! Common for transmission/distribution step-down since there is a neutral on the low voltage side. Even if a = 1 there is a sqrt(3) step-up ratio

34 Y- Connection: Per Phase Model

Exact opposite of the -Y connection, now with a phase shift of -30 degrees.

35 Load Tap Changing Transformers

LTC transformers have tap ratios that can be varied to regulate bus voltages The typical range of variation is 10% from the nominal values, usually in 33 discrete steps (0.0625% per step). Because tap changing is a mechanical process, LTC transformers usually have a 30 second deadband to avoid repeated changes. Unbalanced tap positions can cause "circulating vars"

36 LTCs and Circulating Vars

64 MW slack 14 Mvar

1 1.00 pu 24.1 MW 40.2 MW 12.8 Mvar 1.7 Mvar

A A 1.056 tap 1.000 tap 80% MVA MVA

40.0 MW 24.0 MW -0.0 Mvar -12.0 Mvar 2 0.98 pu 3 1.05 pu

0.0 Mvar

24 MW 40 MW 12 Mvar 0 Mvar

37 Phase Shifting Transformers

Phase shifting transformers are used to control the phase angle across the transformer Since power flow through the transformer depends upon phase angle, this allows the transformer to regulate the power flow through the transformer Phase shifters can be used to prevent inadvertent "loop flow" and to prevent line overloads.

38 Search Wikipedia

Last edited 9 months ago by Yobot

Quadrature booster

A phase angle regulating transformer, phase angle regulator (PAR, American usage), phase- shifting transformer, phase shifter (West coast American usage), or quadrature booster (quad booster, British usage), is a specialised form of transformer used to control the flow of real power on three-phase electricity transmission networks. 400 MVA 220/155 kV phase-shifting For an alternating current transmission line, power transformer. flow through the line is proportional to the sine of the difference in the phase angle of the voltage between the transmitting end and the receiving end of the line.[1] Where parallel circuits with different capacity exist between two points in a transmission grid (for example, an overhead line and an underground cable), direct manipulation of the phase angle allows control of the division of power flow between the paths, preventing overload.[2] Quadrature boosters thus provide a means of relieving overloads on heavily laden circuits and re-routing power via more favorable paths.

Alternately, where an interchange partner is intentionally causing significant "inadvertent energy" to flow through an unwilling interchange partner's system, the unwilling partner may threaten to install a phase shifter to prevent such "inadvertent energy", with the unwilling partner's tactical objective being the improvement of his system's stability at the expense of the other system's stability. As power system reliability is really a regional or national strategic objective, the threat to install a phase shifter is usually sufficient to cause the other system to implement the required changes to his system to reduce or eliminate the "inadvertent energy".

The capital cost of a quadrature booster can be high: as much as four to six million GBP (6–9 million USD) for a unit rated over 2 GVA. However, the utility to transmission system operators in ﬂexibility and speed of operation, and particularly Phase Shifter Example 3.13

345.00 kV 341.87 kV 283.9 MW 283.9 MW 39.0 Mvar 6.2 Mvar 500 MW slack 164 Mvar 500 MW Phase Shifting Transformer 100 Mvar

216.3 MW 216.3 MW 125.0 Mvar 0.0 deg 93.8 Mvar 1.05000 tap

39 ComED Control Center

40 ComED Phase Shifter Display

41 Autotransformers

Autotransformers are transformers in which the primary and secondary windings are coupled magnetically and electrically. This results in lower cost, and smaller size and weight. The key disadvantage is loss of electrical isolation between the voltage levels. Hence autotransformers are not used when a is large. For example in stepping down 7160/240 V we do not ever want 7160 on the low side!

42 Home (http://www.electronics-tutorials.ws) » Transformers (http://www.electronics-tutorials.ws/category/transformer) » The Autotransformer Search

Ads by Google Transformer Coil Winding Auto Transformer Wire Size Calculator

The Autotransformer

Autotransformer Basics Unlike the previous voltage transformer which has two electrically isolated windings called: the primary and the secondary, an Autotransformer has only one single voltage winding which is common to both sides. This single winding is “tapped” at various points along its length to provide a percentage of the primary voltage supply across its secondary load. Then the autotransformer has the usual magnetic core but only has one winding, which is common to both the primary and secondary circuits.

Therefore in an autotransformer the primary and secondary windings are linked together both electrically and magnetically. The main advantage of this type of transformer design is that it can be made a lot cheaper for the same VA rating, but the biggest disadvantage of an autotransformer is that it does not have the primary/secondary winding isolation of a conventional double wound transformer.

The section of winding designated as the primary part of the winding is connected to the AC power source with the secondary being part of this primary winding. An autotransformer can also be used to step the supply voltage up or down by reversing the connections. If the primary is the total winding and is connected to a supply, and the secondary circuit is connected across only a portion of the winding, then the secondary voltage is “stepped-down” as shown.

Autotransformer Design

When the primary current IP is !owing through the single winding in the direction of the arrow as shown, the secondary current, IS, !ows in the opposite direction. Therefore, in the portion of the winding that generates the secondary voltage, V the current !owing out of the winding is the di"erence of I and I . direction. Therefore, in the portion of the winding that generates the secondary voltage, VS the current !owing out of the winding is the di"erence of IP and IS.

The Autotransformer can also be constructed with more than one single tapping point. Auto-transformers can be used to provide di"erent voltage points along its winding or increase its supply voltage with respect to its supply voltage VP as shown.

Autotransformer with Multiple Tapping Points

The standard method for marking an auto-transformer windings is to label it with capital (upper case) letters. So for example, A, B, Z etc to identify the supply end. Generally the common neutral connection is marked as N or n. For the secondary tapping’s, su#x numbers are used for all tapping points along the auto-transformers primary winding. These numbers generally start at number 1 and continue in ascending order for all tapping points as shown.

Autotransformer Terminal Markings

An autotransformer is used mainly for the adjustments of line voltages to either change its value or to keep it constant. If the voltage adjustment is by a small amount, either up or down, then the transformer ratio is small as VP and VS are nearly equal. Currents IP and IS are also nearly equal.

Therefore, the portion of the winding which carries the di"erence between the two currents can be made from a much smaller conductor size, since the currents are much smaller saving on the cost of an equivalent double wound transformer.

However, the regulation, leakage inductance and physical size (since there is no second winding) of an autotransformer for a given VA or KVA rating are less than for a double wound transformer.

Autotransformer’s are clearly much cheaper than conventional double wound transformers of the same VA rating. When deciding upon using an autotransformer it is usual to compare its cost with that of an equivalent double wound type. (http://www.amazon.com/gp/aws/cart/add.html? This is done by comparing the amount of copper saved in the winding. If the ratio “n” is de$ned as the ratio of the lower voltage ASIN.1=1111039135&Quantity.1=1&AWSAccessKeyId=AKIAIOB4VMPIMBIMN7NA&AssociateTag=basicelecttut- to the higher voltage, then it can be shown that the saving in copper is: n.100%. For example, the saving in copper for the two 20) Electrical Transformers and autotransformer’s would be: Rotating Machines (http://www.amazon.com/gp/aws/cart/add.html? ASIN.1=1111039135&Quantity.1=1&AWSAccessKeyId=AKIAIOB4VMPIMBIMN7NA&AssociateTag=basicelecttut- 20) List Price: $149.95 (http://www.amazon.com/gp/aws/cart/add.html? ASIN.1=1111039135&Quantity.1=1&AWSAccessKeyId=AKIAIOB4VMPIMBIMN7NA&AssociateTag=basicelecttut- 20) Current Price: $93.09 (http://www.amazon.com/gp/aws/cart/add.html? ASIN.1=1111039135&Quantity.1=1&AWSAccessKeyId=AKIAIOB4VMPIMBIMN7NA&AssociateTag=basicelecttut- 20)

(http://www.amazon.com/gp/aws/cart/add.html? ASIN.1=1111039135&Quantity.1=1&AWSAccessKeyId=AKIAIOB4VMPIMBIMN7NA&AssociateTag=basicelecttut- 20) Price Disclaimer

Autotransformer Example No1 An autotransformer is required to step-up a voltage from 220 volts to 250 volts. The total number of coil turns on the transformer main winding is 2000. Determine the position of the primary tapping point, the primary and secondary currents when the output is rated at 10KVA and the economy of copper saved.

Then the primary current is 45.4 amperes, the secondary current drawn by the load is 40 amperes and 5.4 amperes !ows through the common winding. The economy of copper is 88%.

Disadvantages of an Autotransformer

The main disadvantage of an autotransformer is that it does not have the primary to secondary winding isolation of a conventional double wound transformer. Then autotransformer’s can not safely be used for stepping down higher voltages to much lower voltages suitable for smaller loads. If the secondary side winding becomes open-circuited, current stops !owing through the primary winding stopping the transformer action resulting in the full primary voltage being applied to the secondary circuit. If the secondary circuit su"ers a short-circuit condition, the resulting primary current would be much larger than an equivalent double wound transformer due to the increased !ux linkage damaging the autotransformer. Since the neutral connection is common to both the primary and secondary windings, earthing of the secondary winding automatically Earths the primary as there is no isolation between the two windings. Double wound transformers are sometimes used to isolate equipment from earth.

The autotransformer has many uses and applications including the starting of induction motors, used to regulate the voltage of transmission lines, and can be used to transform voltages when the primary to secondary ratio is close to unity.

An autotransformer can also be made from conventional two-winding transformers by connecting the primary and secondary windings together in series and depending upon how the connection is made, the secondary voltage may add to, or subtract from, the primary voltage.

The Variable Autotransformer As well as having a $xed or tapped secondary that produces a voltage output at a speci$c level, there is another useful application of the auto transformer type of arrangement which can be used to produce a variable AC voltage from a $xed voltage AC supply. This type of Variable Autotransformer is generally used in laboratories and science labs in schools and colleges and is known more commonly as the Variac.

The construction of a variable autotransformer, or variac, is the same as for the $xed type. A single primary winding wrapped around a laminated magnetic core is used as in the auto transformer but instead of being $xed at some predetermined tapping point, the secondary voltage is tapped through a carbon brush.

This carbon brush is rotated or allowed to slide along an exposed section of the primary winding, making contact with it as it moves supplying the required voltage level.

Then a variable autotransformer contains a variable tap in the form of a carbon brush that slides up and down the primary winding which controls the secondary winding length and hence the secondary output voltage is fully variable from the primary supply voltage value to zero volts.

The variable autotransformer is usually designed with a signi$cant number of primary windings to produce a secondary voltage which can be adjusted from a few volts to fractions of a volt per turn. This is achieved because the carbon brush or slider is always in contact with one or more turns of the primary winding. As the primary coil turns are evenly spaced along its length. Then the output voltage becomes proportional to the angular rotation.

Variable Autotransformer

We can see that the variac can adjust the voltage to the load smoothly from zero to the rated supply voltage. If the supply voltage was tapped at some point along the primary winding, then potentially the output secondary voltage could be higher than the actual supply voltage. Variable autotransformer’s can also be used for the dimming of lights and when used in this type of application, they are sometimes called “dimmerstats”.

Variac’s are also very useful in Electrical and Electronics (http://www.amazon.com/gp/aws/cart/add.html? ASIN.1=0750634707&Quantity.1=1&AWSAccessKeyId=AKIAIOB4VMPIMBIMN7NA&AssociateTag=basicelecttut-20) workshops and labs as they can be used to provide a variable AC supply. But caution needs to be taken with suitable fuse protection to ensure that the higher supply voltage is not present at the secondary terminals under fault conditions.

The Autotransformer have many advantages over conventional double wound transformers. They are generally more e#cient for the same VA rating, are smaller in size, and as they require less copper in their construction, their cost is less compared to double wound transformers of the same VA rating. Also, their core and copper losses, I2R are lower due to less resistance and leakage reactance giving a superior voltage regulation than the equivalent two winding transformer.

In the next tutorial about Transformers we will look at another design of transformer which does not have a conventional primary winding wound around its core. This type of transformer is commonly called a Current Transformer (http://www.electronics-tutorials.ws/transformer/current-transformer.html) and is used to supply ammeters and other such electrical power indicators. Ads by Google Circuit Winding Core Motor Winding Winding Wire Matching Transformer For induction heating, 20-350kHz frequency range, 8% loss, 500kVA

« Multiple Winding Transformers (http://www.electronics-tutorials.ws/transformer/multiple-winding-transformers.html) | The Current Transformer (http://www.electronics-tutorials.ws/transformer/current-transformer.html) »

Other Good Tutorials in this Category Multiple Winding Transformers (http://www.electronics-tutorials.ws/transformer/multiple-winding-transformers.html)

The Autotransformer (http://www.electronics-tutorials.ws/transformer/auto-transformer.html)

The Current Transformer (http://www.electronics-tutorials.ws/transformer/current-transformer.html)

Three Phase Transformers (http://www.electronics-tutorials.ws/transformer/three-phase-transformer.html)

Transformer Basics (http://www.electronics-tutorials.ws/transformer/transformer-basics.html)

Transformer Construction (http://www.electronics-tutorials.ws/transformer/transformer-construction.html)

Transformer Loading (http://www.electronics-tutorials.ws/transformer/transformer-loading.html)

Tags: AC Circuits (http://www.electronics-tutorials.ws/tag/ac-circuits) Electromagnetism (http://www.electronics-tutorials.ws/tag/electromagnetism) Power Device (http://www.electronics-tutorials.ws/tag/power-device) Transformer (http://www.electronics-tutorials.ws/tag/transformers)

5 Responses to “The Autotransformer”

Taonga Good but on the disadvantage which says when secondary windings becomes open circulted current stops !owing resulting in full primary voltage being applied to secondary circult,how come for the voltage to be applied to the secondary side while the secondary side has been open circulted meaning that current amd voltage do not pass to the other side? Reply (/transformer/auto-transformer.html?replytocom=2087#respond) September 19th, 2014 (http://www.electronics-tutorials.ws/transformer/auto-transformer.html/comment-page-1#comment-2087) Wayne Storr (http://www.electronics-tutorials.ws) As stated above, autotransformers consist of just one winding so the secondary output is not isolated from the primary input. If the secondary becomes open-circuited with the primary connected to the supply, the voltage on the secondary tapping can increase to the same level as the primary voltage as there is nothing to control it. No current, no voltage drop. Reply (/transformer/auto-transformer.html?replytocom=2088#respond) September 19th, 2014 (http://www.electronics-tutorials.ws/transformer/auto-transformer.html/comment-page-1#comment-2088) Rajat @Taonga. Voltage and current are two di"erent entities. Voltage is simple the di"erence in the power levels of the electrons, i.e, potential di"erence. When these two sides are joined together by a conductor the current(which is the rate of !ow of electrons) starts to !ow. In an open circuit, the voltage is present, but since no conductor is there the current doesn’t !ow. Reply (/transformer/auto-transformer.html?replytocom=2120#respond) September 22nd, 2014 (http://www.electronics-tutorials.ws/transformer/auto-transformer.html/comment-page-1#comment-2120) uwiincht Electrical and electronic education course. Reply (/transformer/auto-transformer.html?replytocom=905#respond) May 28th, 2014 (http://www.electronics-tutorials.ws/transformer/auto-transformer.html/comment-page-1#comment-905) subbi good Reply (/transformer/auto-transformer.html?replytocom=457#respond) April 20th, 2014 (http://www.electronics-tutorials.ws/transformer/auto-transformer.html/comment-page-1#comment-457)

Leave a Reply Your email address will not be published. Required $elds are marked *

Name *

Email *

Website

What's the Sum * one × 3 =

Comment

You may use these HTML (HyperText Markup Language) tags and attributes:

Post Comment (http://www.addthis.com/bookmark.php?v=300&winname=addthis&pub=ra- 4dabe1c24a1ae8c8&source=tbx32-300&lng=en- us&s=google_plusone_share&url=http%3A%2F%2Fwww.electronics- tutorials.ws%2Ftransformer%2Fauto- transformer.html&title=Autotransformer%20and%20Variable%20Auto%20transformer&ate=AT-ra- 4dabe1c24a1ae8c8/-/- /547ecc7a8d4e"bf/2&frommenu=1&uid=547ecc7a8d96551e&ct=1&tt=0&captcha_provider=nucaptcha) (http://www.addthis.com/bookmark.php?v=300&winname=addthis&pub=ra- 4dabe1c24a1ae8c8&source=tbx32-300&lng=en- us&s=stumbleupon&url=http%3A%2F%2Fwww.electronics-tutorials.ws%2Ftransformer%2Fauto- transformer.html&title=Autotransformer%20and%20Variable%20Auto%20transformer&ate=AT-ra- 4dabe1c24a1ae8c8/-/- /547ecc7a8d4e"bf/3&frommenu=1&uid=547ecc7a5dc97a68&ct=1&tt=0&captcha_provider=nucaptcha) 21 ( http://schematics.com/)