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© 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)
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
Model for studying the voltage control
G
G
Us
r
Thévenin
Es0 Es
IsZs
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
Distribution System Capacitors
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
Conceptual framework for voltage
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
© Alberto Berizzi - Dipartimento di Energia
Conceptual framework for voltage
sensitivities, cont’d
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
© Alberto Berizzi - Dipartimento di Energia
• 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?
Conceptual framework for voltage
sensitivities, cont’d
© Alberto Berizzi - Dipartimento di Energia
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%
© Alberto Berizzi - Dipartimento di Energia
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.
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%
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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.
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
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%
Observe the
dependence on
the slack!
© Alberto Berizzi - Dipartimento di Energia
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
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%
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%
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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”
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
STATCOM
id
Va
Vd
STATCOM
id
Va
Vd
STATCOM
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
Tools and devices to control voltages
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
© Alberto Berizzi - Dipartimento di Energia
Tools and devices to control voltages
cont’d
• Static Synchronous Series Compensator
(SSSC)
• Universal Power Flow Controller (UPFC)
39
© Alberto Berizzi - Dipartimento di Energia
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)
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
Fault close to a generator
Fault clearing in 0.25 s
44
© Alberto Berizzi - Dipartimento di Energia
Fault clearing in 0.34 s
The final part of the transient is determined by
electromechanical oscillations
45Fault close to a generator
© Alberto Berizzi - Dipartimento di Energia
Fault clearing in 0.35 s
46Fault close to a generator
© Alberto Berizzi - Dipartimento di Energia
What is the small-disturbance angle
stability? UCTE, November 200647
© Alberto Berizzi - Dipartimento di Energia
USA Blackout, 199648
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
Block diagram for the IV order model 51
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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+
- -
+
+
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
60Capability chart
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
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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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
How to sum up V-Q characteristics
V
Q Q
V
Qmax 2QmaxV
Q Q
V
Qmax2QmaxQmax
Q1 Qmax+ Q1
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
DC exciter
G3
G_G_
Controller
Instead of the small DC machine, a small synchronous machine + rectifier can be installed
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
Static exciter
G3
AC Controller
DC Controller Ref.
ET
• Fast response• Modularity (lower cost)• Brishless• vexc can be inverted• no maintenance
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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)
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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 ]
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
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
© Alberto Berizzi - Dipartimento di Energia
SVR areas
© Alberto Berizzi - Dipartimento di Energia
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
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Structure of the Hierarchical Voltage
Regulation
© Alberto Berizzi - Dipartimento di Energia
Secondary Voltage Regulation