control of voltage profiles - universidad de...

Control of voltage profiles

Prof. Alberto Berizzi Dipartimento di Energia

Email: [email protected]

© Alberto Berizzi - Dipartimento di Energia

Voltage variations

• Slow voltage variations, due, e.g., to voltage drop caused by load changes (±10%), rms values

• Sudden and short changes: Voltage sags (or dips) (up to 90%, lasting some ms to some s), caused by commutations, breaker operations, clearing of short-circuits

• Repeated and sustained voltage drops, e.g., due to starting of motors, arc furnaces, steel factories. They cause flicker (with a limit of 0.3%-3% as a function of the disturbance frequency)


Goals of the voltage control

• To keep voltages at load busses close to their rated value, to ensure a

proper operation of any connected device

• To keep voltages at HV and EHV busses at values fit for the transfer of

the real power through the transmission grid

• … following any event during normal operation, like motor starting, load

changes, generation changes, non-critical faults


The problem of voltage control

• In radial systems, the voltage depends on:

Voltage profile in the higher voltage network, if an OLTC is not present in the substation

Loads connected, also depending on the point of connection of each load along the feeder

Possible presence of reactive power compensation devices (usually at the substation)

Possible presence of Dispersed Generation and their capability to control voltages

Typically, in the absence of DG, the critical cases are relevant to busses at the starting or at the receiving end of the feeder

• In meshed systems, the voltage depends on how the common resource, i.e. the network, is exploited. In other words, voltage control depends on the behaviour of all loads and all generators


Model for studying the voltage control

G

G

Us

r

Thévenin

Es0 Es

IsZs


Assumptions

• We assume the system as linear, that is small perturbations

• In transmission systems (not including cables), assuming lines not very long, series impedances are lower than shunt impedances. For example: 220 kV overhead line, 150 km long, with

• l=1.3 mH/km e

• c=8.6 mF/km

XL=60W, XC=5000W

• When evaluating Zs, generators must be modeled as solid connections to the ground. This determines the overall inductive feature of Zs

• In distribution systems, and particularly if cables are present, the assumptions are not so suitable: the ratio R/X is a great deal higher than for transmission systems


How to use the linear model?

• According to the linear assumption, it is possible to use the following

approximated formula for the voltage drop

ssssss

sssssss

QXPREV

IXIRV

sincos3

For transmission systems, as usually X»R, it is acceptable to neglect the

first term

• This assumption provides the direct link between voltage magnitudes and

reactive power flows

V can also be regarded as the voltage change when moving from no-

load conditions to loaded conditions


Power System Notation 8

Generators are

shown as circles

Transmission lines are

shown as a single line

Arrows are

used to

show loads

Power system components are usually shown as

“one-line diagrams.”

17.6 MW

28.8 Mvar

16 MW

16 Mvar

16 MW

16 Mvar

17.6 MW

28.8 Mvar

59.7 kV 40 kV


Reactive Power Compensation 9

16.8 MW

6.4 Mvar16 MW

16 Mvar

16 MW

0 Mvar

44.94 kV 40 kV

16.8 MW

6.4 Mvar

0 MW

16 Mvar

Key idea of reactive compensation is to supply reactive power locally.

In the previous example this can be done by adding a 16 Mvar

capacitor at the load

Reactive compensation decreases the line current from 564 A to 400

A, associated to the real power component only.

Also the generator has a benefit and provides better voltage control


Reactive Compensation, cont’d

• Example on reactive compensation with and without Rline

• Reactive compensation has many advantages:

Decreased line losses (i.e., money, less fuel to be burned,

pollution, emissions, etc.), which are equal to I2 R

Lower current allows utility to

• use smaller cross sections for wires, or alternatively,

• supply more load over the same wires, or even

• delay investments for repowering the network

Reduced voltage drop on the line, i.e., better voltage quality

Better operating conditions for large generators

• Reactive compensation is used extensively by utilities

• Capacitors can be used to “correct” a load power factor to an

arbitrary value

../../Politecnico Attività Istituzionale/Corsi Istituzionali/Electric Power Systems/Esempi/Esempi GloverSarmaOverbye/Chapter2/Reactive compensation.PWB


Power Factor Correction Example

1

1desired

new cap

cap

Assume we have 100 kVA load with pf=0.8 lagging,

and would like to correct the pf to 0.95 lagging

80 60 kVA cos 0.8 36.9

pf = 0.95 requires

cos 0.95 18.2

S 80 (60 Q )

60 - Qtan

80

S j

j

cap

cap

18.2 60 Q 26.3 kvar

Q 33.7 kvar


Distribution System Capacitors


Conceptual framework for voltage

sensitivities

• Based on

• We can get

• We observe that, in transmission systems, voltages depend a great deal on reactive power injections

2

in [ ]

% 100 with in [kV]

in [Mvar]

s s s

s

s

s s sn

sn

s

V X Q

XX

V Q VV

Q

W

s s s s s sV E R P X Q



sensitivities, cont’d

• Considering the short-circuit power, Asc s:

• p.u. voltage changes are equal to the changes of Q in p.u. with respect to the short-circuit power

• Q being equal, V is as larger as Asc is lower, that is as weaker the grid: the quality of supply is proportional to the short-circuit power at the connection point

2 23

% 100 %

sn sn

scs

s s

s

s s

scs

E VA

X X

QV Q

A




ss

scs

s scs ns scsscs

s ns ns

QV

A

Q A 3V I3I

V V V

To increase by 1 kV voltage Vs, it

is necessary to inject into bus s a

reactive power in [Mvar] equal to

1.73 Isc s (Isc s in [kA])

Example:

Grid 132 kV, Isc=25 kA

Qs=1.73 Ascs=43 Mvar

Qs=43 Mvar means 1 kV

increase at the same bus

This explains why very significant

loads have to be connected at

high voltages


• In general, in a power system, there are busses where the voltage is controlled, PV busses, and busses where the injections are controlled, PQ busses

• But what about the voltage control of a bus where there are not controllable reactive/voltage resources?




Power Flow Simulation - Before

• One way to determine the impact of perturbation, for example a

generator change, is to compare a before/after PF (perturb and

observe approach)

• For example, below is a three bus case with an overload: how to

mitigate it?

Z for all lines = j0.1

One Two

200 MW

100 MVR200.0 MW

71.0 MVR

Three 1.000 pu

0 MW

64 MVR

131.9 MW

68.1 MW 68.1 MW

124%


Power Flow Simulation - After

Z for all lines = j0.1Limit for all lines = 150 MVA

One Two

200 MW

100 MVR105.0 MW

64.3 MVR

Three1.000 pu

95 MW

64 MVR

101.6 MW

3.4 MW 98.4 MW

92%

100%

Increasing generation at bus 3 by 95 MW (and hence decreasing

it at bus 1 by a corresponding amount), results in a 31.3 drop in

the MW flow on the line from bus 1 to 2.


One Two

200 MW

100 MVR200.0 MW

71.0 MVR

Three 1.000 pu

0 MW

64 MVR

131.9 MW

68.1 MW 68.1 MW

124%


Analytic calculation of sensitivities

• Calculating sensitivities by repeated PF solutions is tedious and

would require many PF solutions (one PF for each control variable)

• An alternative approach is to analytically calculate these values (it is

a linearization!)

The power flow from bus i to bus j is

sin( )

So We just need to get

i j i jij i j

ij ij

i j ijij

ij Gk

VVP

x x

Px P


Analytic Sensitivities

• Exploiting the FD PF equations:

• Therefore, to obtain the changes in [] following a change in [P],

linearization of the conditions of the power system can be exploited

• Starting from a convergent PF operating point, and setting

• Solving the linear system, we obtain the linearized [] , a column,

and eventually the changes in real power flows

] ] ]1

'B P

]

0

1

0

P


Analytic Sensitivities cont’d

• As a general rule, there is a need to control some

state variables [x], i.e.,

• angles,

• voltage magnitudes

• or their combination (currents, power flows, etc.)

by displacing some

control variables [u], e.g.,

• injected powers,

• loads,

• phase-shifters,

• tap-changers,

• generator voltage magnitudes, etc.


Analytic Sensitivities cont’d

• Consider a convergent PF and linearize its behaviour

• [S] is the sensitivity matrix: the element sij gives the changes of state

variable i with respect to control variable j

• In case injected power at each bus are considered as control

variables, [Ju] is the unit matrix

] ]

] ]

] ] ] ]1

( , ) 0

( , ) ( , )( , )

0x u

x u

f x u

f x u f x uf x u x u

x u

J x J u

x J J u S u

]TQP


Analytic Sensitivities Generators (and loads)

as control variables: real power

]

( , ) 0

( , , )( , , ) ( , , )( , , )

0( , , ) ( , , )( , , ) ( , , )

( , , ) ( , , )

( , , ) ( ,

f x u

P P V uP V u P V uP P V u V uV

uQ V u Q V uQ Q V u Q Q V u

Vu

P V u P V u

V V

Q V u Q V

V

]

]

1

1

( ) 1(2 ) ( )

( , , )

, ) ( , , )

If

( , , ) ( , , )

( , , ) ( , , ) 0 u gu g u g

P P V u

uu

u Q Q V u

u

u P

P V u P V u

V IVP

Q V u Q V u

V


Analytic Sensitivities Generators as control

variables: voltage rescheduling

• [Ju] in this case has nonzero elements only in rows relevant to busses

connected to generators busses

]

]

1 ( , , )( , , ) ( , , )

( , , ) ( , , ) ( , , )

If

Assume the g generators are numbered first

( , , ) ( , , )

gg

P P V uP V u P V u

V uVu

Q V u Q V u Q Q V u

Vu

u V

P V u P V u

V V

1

1

(2 )

( , , )

( , , ) ( , , ) ( , , )

g

gg

gu g g

P V u

VV

Q V u Q V u Q V u

V V


Analytic Sensitivities Generators as control

variables: contingency analysis

• [Ju] has non zero entries at two terminal busses of branch ij

• Linearity is hardly true, for contingency

• It could also be studied by changing the P and Q injections at busses i

and j

]

]

1 ( , , )( , , ) ( , , )

( , , ) ( , , ) ( , , )

If

Assume the g generators are numbered first

( , , ) ( , , )

ij

P P V uP V u P V u

V uVu

Q V u Q V u Q Q V u

Vu

u y

P V u P V u

V V

1

(2 ) 1

( , , )

( , , ) ( , , ) ( , , )

ij

ij

iju g

P V u

yy

Q V u Q V u Q V u

V y


Three Bus Sensitivity Example

• Consider the previous three bus example, with zline=j0.1

] ]

1

2

3

20 10 1020 10

10 20 10 '10 20

10 10 20

Consider an unit increase of the injected power at bus 3;

the corresponding increase of voltage angles is:

20 10 0

10 20 1

Y j B

3 1

3 2

2 1

0.0333

0.0667

and the increase of power flows is:

0.0667 0P 0.667

0.1

0.0667 0.0333P 0.333

0.1

0.0333 0P 0.333

0.1


One Two

200 MW

100 MVR200.0 MW

71.0 MVR

Three 1.000 pu

0 MW

64 MVR

131.9 MW

68.1 MW 68.1 MW

124%

Observe the

dependence on

the slack!


Three Bus Sensitivity Example cont’d

• Therefore, if we need to reduce the power flow from bus 1 to bus 2 by

32 MW, it is necessary to increase PG3 by

• Doing that, the following changes also take place:

G3

32P 97MW

0.333


One Two

200 MW

100 MVR200.0 MW

71.0 MVR

Three 1.000 pu

0 MW

64 MVR

131.9 MW

68.1 MW 68.1 MW

124%

3 1

3 2

P 0.667 97 65MW

P 32MW

Z for all lines = j0.1Limit for all lines = 150 MVA

One Two

200 MW

100 MVR105.0 MW

64.3 MVR

Three1.000 pu

95 MW

64 MVR

101.6 MW

3.4 MW 98.4 MW

92%

100%


How to use voltage sensitivities?

• We would like to control voltage at a generic bus s. We can use as control variables, some voltages at busses j and some reactive power injections at busses k

• Once sensitivities are computed, it is possible to determine:

How other voltages change

How to control many voltages at the same time solving a feasibility problem with s equations in u unknown

As usually s<u, we can exploit the remaining degrees of freedom to optimize the system

k

k

k

sj

j j

ss Q

Q

EE

E

EE


EMF connected in series

• As usually R«X, the impedance between p’ and p” is inductive

• Thus, I is lagging p/2 with respect to E

• The network is considered linear and the superposition of effects is exploited to evaluate what is changing when I and – Ichange at p” and p’ respectively

• Changes will be dependent on the equivalent impedance

G

1

p’

n

p”

E

I


Phasor diagrams

(E in phase to Ep)

• If E is in phase to Ep, which is the voltage

at p before the efm is inserted, we obtain:

Injection of Q”= Ep”I into p”

Withdrawal of Q’= Ep’I from p’

• Thus modifying all reactive power flows and

voltage magnitudes in the network

E

Ep

I

I


Voltage changes

(E in phase to Ep)

'

'

"

"'

p

i

p

iii

Q

EQ

Q

EQEE

For what Ep is concerned, different strategies are possible

• To control and keep constant voltage Ep‘

• To control and keep constant voltage Ep’’

• Not to control either of the two

EEp’= Ep

Ep”

E

Ep”= Ep

Ep’

EEp’

Ep”


Network voltage changes if

E in quadrature with Ep (E<<Ep)

• Analogously, in this case it is as if we

injected a real power

• The voltage magnitude at bus p is kept

more or less constant

• The shift is proportional to E

• As usually E» E, we get

E

Ep” Ep’

p

p

p

p

E

E

E

E

2sin2

1


Goals for series voltage connection

• In-phase voltages:

Voltage control

Loss mitigation

Reactive power flow control

• Quadrature voltages:

Real power flow control, which is particularly important in mashed networks and in a market environment


Tools and devices to control voltages

• Shunt devices

Synchronous machines at power plants

On Load Tap Changers

Reactive compensation

• Synchronous compensators (very cool today!)

• Mechanically switched capacitors and reactors

• Shunt SVC (Static var Compensator)

– TCR (Thyristor-Controlled Reactor) or TSR (Thyristor

Switched Reactor)

– TSC (Thyristor Switched Capacitor)

• STATCOM (Static Synchronous Compensator – or Condenser)

• Emf in series:

Series FACTS devices (Universal Power FC, …)

Booster transformers


Static Var Compensators

Nodo di Alta TensioneParametri

misurati

del sistema elettrico

AVR

Filtri TCR

TSC

Nodo di Alta TensioneParametri

misurati

del sistema elettrico

AVR

Filtri TCR

TSC


STATCOM

id

Va

Vd

STATCOM

id

Va

Vd

STATCOM


Properties of SVC, STATCOM

• STATCOM is a voltage source converter (VSC)-based device where a

voltage source is provided by a capacitor behind a thyristor switch.

• If Va is controlled in such a way to be larger than the bus voltage,

reactive power is injected into the grid

• STATCOM has a very little real power capability, unless storage is

provided

• STATCOM is faster than SVCs thanks to the IGBT-based voltage

source and usually works better than SVCs at low voltages, because

SVCs show a quadratic decrease of reactive power injected with bus

voltage, while STATCOM’s Q injected decreases linearly

• On the other side, STATCOMs exhibit larger losses and are more

expensive

37



cont’d

• Series devices:

Thyristor-controlled series reactor

(TCSR): a series reactor bank is

shunted by a thyristor-controlled

reactor

Thyristor-switched series reactor

(TSSR): a series reactor bank is

shunted by a thyristor-switched reactor

Thyristor-controlled series capacitor

(TCSC): a series capacitor bank is

shunted by a thyristor-controlled

reactor

Thyristor-switched series capacitor

(TSSC): a series capacitor bank is

shunted by a thyristor-switched reactor



cont’d

• Static Synchronous Series Compensator

(SSSC)

• Universal Power Flow Controller (UPFC)

39


Most common ways to control reactive

power

• Shunt compensation (mechanical switched capacitors) at load busses

• Synchronous generators at power plants

• Synchronous compensators: synchronous machines that

withdraw real power from the system to ensure rotation,

control excitation, thus providing full reactive power control

provide inertia and short-circuit capability (useful for RES

integration)


Voltage control in power plants

• Assumptions: We neglect RL

Voltage VG is controlled

• When QU changes, the voltage change at load bus depends on Xe,i.e., on the electrical distance of the load bus from the bus where voltage is controlled

• In absence of control, Vi is constant, and not VG

Xe includes also Xd, with Xd>> (XT+Xl)

The result is that voltage variations are larger

G

XL

U

VUVG

XT

Vi, Xd

UeU

UeGU

ULTUG

QXV

QXVV

QXXVV

)(

VT


Control of voltage at load busses

• In order to keep constant the voltage at a load bus, when the load changes, it is usually necessary to:

Keep the generator voltage (generally high)

Increase the excitation voltage as the reactive load increases

• At low load or capacitive load,

The voltage at the load bus is higher than the voltage at the generator terminals

It is necessary then to keep the voltage low, underexciting the machine


Goals of the excitation control

• At steady-state:

To keep voltage constant

• At the generator terminals

• At the HV busbar of the power plant

• At the end of a line with/without real time measurements

To control the reactive power sharing among generators

To control the fulfillment of the capability chart

To contribute to power system voltage security and efficiency

The normal load of the excitation system is 2÷3.5kW/MVA

• During transients:

To guarantee the proper operation large perturbations

• Short-circuits

• Avoid overvoltages in case of load disconnection

To improve the stability of transmission

To ensure a suitable damping of electromechanical in case of small angle perturbations

To participate to the hierarchical voltage control


Fault close to a generator

Fault clearing in 0.25 s

44



The final part of the transient is determined by

electromechanical oscillations

45Fault close to a generator



46Fault close to a generator


What is the small-disturbance angle

stability? UCTE, November 200647


USA Blackout, 199648


Types of small-angle perturbation stability

• The power system behaviour can be linearized

• Aperiodic behaviour: the problem is lack of synchronizing torque

• Periodic behaviour (electromechanical oscillations): lack of damping

torque:

Increasing oscillations (positive damping)

Not well damped oscillations (negative, but too small damping)

49


Block diagram representation

• Representation of

• pGS is the synchronising power, in phase to the angle change

• pGD is the damping power; it is in phase to the angular speed

change, and in quadrature to the change in the angle

50

2

2

m ps

m ps

dDp S

dt

d dH Dp S

f dtdt

p


Block diagram for the IV order model 51


Comments on the block diagram

• The block diagram is the result of a linearisation and therefore it

depends on the initial point (in particular, Sp)

• pGS and pGD compensate pm, and if they are positive (e.g., Sp>0)

they increase stability

They are shifted by 90° to each other

• Considering contribution 3, it could be negative, depending on the

combination of blocks 4 and 5: it could result in reduced or even

negative damping:

in the presence of long lines and fast AVRs, the contribution from

3 can be equal and opposite to pGD, because the AVR induces a

voltage in the damping windings which is opposite to the natural

voltage induced by the speed

• The latter problem can be solved by the design of suitable PSS

controllers

52


Comments on the block diagram cont’d

• In case of constant e’q, that is constant excitation flux, contribution 3 is

neglected

• In case of constant ef, which is the case of generator reaching its

reactive power limit, it can be demonstrated that, for typical

frequencies of 1 Hz,

The equivalent synchronising coefficient decreases from the value

Sp to a decreased value

The equivalent damping coefficient increases

53


The role of the AVR

• The presence of the AVR

increases the power in phase to the angle change, synchronising

power, thus decreasing the risk of aperiodic instability

BUT it reduces the natural damping of the generator, depending

on the gain: this problem can be overcome by the PSS

• Therefore the role of the AVR is

For large perturbations, to guarantee a sufficient synchronising

power

For small perturbations, to guarantee a sufficient damping,

especially for low frequency oscillations

54


Practical cases 55

• Transferring large power from a weak to a powerful system can

induce oscillations

• In that case, reduction of the transmitted power must be achieved

• PSS can solve the problem


Negative ceiling voltage

• It is useful to be able to invert the excitation voltage to force to zero the current as soon as possible

t

iecc

No negative ceiling

Negative ceiling


Loss of load

• During a load disconnection, when the breaker opens, we can measure a step increase of the voltage at the generator terminals

• Then the voltage further increases, due to:

Armature reaction

Speed increase (emf=2f)

Zeroing of the voltage drop in the synchronous reactance

• With static exciters, the voltage is brought back to rated value in about 0.5s

t

V

Vi VMAX

Vn


Excitation control system

Generator GridExciterAmplifier

Transducer

Transient feedback

Compound and droop

Limitation and protection

Power SystemStabilizer (PSS)

Regulator

Excitation system

Voltage control system

vrif ev+

- -

+

+


Limitation and protection system

• They are nonlinear systems that must be included into the long term stability and voltage stability analysis; they can be neglected only during small perturbation stability analysis

• They ensure that capability limits are fulfilled, particular: Rotor current in underexcitation conditions

• Stability

• End-core heating limit: it is a consequence of the end turn leakage flux existing in the end region of a generator, perpendicular to the stator lamination. Eddy currents will then flow in the lamination and will be the cause of localized heating in the end region

Maximum overexcitation limit

Maximum stator limit

Maximum voltage

• Checking temporary temperature limits (short-term capability)

• Limiters can either Generate a signal which is superimposed to other signals

By pass the signal coming from the regulator


60Capability chart


Underexcitation limits (UEL)

• Usually the limiter has either P and Q or V and I as inputs

• The voltage control is by-passed until normal operating conditions are re-gained

• It must be coordinated to the protection system

For example, in case of loss of field, the limiter has not any effect and the protection must trip, otherwise:

Asynchronous operation

Abnormal Q withdrawal (Q=2-4 An)

Low voltage

High currents (2-3 pu)

High steady-state currents in the dampersQ

P

Protection relais

UEL limitermodel

Underexcitation limit


Overexcitation limits

• When excitation voltage and current increase, circuits can result heated For example, these can be the value to be limited:

iecc=112% tMAX=120 s

iecc=125% tMAX=60 s

iecc=208% tMAX=10 s

• Due to thermal time constants, it is not always necessary to immediately trip the generator: we can try to bring back the current

• If this does not succeed, the generator is tripped

• Usually, 105% of the current is allowed permanently

• Limiters are usually very fast

• Current 1.325 pu is tolerated for 15s, and it will be brought back to 1.05 in the next 15s

iecc

t[s]

Thermal behaviour

Time-dependentlimit

Fixed limit

15 30 t[s]

iecc IFLM1=1.6 ieccn

IFLM2=1.05 ieccn

1.325


63

Power System Stabilizer (PSS)

• PSSs produce a stabilizing signal to increase damping of oscillations

• Its inputs are:

Speed changes

Accelerating power

Frequency and voltage deviations

• At steady state this signal is zero


Load compensation

• When the load increases, i.e., the output Q increases, the voltage set point VREG is updated as a function of parameter a

a>0 compound

a<0 droop (like for frequency control)

• Compound and droop can be obtained by suitable connections of CT and VT

Q

VREG

VREG 0

VREG=V+aQ


How to get a compounded characteristic

• The regulator receives VMeas: at no load, VMeas~V21

• At load Q (red), VMeas decreases when Q increases: the regulator increases voltage, because VMeas<V21REF

• The in-phase component associated to P is not negligible

• R should be the image of the series reactance of components that are to be compensated

• If we liked to compensate P, it would be sufficient to change R with a reactance, or insert the CT on phase 2

G3

1

2

3

V21

I3

kII3

kVV21

VMeas=kVV21-kII3

12

3

kII3

kVV21

VMeas

R


66

Compound

• Things go as if the measure of voltage occurred inside the transformer

• The compensated part is in red

• For stability reasons it is not advisable to compensate 100%

GridE

xg xT


Droop: dynamic issues

• Let us assume we have zero droop and meters not perfectly equal

G1 measures a lower voltage and tries to increase it, increasing Qg1

G2 measures an increasing voltage and tries to decrease it, decreasing Qg2

• This behaviour is unstable and stops when a limit is reached (over or underexcitation)

• Moreover, even though this was neglected, a zero droop would result in an undetermined sharing of the total reactive power generated by the generators

E1

xg1

xg2

E2

Q


Droop: sharing of total reactive power

• If the grid requires a total Qtot, the two generators will share it depending on their own droop with

• Qtot =Q1+Q2

• If one of the two has zero droop, it will take completely Qtot

• In this case, a measurement error results in a not perfect sharing, but nothing else.

• A manual adjustment can be carried out

Q

VREG

Q

VREG

Qtot

Veq

Veq

Q1 Q2


How to sum up V-Q characteristics

V

Q Q

V

Qmax 2QmaxV

Q Q

V

Qmax2QmaxQmax

Q1 Qmax+ Q1


Droop and compound

• From the PoC, the characteristic must have nonzero droop: Assume a pure reactive load: QLOAD=V2/X

• If there was compound (a>0), a QLOAD increase would correspond to a VREG increase, which in turn would result in a further QLOADincrease, thus leading to instability

• With a negative characteristic, viceversa, an increase of QLOADleads to a V decrease, thus resulting in a new equilibrium point

• A system with droop is like to regulate a fictitious voltage inside the transformer: in this way, a reactance is seen between the PoC and the point where the voltage is kept regulated

xg1

xg2


Natural droop and compound

• A zero droop regulator can be used with some schemes. For example, with this scheme, the transformer introduces a natural droop, with respect to the PoC

The reactance can be seen as an elastic, able to compensate any mismatch

The two generators produce

Qi=(Vregi-V)2/XTi;

for XT→0 the unstable case results

• Therefore, the regulator with compound can be used provided that the transformer compensation is less than 100%

• Usually, it is about 50%-80% xT.

• The complete compensation can be set up manually

• The secondary voltage control is a particular type of compound

xg1 xT1

xg2 xT2


Compensation of the load

• Both Compound and droop have the goal to change the reactive

power produced by means of a signal proportional to the reactive

load, in order to keep constant the voltage not at the generator

terminals, but

Inside the transformer windings (compound), to compensate the

voltage drop on the transformer reactance or along a long line

Inside the generator (droop) when two or more transformers are

directly connected at their terminals, that is, inserting a fictitious

reactance among different generators to make it possible to

share the reactive production


Exciters

• Rotating exciters:

in DC

• The exciter is a DC machine, on the generator and turbine shaft

in AC

• The exciter is an AC machine, whose voltage is rectified. The power comes from the turbine-generator shaft.

• Static exciter

The excitation current comes from a rectifier supplied by the generator terminals or from the auxiliary service busbars. Only in the latter case, if there is an alternative source, black start capability can be provided


DC exciter

G3

G_G_

Controller

Instead of the small DC machine, a small synchronous machine + rectifier can be installed


DC exciter cont’d

• In use since 1920, installed until ’60s

• The field is supplied by a dc main machine, while field is supplied by an auxiliary dc machine, with gain 10000-100000 and T=0.02s-0.25s

• The main dc generator is usually self-excited and if the auxiliary generator is out of order, a rheostat can be used

• Pros:

Security of supply

Very well-know and consolidated approach

Possibility to quick force excitation to zero by inverting Vexc

• Cons:

Very long shaft and decrease of reliability

Not able to face very fast transients

The main dc exciter has to be largely sized to deal with transients: 0.3%-1% Sn of the main generator

Auxiliary dc generator is rated 1%-3% Pn of the main dc exciter


AC exciter with diode rectifier

G3

DC controller

G3

reference

AC controller

• Speed of response increased• Modularity• Security of supply• Brushless

Inversion of vexc not possible


AC exciter with controlled rectifier

G3

Controller of the bridge supply

G3

AC controller

DC controller Ref.

• Speed of response• Modularity• Security of supply• No brushes• vecc can be inverted


Brushless exciter

G3

G3

Controllore AC

G3

N

S

• Initially in high power applications (660 MW), then on small machines and explosive environment

• No brushes at all• limited possibility of control


Static exciter

G3

AC Controller

DC Controller Ref.

ET

• Fast response• Modularity (lower cost)• Brishless• vexc can be inverted• no maintenance


Properties of the static exciter

• It is the most advanced and used solution, today

• The field is supplied by a rectifier

• The source for the power is:

Voltage only, by means of the excitation transformer connected to:

• Generator terminals

• Auxiliary service busbar, which usually have a reserve supply

• For starting only, sometimes busbar specially supplied for the starting (TAG) unless GCB is available

• Ceiling voltage depends on the voltage available, which is minimum in case of close short-circuit

Voltage/current supply, useful in case of short-circuit close to the generator

• They can provide negative excitation voltage

• They are very fast


Off-nominal ratio transformers

• When the turn ratio is different from the rated ratio or from the ratio

between reference voltages, the transformer model is modified

• LTC transformers have tap ratios that can be changed to regulate bus

voltages and keep them within acceptable limits

• Taps are typically located on the HV side

• The typical range of variation is 10% (from 0.9 to 1.1 pu), for

example in 32 discrete steps (0.0625% per step)


Load Tap-Changers (OLTC)

• LTC can be

Off-load, moved at no load: breakers must be opwn before moving

taps

On-load (OLTC), typically controlled automatically to keep the

voltage at a reference value. As tap-changing is a mechanical

process, LTC transformers usually have a 30 second dead band

to avoid repeated changes. Their regulator is an integrator, usually

with time constant around 10 s.

• Unbalanced tap positions of parallel transformers can cause

"circulating vars"

82


pu transformation for off nominal tap ratio

• pu transformation is very useful when considering transformers with

voltage ratio equal to the ratio of reference base voltages

• When the ration can change, it is necessary to model it

• Let us define the following ratios:

83

1

2

1

2

the actual turn ratio

N= the ratio between base voltages b

b

Nn

N

V [V ]

V [V ]


pu transformation: ideal transformer

off-nominal tap ratio

the above pu equations are the same as the ideal transformer

equations in absolute values, but here a is dependent on the actual

ratio modified by the ratio between reference voltages

a=1 iff the actual ratio is the same as the ratio of reference voltages

a does not depend only on the ratio among nominal voltages (plate

values) of the transformer

a can be interpreted as the pu transformation ratio

84

22 2 22

2 21 1 2

22 22 2 2

2

1 1 2

2 2

22

1

with

b''

'b b b

' b''

b b b

'

'

VV nV nvvV nV NV V V

II II I i

i Nnn nI I I

v avn

aiNi

a


Complete pu model of the off-nominal ratio

transformer (a complex, general case)

• For the sake of generality, let us consider

a P model

a complex pu ratio : the case of nonzero imaginary part corresponds

to the phase-shifter transformer or, f.i., DY transformer

85

2

2 2 2 2 222 2 2 2

2 22 2 2 2

2

1

'

' ' ' '' '

' '

va

s v i i vvv i v i a

v is v i i

i a

a


Derivation of an equivalent circuit

(a complex, general case)86

2

2

2

2

0 01

1 1 1

22 20 02

1and

1

2 2

2 2

'

cc'cc''

' 'cc' cc' cc' cc'

'' ''cc' cc' cc' cc'

va

vy

zi

i a

y yi y y y yi v v

iv avy yi

y y y ya


Derivation of an equivalent circuit cont’d

(a complex, general case)87

01

1

220

0

1 1

0 22

2

2

2

2

'cc' cc'

'cc' cc'

'cc' cc'

'cc' cc'

yi y yv

iavy

y ya

yy ay

i v

y viay aa y


Complete model of the off-nominal ratio

transformer (a real)

• In this case, a is a real number

• Corresponding to the following equivalent circuit (without ideal transformer)

• The shunt admittance is added as it is on the tapped side, and it is multiplied

by a2 on the other side

• The admittance matrix is symmetrical: an equivalent circuit can be drawn

88

012

'cc'

yy a 201

2

'cc'

yy a a a

cc'ay

0

1 1

2 0 22

2

2

'cc' cc'

'cc' cc'

yy ay

i v

y viay a y


Simplified model of the off-nominal ratio

transformer

• If the actual transformer shunt admittance is neglected,

• Corresponding to the following equivalent circuit

• The equivalent circuit do have two shunt branches all the same

• The two shunt admittances have opposite sign

• As a →1, the model becomes the series impedance model

89

1cc'y a 1cc'y a a

cc'ay

1 1

222

cc' cc'

cc' cc'

i y ay v

vi ay a y


Tap on the left side, y” on the right side

• If the tap is installed at bus #1,

the equivalent circuit as a function

of ycc” is obtained by dividing by a2

90

21 1

22

cc'' cc''

cc''cc''

y y

i vaa

vi yy

a

2

1cc''

ay

a

1cc''y a

a

cc''y

a

cc''y


Example for automatic tap-changer

• Example

• Typically, OLTC are used to control voltage at load busses, e.g., by

Distributors

• In this framework, they have a fixed set point and they are

automatically adjusted

• However, taps are discrete variables

91

../../Politecnico Attività Istituzionale/Corsi Istituzionali/Electric Power Systems/Esempi/Esempi GloverSarmaOverbye/Chapter3/Example3_12.pwb


The hierarchical voltage control strategy

• First level: local level (primary voltage regulation: very fast; AVR)

Changing the excitation (field) current of the synchronous machine

it is possible to control the voltage at the generator terminals or at

the PoC of the power plant with the transmission system

• Secondary level (secondary voltage regulation):

The transmission system is organized in different control areas

and for each of them a pilot bus is defined. By means of the

control generators belonging to a specific area, the voltage

magnitude of the pilot bus is kept at an optimized set point

Pilot bus set points are computed by an OPF and can be

computed on-line, or by…

• Third level (Tertiary voltage regulation):

In real time, the voltage set points for the pilot busses are updated

to take into account the actual condition of the power system,

likely to be different from forecasted conditions


Secondary Voltage Regulation

• Pilot busses: load busses, with significant short-circuit power, such that they can be considered representative of voltages in that area

• Goal: to regulate automatically the voltage of pilot busses in such a way that:

Pilot bus voltages are kept constant at an optimum value computed by a SCOPF based on the day ahead forecast or in the very short-term horizon

• Tools:

Regulating generators of the area of pilot busses

• Constraints:

All technical operating constraints

Alignment constraints: all regulating generators are loaded at the same pu reactive power


SVR areas


Tertiary Voltage Regulation

• It is necessary to take into account differences between the optimal

operation determined based on day-ahead forecasted conditions and

the real-time conditions: in real time, to keep pilot bus voltages at the

optimal set-point, reactive levels will be different from optimal values

• TVR moves all pilot bus set points and reactive levels in such a way that

differences to the optimal values computed with reference forecasted

values are minimized

• The following quadratic OF is minimized automatically (a and b are

weight diagonal matrices)

• This optimization is carried out every 5 minutes and computes new

values of VP and QA, taking into account constraints on sentinel busses

and capability constraints (linearized constraints).

• Alternatively, an on-line voltage re-scheduling can be carried out

] ] ] ] ] ]ToptAAoptAA

T

optppoptpp QQQQVVVVFO ba


Structure of the Hierarchical Voltage

Regulation


Secondary Voltage Regulation

control of voltage profiles - universidad de...

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