STABILITATEA SISTEMELOR ELECTROENERGETICEiota.ee.tuiasi.ro/~mgavril/SCSEE/SCSEE_11.pdf · 1...
Transcript of STABILITATEA SISTEMELOR ELECTROENERGETICEiota.ee.tuiasi.ro/~mgavril/SCSEE/SCSEE_11.pdf · 1...
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STABILITATEA SISTEMELOR ELECTROENERGETICE
STABILITATEA DE TENSIUNE
(Voltage Stability)
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classifications and definitions
Load characteristics of the radial transmission system
The Voltage – Power characteristic of the system
C
O
N
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Stability criteria
Voltage collapse
Examples
T
E
N
T
FA C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classifications and definitions
Load characteristics of the radial transmission system
The Voltage – Power characteristic of the system
C
O
N
STABILITATEA DE TENSIUNE 3
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Stability criteria
Voltage Collapse
Examples
T
E
N
T
2
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
STABILITATEA DE TENSIUNE 4
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Classification of power system stability concepts
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classification of power system stability on time scale and driving force criteria.
STABILITATEA DE TENSIUNE 5
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
DEFINITION 1 ‐ STABILITY
Voltage stability may be described as the ability of a power system to maintain
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
steady acceptable voltages at all buses in the system under normal operating conditions and after being subjected to a disturbance [Kundur, 1994].
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
DEFINITION 2 ‐ STABILITY
A power system is voltage stable if
STABILITATEA DE TENSIUNE 7
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
p y gvoltages after a disturbance are close to voltages at normal operating conditions [Repo, 2001].
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
DEFINITION 3 ‐ INSTABILITY
Voltage instability stems from the attempt of load dynamics to restore power
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
of load dynamics to restore power consumption beyond the capability of the combined transmission and generation system [Van Custem, 1998].
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
DEFINITION 4 ‐ INSTABILITY
A power system becomes unstable when voltages uncontrollably decrease due to
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
outage of equipment (generator, line, transformer, bus bar, etc), increment of load, decrement of production and / or weakening of voltage control [Repo, 2001].
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
DEFINITION 5 ‐ INSTABILITY
Voltage instability is generally characterized by loss of a stable operating
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
point as well as by the deterioration of voltage levels in and around the electrical center of the region undergoing voltage collapse [Guide, 2006].
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN Disturbance type
Large ‐disturbance
Voltage Stability
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Disturbance typeSmall‐
disturbance Voltage Stability
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Large‐disturbance Voltage Stability
… system's ability to maintain steady voltages following large disturbances such as system faults loss of generation or
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
as system faults, loss of generation, or circuit contingencies.
The study period of interest may extend from a few seconds to tens of minutes.
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Small‐disturbance Voltage Stability
… system's ability to maintain steady voltages when subjected to small perturbations such as incremental changes
STABILITATEA DE TENSIUNE 13
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
perturbations such as incremental changes in system load.
This concept is useful in determining how the system voltages will respond to small system changes.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN Timeframes
Short‐term Voltage Stability
Mid‐term
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
TimeframesVoltage Stability
Long‐term Voltage Stability
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Short‐term Voltage Stability (1)
… involves the time taken between the onset of a system disturbance to just prior to the activation of the automatic LTC
STABILITATEA DE TENSIUNE 15
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
to the activation of the automatic LTC (Load Tap Changers).
Rotor angle instability and voltage instability can occur within this timeframe.
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Short‐term Voltage Stability (2)
… involves dynamics of fast acting load or system components such as:
• Synchronous Condensers h d h
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
• Automatic switched shunt capacitors • Induction motor dynamics • Static VAr Compensators • Flexible AC Transmission System (FACTS) devices • Excitation system dynamics • Voltage‐dependent loads
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Short‐term Voltage Stability (3)
The study period of interest is in the order of several seconds, and analysis requires solution of appropriate system differential
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
solution of appropriate system differential equations; this is similar to the analysis of rotor angle stability. In contrast to angle stability, short circuits near loads are important.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Mid‐term Voltage Stability
… refers to the time from the onset of the automatic LTC operation to just prior to
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
automatic LTC operation to just prior to the engagement of over‐excitation limiters (OEL). During this time, frequency and voltage stability may be of interest.
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Long‐term Voltage Stability
… refers to the time after OELs engage and includes manual operator‐initiated action. D i thi ti f l t
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
During this timeframe, longer‐term dynamics come into play such as governor action and load‐voltage and/or load‐frequency characteristics in addition to operator‐initiated manual adjustments.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Voltage Collapse
Voltage control and instability – local problems but widespread impact.
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Definition: the result of a cascading sequence of events accompanying voltage instability leading to an unacceptable low voltage profile in a significant part of the power system.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Voltage Collapse
… commonly occurs as a result of reactive
Main cause of …
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GGHH
AASSAACCHHII
IIAASSII
power deficiency.Due to a combination of events and system conditions the lack of reactive power reserve may lead to voltage collapse.
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Voltage Collapse
• Insufficient reserves in generators reactive power/voltage control limits
Factors that contribute to …
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
p / g• Unfavorable load characteristics• Characteristics of reactive compensation devices • Action of voltage control devices such as transformer under‐load tap changers (ULTCs)
•Poor coordination between various control and protective systems
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
• Increasing power demands, coupled with a local or regional shortage of reactive power.
• Small gradual changes such as natural increase in system load.
Main causes of voltage instability:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
system load.• Large sudden disturbances such as loss of a generating unit or a heavily loaded line.
• Malfunctioning or erroneous functioning of transformer on‐load tap changers.
• The inability of the system to meet reactive demands.• Cascading events
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
How does voltage collapse occurs?‐ A possible scenario ‐
• The reactive power reserve in the system is scarce (close to minimum).
Initial conditions:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
( )• Some EHV lines in the system are already heavily loaded.
Primary cause:• One of the heavily loaded EHV line is tripped.
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
How does voltage collapse occurs?‐ A possible scenario ‐
• The power flow from the tripped EHV line is redistributed through other EHV lines, causing an
Primary effects:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
g , gincrease in the loading of these lines.
• The additional loading determines an increase in the reactive power losses in the EHV lines.
• Consequence: the system reactive power demand is increased.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
How does voltage collapse occurs?‐ A possible scenario ‐
• Excessive reactive power flows determine higher voltage drops and a reduction of voltage at substation buses.R d ti i lt d t i l d d ti d
Intermediate effects:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
• Reduction in voltage determines a load reduction and consequently a reduction in power flows through EHV lines. These actions could have a stabilizing effect.
• AVRs at generators will restore terminal voltages to their prescribed values and more reactive power generation.
• Additional reactive power flows will determine greater voltage drops and the voltage will drop in avalanche.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
How does voltage collapse occurs?‐ A possible scenario ‐
• Low voltage levels are reflected in the distribution system.• The ULTC (Under‐Load Tap Changer) systems from
b t ti t f ill t di t ib ti lt
Effects in the distribution system:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
substation transformers will restore distribution voltages and loads to their pre‐fault levels in few minutes.
• Re‐increasing active and reactive powers based on tap changing actions will cause greater voltage drops in the EHV network again.
• The AVRs at generators will act to restore terminal voltages and will produce more reactive power.
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
How does voltage collapse occurs?‐ A possible scenario ‐
• Gradually all or part of the generators in the system will reach their reactive power limits (the maximum field current)
Cascading effect:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
current).• Suppose the first generator has reached its limits. At this moment the AVR could no more maintain the prescribed value of the terminal voltage, which will drop down.
• To continue to produce the same power with lower voltages, the armature current will increase causing additional reduction in the generator’s reactive power.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
How does voltage collapse occurs?‐ A possible scenario ‐
• Hence the initial share of reactive power of this
Cascading effect ‐ continued:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
generator will be transferred to other generators, leading to overloading more and more generators.
• This process will eventually lead to voltage collapse and possibly to loss of synchronism of generating units.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classifications and definitions
Load characteristics of the radial transmission system
The Voltage – Power characteristic of the system
C
O
N
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Stability criteria
Voltage collapse
Examples
T
E
N
T
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The simple radial transmission system
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
System impedance:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
is the load factor:
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Load characteristics ‐ formulae:
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NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
or
12
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Load characteristics ‐ formulae:
Active power maximum value:
STABILITATEA DE TENSIUNE 34
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Voltage critical value:
Isc ‐ the short‐circuit current;U1 = E ‐ the sending end voltage;
PL,max ‐ the maximum active power at the receiving end
Changing from absolute units to p.u. – reference values:
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Load characteristics ‐ graphics
STABILITATEA DE TENSIUNE 35
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Variation of active power
• For ZL > Z the increase in current is dominant PL = U2∙I∙coswill increase too;
STABILITATEA DE TENSIUNE 36
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
U2 I coswill increase too;• For ZL < Z the decrease in voltage is dominant PL = U2∙I∙coswill decrease too;
• When ZL = Z , PL PL,max
and U2 Ucr.
13
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Possible operating points
•Point A (a lower value of the current and a higher value of the voltage). This point describes normal operating conditions for
STABILITATEA DE TENSIUNE 37
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
operating conditions for the system.
•Point B (very high values of the current and very low values of the voltage). It describes abnormal operating conditions.
Feasibleregion
Unfeasibleregion
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classifications and definitions
Load characteristics of the radial transmission system
The Voltage – Power characteristic of the system
C
O
N
STABILITATEA DE TENSIUNE 38
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Stability criteria
Voltage collapse
Examples
T
E
N
T
FA C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The Voltage – Power characteristics (1)
The new one‐line diagram …
STABILITATEA DE TENSIUNE 39
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
… and its phasor diagram.
14
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The Voltage – Power characteristic (2)
Active and reactive power loads:
STABILITATEA DE TENSIUNE 40
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
The static power‐voltage equation / characteristic:
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The case of an ideally stiff load ‐ 1
For an ideally stiff load the power demand of the load is independent of voltage and is constant:
STABILITATEA DE TENSIUNE 41
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Based on the P‐Q relationship :
… and after some simple maths:
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The case of an ideally stiff load ‐ 2
[in p.u.]
where the base‐values are:
STABILITATEA DE TENSIUNE 42
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
The U‐P characteristic
(nose curves)‐ critical point
15
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The case of an ideally stiff load ‐ 3
Characteristics using voltage as a parameter:
For U2 = ct, equation: describes a circle in the
plane (Pn ‐ Qn).
STABILITATEA DE TENSIUNE 43
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Influence of the load characteristics ‐ 1
STABILITATEA DE TENSIUNE 44
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Influence of the load characteristics ‐ 2
STABILITATEA DE TENSIUNE 45
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
16
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classifications and definitions
Load characteristics of the radial transmission system
The Voltage – Power characteristic of the system
C
O
N
STABILITATEA DE TENSIUNE 46
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Stability criteria
Voltage collapse
Examples
T
E
N
T
FA C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Stability criteria
Th Th Th
STABILITATEA DE TENSIUNE 47
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
The dΔQ/dUcriterion
The dE/dUcriterion
The dQG/dQLcriterion
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Stability criteria
Th Th Th
STABILITATEA DE TENSIUNE 48
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
The dΔQ/dUcriterion
The dE/dUcriterion
The dQG/dQLcriterion
17
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dΔQ/dU criterion ‐ 1
The classical stability criterion.
Separate notionally:‐ Active from reactive power;‐ Power supplied from power consumption
STABILITATEA DE TENSIUNE 49
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
‐ Power supplied from power consumption
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dΔQ/dU criterion ‐ 2
The relationship between active and reactive power:
STABILITATEA DE TENSIUNE 50
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Solving for QS(U) gives:
U
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dΔQ/dU criterion ‐ 3
NOW reconnect to the system the notionally separated reactive
STABILITATEA DE TENSIUNE 51
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
power load and superimpose both the QS(U) and QL(U) characteristics on the same diagram.
18
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dΔQ/dU criterion ‐ 4
ANALYZE the stability of the two equilibrium points.
STABILITATEA DE TENSIUNE 52
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
S ‐ stable
U ‐ unstable
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dΔQ/dU criterion ‐ 5
OBTAIN the classic voltage stability criterion.
STABILITATEA DE TENSIUNE 53
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
or
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dΔQ/dU criterion ‐ 6
The equivalent form of the stability condition:
STABILITATEA DE TENSIUNE 54
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
where the derivatives dQL/dU and dPL/dU are calculated from the functions used to approximate the load characteristics.
19
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Stability criteria
Th Th Th
STABILITATEA DE TENSIUNE 55
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
The dΔQ/dUcriterion
The dE/dUcriterion
The dQG/dQLcriterion
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dE/dU criterion ‐ 1
Consider again the relationship between active and reactive powers supplied to the load:
STABILITATEA DE TENSIUNE 56
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
and solve it for E:
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dE/dU criterion ‐ 2ANALYZE the stability of the two equilibrium points.
Conclusion:
STABILITATEA DE TENSIUNE 57
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
The E – U characteristic
20
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Stability criteria
Th Th Th
STABILITATEA DE TENSIUNE 58
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
The dΔQ/dUcriterion
The dE/dUcriterion
The dQG/dQLcriterion
FA C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dQG / dQL criterion ‐ 1
Considers the behavior of the reactive power generation QG(U) as the load reactive demand QL(U) varies.
STABILITATEA DE TENSIUNE 59
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
QG(U) now includes the reactive power demand of both the load, QL(U), and the network, I
2X:
E U(U)
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The dQG / dQL criterion ‐ 2
Substituting argument δand magnitude U as function of PL(U) and QL(U), h b i i
STABILITATEA DE TENSIUNE 60
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
the above equation gives:
21
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
ANALYZE the stability of the two equilibrium points.
The dQG / dQL criterion ‐ 3
Conclusion:
STABILITATEA DE TENSIUNE 61
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classifications and definitions
Load characteristics of the radial transmission system
The Voltage – Power characteristic of the system
C
O
N
STABILITATEA DE TENSIUNE 62
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Stability criteria
Voltage collapse
Examples
T
E
N
T
FA C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The case of 2 equilibrium points
Critical Load Demand and Voltage Collapse
Point A and voltage U2
STABILITATEA DE TENSIUNE 63
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
S
U
U
Point A and voltage U1
dΔQ / dU criterion
22
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The case of 1 equilibrium point
Critical Load Demand and Voltage Collapse
U
STABILITATEA DE TENSIUNE 64
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
U
Point B and voltage V2
dΔQ / dU criterionUcr
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
The case of no equilibrium point
U
A point outside the network solution area
Critical Load Demand and Voltage Collapse
STABILITATEA DE TENSIUNE 65
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
STABILITATEA DE TENSIUNE
?
U
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
AA”
Q Q’L
QL
How a Voltage Collapse Occurs ?
P (U) increases
STABILITATEA DE TENSIUNE 66
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
A’
BB’
B”
QSQ’S
U
PL(U) increases
QS (U) becomes lower
PL(U) increases
QL (U) becomes raiser
23
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
How Does a Voltage Collapse Looks Like?
STABILITATEA DE TENSIUNE 67
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
(1) voltage variations during the day of the voltage collapse;(2) voltage variations during the previous day (Nagao, 1975).
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Estimating critical power and voltage (1)
It’s impossible to derive a general formula, due to nonlinearities of voltage characteristics.
An iterative approach is possible if the following assumptions are made:
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are made:‐ The power factor of the consumer load is maintained constant when the load demand increase.
‐ The composite load has a parabola form for the reactive power characteristic and a linear form for the active power characteristic.
‐ The load composition is constant.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Estimating critical power and voltage (2)The load model:
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
Critical values:
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24
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Classifications and definitions
Load characteristics of the radial transmission system
The Voltage – Power characteristic of the system
C
O
N
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IIAASSII
Stability criteria
Voltage collapse
Examples
T
E
N
T
FA C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Example 1
Effect of Increasing the Load‐‐‐‐‐‐‐‐‐ The network ‐‐‐‐‐‐‐‐‐
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IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Effect of Increasing the Load‐‐‐‐‐‐‐‐‐ The load‐‐‐‐‐‐‐‐‐
Active power:
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AASSAACCHHII
IIAASSII
PL = 0.682∙ξ∙U
Reactive power:
QL = ξ∙ (0.0122 ∙U2 − 4.318∙U + 460)
25
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Solution – Normal operating conditionsStable operating
point:
U = 207.63 kVQ = 89.40 MVAr
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Unstable operating point:
U = 92.42 kVQ = 165.12 MVAr
Overloading capacity – active power: 66.72 %
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
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TTEEHHNN
Solution – Calculate critical values
U cr [kV]: 150.03 150.03 153.39
Critical Voltage and Critical Overloading Factor ‐ successive approximations:
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U_cr [kV]: 150.03 150.03 153.39ξ _cr [%]: 0.00 42.90 60.13
U_cr [kV]: 154.27 154.49 154.54ξ _cr [%]: 65.14 66.41 66.72
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
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TTEEHHNN
Solution – Critical operating conditions
Critical operating point:
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IIAASSII
point:
U = 154.54 kVQ = 140.15 MVAr
26
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Example 2
Effect of Network Outages‐‐‐‐‐‐‐‐‐ The network ‐‐‐‐‐‐‐‐‐
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GGHH
AASSAACCHHII
IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Effect of Network Outages‐‐‐‐‐‐‐‐‐ The load‐‐‐‐‐‐‐‐‐
Active power:
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GGHH
AASSAACCHHII
IIAASSII
PL = 1.09∙U
Reactive power:
QL = 0.0195 ∙U2 − 6.9∙U + 736
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Solution
NORMAL OPERATING CONDITIONSStable operating point: U=202.35 kV Q=138.23 MVArUnstable operating point: U=99.76 kV Q=241.72 MVArO l di it ti CSI 49 37 %
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Overloading capacity ‐ active power: CSI=49.37 %
AFTER TRIPPING THE LINEStable operating point: U=170.08 kV Q=126.53 MVArUnstable operating point: U=138.38 kV Q=154.56 MVArOverloading capacity ‐ active power: CSI=3.62 %
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
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TTEEHHNN
Solution – graphic representation
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Example 3
Effect of the Shape of the Load Characteristics
The network
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‐‐‐‐‐‐‐‐‐ The network ‐‐‐‐‐‐‐‐‐
The same network data from Example 2.
Effect of the Shape of the Load Characteristics‐‐‐‐‐‐‐‐‐ The load‐‐‐‐‐‐‐‐‐
(1) P 240 t
Active power:
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN (2) P 16 18 t(U)
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(1) PL = 240 = ct
Reactive power:
QL = 0.0195 ∙U2 − 6.9∙U + 736
NNIICCAA
GGHH
AASSAACCHHII
IIAASSII
(2) PL = 16.18∙sqrt(U)
(3) PL = 1.09∙U (4) PL = 0.004859 ∙U2
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F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Solution
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IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Example 4
Effect of the Voltage Control‐‐‐‐‐‐‐‐‐ The network ‐‐‐‐‐‐‐‐‐
The same network data from Example 2.
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p
UL = 208 kVUg = 245 kV
(constant)
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
NORMAL OPERATING CONDITIONSStable operating point: U=202.35 kV and Q=138.23 MVArUnstable operating point: U=99.76 kV and Q=241.72 MVArOverloading capacity ‐ active power: CSI=49.37 %
AFTER TRIPPING THE LINE (E=ct)
Solution
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( )Stable operating point: U=170.07 kV and Q=126.53 MVArUnstable operating point: U=138.38 kV and Q=154.58 MVArOverloading capacity ‐ active power: CSI=3.62 %
AFTER TRIPPING THE LINE (U_g=ct)Stable operating point: U=182.15 kV and Q=126.15 MVArUnstable operating point: U=120.99 kV and Q=186.61 MVArOverloading capacity ‐ active power: CSI=22.51 %
29
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Solution
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IIAASSII
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
• Generation centralized in fewer, larger power plants:o fewer voltage controlled buseso longer electrical distances between generation and load
Why Voltage Stability is Important Today ?
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and load • Generation decentralized in more, smaller power plants:
o difficulties to take part in the voltage control process
o growing complexity in voltage control coordination.
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
• Extensive use of shunt capacitor compensation.• Voltage instability caused by line and generator
t
Why Voltage Stability is Important Today ?
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AASSAACCHHII
IIAASSII
outages• Many incidents throughout the world (USA and Canada ‐ 2003, Denmark and Sweden ‐ 2003, Greece ‐ 2004 etc.)
• Operation of systems closer to their limits
30
F A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T AF A C U L T A T E A D E I N G I N E R I E E L E C T R I C A , E N E R G E T I C A S I I N F O R M A T I C A A P L I C A T A
UUNNIIVVEERRSSIITTAATTEEAA
TTEEHHNN
Bulac C., Eremia M., “Dinamica sistemelor electroenergetice”, Editura Printech, Bucureşti, 2006.
Guide, „Guide to WECC/NERC Planning Standards I.D: Voltage Support and Reactive Power”, Western Electricity Coordinating Council, March 2006.
Kundur P., “Power System Stability and Control”, McGraw‐Hill Inc., New York, 1994.
Kundur P., Paserba J., Ajjarapu V., Andersson G., Bose A., Canizares C., Hatziargyriou N., Hill D., Stankovic A.,Taylor C., Van Cutsem T., Vittal V., “Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions”. Power Systems, IEEE
REFERENCES
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y / j y y ,Trans. Vol. 19. 2004; pp. 1387 – 1401.
Machovsky J., Bjalek J., Bumby J., “Power Systems Dynamics: Stability and Control”, John Wiley and Sons Ltd., London, 2008.
Repo S., “On‐line Voltage Stability Assessment of Power Systems – An Approach of Black‐Box Modeling”, Tampere University of Technology, PhD Thesis, 2001.
Taylor C.W., “Power System Voltage Stability”, McGraw‐Hill, New York, 1994.
Van Cutsem T., Vournas C., “Voltage stability of electric power systems”, Kluwer Academic Publisher, Boston, USA, 1998.