Electrical Engineering in Power Plants I (1)

Brandenburg University of Technology Cottbus Department of Decentralised Power Generation and Electrical Engineering in Power Plants

Electrical Engineering in Power Plants I

Prof. Dr.-Ing. Klaus Pfeiffer LG 3 Walther-Pauer-Straße 5 03046 Cottbus Phone: (0355) 69-4035 [email protected] February, 2009

Brandenburg University of Technology Pfeiffer Department of Decentralised Power Generation and Electrical Engineering in Power Plants 1

Contents

1 Network connection of power plants

2 Basic circuits

3 Reliability requirements to the power plant auxiliaries system

4 Single-line diagrams

5 Low-voltage distributions

6 Auxiliary voltage supply

7 Parameter of the main electrical equipment

8 Selective protection in the auxiliaries system

Exercises



1. Network connection of power plants

Overview

English German

A Direct generator bus connection Sammelschienenschaltung B Unit connection Blockschaltung C Group unit connection Gruppenblockschaltung

Figure 1.1: Direct generator bus connection

Figure 1.2: Unit connection

Figure 1.3: Group unit connection



Application

Network connection type Generator power PrG

[MW]

A Direct generator bus connection 50 … 100 B Unit connection > 100

C Group unit connection 100 … 200

Properties

Advantage of the unit connection (B)

Faults doesn’t affect other generators in the power plant

Disadvantage of the direct generator bus connection (A)

1. For faults on – the power plant busbar – the transformer – the line between transformer and grid

switchgear all the generators will be switched off. 2. High short-circuit currents at power plant busbar.

Disadvantage of the group unit connection (C)

1. For faults on – the power plant busbar – the line between power plant busbar and

grid switchgear all the generators will be switched off. 2. High short-circuit currents at power plant busbar.

System voltages at normal operation

Un [kV]

Un [kV]

MIN MAX

110 100 123 220 200 245 380 360 420



Type of constructions

Electrical equipment Type

A Busbar of non-encapsulated type (indoor installation)

Eng

Ger

Generator leads

Generatorausleitung GAL B, C Busbar of encapsulated type

A Busbar of non-encapsulated type (indoor installation)

Eng

Ger

Power plant busbar

Kraftwerks-Sammelschiene C Outdoor installation with

switching devices in the generator branches

A Cable or overhead line Eng

Ger

Line between - transformer and switchgear (A and B) - power plant busbar and grid switchgear (C)

Energieabführungsanlage (EAF)

B Overhead line or Cable inside the territory of the power plant, outside overhead line

C Cable inside the territory of the power plant, outside overhead line

Eng

Ger

Transformer

Transformator (T)

A Vector group Yd5 (to avoid zero sequence system on the generator side)

Eng

Ger

Unit transformer

Blocktransformator (BT)

B, C Vector group Yd5 (to avoid zero sequence system on the generator side)



Circuit breakers

Terms

English German Generator circuit breaker Generatorleistungsschalter (GLS) Generator switch Generatorlastschalter (GLaS) Grid circuit breaker Netzleistungsschalter (NLS)

Direct generator bus connection (A) and group unit connection (C): Generator circuit breakers (one c.b. in every generator branch) are absolutely required for the commissioning and withdrawal from service of each generator separately.

Figure 1.4: Direct generator bus connection

Figure 1.5: Group unit connection

Generator circuit breakers are not urgently required for the unit connection type. There exist some older installations where generator circuit breakers are not existent.

Figure 1.6: Unit connection



2. Basic circuits

The basic circuits of power plants include the network connection and the circuits for the power plant auxiliaries system.

Object of the power station auxiliaries: To supply the technological process in the power plant with electrical energy.

Example: Coal-fired power station

– feed in of fuel, air, water (by coal-mills, induced-draught, forced draught, feed-water pumps)

– disposal of flue gas and ash o flue gas cleaning system (desulphurisation) o ash filter o C02-capturing

Furthermore the power plant auxiliaries system is needed for

– the start-up of power station units (before connecting the generator to the grid)

– the shut-down of power station units (after disconnecting the generator from the grid)

In the following we examine only generators in unit connection (because this is the most favoured type of network connection of power plants) and its corresponding auxiliaries system.

For the start-up or the shut-down process respectively the covering of the load demand of the power plant auxiliaries system is done by the unit auxiliary transformer or the visited network transformer (depends on the equipping with generator c.b.). The consumers (outgoing feeders) are connected to the unit distribution. The distribution for starting-up/shut-down can be coupled with the unit distribution.

Figure 2.1: Overview



There are two possibilities for the equipping with switching devices:

1. Application of generator circuit breakers or generator switches (fig. 2.2.1)

2. Renunciation of generator circuit breaker (fig. 2.2.2)

Figure 2.2.1: Overview about the basic circuit for the auxiliaries system with generator circuit breaker

Figure 2.2.2: Overview about the basic circuit for the auxiliaries system without generator circuit breaker



Breaker position GLS NLS ELS KLS Figure

Starting-up procedure OFF ON ON OFF 2.3 Normal operation after connecting the generator to the grid

ON ON ON OFF 2.4 GLS or GLaS

Technological fault OFF ON ON OFF 2.5 GLS Electrical fault OFF OFF OFF ON 2.6 GLaS Electrical fault ON OFF OFF ON 2.7 ---- Starting-up procedure ---- OFF OFF ON 2.8

---- Normal operation after connecting the generator to the grid

---- ON ON OFF 2.9

---- Technological fault ---- OFF OFF ON 2.10 ---- Electrical fault ---- OFF OFF ON 2.10

Note:

Technological faults (no short-circuit!)

– disturbance in the boiler – disturbance in steam pipe – disturbance in the turbine

Electrical faults – all possible faults in the zone between generator and incoming feeder circuit breaker in the grid switchgear

Generator circuit breakers are very expensive and usually applied for unit capacities greater than 500 MW only. They must have a very high reliability.

Example: Power plant Jänschwalde (one generator: SrG = 588 MVA, UrG = 20 kV)

IrG = 17 kA

Terms

English German Unit auxiliary transformer Blockeigenbedarfstransformator (BET) Visited network transformer Fremdnetztransformer (FNT) Unit distribution Blockverteilung (BV) Distribution for starting-up/shut-down Anfahr-/Abfahrverteilung (AV) Bus coupler circuit breaker Kuppelleistungsschalter (KLS) Incoming feeder circuit breaker Einspeiseleistungsschalter (ELS)



Figure 2.3: Starting-up of a power plant unit with generator circuit breaker or generator switch

Figure 2.4: Normal operation of a power plant unit with generator circuit breaker or generator switch



Figure 2.5: Breaker position after a technological fault (power plant unit with generator circuit breaker of generator switch)

Figure 2.6: Breaker position after an electrical fault (power plant unit with generator circuit breaker)



Figure 2.7: Breaker position after an electrical fault (power plant unit with generator switch)

Figure 2.8: Starting-up of a power plant unit (power plant unit without generator switch)



Figure 2.9: Normal operation of a power plant unit (power plant unit without generator switch)

Figure 2.10: Breaker position after a technological or electrical fault (power plant unit without generator switch)



Power rating of the visited network transformer

Power plant unit with generator circuit breaker/generator switch

Visited network transformer has to supply only these drives and machines which are necessary for the shut-down of the generator unit after electrical faults ⇒ Power rating of the visited network transformer according to the required power for the shut-down process

Power plant unit without generator circuit breaker/generator switch

Power rating of the visited network transformer according to the required power in the auxiliaries system for the starting-up/shut-down process of the generator

Changeover procedures between unit distribution and distribution for starting-up/shut-down

Eng

Ger

Instantaneous changeover

Sofortumschaltung

– after technological faults (supply of the unit distribution via the distribution for starting-up/shut-down

– after connecting the generator to the grid (at the end of starting-up process)

Eng

Ger

Slow changeover

Langsamumschaltung

– after electrical faults

Note: The determination of the making time for slow changeover procedures has to consider different phase angles of the voltages at the unit distribution and at the distribution for starting-up/shut-down. The slow changeover has to be processed out in that time window where the phase angles of the voltages at the unit distribution and at the distribution for starting-up/shut-down are in such a range that unacceptable high currents at re-acceleration of the machines will not occur. Measures for a successful changeover:

– short-circuit power of the visited network must be sufficient to keep the voltage drop at motor re-acceleration after changeover inside the limit range

– switch-off of some machines before the changeover procedure to reduce the total power to be changed over simultaneously



Faults in the transmission grid

Primary protection For faults in the transmission grid the grid circuit breaker performs the system decoupling. This means a sudden off-loading to the generator. Regardless of the availability of the generator circuit breaker or generator switch the generator output will be adjusted to the load demand of the auxiliaries system. The generator is only feeding into the distributions of the auxiliaries system. We speak about a generator in isolated operation. If the generator is incapable for the isolated operation, the unit has to be shutted-down, feeding the necessary drives and machines for the shut-down process over the visited network. Note: The ability of a generator unit for the isolated operation depends on the technological process. In most cases the isolated operation is limited to a certain time period only.

Back-up protection The circuit breakers in the outgoing feeders of the grid switchgear have to be included into the back-up protection, if the grid circuit breaker fails. If no generator circuit breaker is existing and in case of a primary protection failure (grid circuit breaker fails) the generator would be remaining connected to the grid, if no back-up protection is available.

Unit distribution

All the consumers in the auxiliaries system (machines/drives) will be supplied from the unit distribution. The rating of the unit distribution is mostly done for a rated operational voltage of Ue = 10 kV (rated voltage Ur = 12 kV). The majority of the consumers have a rated voltage lower than 1 kV. Therefore the two low-voltage levels 690 V and 400 V were introduced (former 6 kV and 380 kV). The auxiliary voltage is formed from the low-voltage busbars (chapter 6).

Figure 2.11: Basic circuit of the unit distribution



3. Reliability requirements to the power plant auxiliaries system

General task of the auxiliaries system: Provide electrical energy for

– starting-up

– normal operation

– shut-down

of the power plant. Besides these general tasks the auxiliaries system has to meet the following requirements:

– to guarantee the system function to ensure a high availability of the power plant

– to ensure the safety function to avoid accidents with negative consequences (In case of an arbitrary breakdown or any other disturbance the necessary equipment for a safe shut-down of the power plant must be always available. Important for nuclear power plants: permanent availability of the circular pump of the first circulation.)

Note: To guarantee the safety function it is necessary to install two independent protection systems for the electrical circuits.

The process engineering of the power plant influences the design specifications of the auxiliaries systems, considering

– type

– capacity

– significance

of the power plant to ensure system and safety function. The result is the number of systems which have to be realised by the electrical engineering. The following design specifications will be applied:

– n-criterion

– (n+1)-criterion

– (n+2)-criterion

n is the minimum number of systems or subsystems which are required for a 100%-system function, e.g. 1 x 100% or 2 x 50%.

The (n+1)-criterion contains a redundancy (additional system function). In case of any random failure or disturbance the 100%-system function is still available. This criterion is also called individual failure criterion.

The n-criterion and the (n+1)-criterion is applied to conventional power plants.



The (n+2)-criterion considers random failures and additional the non-availability (outage) of equipment due to repair. This criterion is applied for the design of safety systems in nuclear power plants.

The determination of the number of systems is as follows:

Important for the reliability of the auxiliaries system is also the number of independent (electrical) routes to a consumer (equipment). In figure 3.1 it is to be seen that the machines at the unit distributions A and B can be supplied either from the unit auxiliary transformer of from the visited network transformer.

Figure 3.1: Two-way supply (double circuit) (ger.: Zweisträngigkeit)

Variants:

n = 2 x 50% n-criterion

n = 2 x 100% (n+1)-criterion

In conventional power plants both of the criteria will be applied in one and the same power plant.

Let n equal to 1 x 100% n-criterion 1 system

(n+1)-criterion 2 systems


Let n equal to 2 x 50% n-criterion 2 systems



i.e. the following systems are existent:

n-criterion 2 x 50%

(n+1)-criterion 3 x 50%

(n+2)-criterion 4 x 50%



Note:

The term “two-way supply” or “double circuit” respectively does not contain a definition of the availability or power output of the power plant during operation. If the equipment (consumers) is installed in the 2 x 50%-variant and one equipment fails, the power plant can only operate at reduced (half) power output.



4. Single-line diagrams

Examples

Figure 4.1: Conventional coal-fired power plant with one generator unit Rated generator apparent power: SrG = (500 … 900) MVA

The distributions for the coal feeding are located in a distance (approx. 1000 m) from the plant building. For the supply of the distributions for the coal feeding exist sub-distributions. These sub-distributions are connected to the unit distributions.

In the following table the 10-kV-consumers in a real existing 800-MW-coal-fired power plant with two boilers are shown (connection to the unit distributions A – D).

Consumer type number Capacity

Unit distribution A Distribution transformer 1 3,15 MVA (10 / 0,73 kV) Distribution transformer 1 5 / 2,5 / 2,5 MVA (10 / 0,73 / 0,73 kV) Distribution transformer 1 3,15 MVA (10 / 0,73 kV) Distribution transformer 2 2,5 MVA (10 / 0,73 kV) Distribution transformer 2 2,0 MVA (10 / 0,42 kV) Main condensate pump 2 2 / 1 / 1 MVA (freq. converter transf.) Coal mill (for boiler 1) 4 2 x 2 / 1,25 / 1,25 MVA (freq. converter transf.) Feed-water pump 1 13,5 MW Forced draught (for boiler 1) 1 4,1 MW Intermediate cooling circuit pump 1 0,67 MW Sub-distribution 1



Unit distribution B Distribution transformer 1 3,15 MVA (10 / 0,73 kV) Distribution transformer 1 5 / 2,5 / 2,5 MVA (10 / 0,73 / 0,73 kV) Distribution transformer 1 3,15 MVA (10 / 0,73 kV) Distribution transformer 2 2,5 MVA (10 / 0,73 kV) Distribution transformer 2 2,0 MVA (10 / 0,42 kV) Main condensate pump 2 2 / 1 / 1 MVA (freq. converter transf.) Coal mill (for boiler 2) 4 2 x 2 / 1,25 / 1,25 MVA (freq. converter transf.) Feed-water pump 1 13,5 MW Forced draught (for boiler 2) 1 4,1 MW Intermediate cooling circuit pump 1 0,67 MW Boiler circulating pump 1 1,0 MW Sub-distribution 1 Unit distribution C Distribution transformer 3 2,5 MVA (10 / 0,73 kV) Distribution transformer 1 2,0 MVA (10 / 0,42 kV) Distribution transformer 1 6,4 / 3,2 / 3,2 MVA (10 / 0,73 / 0,73 kV) Absorbing pump 4 0,7 MW Induced draught 1 9,5 MW Oxi-Blower 1 0,6 MW Main cooling-water pump 1 3,5 MW Sub-distribution 1 Sub-distribution 1 Unit distribution D Distribution transformer 3 2,5 MVA (10 / 0,73 kV) Distribution transformer 1 2,0 MVA (10 / 0,42 kV) Distribution transformer 1 6,4 / 3,2 / 3,2 MVA (10 / 0,73 / 0,73 kV) Absorbing pump 4 0,7 MW Induced draught 1 9,5 MW Oxi-Blower 1 0,6 MW Main cooling-water pump 1 3,5 MW Sub-distribution 1 Sub-distribution 1

For comparison: examples for the 10-kV-drives in a 500-MW-coal-fired power plant

number

PrM [MW]

Feed-water pump 1 6,0 Cooling-water pump 1 3,5 Condensate pump 2 0,6 Coal mill 6 0,8 Induced draught 1 3,2 Forced draught 2 2,0



Figure 4.2: Conventional coal-fired power plant with two generator units (A and B)

Figure 4.3: Nuclear power plant approx. rated generator apparent power: SrG = 1300 MVA

Security relevant consumers connected to the unit sub-distributions: after-cooler pumps, emergency feeder pumps



Figure 4.4: Combined cycle power plant

AU: automatic changeover facility U changeover facility

Figure 4.5: Biomass power plant

U changeover facility



5. Low-voltage distributions

Principles for the low-voltage distributions:

1. Each low-voltage distribution has its own transformer infeed. Two neighbouring low-voltage distributions can be coupled.

2. The maximum power demand (total of the power of all the consumers connected to one low-voltage distribution does not exceed the half of the transformer capacity of the infeeding transformer.

∑ Sr consumer ≤ 0,5 · SrT

3. In case of a failure of the transformer infeed an automatic changeover (ger.: automatische Umschaltung AU) to the neighbouring distribution will be executed. The transformer of the remaining transformer infeed can supply the coupled distribution without any problems due to principle 2 (German term: Halbschienenbauweise).

4. The two transformers are not connected to the same upstream unit distribution.

These principles can be realised by means of two variants (fig. 5.1 and 5.2).

Figure 5.1: Supply of low-voltage distributions; variant 1: with coupling

Figure 5.2: Supply of low-voltage distributions; variant 2: without coupling



A comparison of variant 1 and variant 2 is to be seen in the following table and in figure 5.3. Criteria for the comparison are

– Selective protection

– Costs for the circuit breakers

– Switching capacity of the circuit breakers

Variant 1 Variant 2

Max. power demand of the low-voltage distribution

∑ Sr consumer / SrT ≤ 0,5 ∑ Sr consumer / SrT ≤ 0,5

Failure of one transformer infeed

Incoming feeder circuit breaker: OFF

Bus coupler circuit breaker: ON

Incoming feeder circuit breaker 1: OFF

Incoming feeder circuit breaker 2: ON

Max. continuous current IUmax of circuit breaker

Incoming feeder circuit breaker: IUmax / IrT = 1

Bus coupler circuit breaker: IUmax / IrT = 0,5

All circuit breakers: IUmax / IrT = 0,5

Number of circuit breaker 3 4

Number of grading steps (for selective protection)

2 1

Interruption of short-circuit currents (fig. 5.3)

Incoming feeder circuit breaker: IkN

Incoming feeder circuit breaker: IkN + IkM

Figure 5.3: Interruption of short-circuit currents Switching status: one transformer supplies two low-voltage distributions



Three-winding transformers will be applied instead of two-winding transformers to save costs (fig. 5.4). A reduction of reliability or availability is not to be expected because transformer failures are very rare. The reason for a changeover in the low-voltage level (coupling of two low-voltage distributions) is in most cases a power outage at the unit distribution.

Figure 5.4: Supply of low-voltage distributions with three-winding transformers



6. Auxiliary voltage supply

Auxiliary supply voltages are

– 220 V DC

– 400 V AC

They are needed for the voltage supply of the following functions:

– actuation

– protection

– control

– signalling

– interlocking

Figure 6.1 presents the circuit for the generation of the auxiliary voltages.

Figure 6.1: Auxiliary voltage supply Figure 6.2: Battery room

The 220-V-DC busbar can be supplied either from the rectifier or from the battery. The battery is feeding the 220-V-DC busbar in case of rectifier failure or an outage of the 400 V AC supply of the upstream switchgear . The duration depends on the capacity of the battery. In the second stage an inverter generates from 220 V DC the output voltage of 400 V AC (busbar ). Due to the battery back-up the 400-V-AC busbar is called safe busbar or busbar of uninteruptable power supply (UPS).



The electronic transfer switch (German: Elektronische Umschalteinheit EUE) is a thyristor switch which connects busbar and directly. The thyristor switches on in case of

– overload of the inverter

– fault in the connection between battery and inverter

– outage of the inverter

In case of maintenance work at the inverter or at the electronic transfer switch the double-throw switch will be switched manually into position 2 (connecting upstream 400-V-AC switchgear with the safe busbar).

The basic scheme for the auxiliary voltage supply according to figure 6.1 is multiple existent in the power plant due to

– redundancy concept

– covering the load demand of the necessary consumers

Other auxiliary voltage levels, e.g. 24 V DC will be generated locally by means of DC/DC-transformers.

Examples:

220 V DC Low-voltage switchgears:

– Actuation of ACB’s (supply voltage of the trip coil)

– Supply of the protection relays ( in some cases 24 V DC are needed for some electronic protection relays)

400 V AC – Process I&C

– Substation automation (M.V. and L.V.)

Tolerance band for the auxiliary voltages: (0,85 … 1,1) U



7. Parameter of the main electrical equipment

7.1 Generator

Parameters

Table 7.1 presents guidance values for

– rated (active) generator power PrG

– rated generator voltage UrG

– rated generator current IrG

The table also contains the initial three-phase short-circuit current for terminal fault, roughly calculated from the subtransient generator reactance dx ′′ .

The generator resistance can be neglected in most cases.

PrG [MW]

UrG [kV]

IrG [kA]

kI′′

[kA] dx ′′

[%]

25 6,3 3 30 10

50 10,5 4 35 11

100 10,5 7 60 12

200 15,75 9 60 15

500 20 17 70 24

800 27 21 85 26

Table 7.1: Guidance values for generator parameters

The rated power output of the generator must be possible at continuous operation at

– rated voltage UrG ±5%

– rated frequency frG ±2%

At f = 47,5 Hz an immediate shutdown of the generator will be executed.



Equivalent circuit

Figure 7.1: Equivalent circuit and corresponding phasor diagram

Xh direct-axis magnetizing reactance (Hauptfeldreaktanz) Xσ stator leakage reactance (Ständerstreureaktanz)

pU synchronous generated voltage (synchronous internal voltage)

(Polradspannung)

E armature voltage (Ankerspannung) U terminal voltage (Klemmenspannung) ϕ phase angle (Phasenwinkel) ϑ angular displacement (Polradwinkel)

Synchronous reactance: σhd XXX +=

(Ger.: synchrone Reaktanz, Ankerreaktanz)

Generator resistance: dXR <<

Figure 7.2: Simplified equivalent circuit and corresponding phasor diagram

IX jUU dp ⋅+= ( )pd

UUX1jI −⋅=

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅⋅=⋅⋅= *

p*

d

* UUX1j- U3IU3S

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⋅−⋅−=

d

*p

d

2

XUU

jXUj3S



( )ϑϑϑ sin jcosUUU pp*p −⋅=−∠=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

⋅+

⋅⋅=

d

2

d

p

d

p

XUcos

XUU

jsinX

UU3S ϑϑ

Active power: ϑsinX

UU3P

d

p⋅⋅=

Reactive power: ⎟⎟⎠

⎞⎜⎜⎝

⎛−

⋅⋅=

d

2

d

p

XUcos

XUU

3Q ϑ

Dependencies: P ~ Pturb ~ ∆Uq ~ Iw ~ ϑ for U, Up = const.

Q ~ If ~ ∆Ul ~ Ib ~ Up for U, ϑ = const.

Pturb turbine power output (Turbinenleistung) If excitation current (Erregerstrom)

The equation for active and reactive power is presented in figure 7.3:

Figure 7.3: Power – angle characteristic of the synchronous generator

From figure 7.3 the following is to be seen:

– The stationary operation is characterized by the balance between turbine power output (mechanical power output) and electrical power output of the generator (operating point A).

– The maximum active power output (pull-out power; Ger.: Kippleistung) d

p

XUU

3P⋅

⋅=

is achieved for ϑ = 90°. This angle is called pullout rotor angle.

– Reactive power output (infeed of inductive reactive power into the grid) is only possible for Up > U (overexcitation). The reactive power output is decreasing with increasing active power output (increase of ϑ).



The capability curve of the generator can be drawn by means of the equation for the apparent power.

Figure 7.4: Capability curve of a synchronous generator

From the capability curve the permissible operating area is to be seen (fig. 7.5).

Legend:

overexcited

underexcited section A section B section C section D section E section F

infeed of inductive reactive power

consumption of inductive reactive power power limitation due to maximum turbine power output power limitation due to temperature rise of the stator power limitation due to limiting temperature rise of the rotor reverse power protection minimum excitation power limit due to stability (maximum angular displacement ϑ)

Figure 7.5: Operating area of a synchronous generator



Parameter for short-circuit calculation

Subtransient reactance rG

2rG2

dd SU10xX ⋅⋅′′=′′ −

Resistances according to VDE 0102

UrG [kV]

SrG [MVA]

RG / dX ′′

> 1 ≥ 100 0,05 > 1 < 100 0,07 ≤ 1 0,15

Impedance dGG XjRZ ′′+=

Correction factors kG according to VDE 0102 must be considered.

( )dGGGK XjRkZ ′′+⋅=

rGd

max

rG

nG sinx1

cUUk

ϕ⋅′′+⋅=

Subtransient three-phase short-circuit current (neglecting resistance)

dk X

EI′′′′

=′′

Subtransient electromotive force (e.m.f.) 3

U1,1E rG⋅=′′

Peak short-circuit current kp I2i ′′⋅⋅= κ

)dX/(R f G ′′=κ peak factor

The peak short-circuit current is given by the manufacturer. Tolerances of ±30% are permissible.



Load unbalance Negative sequence currents I2 occur in the generators at asymmetrical faults in the grid. The negative sequence currents cause contrarotating fields which stress the generator windings thermally.

The highest negative sequence currents occur at phase-to-phase short circuits.

The percentage negative sequence current is called load unbalance:

100IIsrG

2 ⋅= [%]

Permissible values:

continuous load unbalance: s = 5%

short-term load unbalance: 100t

5ss21

⋅⎟⎠⎞

⎜⎝⎛= [%]

t: duration of the load unbalance [s]



7.2 Transformer

7.2.1 Unit transformer

Types of construction

Figure 7.6: Types of construction for unit transformers

Properties:

Variant 1 in comparison with variant 2 and 3

– reduced costs

– reduced losses

– one three-phase reserve transformer needed

Variant 3 in comparison with variant 1 and 2

– maximum space required

– one single-phase reserve transformer needed

– high expenses for the interconnection of the single-phase windings



Figure 7.7: Interconnection of three single phase transformer windings (vector group Yd5)

For the unit connection type always transformers with vector group Yd5 are applied.

Vector group Yd5

Neutral point connection: depends on the desired phase-to-ground short-circuit current in the grid

Variants:

ZME = 0

Solid earthing

ZME = XD Low-impedance earthed neutral

Rated power output:

– power output of the transformer depends on the cooling

⇒ rated power output for continuous operation is given for the designed (rated) cooling

– overload capability is a function of the time and additional cooling

– transformer temperature is monitored continuously

Further important criteria:

– changing of the transformation ratio by on-load tap changer (reactive power consumption or infeed in dependency of the grid voltage)

– transport

– acoustic power level

– insulation level



7.2.2 Unit auxiliary transformer

Determination of percentage impedance

Three-winding transformers will be often applied for unit auxiliary transformers (figure 7.5).

Figure 7.8: Three-winding transformer

The determination of the percentage impedances uk has to consider the following:

– short-circuit currents at busbar 1 and 2 should not exceed defined values

– low mutual influence of the busbars 1 and 2 ⇒ starting operations of machines connected at busbar 1 should cause only small

voltage drops at busbar 2

The equivalent circuit for three-winding transformers is shown in figure 7.6.

Figure 7.9: Equivalent circuit of a three-winding transformer (Z0, Z1, Z2 are not symmetrical impedances)

For

20 k10 k uu −− =

10 k21 k uu −− ⋅= 2

we get

0Z0 =

For this case the sides US 1 and US 2 are independent from each other.



Voltage control

Unit auxiliary transformers will be often stressed by high motor starting currents. This is one of the reasons why unit auxiliary transformers are not equipped with a tap changer. The voltage at US 1 and US 2 can be only controlled by the generator voltage control. The following requirement has to be met:

mGmax Uü

U≤

Um maximum permissible voltage at sides US 1 and US 2

Further properties

Vector group: Yy0 or

Dy0

Neutral point treatment: Low-impedance earthed neutral or

Isolated neutral

7.2.3 Distribution transformer

In case of application of three-winding transformers the above mentioned statements are valid too.

Properties

Three-winding transformer Two-winding transformer

Vector group: Dy5y5 Dy5

Neutral point treatment: Solid earthing ZME = 0

Maximum transformer power: 2 MVA (0,4 kV)

3,15 MVA (0,69 kV)

(due to limited arcing fault withstand capability of the low-voltage switchgears)



7.2.4 Guidance values for transformer parameter

Type Transformation ratio SrT [MVA]

uk [%]

uR [%]

Unit transformer UrG / (Un ±12%) 1) 600 – 1000 12 – 16 0,1 – 0,2

Unit auxiliary transformer UrG / 10,5 2) 20 – 45 8 – 12 0,3 – 0,4

Distribution transformer 10,5 / 0,40 ±2x2,5% 3) 10,5 / 0,69 ±2x2,5% 3)

1 – 2 2 – 3,2

6 6 – 7

0,5 – 0,8 0,4 – 0,7

Table 7.2: Guidance values for transformer parameters 1) on-load tap changer 2) change of the transformation ratio by generator voltage control 3) off-circuit tapping Un nominal voltage of the transmission grid

Permissible tolerances for the percentage impedances

principal tapping: ±10% other tapping: ±14%

Impedances

Two-winding transformer TTT jXRZ +=

rT

2rT2

RT SU10uR ⋅⋅= −

rT

2rT2

kT SU10uZ ⋅⋅= −

2T

2TT RZX −=

According to VDE 0102 correction factors have to be considered:

( )TTTTK jXRkZ +⋅=

kT for maximum short-circuit currents:

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ ⋅+

⋅=

2rT

rTT

maxT

U

SX0,61

c0,95k

Three-winding transformer For short-circuit calculation each side can be considered separately. According to figure 7.6 we get:

10T ZZ += Z or

20T ZZ += Z



7.3 Motor

For the drive of pumps, fans, mills etc. asynchronous motors are applied.

Un [kV]

PrM [kW]

10 > 500

0,69 < 500

0,40 < (200 … 250)

Table 7.2: Guidance values for motor power

Requirements

1. Secure start-up at UN = 0,75 · UrM and fN = 0,95 · fr

2. No interruption of operation at short-term voltage deviations of UN = 0,70 · UrM (no stall/pulling out)

3. Re-connection at UM = 0,4 · UrM and phase opposition between motor voltage and grid voltage

4. Secure continuous operation at voltage deviations to UN = 0,85 · UrM

Parameters

Rated motor current rMrMrM

rMrM ηcosU3

PI⋅⋅⋅

=ϕ

Quasi-steady starting current rMAM IaI ⋅=

a starting current ratio (given by the manufacturer) permissible tolerance: +20%

guidance values: M.V.-motors: a = 4 … 5 L.V.-motors: a = 2,5 … 7,5 a = 2,5 for PrM < 1 kW

Subtransient starting current (peak values of the starting current)

AMMAM I2i ⋅⋅= κ

κM peak factor (dependent on RM / XM) in most cases manufacturer information are not available

κM max = 1,8



Start-up L.V.-motors:

M.V.-motors:

– direct start-up

– direct start-up

– application of frequency converters to reduce the motor starting currents (fig. 7.7)

⇒ the starting currents will be reduced to 2 · IrM

Figure 7.10: Connection of motors using frequency converters

Impedances

rM

2rM

M SU

a1Z ⋅=

rMrM

rMrM ηcos

PS⋅

=ϕ

This impedance is the initial motor impedance (after switch-on, after fault begin)

2

M

M

MM

XR1

ZX

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

According to VDE 0102 the following values in table 7.3 can be applied.

UrM [kV]

PrM / p [MW]

RM / XM XM [Ω]

> 1 >1 0,10 0,995 > 1 < 1 0,15 0,989 < 1 all 0,42 0,922

Table 7.3: Guidance values for motor resistances and reactances

p number of pole pairs



Short-circuit current rMM

rMkM Ia

Z3UI ⋅≈⋅

≈′′

kMMpM I2i ′′⋅⋅= κ

The impedances of the cable connections can be neglected.

The motor short-circuit currents decay very fast. Hence the

– breaking current

– thermal equivalent short-circuit current

are very small compared to the short-circuit currents feeded from the grid.

7.4 Switchgears

Rated switchgear parameters

Rated short-time withstand current Icw(1s)

Rated peak short-circuit current Ipk

The switchgear parameters have to meet the following requirements:

Withstand capability > Stress parameter

Icw(1s) > Ith(1s)

Ipk > ip

Safety factors will be applied to consider possible future changes (increases) in motor power.

The arcing fault stress to the switchgear is not a formal selection criterion. The arcing fault withstand capability of a switchgear has to be proofed in a test field. The test parameters

– prospective kI′′ (three-phase, dead short circuit)

– fault duration tag

are set by the user of the switchgear. The determination of these test parameters has to consider the real maximum short-circuit current and the total fault duration according to the protection concept.



The rated parameters for switchgears are given in table 7.4 and 7.5.

Un [kV]

Icw(1s) [kA]

Ipk [kA]

10 25 63 10 31,5 80 10 40 100 10 50 125

Un [kV]

Icw(1s) [kA]

Ipk [kA]

<1 50 110 <1 80 176 <1 100 220

Table 7.4: Rated parameters of M.V.-switchgears Ipk = 2,5 · Icw(1s)

Table 7.5: Rated parameters of L.V.-switchgears

Ipk = 2,2 · Icw(1s)

Rated M.V.-circuit breaker parameters

Rated short-circuit breaking capacity Iar

Rated short-circuit making capacity Icm


Circuit breakers with

Iar = Icw(1s)

Icm = Ipk

are applied in M.V.-switchgears.

Rated L.V.-circuit breaker parameters

Rated service short-circuit breaking capacity Ics

Rated short-circuit making capacity Icm


The circuit breaker parameters have to meet the following requirements:

Ics > kI′′

Icm > ip

Icw(1s) > Ith(1s)



8. Selective protection in the auxiliaries system

8.1 Types of protection

The protection relays mentioned in the following are definite-time overcurrent-time relays (Ger.: UMZ-Schutz; Unabhängiger Maximalstrom-Zeitschutz).

8.1.1 Primary protection (German: Hauptschutz)

The assigned circuit breaker (closest to the fault) will trip.

Figure 8.1: Principle of the primary protection

I> threshold current t(I>) time delay

8.1.2 Back-up protection (German: Reserveschutz)

In case of

– malfunction of the protective equipment in the outgoing feeder

– failure of the assigned circuit breaker (c.b. A)

the upstream circuit breaker (c.b. E) will trip.

Figure 8.2: Principle of the back-up protection



8.1.3 Breaker failure protection (German: Schalterversagerschutz)

If the circuit breaker in the outgoing feeder (c.b. A) will not trip according to t(I>), then after t(I>) + ∆t a trip command will be send from the same protective equipment to the upstream circuit breaker c.b. E.

Figure 8.3: Principle of the breaker failure protection

8.1.4 Second protective system

For the increase of the reliability of the feeder protection an additional protective system will be installed. The second protective system sends a parallel tripping command to the outgoing feeder circuit breaker (c.b. A).

The second protective system is independent of the primary protection. Each protective system has its own current transformers and its own auxiliary voltage supply.

Figure 8.4: Principle of the protection with a second protective system inclusive breaker failure protection function



8.2 Definitions

tag total break time or total fault duration

time from the beginning until the end of the fault

(Gesamtausschaltzeit oder Kurzschlussdauer)

tag = tan + tv + tSE + tLi = ts + tSA

tan response time of the protective device (Ansprechzeit)

tv (adjustable) delay time (Verzögerungszeit)

tSE mechanical delay of the circuit breaker (time to contact separation)

(Eigenzeit des Leistungsschalters)

tLi arcing time (Lichtbogenzeit)

ts operating time of the protection relay (Kommandozeit)

ts = tan + tv

tSA operating time of the circuit breaker (Schalterausschaltzeit)

tSA = tSE + tLi

The grading time (selective time interval) ∆t is the time difference between the operating times of two neighbouring protective devices (fig. 8.5)

Figure 8.5: Description of grading time

∆tv1 tolerance of delay time tv1 ∆tv2 tolerance of delay time tv2 tR release time (Rückfallzeit)

From figure 8.5 it is to be seen, that

SAR2v1v ttttt +++= ∆∆∆

Selectivity exists, if

tv2 ≥ tv1 + ∆t



8.3 Types of selective protection

8.3.1 Time grading selectivity

Time grading of the delay times of the tripping devices in series

tv4 > tv3 > tv2 > tv1

tv2 ≥ tv1 + ∆t

tv3 ≥ tv2 + ∆t

tv4 ≥ tv3 + ∆t

Figure 8.6: Principle of time grading

If selectivity between c.b. 2 and c.b.3 is not required, then tv2 = tv3

Back-up protection can be ensured, dependent on the threshold currents.

Property: total fault duration is increasing in upstream direction to the infeed.



8.3.2 Zone selectivity (German: Gesteuerte Selektivität GS)

Zone selectivity is a method to reduce the trip times of the protection relay closest to the fault in relation to the times foreseen by time grading selectivity. The word “zone” is used to refer to the part of the installation between two circuit breakers in series (fig. 8.7). The protection relays in series are connected by communication lines.

Function principle: Each protection relay that detects a fault, communicates this to the upstream protection relay using the zone selectivity communication line. This cause in the upstream protection relay a switchover of the time delay from tvGS (fixed value; time depending on the relay type; tvGS ≈ 40 ms) to tv (adjustable). The protection relay closest to the fault does not receive a zone selectivity signal. The corresponding circuit breaker trips after tvGS. Therefore the fault zone is the zone immediately to the load side of the protection relay that detects the fault, but does not receive a signal from a downstream protection relay.

The back-up protection is ensured similarly to the time grading selectivity.

To ensure selectivity – between primary protection and back-up protection – within the back-up protection

the delay times have to meet the following requirements: tv1 = tvGS tv2 ≥ tv1 + ∆t tv3 ≥ tv2 + ∆t

Figure 8.7: Principle of zone selectivity

tvGS time delay of the zone selectivity



Properties of zone selectivity

– the total fault duration (total break time) is the same in each zone

– the total fault duration is considerably lower compared to the total fault duration of the time grading selectivity

The zone selectivity function is an integrated part of the protection relays.

8.3.3 Requirements to the total fault duration

The thermal stresses and the arcing fault stresses define the requirements to the total fault duration. The times (total fault durations), for which the thermal withstand capability and the arcing fault withstand capability of an arbitrary electrical equipment has been verified, must not be exceeded by the protection system.

The verification of arcing fault withstand capability of switchgears is carried out in a test lab with the following test durations tp:

M.V.-switchgears: tp = 1 s

L.V.-switchgears: tp = 0,3 s

These requirements to the total fault duration (tag ≤ tp) can be met usually with the following times:

grading times U > 1 kV ∆t = (200 … 250) ms

U < 1 kV ∆t = (70 … 100) ms

(fix) delay time of zone selectivity U < 1 kV tvGS = (50 … 60) ms

operating times of circuit breaker M.V.-c.b. tSA = (60 … 70) ms

L.V.-c.b. tSA = (30 … 40) ms

It is to be seen, that due to tag - requirements the number of protection relays in a selectivity chain is limited.

The application of zone selectivity yields to the following total fault durations:

primary protection tag ≤ 100 ms (for each fault location)

back-up protection tag ≈ 300 ms (at incoming feeder circuit breaker)



8.4 Zero current protection

Low resistance neutral point earthing usually is applied in the M.V.-level of the auxiliaries system. The goal of the neutral point earthing is the limitation of the earth fault current to

A100 Ik1 ≈ .

The value of the star point resistance has to meet the requirement of Ik1.

The earth fault current (= 3 x zero current) is measured by means of single-pole current transformers (star-point current transformers – Ger.: Sternpunktwandler) and cable-type current transformers (Ger.: Kabelumbauwandler) in the outgoing feeders.

Figure 8.8: Principle of zero current protection

In the outgoing feeders usually exist two settings for the zero current protection:

threshold current I0>> for earth fault currents in the grid corresponding delay time: t(I0>>) < 50 ms

threshold current I0> for inner faults in electrical equipment (motors) corresponding delay time: t(I0>) ≈ some seconds

The time grading for the zero current protection is done as for the time grading selectivity.



8.5 Selective protection of distribution transformers

8.5.1 Fundamental statements about operating currents and short-circuit currents

Principles

To find the settings for the protection relays, the

– maximum operating currents

– minimum short-circuit currents

are required.

The maximum operating currents usually occur at changeover procedures. Starting currents (motors) and inrush currents (transformers) belong to the maximum operating currents too.

Figure 8.9: Explanation of maximum operating currents (changeover currents)

Figure 8.10: Explanation of minimum short-circuit currents

IkLB minimum arcing fault current (Ger.: Lichtbogenkurzschlusstrom) Ik1 minimum single-pole short-circuit current

Note:

Due to vector group Dy5 the single-pole short-circuit will be transformed by )ü3(1 ⋅ to the

H.V.-side (see lecture note EDS 1).



Busbar impedances usually can be neglected for the calculation of minimum short-circuit currents, if the busbar length doesn’t exceed 5 m.

The minimum arcing fault currents will be calculated by means of the minimum three-phase short-circuit currents:

mink3 BkLB IkI ⋅=

The minimum short-circuit current for a fault at the H.V.-side of the transformer is the minimum phase-to-phase short circuit.

Figure 8.11: Explanation of maximum short-circuit currents

IkM motor short-circuit currents (Ger.: Motorkurzschlussstrom) IkN short-circuit currents feeded from the transformer (Ger.: Netzkurzschlussstrom)



8.5.2 Protection of three-winding transformers

For the selective protection of three-winding transformers a differential protection relay is applied in addition to definite-time overcurrent protection relays.

Figure 8.12: Principle of the selective protection of three-winding transformers

(without zero current protection)

∆I differential protection relay UMZ definite-time overcurrent protection

Note: UMZ 4 and UMZ 5 protection relays as well as the corresponding current transformers are an integrated part of the L.V.-circuit breaker

The detection of the short-circuit currents at different fault locations is shown in table 8.1.

Fault location Primary protection Back-up protection

K1 UMZ 4 UMZ 2

K2 UMZ 5 UMZ 3

K3 ∆I UMZ 1

K4 ∆I UMZ 1

K5 ∆I UMZ 1

Table 8.1: Effect of the protection relays in fig. 8.12



Requirements to the current threshold values of the protection relays

UMZ 1 Protection function: I> Back-up protection for faults at L.V.-side

( ) H.V.k

H.V.rTn I

s1IIs ⋅≤>≤⋅

H.V.rTI rated current of the transformer (referred to the H.V.-side) H.V.kI minimum short-circuit current for a fault at L.V.-side, referred to H.V.-side

sn safety factor for non-starting the relay s safety factor for starting the relay

A possible starting of the protection relay at changeover currents (maximum operating currents) has to be considered at the selection of the delay time t(I>).

t(I>) > t (Ichangeover)

Protection function: I>> (t(I>>) ≈ 0)

( )>>≤⋅ IIsH.V.

Un

H.V.UI changeover current for a changeover at L.V.-side (referred to H.V.-side)

The simultaneous changeover of the two L.V-sides must be considered (see figure 8.9)

( )>>≤⋅ IIsH.V.

max kn to ensure selectivity between UMZ2/4 or UMZ3/5 and UMZ 1

H.V.maxk I maximum short-circuit current for a fault at L.V.-side (referred to H.V.-side)

.kminI

s1(I ⋅<>>)

minkI minimum short-circuit current for a fault at H.V.-side (fault location K5)

UMZ 2 Protection function: I>

( ) 1 L.V.kLB

1 L.V.Un I

s1IIs ⋅≤>≤⋅

1L.V. UI changeover current at L.V.-side 1

1L.V. kLBI arcing fault current for fault at L.V.-side 1

Protection function: I>>

I>> - function is used for breaker failure protection. The I>> - threshold is the same as for I> - function, but the time delay is greater.

t(I>>) > t(I>)




( ) 2 L.V.kLB

2 L.V.Un I

s1IIs ⋅≤>≤⋅


I>>-function is used for breaker failure protection. The I>> threshold is the same as for I>-function, but the time delay is greater

t(I>>) > t(I>)

8.5.3 Protection of two-winding transformers

In comparison with three-winding transformer only two definite-time overcurrent relays (UMZ) will be needed at H.V.-side (fig. 8.13). The definite-time overcurrent relays are responsible for the primary protection as well as for the back-up protection (table 8.2).

Figure 8.13: Principle of the selective protection of two-winding transformers

(without zero current protection)

Fault location Primary protection Back-up protection

K1 UMZ 3 UMZ 1/2

K2 UMZ 1 UMZ 2

K3 UMZ 1 UMZ 2

Table 8.2: Effect of the protection relays in fig. 8.13



Requirements to the current threshold values of the protection relays


Back-up protection (for faults at L.V.-side)

( ) H.V.k

H.V.Un I

s1IIs ⋅≤>≤⋅

H.V.UI changeover current (referred to the H.V.-side) H.V.kI minimum short-circuit current for a fault at L.V.-side

(fault location K1 and K2), referred to H.V.-side

s0,30 )t(I ≈>


Primary protection

( ) kminH.V.kmaxn I

s1IIs ⋅≤>>≤⋅


minkI minimum short-circuit current for a fault at H.V.-side (fault location K3)

s0,03 )t(I ≈>>

Breaker failure protection: +∆t ≈ 0,30 s

UMZ 2 UMZ 2 is a second protective system and gets the same settings as UMZ 1. The breaker failure protection is being omitted at UMZ 2.



Exercises

1. Infeed of active and reactive power in the transmission grid

Given is the following single-line diagram:

The generator generates (according to its capability curve)

PG = 920 MW

QG = 400MVar

Find: PN QN UN

Solution:

The calculation is referred to one phase of the three-phase system (Index 1p):

MW 306,673MW920 P 1p G ==

MVar133,33 3MVar400 Q 1p G ==

( ) ( ) MVA334,4 MVar133,33 MW 306,67S 221p G =+=

kV 15,593kV 27U G =Y (Index Y: phase-to-ground voltage)

0,917MVar334,4

MW 306,67SP

cos1p G

1p G ===ϕ

0,399MVar334,4 MW133,33

SQ

sin1p G

1p G ===ϕ

kA 21,45kV 15,59

MVA334,4 US

IY G

1p GG ===

kA 19,670,917kA 21,45cosII Gw G =⋅=⋅= ϕ

kA 80,399kA 21,45sinII Gb G 56,=⋅=⋅= ϕ



( ) 0,0012 ΩMVA1000

kV 27100,17SU

10uR2

2

rT

2

rT2RrT =⋅⋅=⋅⋅= −−

( ) 0,142 ΩMVA1000

kV 271019,6SU

10uZ2

2

rT

2

rT2krT =⋅⋅=⋅⋅= −−

( ) ( ) T222

T2TT Z0,142 Ω0,0012 Ω0,142 ΩRZX ==−=−=

GTT IZU∆ ⋅=

( ) ( ) ( )b Gw GTTql I jIX jRU jU −⋅+=+ (inductive generator current; see phasor diagram)

b GTw GTl IXIRU ⋅+⋅=

b GTw GTq IRIXU ⋅−⋅=

kV1,243 kA8,56 0,142 ΩkA 19,670,0012 ΩUl =⋅+⋅=

kV 2kA8,56 0,0012 ΩkA 19,670,142 ΩUq 783,=⋅−⋅=

TY GY N U∆UU −=′

( ) ( )qlY GwY NbY Nw U jUUU jU +−=′+′ 0U Y Gb = (see phasor diagram above)

lY GlY GwY Nw UUUUU −=−=′

qY Nb UU −=′

kV 14,35kV1,243 -kV 15,59U Y Nw ==′

kV2,78 U Y Nb −=′



*NY N1p N IUS ⋅=

*GY N

*GY N1p N IUI

ü1UüS ⋅′=⋅⋅′⋅= ( )b Gw GG I jII −= (inductive generator current)

( ) ( ) ( )b Gw GY NbY Nw1p N1p N I jIU jUQ jP +⋅′+′=+

GbY NbGwY Nw1p N IUIUP ⋅′−⋅′=

GbY NwGwY Nb1p N IUIUQ ⋅′+⋅′=

( ) MW306,06 kA8,56 kV2,78 kA 19,67kV 14,35P 1p N =⋅−−⋅=

MVar68,16 kA8,56 kV 14,35kA 19,67kV2,78 Q 1p N =⋅+⋅−=

MW918,2 P3P 1p NN =⋅=

MVar 204,53Q 1p NN =⋅= Q

( ) ( )( ) kV 216,5kV2,78 jkV 14,3527400U jUüU Y NbY NwY N =−+⋅=′+′⋅=

kV 375U3U Y NN =⋅=

Result:

– a reactive power of QN = 204,5 MVar is available for the infeed in the grid

– the voltage at the secondary side (gride side) of the unit transformer is UN = 375 kV

⇒ this operating state doesn’t meet the requirement of the voltage tolerance band (minimum level: 380 kV)

⇒ the transformation ratio of the unit transformer has to be adjusted (increased)

Selection of 27420ü =

( )( ) kV 227,5kV2,78 jkV 14,3527420U Y N =−+⋅=

kV394 U3U Y NN =⋅=

Conclusion:

– the necessity of (on-load) tap changing for unit transformers is clearly to be seen

– the control band of the tap changing depends on the reactive power infeed



Power balance:

Reactive power demand of the unit transformer

1p N1p G1p T QQQ −=

MVar 65,17MVar68,16 MVar133,33 Q 1p T =−=

Check: ( ) MVar65,33 kA 21,450,142 ΩIXQ 22GT1p T =⋅=⋅=

Unit transformer losses

1p N1p G1p T PPP −=

MW 0,61MW306,06 MW 306,67P 1p T =−=

Check: ( ) MW 0,55kA 21,450,0012 ΩIRP 22GT1p T =⋅=⋅=

(slight difference due to manual calculation)



2. Voltage drop at motor start-up

Given is the following single-line diagram:

The 13,5-MW-motor at unit distribution B is starting.

Find:

Voltage at unit distribution B during the motor start-up (rough calculation).

For the rough calculation the complete single-line diagram can be simplified.

Assumptions:

– short-circuit power at the primary side (27 kV) of the unit auxiliary transformer is infinite

– base load of the equivalent motors (EM) will be neglected ⇒ hence the three-winding transformer can be transformed in a

two-winding transformer

– cable impedances will be neglected (ZK << ZT; ZK << ZM)



Simplified equivalent circuit:

( ) Ω0,27MVA 45kV 10,51011Z

22

T =⋅⋅= −

( ) Ω0,01MVA 45kV 10,5100,4R

22

T =⋅⋅= −

TT ZX ≈

rM

2rM

M SU

a1Z ⋅=

rMrM

rMrM ηcos

PS⋅

=ϕ

( ) 1,58 ΩMW 13,5

0,970,88kV10 41Z

2

M =⋅⋅

⋅=

0,24 Ω0,151,58 ΩcosZR ANMM =⋅=⋅= ϕ

1,56 Ω0,991,58 ΩsinZX ANMM =⋅=⋅= ϕ

⇒ the resistances can be neglected and the equivalent circuit can be simplified

Derivation of formula for ∆UB

MT

QTM XX

UI

+

′=

TTMQB XIUU ⋅−′=



Q

TTM

Q

B

UXI1

UU

′⋅

−=′

MT

T

MTMTTM

TTM

Q

B

XXX1

XIXIXI1

UU

+−=

⋅+⋅⋅

−=′

Q

B

Q

BQB U

U1U

UUU

′−=

′−′

=∆

MT

TB XX

XU+

=∆

100XX

XUMT

TB ⋅

+=∆ [%]

Calculation:

( )kA 3,31

1,56 Ω Ω0,273kV 10,5ITM =+⋅

=

( ) kV 5,17 Ω0,27kA 3,313kV 10,5UB =⋅−=

kV 8,953kV 5,17U ∆ B =⋅=

%14,8 kV 10,5kV 8,951UB =−=∆

Test: %14,8 100%1,56 Ω Ω0,27 Ω0,27100%

XXXU

MT

TB =⋅

+=⋅

+=∆



3. Selective protection of a two-winding transformer

Given is the following single-line diagram. The single-line diagram includes the transformer parameter and the minimum short circuit currents.

Find

– Maximum short-circuit current at L.V.-distribution Assumption: impedance of the grid and cable impedances can be neglected; transformer resistance can be neglected)

– Maximum operation current (changeover current)

– Settings for the UMZ 1 and UMZ 2 protection relays (according to chapter 8.5.3) Assumption: Safety factor s for starting the relay s ≥ 1,3 (Ger.: Ansprechsicherheitsfaktor) Safety factor sn for non-starting the relay sn ≥ 1,3 (Ger.: Nichtansprechsicherheitsf.)



Solution

Maximum short-circuit current ⇒ 3-phase short-circuit current

rT

2rT

kTTk SUukZ ⋅⋅=

0,9630,060,61

1,050,95x0,61

c0,95kT

maxT =

⋅+⋅=

⋅+⋅=

( ) mΩ11,98 MVA 2,5kV0,72 0,060,963Z

2

Tk =⋅⋅=

kA 34,9mΩ11,98 3kV 0,691,05

Z3UcITk

nmaxkNmax =

⋅⋅

=⋅⋅

=

Changeover current

The changeover current consists of two parts:

– steady-state operation current of L.V.-distribution A

– starting current of the motors connected to L.V.-distribution B after the changeover procedure

rTrTU Ia0,5I0,5I ⋅⋅+⋅=

rTU I3I ⋅=

kA6,0 A2004 3kV0,72 3

MVA 2,53U3

S3IrT

rTU =⋅=

⋅⋅=

⋅⋅=

Settings for the protection relays

UMZ 1 Protection function: I> (Back-up protection for faults at L.V.-side)

( ) H.V.k

H.V.Un I

s1IIs ⋅≤>≤⋅

H.V.UI changeover current (referred to the H.V.-side) H.V.kI minimum short-circuit current for a fault at L.V.-side (referred to H.V.-side)

( )13,91,3kA 15,1)I

13,9kA6,0 1,3

⋅≤>≤⋅

( ) kA0,84 )IkA0,56 ≤>≤

The determination of the setting values tends to the lower value. This increases the chance to detect inner faults of the electrical equipment with fault currents lower than the minimum short circuit current.



Determination of I>:

I> = 0,6 kA

Current transformer: 200/1 ⇒ setting value: 3 · ICT

Protection function: I>> (Primary protection for faults at H.V.-side)

( ) kminH.V.kmaxn I

s1IIs ⋅≤>>≤⋅


minkI minimum short-circuit current for a fault at H.V.-side

( )1,3

kA 13,5)I13,9

kA 34,91,3 ≤>>≤⋅

( ) kA10,4 )IkA3,3 ≤>>≤

Determination of I>>:

I>> = 4,5 kA

Current transformer: 200/1 ⇒ setting value: 22,5 · ICT

Determination of the delay times:

Conditions:

– total fault duration must be lower than the test duration at arcing fault tests ⇒ usually this yields to t(I>) ≈ 240 ms (tSA ≈ 60 ms for M.V.-circuit breaker)

– time grading between I> and I>> - function

⇒ ( ) ( )SAp tt)t(I)t(I∆t −≤>≤>>+

Empirical values:

t(I>>) ≥ 30 ms begin of the time grading

∆t ≥ 200 ms grading time

⇒ selection of t(I>) = 300 ms

+∆t ≥ 300 ms time delay of breaker failure protection

UMZ 2 is the second protective device (redundancy) and will get the same settings as UMZ 1.



Time grading schedule

Documents

Electrical Engineering in Power Plants I (1)