Note: Descriptions are shown in the official language in which they were submitted.
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METHODS OF PATEL LOADFLOW COMPUTATION FOR ELECTRICAL POWER
SYSTEM
FIELD OF THE INVENTION
[001] The present invention relates to a method of loadflow computation in
power flow control
and voltage control for an electrical power system.
BACKGROUND OF THE INVENTION
[002] The present invention relates to power-flow/voltage control in
utility/industrial power
networks of the types including many power plants/generators interconnected
through
transmission/distribution lines to other loads and motors. Each of these
components of the power
network is protected against unhealthy or alternatively faulty, over/under
voltage, and/or over
loaded damaging operating conditions. Such a protection is automatic and
operates without the
consent of power network operator, and takes an unhealthy component out of
service by
disconnecting it from the network. The time domain of operation of the
protection is of the order
of milliseconds.
[003] The purpose of a utility/industrial power network is to meet the
electricity demands of its
various consumers 24-hours a day, 7-days a week while maintaining the quality
of electricity
supply. The quality of electricity supply means the consumer demands be met at
specified voltage
and frequency levels without over loaded, under/over voltage operation of any
of the power
network components. The operation of a power network is different at different
times due to
changing consumer demands and development of any faulty/contingency situation.
In other words
healthy operating power network is constantly subjected to small and large
disturbances. These
disturbances could be consumer/operator initiated, or initiated by overload
and under/over voltage
alleviating functions collectively referred to as security control functions
and various optimization
functions such as economic operation and minimization of losses, or caused by
a
fault/contingency incident.
[004] For example, a power network is operating healthy and meeting quality
electricity needs
of its consumers. A fault occurs on a line or a transformer or a generator
which faulty component
gets isolated from the rest of the healthy network by virtue of the automatic
operation of its
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protection. Such a disturbance would cause a change in the pattern of power
flows in the network,
which can cause over loading of one or more of the other components and/or
over/under voltage
at one or more nodes in the rest of the network. This in turn can isolate one
or more other
components out of service by virtue of the operation of associated protection,
which disturbance
can trigger chain reaction disintegrating the power network.
10051 Therefore, the most basic and integral part of all other functions
including optimizations
in power network operation and control is security control. Security control
means controlling
power flows so that no component of the network is over loaded and controlling
voltages such
that there is no over voltage or under voltage at any of the nodes in the
network following a
disturbance small or large. As is well known, controlling electric power flows
include both
controlling real power flows which is given in MWs, and controlling reactive
power flows which
is given in MVARs. Security control functions or alternatively overloads
alleviation and
over/under voltage alleviation functions can be realized through one or
combination of more
controls in the network. These involve control of power flow over tie line
connecting other utility
network, turbine steam/water/gas input control to control real power generated
by each generator,
load shedding function curtails load demands of consumers, excitation controls
reactive power
generated by individual generator which essentially controls generator
terminal voltage,
transformer taps control connected node voltage, switching in/out in
capacitor/reactor banks
controls reactive power at the connected node.
1006] Control of an electrical power system involving power-flow control and
voltage control
commonly is performed according to a process shown in Fig. 5, which is a
method of
forming/defining a loadflow computation model of a power network to affect
control of voltages
and power flows in a power system comprising the steps of:
Step-10: obtaining on-line/simulated data of open/close status of all switches
and circuit breakers
in the power network, and reading data of operating limits of components of
the power
network including maximum power carrying capability limits of transmission
lines,
transformers, and PV-node, a generator-node where Real-Power-P and Voltage-
Magnitude-V are given/assigned/specified/set, maximum and minimum reactive
power
generation capability limits of generators, and transformers tap position
limits, or stated
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alternatively in a single statement as reading operating limits of components
of the
power network,
Step-20: obtaining on-line readings of given/assigned/specified/set Real-Power-
P and Reactive-
Power-Q at PQ-nodes, Real-Power-P and voltage-magnitude-V at PV-nodes, voltage
magnitude and angle at a reference/slack node, and transformer turns ratios,
wherein
said on-line readings are the controlled variables/parameters,
Step-30: performing loadflow computation to calculate, depending on loadflow
computation
model used, complex voltages or their real and imaginary components or voltage
magnitude corrections and voltage angle corrections at nodes of the power
network
providing for calculation of power flow through different components of the
power
network, and to calculate reactive power generation and transformer tap-
position
indications,
Step-40: evaluating the results of Loadflow computation of step-30 for any
over loaded power
network components like transmission lines and transformers, and over/under
voltages
at different nodes in the power system,
Step-50: if the system state is acceptable implying no over loaded
transmission lines and
transformers and no over/under voltages, the process branches to step-70, and
if
otherwise, then to step-60,
Step-60: correcting one or more controlled variables/parameters set in step-20
or at later set by
the previous process cycle step-60 and returns to step-30,
Step-70: affecting a change in power flow through components of the power
network and voltage
magnitudes and angles at the nodes of the power network by actually
implementing the
finally obtained values of controlled variables/parameters after evaluating
step finds a
good power system or stated alternatively as the power network without any
overloaded
components and under/over voltages, which finally obtained controlled
variables/parameters however are stored for acting upon fast in case a
simulated event
actually occurs or stated alternatively as actually implementing the corrected
controlled
variables/parameters to obtain secure/correct/acceptable operation of power
system.
[007] Overload and under/over voltage alleviation functions produce changes in
controlled
variables/parameters in step-60 of Fig.5. In other words controlled
variables/parameters are
assigned or changed to the new values in step-60. This correction in
controlled
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variables/parameters could be even optimized in case of simulation of all
possible imaginable
disturbances including outage of a line and loss of generation for corrective
action stored and
made readily available for acting upon in case the simulated disturbance
actually occurs in the
power network. In fact simulation of all possible imaginable disturbances is
the modem practice
because corrective actions need be taken before the operation of individual
protection of the
power network components.
[008] It is obvious that loadflow computation consequently is performed many
times in real-
time operation and control environment and, therefore, efficient and high-
speed loadflow
computation is necessary to provide corrective control in the changing power
system conditions
including an outage or failure of any of the power network components.
Moreover, the loadflow
computation must be highly reliable to yield converged solution under a wide
range of system
operating conditions and network parameters. Failure to yield converged
loadflow solution
creates blind spot as to what exactly could be happening in the network
leading to potentially
damaging operational and control decisions/actions in capital-intensive power
utilities.
[009] The power system control process shown in Fig. 5 is very general and
elaborate. It
includes control of power-flows through network components and voltage control
at network
nodes. However, the control of voltage magnitude at connected nodes within
reactive power
generation capabilities of electrical machines including generators,
synchronous motors, and
capacitor/inductor banks, and within operating ranges of transformer taps is
normally integral part
of loadflow computation as described in "LTC Transformers and MVAR violations
in the Fast
Decoupled Load Flow, IEEE Trans., PAS-101, No.9, PP. 3328-3332, September
1982." If
under/over voltage still exists in the results of loadflow computation, other
control actions,
manual or automatic, may be taken in step-60 in the above and in Fig.5. For
example, under
voltage can be alleviated by shedding some of the load connected.
[010] The prior art and present invention are described using the following
symbols and terms:
Ypq = Gpq Bpq : (p-q) th element of nodal admittance matrix without shunts
Ypp ¨ Gpp + Bpp : p-th diagonal element of nodal admittance matrix without
shunts
yp = gp + jbp : total shunt admittance at any node-p
Vp = ep + jfp = VpZ0p : complex voltage of any node-p
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Ypq = Gm+ jBpq : (p-q) th element of nodal admittance matrix without shunts
Ypp Gpp+ iBpp p-th diagonal element of nodal admittance matrix without
shunts
yp = gp + jbp : total shunt admittance at any node-p
VP = ep + jfp= VpZ0p : complex voltage of any node-p
Vs = e + jfs= Vs/Os : complex slack-node voltage
AO, AV p : voltage angle, magnitude corrections
Afp, Aep : imaginary, real part of complex voltage corrections
PP +.0p : net nodal injected power, calculated
AP p + jAQp : nodal power residue or mismatch
RP p + jRQp : modified nodal power residue or mismatch
RI p +Pp : net nodal injected current, calculated
ARID + jAllp : nodal current residue or mismatch
RRIp + jRIlp : modified nodal current residue or mismatch
PSHp + jQSHp : net nodal injected power, scheduled/specified
Cp = 1Z= CoscDp+ jSineop= 1+1Tanelp: Unitary rotation/transformation
: number of PQ-nodes
: number of PV-nodes
n=m+k+1 : total number of nodes
q>p : node-q is connected to node-p excluding the case of q=p
[ : indicates enclosed variable symbol to be a vector or matrix
LRA : Limiting Rotation Angle, -36 for prior art, -48 for
invented models
PQ-node: load-node, where, Real-Power-P and Reactive-Power-Q are specified
PV-node: generator-node, where, Real-Power-P and Voltage-Magnitude-V are
specified
Loadflow Computation: Each node in a power network is associated with four
electrical
quantities, which are voltage magnitude, voltage angle, real power, and
reactive power. The loadflow computation involves calculation/determination
of two unknown electrical quantities for other two
given/specified/scheduled/set/known electrical quantities for each node. In
other words the loadflow computation involves determination of unknown
quantities in dependence on the given/specified/scheduled/set/known
electrical quantities.
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Loadflow Model: a set of equations describing the physical power network and
its operation for
the purpose of loadflow computation. The term loadflow model' can be
alternatively referred to as 'model of the power network for loadflow
computation'. The process of writing Mathematical equations that describe
physical power network and its operation is called Mathematical Modeling. If
the equations do not describe/represent the power network and its operation
accurately the model is inaccurate, and the iterative loadflow computation
method could be slow and unreliable in yielding converged loadflow
computation. There could be variety of Loadflow Models depending on
organization of set of equations describing the physical power network and its
operation, including Decoupled Loadflow Models, Super Decoupled
Loadflow Models, Fast Super Decoupled Loadflow (FSDL) Model, and Super
Super Decoupled Loadflow (SSDL) Model.
Loadflow Method: sequence of steps used to solve a set of equations describing
the physical
power network and its operation for the purpose of loadflow computation is
called Loadflow Method, which term can alternatively be referred to as
loadflow computation method' or 'method of loadflow computation'. One
word for a set of equations describing the physical power network and its
operation is: Model. In other words, sequence of steps used to solve a
Loadflow Model is a Loadflow Method. The loadflow method involves
definition/formation of a loadflow model and its solution. There could be
variety of Loadflow Methods depending on a loadflow model and iterative
scheme used to solve the model including Decoupled Loadflow Methods,
Super Decoupled Loadflow Methods, Fast Super Decoupled Loadflow
(FSDL) Method, and Super Super Decoupled Loadflow (SSDL) Method. All
decoupled loadflow methods described in this application use either
successive (10, IV) iteration scheme or simultaneous ( I V, 10) iteration
scheme, defined in the following.
[011] Prior art method of loadflow computation of the kind carried out as step-
30 in Fig. 5,
include a class of methods known as decoupled loadflow. This class of methods
consists of
decouled loadflow and super decoupled loadflow methods including Super Super
Decoupled
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Loadflow method all formulated involving Power Mismatch computation and polar
coordinates.
Prior-art Loadflow Computation Methods are described in details in the
following documents of
Research publications and granted patents. Therefore, prior art methods will
not be described
here.
MAJOR RESEARCH PUBLICATIONS
1) "Super Super Decoupled Loadflow" Presented at IEEE Toronto International
Conference ¨
Science and Technology for Humanity (TIC-STH 2009), pp.652-659, 26-27
September,
2009
2) "Fast Super Decoupled Loadflow" IEE Proceedings Part-C, Vol.139, No.1,
pp.13-20, Jan
1992
PATENTS
I. "Method of Fast Super Decoupled Loadflow Computation for Electrical Power
System",
Canadian Patent #2107388 issued July 5,2011
2. "Method of Super Super Decoupled Loadflow Computation for Electrical Power
System",
Canadian Patent # 2548096 issued January 5, 2011
3. "Method and Apparatus for Parallel Loadflow Computation for Electrical
Power System",
Canadian Patent # 2564625 issued March 9, 2011
4. "Method of Loadflow Computation for Electrical Power System", Canadian
Patent #
2661753 issued October 11,2011
SUMMARY OF THE INVENTION
[012] It is a primary object of the present invention to improve convergence
and efficiency of
the prior art Super Super Decoupled Loadflow computation method under wide
range of system
operating conditions and network parameters for use in power flow control and
voltage control in
the power system. A further object of the invention is to reduce computer
storage/memory or
calculating volume requirements.
[013] The above and other objects are achieved, according to the present
invention, Newton-
Raphson-Patel Loadflow (NRPL) Patel Loadflow (PL), Y matrix ¨ Patel Loadflow
(YPL), Z
matrix - Patel Loadflow (ZPL) Methods and their many variants, for loadflow
calculation for
Electrical Power System. In context of voltage control, one of the inventive
system of NRPL and
others listed in the above methods of loadflow computation for Electrical
Power system
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consisting of plurality of electromechanical rotating machines, transformers
and electrical loads
connected in a network, each machine having a reactive power characteristic
and an excitation
element which is controllable for adjusting the reactive power generated or
absorbed by the
machine, and some of the transformers each having a tap changing element,
which is controllable
for adjusting turns ratio or alternatively terminal voltage of the
transformer, said system
comprising:
means defining and solving loadflow model of the power network characterized
by
inventive CIPSDL and other listed in the above methods of loadflow computation
models for providing an indication of the quantity of reactive power to be
supplied
by each generator including the reference/slack node generator, and for
providing
an indication of turns ratio of each tap-changing transformer in dependence on
the
obtained-online or given/specified/set/known
controlled network
variables/parameters, and physical limits of operation of the network
components,
machine control means connected to the said means defining and solving
loadflow model
and to the excitation elements of the rotating machines for controlling the
operation of the excitation elements of machines to produce or absorb the
amount
of reactive power indicated by said means defining and solving loadflow model
in
dependence on the set of obtained-online or given/specified/set controlled
network
variables/parameters, and physical limits of excitation elements,
transformer tap position control means connected to the said means defining
and solving
loadflow model and to the tap changing elements of the controllable
transformers
for controlling the operation of the tap changing elements to adjust the turns
ratios
of transformers indicated by the said means defining and solving loadflow
model
in dependence on the set of obtained-online or given/specified/set controlled
network variables/parameters, and operating limits of the tap-changing
elements.
[014] The method and system of voltage control according to the preferred
embodiment of the
present invention provide voltage control for the nodes connected to PV-node
generators and tap
changing transformers for a network in which real power assignments have
already been fixed.
The said voltage control is realized by controlling reactive power generation
and transformer tap
positions.
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[015] One of the inventive system of NRPL, PL, YPL, ZPL Loadflow methods of
computation
can be used to solve a model of the Electrical Power System for voltage
control. For this purpose
real and reactive power assignments or settings at PQ-nodes, real power and
voltage magnitude
assignments or settings at PV-nodes and transformer turns ratios, open/close
status of all circuit
breaker, the reactive capability characteristic or curve for each machine,
maximum and minimum
tap positions limits of tap changing transformers, operating limits of all
other network
components, and the impedance or admittance of all lines are supplied. A
decoupled loadflow
system of equations (1) and (2) is solved by an iterative process until
convergence. During this
solution the quantities which can vary are the real and reactive power at the
reference/slack node,
the reactive power set points for each PV-node generator, the transformer
transformation ratios,
and voltages on all PQ-nodes nodes, all being held within the specified
ranges. When the iterative
process converges to a solution, indications of reactive power generation at
PV-nodes and
transformer turns-ratios or tap-settings are provided. Based on the known
reactive power
capability characteristics of each PV-node generator, the determined reactive
power values are
used to adjust the excitation current to each generator to establish the
reactive power set points.
The transformer taps are set in accordance with the turns ratio indication
provided by the system
of loadflow computation.
[016] For voltage control, system of NRPL or others and many variants listed
in the above
Methods of Loadflow computation can be employed either on-line or off-line. In
off-line
operation, the user can simulate and experiment with various sets of operating
conditions and
determine reactive power generation and transformer tap settings requirements.
A general-
purpose computer can implement the entire system. For on-line operation, the
loadflow
computation system is provided with data identifying the current real and
reactive power
assignments and transformer transformation ratios, the present status of all
switches and circuit
breakers in the network and machine characteristic curves in steps-10 and -20
in Fig. 5, and steps
12, 20, 32, 44, and 50 in Fig 6 described below. Based on this information, a
model of the system
based on gain matrices of invented loadflow computation systems provide the
values for the
corresponding node voltages, reactive power set points for each machine and
the transformation
ratio and tap changer position for each transformer.
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[017] The present inventive system of loadflow computation for Electrical
Power System
consists of, one of the Current Injection Patel Super Decoupled Loadflow: YY-
version (CIPSDL-
YY) or CIPSDL-XX, or others listed in the above Methods characterized in that
1) it is possible
to have single decoupled coefficient matrix solution requiring only 50% of
memory used by prior
art methods, 2) the presence of transformed values of
known/given/specified/scheduled/set
quantities in the diagonal elements of the gain matrices [Yf] and [Ye] of the
decoupled loadflow
sub-problem, and 3) transformation angles are restricted to maximum of ¨36 to
¨900 to be
determined experimentally, 4) PV-nodes being active in both RI-f and II-e sub-
problems, PQ-
node to PV-node and PV-node to PQ-node switching is simple to implement, and
these inventive
loadflow computation steps together yield some processing acceleration and
consequent
efficiency gains, and are each individually inventive, and 5) modified real
current mismatches at
PV-nodes are determined as RRIp = (epAPp )/[Kp(ep2 + fp2)] and RIIp = (-
fpAPp) / [Kp(ep2+ fp2)]
in order to keep gain matrices [Yf] and [Ye] symmetrical. If the value of
factor K=1, the gain
matrices [Yf] and [Ye] becomes unsymmetrical in that elements in the rows
corresponding to PV-
nodes are defined without transformation or rotation applied, as Yfpq= Yepq= -
13pq. It is possible
that Current Injection Patel Super Decoupled methods can be formulated in
polar coordinates by
simply replacing correction vectors [M] and [Ae] in equations (I) and (2) and
subsequently
followed equations by correction vectors [AO] and [AV]. However, it will not
be easy to have
single gain matrix model, because [AV] for PV-nodes is zero and absent.
BRIEF DESCRIPTION OF DRAWINGS
[018] Fig. 1 is a flow-chart of invented NRPL method.
[019] Fig. 2 is a flow-chart embodiment of the invented PL computation method.
[020] Fig. 3 is a flow-chart embodiment of the invented Y matrix based Patel
Loadflow (YPL)
computation method using complex algebra.
[021] Fig. 4 is a flow-chart embodiment of the invented method of Z matrix
based Patel
Loadflow (ZPL) computation method using complex algebra.
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[022] Fig. 5 is a flow-chart of the overall controlling method for an
electrical power system
involving loadflow computation as a step which can be executed using one of
the
loadflow computation methods embodied in Figs. 1, 2, 3 or 4
[023 Fig. 6 is a flow-chart of the simple special case of voltage control
system in overall
controlling system of Fig. 5 for an electrical power system
[024] Fig. 7 is a one-line diagram of an exemplary 6-node power network having
a
reference/slack/swing node, two PV-nodes, and three PQ-nodes
DESCRIPTION OF A PREFERED EMBODYMENT
[025] A loadflow computation is involved as a step in power flow control
and/or voltage control
in accordance with Fig. 5 or Fig. 6. A preferred embodiment of the present
invention is described
with reference to Fig. 7 as directed to achieving voltage control.
[026] Fig. 7 is a simplified one-line diagram of an exemplary utility power
network to which the
present invention may be applied. The fundamentals of one-line diagrams are
described in section
6.11 of the text ELEMENTS OF POWER SYSTEM ANALYSIS, fourth edition, by William
D.
Stevenson, Jr., McGrow-Hill Company, 1982. In Fig. 7, each thick vertical line
is a network node.
The nodes are interconnected in a desired manner by transmission lines and
transformers each
having its impedance, which appears in the loadflow models. Two transformers
in Fig.7 are
equipped with tap changers to control their turns ratios in order to control
terminal voltage of
node-1 and node-2 where large loads are connected.
[027] Node-6 is a reference/slack-node alternatively referred to as the slack
or swing -node,
representing the biggest power plant in a power network. Nodes-4 and ¨5 are PV-
nodes where
generators are connected, and nodes-1, -2, and ¨3 are PQ-nodes where loads are
connected. It
should be noted that the nodes-4, -5, and ¨6 each represents a power plant
that contains many
generators in parallel operation. The single generator symbol at each of the
nodes-4, -5, and ¨6 is
equivalent of all generators in each plant. The power network further includes
controllable circuit
breakers located at each end of the transmission lines and transformers, and
depicted by cross
markings in one-line diagram of Fig. 7. The circuit breakers can be operated
or in other words
opened or closed manually by the power system operator or relevant circuit
breakers operate
automatically consequent of unhealthy or faulty operating conditions. The
operation of one or
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more circuit breakers modify the configuration of the network. The arrows
extending certain
nodes represent loads.
[028] A goal of the present invention is to provide a reliable and
computationally efficient
loadflow computation that appears as a step in power flow control and/or
voltage control systems
of Fig. 5 and Fig. 6. However, the preferred embodiment of loadflow
computation as a step in
control of terminal node voltages of PV-node generators and tap-changing
transformers is
illustrated in the flow diagram of Fig. 6 in which present invention resides
in function steps 42
and 44.
[029] Short description of other possible embodiment of the present invention
is also provided
herein. The present invention relates to control of utility/industrial power
networks of the types
including plurality of power plants/generators and one or more motors/loads,
and connected to
other external utility. In the utility/industrial systems of this type, it is
the usual practice to adjust
the real and reactive power produced by each generator and each of the other
sources including
synchronous condensers and capacitor/inductor banks, in order to optimize the
real and reactive
power generation assignments of the system. Healthy or secure operation of the
network can be
shifted to optimized operation through corrective control produced by
optimization functions
without violation of security constraints. This is referred to as security
constrained optimization
of operation. Such an optimization is described in the United States Patent
Number: 5,081,591
dated Jan. 13, 1992: "Optimizing Reactive Power Distribution in an Industrial
Power Network",
where the present invention can be embodied by replacing the step nos. 56 and
66 each by a step
of constant gain matrices [Yf] and [Ye], and replacing steps of "Exercise
Newton-Raphson
Algorithm" by steps of "Exercise NRPL or PL or YPL or ZPL Computation" in
places of steps 58
and 68. This is just to indicate the possible embodiment of the present
invention in optimization
functions like in many others including state estimation function. However,
invention is being
claimed through a simplified embodiment without optimization function as in
Fig. 6 in this
application. The inventive steps-42 and ¨44 in Fig.6 are different than those
corresponding steps-
56, and ¨58, which constitute a well known Newton-Raphson loadflow method, and
were not
inventive even in United States Patent Number: 5,081,591.
[030] In Fig. 6, function step 12 provides stored impedance values of each
network component
in the system. This data is modified in a function step 14, which contains
stored information
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about the open or close status of each circuit breaker. For each breaker that
is open, the function
step 14 assigns very high impedance to the associated line or transformer. The
resulting data is
than employed in a function step 16 to establish an admittance matrix for the
power network. The
data provided by function step 12 can be input by the computer operator from
calculations based
on measured values of impedance of each line and transformer, or on the basis
of impedance
measurements after the power network has been assembled.
[031] Each of the transformers T1 and T2 in Fig. 7 is a tap changing
transformer having a
plurality of tap positions each representing a given transformation ratio. An
indication of initially
assigned transformation ratio for each transformer is provided by function
step 18 in Fig. 6.[[.]]
[032] The indications provided by function steps 14, and 22 are supplied to a
function step 42 in
which constant gain matrices [Yf] and [Ye], or [Y] or [Y*] of any of the
invented CIPSDL or
CNRPL models are constructed, factorized and stored. The gain matrices [Yf]
and [Ye], or [Y] or
[Y*] are conventional tools employed for solving CIPSDL or CNRPL models
defined by
equations (1) and (2), or (73) or (77) of a power system.
[033] Indications of initial reactive power, or Q on each node, based on
initial calculations or
measurements, are provided by a function step 22 and these indications are
used in function step
24, to assign a Q level to each generator and motor. Initially, the Q assigned
to each machine can
be the same as the indicated Q value for the node to which that machine is
connected.
[034] An indication of measured real power, P, on each node is supplied by
function step 32.
Indications of assigned/specified/scheduled/set generating plant loads that
are constituted by
known program are provided by function step 34, which assigns the real power,
P, load for each
generating plant on the basis of the total P, which must be generated within
the power system.
The value of P assigned to each power plant represents an economic optimum,
and these values
represent fixed constraints on the variations, which can be made by the system
according to the
present invention. The indications provided by function steps 32 and 34 are
supplied to function
step 36 which adjusts the P distribution on the various plant nodes
accordingly. Function step 38
assigns initial approximate or guess solution to begin iterative method of
loadflow computation,
and reads data file of operating limits on power network components, such as
maximum and
minimum reactive power generation capability limits of PV-nodes generators.
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[035] The indications provided by function steps 24 36, 38 and 42 are supplied
to function step
44 where inventive CIPSDL computation or NGSPL or DGSPL or CNRPL computation
is
carried out, the results of which appear in function step 46. The loadflow
computation yields
voltage magnitudes and voltage angles at PQ-nodes, real and reactive power
generation by the
reference/slack/swing node generator, voltage angles and reactive power
generation indications at
PV-nodes, and transformer turns ratio or tap position indications for tap
changing transformers.
The system stores in step 44 a representation of the reactive capability
characteristic of each PV-
node generator and these characteristics act as constraints on the reactive
power that can be
calculated for each PV-node generator for indication in step 46. The
indications provided in step
46 actuate machine excitation control and transformer tap position control.
All the loadflow
computation methods using inventive CIPSDL or NGSPL or DGSPL or CNRPL
computation
models can be used to effect efficient and reliable voltage control in power
systems as in the
process flow diagram of Fig. 6.
[036] Particularly inventive CIPSDL models in terms of equations for
determining elements of
vectors [RRI], [RII], and elements of gain matrices [yq, and [Ye] of equations
(1) and (2) are
described followed by computation steps of the CIPSDL methods are described.
The same is
repeated for all other inventive models and methods.
[037] The presence of transformed values of
known/given/specified/scheduled/set quantities in
the diagonal elements of the gain matrix [Yf] and [Ye] of equations (I) and
(2), which takes
different form for different methods, is brought about by such formulation of
loadflow equations.
The said transformed quantities in the diagonal elements in the gain matrices
improved
convergence and the reliability of obtaining converged loadflow computation
[038] The slack-start is to use the same voltage magnitude and angle as those
of the
reference/slack/swing node as the initial guess solution estimate for
initiating the iterative
loadflow computation. With the specified/scheduled/set voltage magnitudes, PV-
node voltage
magnitudes are adjusted to their known values after the first P-0 iteration.
This slack-start saves
almost all effort of mismatch calculation in the first P-f iteration. It
requires only shunt flows
from each node to ground to be calculated at each node, because no flows
occurs from one node
to another because they are at the same voltage magnitude and angle.
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New Application dated May 31, 2017
Newton-Raphson-Patel Loadflow (NRPL)
1039] This NRPL model comprises equations (1) to (15) provided in the hand
written form in both
rectangular and polar versions.
10401 The steps of loadflow computation method, Newton-Raphson-Patel Loadflow
(NRPL)
method are shown in the flowchart of Fig. 1. Referring to the flowchart of
Fig.1, different steps
are elaborated in steps marked with similar letters in the following. Double
lettered steps are the
characteristic steps of NRPL method. The words "Read system data" in Step-a
correspond to
step-10 and step-20 in Fig. 5, and step-16, step-18, step-24, step-36, step-38
in Fig. 6. All other
steps in the following correspond to step-30 in Fig.5, and step-42, step-44,
and step-46 in Fig. 6.
a. Read system data and assign an initial approximate solution. If better
solution estimate is
not available, set voltage magnitude and angle of all nodes equal to those of
the slack-
node, referred to as the slack-start.
b. Form nodal admittance matrix, and Initialize iteration count ITR = 0
cc. Form (2m+k) x (2m+k) size coefficient constant matrix of (1). The
matrix is formed using
equations (6) to (11). Factorize coefficient constant matrix of (1) and store
in a compact
storage exploiting sparsity.
d. Compute residues [AP] at PQ- and PV-nodes and [AQ] at only PQ-nodes. If
all are less
than the tolerance (6), proceed to step-n. Otherwise follow the next step.
ee. Compute the vector of residues [AR1 1M1] using equations (4) and (5)
for PQ-nodes, and
using equations to be provided on a later date for PV-nodes.
f. Solve (2) for the vector [Af Ae] and update components of voltage using,
[f] = [f] + [Af],
[e] = [e] + [Ae].
gg= Compute (12) to (15) for each PQ-node, and each PV-node.
h. Set voltage magnitudes of PV-nodes equal to the specified values, and
Increment the
iteration count ITR=ITR+1, and Proceed to step-d
i. Calculate reactive power generation at PV-nodes and tap positions of tap-
changing
transformers. If the maximum and minimum reactive power generation capability
and
transformer tap position limits are violated, implement the violated physical
limits and
adjust the loadflow solution by the method like one described in "LTC
Transformers and
MVAR violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9,
PP.
CA 2968813 2017-05-31
New Application dated May 31, 2017
3328-3332, September 1982".
n. From calculated values of voltage magnitude and voltage angle at PQ-
nodes, voltage
angle and reactive power generation at PV-nodes, and tap position of tap
changing
transformers, calculate power flows through power network components.
Patel Loadflow (PL)
[041] Propounding Statement of Patel Numerical Method:
1. Organize linear or nonlinear equations as mismatch functions equated to
zero.
2. Club any term with known quantities or value in to a diagonal term with
simple algebraic
manipulations.
3. Express the mismatch function as a product of coefficient matrix and a
vector of unknown
variables, which can sometimes be treated as correction vector of unknown
variables.
4. Equate vector of mismatch functions to the product of coefficient matrix
and vector of
unknown variables or correction vector of unknown variables.
5. Solve such a matrix equation by iterations for the vector of unknown
variables or the
correction vector of unknown variables using evaluation of mismatch functions
with guess
values of unknown variables to begin with, and inverting or factoring the
coefficient
matrix.
[042] The following inventions are based on Patel Numerical Method propounded
by this
inventor in 2007. The invented class of methods of forming/defining and
solving loadflow
computation models of a power network are the methods that organize a set of
nonlinear algebraic
equations in linear form as a product of coefficient matrix and unknown vector
on one side and
the corresponding mismatch vector on the other side. and then solving the
linear matrix equation
for unknown vector in an iterative fashion.
[043] It is about organizing load flow equations in the mismatch form and
putting them as a
product of a coefficient matrix and an unknown vector to be calculated.
Similar model was
originally propounded by this inventor in the year 2007 in the international
PCT patent filing and
consequent national phase filings which is granted patent in both USA and
Canada. This PL
model comprises equations (16) to (25). Super Decoupled versions will be
provide in about one
year time when this application is finalized. Also provided its YPL and ZPL
versions in complex
formulations. The model YPL comprised equations (26) to (33), and the model
ZPL comprises
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CA 2968813 2017-05-31
New Application dated May 31, 2017
equations (35) and (36). Again this models are proved in hand written form,
and formally typed
version will be provided in about a month time.
[044] The steps of loadflow computation method, Patel Loadflow (PL) method are
shown in the
flowchart of Fig. 2. Referring to the flowchart of Fig.2, different steps are
elaborated in steps
marked with similar letters in the following. Triple lettered steps are the
characteristic steps of PL
method. The words "Read system data" in Step-a corresponds to step-10 and step-
20 in Fig. 5,
and step-16, step-18, step-24, step-36, step-38 in Fig. 6. All other steps in
the following
correspond to step-30 in Fig.5, and step-42, step-44, and step-46 in Fig. 6.
a. Read system data and assign an initial approximate solution. If better
solution estimate is
not available, set voltage magnitude and angle of all nodes equal to those of
the slack-
node, referred to as the slack-start.
b. Form nodal admittance matrix, and Initialize iteration count ITR = 0
ccc. Form (2m+2k) x (2m+2k) size coefficient constant matrix of (1) or
(22). The matrix is
formed using equations (18) to (21). Factorize coefficient constant matrix of
(1) or (22),
and store in a compact storage exploiting sparsity
d. Compute residues [AP] at PQ- and PV-nodes and [AQ] at only PQ-nodes. If
all are less
than the tolerance (s), proceed to step-10. Otherwise follow the next step.
eee. Compute the vector of residues [AR! Al!] using equations (16) and (17)
for PQ-nodes,
and using equations to be provided on a later date for PV-nodes.
fff. Solve (2) or (23) for the vector [Af Ae] or [f e] respectively and
update components of
voltage using, [f] = [f] + [An, [e] = [e] + [Ae].
ggg. Compute (24) and (25) for each PQ-node, and each PV-node.
h. Set voltage magnitudes of PV-nodes equal to the specified values, and
Increment the
iteration count ITR=ITR+1, and Proceed to step-4.
i. Calculate reactive power generation at PV-nodes and tap positions of tap-
changing
transformers. If the maximum and minimum reactive power generation capability
and
transformer tap position limits are violated, implement the violated physical
limits and
adjust the loadflow solution by the method like one described in "LTC
Transformers and
MVAR violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9,
PP.
3328-3332, September 1982".
17
CA 2968813 2017-05-31
New Application dated May 31, 2017
n. From calculated values of voltage magnitude and voltage angle at PQ-
nodes, voltage
angle and reactive power generation at PV-nodes, and tap position of tap
changing
transformers, calculate power flows through power network components.
[045] The steps of loadflow calculation by YPL method are shown in the
flowchart of Fig. 3.
Referring to the flowchart of Fig.3, different steps are elaborated in steps
marked with similar
numbers in the following. Four lettered steps are the inventive steps. The
words "Read system
data" in Step-a correspond to step-10 and step-20 in Fig. 5, and step-16, step-
18, step-24, step-36,
step-38 in Fig. 6. All other steps in the following correspond to step-30 in
Fig.5, and step-42,
step-44, and step-46 in Fig. 6.
a. Read system data and assign an initial approximate solution. If better
solution estimate is
not available, set voltage magnitude and angle of all nodes equal to those of
the slack-
node, referred to as the slack-start.
b. Form nodal admittance matrix, and Initialize iteration count ITR = 0
cccc. Form (m+k) x (m+k) size complex matrices [Y] of (26) in a compact
storage exploiting
sparsity. The complex matrix is formed using equations (27) and (28), or (31)
and (32).
d. Compute residues [AP] at PQ- and PV-nodes and [AQ] at only PQ-nodes. If
all are less
than the tolerance (c), proceed to step-n. Otherwise follow the next step.
eeee. Compute the vector of complex current injection vectors using equations
(29) or (30). The
value of QSHp at PV-nodes is calculated with the latest available [V], and
violated
reactive power generation capability limit of generator of a PV-node is
implemented by
setting the value of QSHp equal to the violated limit.
ffff. Solve (26) for [V] or [AV] and update voltage using, [V] = [V] + [AV].
ggg. Compute (33) for each PQ-node, and each PV-node.
h. Set voltage magnitudes of PV-nodes equal to the specified values, and
Increment the
iteration count ITR=ITR+1.
i. Calculate reactive power generation at PV-nodes and tap positions of tap-
changing
transformers. If the maximum and minimum reactive power generation capability
and
transformer tap position limits are violated, implement the violated physical
limits and
adjust the loadflow solution by the method like one described in "LTC
Transformers and
MVAR violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9,
PP.
3328-3332, September 1982".
18
CA 2968813 2017-05-31
New Application dated May 31, 2017
n. From calculated values of complex voltage, voltage angle and reactive
power
generation at PV-nodes, and tap position of tap changing transformers,
calculate power
flows through power network components.
10461 The steps of loadflow calculation by ZPL method are shown in the
flowchart of Fig. 4.
Referring to the flowchart of Fig.4, different steps are elaborated in steps
marked with similar
numbers in the following. Five lettered steps are the inventive steps. The
words "Read system
data" in Step-a correspond to step-10 and step-20 in Fig. 5, and step-16, step-
18, step-24, step-36,
step-38 in Fig. 6. All other steps in the following correspond to step-30 in
Fig.5, and step-42,
step-44, and step-46 in Fig. 6.
a. Read system data and assign an initial approximate solution. If better
solution estimate is
not available, set voltage magnitude and angle of all nodes equal to those of
the slack-
node, referred to as the slack-start.
b. Form nodal admittance matrix, and Initialize iteration count ITR = 0
ccccc. Form (m+k) x (m+k) size complex matrix [Z] of (34) in a compact storage
exploiting
sparsity. The complex matrix is formed using standard Z matrix building
algorithm or is
obtained by building and inverting [Y].
d. Compute vector of complex current injections by S*/V*
eeeee. Solve (34) or (35) for [V] or [AV] and update voltage using, [V] = [V]
+ [AV].
fffff. Compute (39) for each PQ-node and each PV-node
g. Set voltage magnitudes of PV-nodes equal to the specified values and
Increment the
iteration count ITR=ITR+1.
h. Calculate reactive power generation at PV-nodes and tap positions of tap-
changing
transformers. If the maximum and minimum reactive power generation capability
and
transformer tap position limits are violated, implement the violated physical
limits and
adjust the loadflow solution by the method like one described in "LTC
Transformers and
MVAR violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9,
PP.
3328-3332, September 1982".
i. Calculate Abs ([Vr1) ¨ [V](r)), and if all components are not less than
the specified
tolerance, go to step-d or else follow the next step-n.
n. From calculated values of complex voltage, voltage angle and reactive
power
generation at PV-nodes, and tap position of tap changing transformers,
calculate power
19
CA 2968813 2017-05-31
New Application dated May 31, 2017
flows through power network components.
General Statements
10471 The system stores a representation of the reactive capability
characteristic of each machine
and these characteristics act as constraints on the reactive power, which can
be calculated for each
machine.
1048] While the description above refers to particular embodiments of the
present invention, it
will be understood that many modifications may be made without departing from
the spirit
thereof. The accompanying claims are intended to cover such modifications as
would fall within
the true scope and spirit of the present invention.
10491 The presently disclosed embodiments are therefore to be considered in
all respect as
illustrative and not restrictive, the scope of the invention being indicated
by the appended claims
in addition to the foregoing description, and all changes which come within
the meaning and
range of equivalency of the claims are therefore intended to be embraced
therein.
