ECE 6378 Power System Analysis Projects and HW

7/25/2019 ECE 6378 Power System Analysis Projects and HW

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HW/Project # 2

For the RPSs three-phase symmetrical steady-state operation(positive sequence):

1. For each equivalent power system component calculateparameters and represent the corresponding equivalent circuit.

Parameters to be defined in per unit at the power system level.

The equivalent power system component means the equivalent ofall power system components of the same type (as generators, or

transformers, or lines circuits, or loads) that are parallelconnected to the same bus (as generators or loads are) or betweenthe same two buses (as transformers or lines circuits are).

2. At a proper scale draw the RPSs corresponding impedancediagram.

The parameters of the equivalent power system componentsand the impedance diagram are defined within the following

assumptions:

- All main power components installed within RPS are inoperation.

- On each power plant the generating units are parallel connectedto a common bus, and they are equally loaded with the active andreactive powers.

- On each power substation the transformer units are parallelconnected to common buses.

- Transformers are operating at the rated turn-ratio.

- For loads are considered the initial given data, which correspondto the annual peak load.


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- At the 345 /kV/ level the base quantities are selected as Vb =345 /kV/ and Sb = 100 /MVA/. They also are considered asthe base quantities at the power system level.

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It is added that:

- The equivalent circuit and the corresponding parameters for theequivalent generating unit are included in the impedance diagram.At this moment the generators parameters are defined as for asteady-state normal operation.

- The transformers parameters are defined assuming that for 1/pu/ turn-ratio magnitude, the transformer is modelled with agamma equivalent circuit, with the shunt branches represented tothe higher voltage side.

- The line parameters are defined assuming that the line ismodelled as a symmetrical pi equivalent circuit.

- The load parameters are defined assuming that the load is

modeled as a constant shunt impedance/admittance. For defining the load parameters are counted the given data,which are the rated voltage, maximum active power, and theaverage power factor. The load equivalent circuit and the corresponding parameters areincluded on the impedance diagram.

- For those voltage levels that are different of 345 /kV/, the basevoltage can be selected as:

a) The actual rated voltage at that level that is different of345 /kV/. Then the equivalent circuit and parameters for thecorresponding equivalent transformer are modelled consideringthe actual turn-ratio magnitude, which in per unit can bedifferent of 1.0, or

b) In agreement with the actual (rated) turn-ratio magnitude ofthe transformer connected between the 345 /kV/ level and the


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other voltage level. Then the equivalent circuit and parametersfor the corresponding equivalent transformer is the normal one(gamma, as required).

- Regarding the above subject, for sure a such case appears inconnection to the power substation PS45 and the correspondingpower plant G5. Here, the transformers rated turn ratiomagnitude, defined from 345 /kV/ side, is 362.25/24 /kV/.a) One version is to select the base voltage at the lower voltage

side as the rated voltage at that level, that is 24 /kV/. Then,with the base voltages as 345 /kV/ and 24 /kV/, respectively, the

transformers PS45 turn ratio magnitude in per unit results as(362.25/345)/(24/24) = 1.05 /pu/. In this case for the transformerequivalent circuit it must be counted that the turn ratiomagnitude is different of 1 /pu/. At the generator level the basevoltage will equal the generator rated voltage.

b) Another version is to select the base voltage at the generatorlevel such that the transformers turn ratio magnitude equals 1

/pu/. That is, the base voltage at the generator level to be24/1.05 = 22.857. /kV/. Then the transformers turn ratiomagnitude in per unit results as (362.25/3450/(24/22.857 ..) = 1

/pu/. Then the transformers equivalent circuit will be agamma equivalent circuit, as for the turn ratio magnitude in perunit equal to 1 /pu/. But the generators parameters in perunit must be calculated counting the new base voltage at thatlevel, that now is different from the generators rated voltage.

- It is reminded that for the positive sequence (that correspondsto the three-phase symmetrical steady-state operation), and

according to the USA standards, for the Y/Y and transformers windings connection, the line-to-neutral voltage at thehigher voltage side is in phase with the line-to-neutral voltage at

the lower voltage side. But for the Y/ or /Y windingsconnection, the line-to-neutral voltage to the higher voltage sideleads with 30 degrees the line-to-neutral voltage to the lowervoltage side. Such, just if the transformers turn-ratio magnitudein per unit is 1.0, and there is not a phase-shifter installed, a


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corresponding phase shift must be included in the transformer

equivalent circuit for a Y/ or /Y windings connection.

- For each individual and/or equivalent power system componentyou must show the corresponding final equivalent circuit and thecomputation steps used to obtain the given parameters. For eachpower system component the corresponding equivalent circuit mustbe shown along with its parameters computation steps. Do notshow that equivalent circuit to another location. On that finalequivalent circuit it must be specified the location and thenumber/symbol of the corresponding terminal bus/buses of thatequivalent power component. The branch parameters of the final

equivalent circuit to be defined as and Y (here theimpedance or the admittance is shown with bolded letter, as Z

or Y, respectively, and their magnitude is shown with regularletters, as Z and Y; you have to take care to use thecorrect notation), each of them shown in the rectangular andangle notation. Parameters value shown on the final equivalentcircuit to be the final rounded value.

- For each quantity involved show the units used.

- It is reminded that in the computation steps all decimals mustbe used, and only the final result is rounded to four decimals for

the component terms of the algebraic notation and for themagnitude, and two decimals for the corresponding angle. Theangle is to be defined in degrees.

- The impedance diagram to be drawn large enough, such to beclear and readable!!!!!! It will be frequently used on the next steps.

- On the impedance diagram, for each branch to be specified the

corresponding parameter value (both Z and Y ) in therectangular and angle notation, with the algebraic componentterms and the magnitude defined in per unit at the power systemlevel, and the angle in degrees.

- On the impedance diagram the parameters value to be shownwith four decimal digits for magnitude and two decimal digits for


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angle.

- Regarding the other details, review the set with the initial data.

- Since the obtained parameters are to be used for the next stepsof the project, it is recommended to store the calculatedparameters in a data file.

- SINCE DATA AND THE IMPEDANCE DIAGRAMOBTAINED AT THIS STEP ARE TO BE USED FORTHE NEXT STEP(S), SAVE A COPY OF THEM.

ALONG THE SEMESTER, THIS RULE APPLIES FORANY OTHER PROJECT STEP THAT FOLLOWS !

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Some general comments about the specified configuration anddata:

It must be known that, just if some of the specifiedinformation and assumptions provided here could be satisfied inthe real life, they are not always in agreement with the actualpractice. The only reason that they have been accepted here is

to simplify the project solution.

Such, it is mentioned that, normally:

- Each synchronous generator is directly connected to its step-uptransformer. Such, on the lower voltage side the transformers arenot connected to the same bus.

- On the higher voltage side, the step-up transformers are or arenot connected to the same bus. Or, maybe only some of them

are connected to a common bus.

- The (step-up or step-down) transformers are not necessarilyoperating at the rated turn-ratio.

- For the parallel transmission lines circuits, just if they followthe same right-of way, it does not mean that they always have


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both terminals connected to common buses.

- Modelling the load with constant parameters is not the only wayand it is not always the correct one of the loads modelling.

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Regarding how the impedance/admittance exact and roundedvalue calculation has to be handled:

- Before the procedure is described, some comments about thegiven data are added.

As it is required here, by starting with data provided for the

Reference Power System (RPS), the branch parameters are to bedefined in per unit, based on their /rpu/ value (generators), or thecomponent rated data (loads), or their value in actual units(transformers and lines).

Such, to define the branch parameters in per unit at the powersystem level, the first step is to define the base voltage to be usedfor each power system component, and then to calculate the valuefor the corresponding base admittance/impedance.

After that it is defined the parameters value for each individualbranch.

You have to know that when the parameters (impedance,admittance) of a branch are calculated, it must be taken allmeasures such to have the product (Z x Y) as close as possible to1.0000000 ./0.0000000. .

- For that purpose, and based on what data are given, first youcalculate the branch impedances value (when R and Xare given), or the branch admittances value (when G andB are given) in per unit at the power system level. For thatpurpose use all decimals that your calculator can carry. At thismoment on the angle notation your branchs Z or Y lookslike Z/a or Y/b, that is x.xxxxxxxxxxxxxx../x.xxxxxxxxxxx

.., and on the algebraic notation as r.rrrrrr. + j i.iiiiiiii

Also, it is added that when you calculate one parameter in perunit at the power system level, it is recommended to use only oneequation, and the parameter to be defined at once for the


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equivalent power system component.

- On the next step round to four decimals the algebraiccomponents of the exact value obtained for Z or for Y.They will look like R.RRRR + j I.IIII. This will be the final,rounded value for the algebraic components of Z or of Y.

- With these rounded algebraic components calculate thecorresponding magnitude and angle for Z or for Y, that willresult as M.MMMMMM ./A.AAAAA.

- Round the corresponding magnitude to four decimals andangle to two decimals, that will look like as M.MMMM/A.AA.

- With this magnitude and angle for Z or for Y, calculatethe angle notation for the corresponding Y or Z , that willlook like m.mmmmm/a.aaaaaa..

- By using this value for Y or Z, calculate thecorresponding real and imaginary components of the algebraicnotation, and round them to four decimals, that will look likeR.RRRR + j I.IIII. This will be the final rounded algebraic notation for Y or for Z.

- With these algebraic components calculate the magnitude andangle for the corresponding Y or Z, and round themagnitude to four decimals and the angle to two decimals.

- At this moment it will be available the branch impedance andadmittance in the rectangular and the polar (angle) notation.

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Also, it must be understood that:

- Four decimal digits means: x.xxxx, not x.xxxxE-275.

- A generator, a transformer, a lines circuit, or a load is not abranch of the power system. In an electric circuit a branch is a section between two buses


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(defined by the corresponding parameter, as impedance oradmittance). For example, for a pi equivalent circuit of a line,there is a series branch and two shunt branches.


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O. Crisan, ECE 6378 Power System Analysis

1

HW/ PROJECT # 3

For the RPS Network:

1. By a direct inspection of the impedance diagram build the networks

bus admittance matrix [Y].

2.

By the inversion of the bus admittance matrix define the networks bus

impedance matrix [Z].

3.

Check that the product [Y] x [Z] = [I].

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Important:

To the HW/Project # 3s solution it must be attached the final version of the

HW/Project # 2!

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It is added:

- The steps required for solving the present HW/Project # 3 are applied

only to the RPSs power network, that is, the generators and loads (the

terminal power system components) are not included.

- The Task # 1 shown above is solved by hand, and Tasks # 2 and # 3 are

solved by using computers.

- For Tasks # 2 and # 3 attach the source program and the initial,

intermediate and the final data printouts.


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2

- For Task # 3, if the product does not come as [I], it means that there

is/there are some a mistakes on the component matrices. You have to

review and correct them and then try the product again.

-

For defining the corresponding driving point and transfer bus admittancesfor buses where transformers are involved, look to the transformer bus

equations shown on Chapter 3, Section 3.7, page 2 or page 2 (which

one do you have to use, depends on which equivalent circuit you

considered for that transformer).

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- Before you start solving HW/Project # 3, you must correct all mistakes

recorded (if it is the case) on the HW/Project # 2!!!!

- But, when the assignment for the HW/Project # 3 is received, you do not

have yet the graded HW/Project # 2, and such you do not know yet if

there are or not corrections to be made. Just if it is so, it is

recommended for you to start working on solving the above Task # 1,

and prepare the computer programs for the subroutines utilization for

solving Tasks # 2 and # 3.

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Other supplementary explanations:

- In the case that it must be made corrections to the HW/Project # 2, do not

forget that along to the corrected sections you also have to turn in the

initial graded version of the HW/Project # 2.

- The final value of a branch parameter defined on HW/Project # 2 (that is

that value with the magnitude rounded to four decimals and the angle in

degree rounded to two decimals, and the corresponding real and imaginarycomponents rounded to four decimals) is considered as the correct value for

defining other parameters, as required in the present HW/Project.

- To define the bus admittances (Task # 1 of the present HW/Project), are

used the component branch admittances defined on HW # 2 in a rectangular


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3

form and with those components calculate admittance magnitude and

angle!!!!!

- Be very careful and include the correct value for parameters that you have

on the impedance diagram. It is a common mistake that, just if the

parameters value on the impedance diagram is the correct one, when it is

inserted as the input data it is taken a wrong value.

And clearly show the analytical and the numerical equation used to obtain

the value for each bus admittance term!!!!

- The elements of the bus admittance/impedance matrix to be shown as a

rectangular and as an angle notation. For the angle notation the magnitude

to be shown as rounded to four decimals and the angle to be shown in

degrees rounded to two decimals.

- In the intermediate steps all decimals are carried up, and only the final

result is rounded to four decimals for magnitudes and two decimals for

angles.

- The shunt branches connected to the same bus can be replaced with an

equivalent branch of a corresponding Z or Y. Show how you have

obtained these parameters.

- The final form of the bus admittance matrix (Task # 1), of the bus

impedance matrix (Task # 2), and of their product (Task # 3) to be shown

in a matriceal format.

- The bus admittance/impedance data to be stored in data files. They are to

be used with the next Projects.

- Start the solution as soon as possible.


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HW/PROJECT # 5

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For the RPSs steady-state operation, analyze the effect of only thespeed-governors upon the frequency magnitude.

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It is specified that:

- The RPSs initial steady-state corresponds to the final power flowsolution obtained with your HW/PROJECT # 4. That is, the generated, consumed and the lost active and reactivepowers, including the reactive power supplied by the supplementarysources, are the same as those obtained with HW/PROJECT # 4.

- It is known that the initial steady-state power system frequency is therated one, that is fRPS.0= 60 /Hz/.

- The generating units rated active power is defined with the ratedapparent power and the rated power factor, by using the initialspecified set of data.

Also, this time the maximum active power is considered as that onegiven with the initial set of data (Pmax)!! The minimum active power is defined as on HW/Project # 4.

- The speed regulation for each generating unit installed on the powerplant G1 is RG1% = 5 /%/, and for each generating unit installedon the power plant G5 is RG5% = 6 /%/. It is reminded that if the loading of a unit is within the active powerlimits, then the value of the speed regulation remains the same for anyloading of that unit!!!

- The active (electrical and/or mechanical) power lost in the generating


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units and prime-movers is neglected, that is, it is assumed that themechanical power supplied by a prime-mover equals the electricalpower supplied by the corresponding electrical generator.

- All installed generating units are considered in operation.

- For solution, to each power plant it will be considered an equivalentgenerating unit.

- Here it is considered that the active power-speed-frequency control ofthe RPS is achieved only by the speed governors control.

- In what follows by active load or loading it is understood thetotal active power that must be supplied by the generating unit. That is

the total active power consumed plus total active power lost on the RPSnetwork.

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The following are to be calculated and presented on the ProjectSolution:

1. For the equivalent generating unit of each power plant, calculate

the available rated, maximum and minimum active powers in /MW/. Also, calculate the available rated, maximum and minimumgenerating active powers per total power system (it is like for anequivalent generating unit at the RPS level) in /MW/.

For each power plant-equivalent generating unit calculate the ratio ofits rated active power to the generating rated active power at the RPSlevel.

2. With the initial steady-state active power loading of thegenerating units (according to the power flow results obtained on yourHW/Project # 4), calculate the mechanical power setting and thefrequency setting, in /MW/ and /Hz/, respectively, for the speed-governor of each power plant-equivalent generating unit, and for theequivalent generating unit at the power system level.Also, considering that each power plants equivalent generating unit isoperating within the given active power constraints, calculate the valueof the speed regulation at the power system level.


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3. If, starting with the initial steady-state, the total load active powerof the RPS, including the active power lost (it means the total activepower generated), has an initial increment of ( - 10) /%/, and there isno change on the speed-governors setting, calculate the value of the newsteady-state frequency in /Hz/. This time assume that the speed (frequency) regulation of the load

active power, including the active power lost, is Rl% =

(infinite). That is, after the load (including losses) increment/decrement isapplied, just if the frequency changes, the new load remains unchanged. Also, calculate the new steady-state active power in /MW/, deliveredby each power plant-equivalent generating unit, and by the equivalentunit at the RPS level.

Check if the new steady-state generated active power equals the newsteady-state load (plus losses) active power.

4. With the same loads characteristics as specified at item # 3 (loadspeed regulation equal to infinity), repeat the calculation steps shown atposition # 3, for when the total active power of the RPS, including theactive power lost, has an initial increment of (+ 20) /%/.

5. Repeat the calculation steps shown at position # 3 (for when fromthe initial steady-state there is an initial increment of (- 10 %) on the

load total active power, including the active power lost), for when theload speed regulation is Rl% = 100 /%/, and for when there is nochange on the speed-governor setting.

6. For the case specified at position # 5, calculate the needed changein the speed-governors mechanical power setting, such that thefrequency to be recovered to the initial, rated frequency (this is the jobthat the frequency and/or Economic Dispatch will handle).

7. On one graph to be represented the speed-governorcharacteristics for the following cases:

- Case shown at the above item # 2, that corresponds to the initialsteady-state operation.

- Case shown at the above item # 6, that corresponds to when thespeed-governor setting was changed accordingly, such to recover


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the frequency change.

The speed-governor characteristics to be drawn at a correspondingscale, and on each characteristic to be shown the data (the rotorspeed/frequency and the prime-mover mechanical/active power value),corresponding to cases shown above at items # 2 (the initial loading), # 3(the load increment of 10% and its speed-regulation as infinity), # 4(the load increment of + 20% and its speed-regulation as infinity), # 5(the load increment of 10% and its speed regulation as 100%), and # 6(the load increment -10%, its speed-regulation 100%, and the speed-governor setting readjusted).

Also, on the speed-governor characteristics to be shown the minimumand the maximum loading for the equivalent generating unit of each

power plant.

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It is added:

- On solving use all decimal digits and results to be shown with four

decimal digits.

-To the present Project attach a table with the final results (buses

number, V, , and calculated P and Q values) obtained withHW/PROJECT # 4.

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Documents

ECE 6378 Power System Analysis Projects and HW