CA2107388C

CA2107388C - Method of fast super decoupled loadflow computation for electrical power system

Info

Publication number: CA2107388C
Application number: CA2107388A
Authority: CA
Inventors: Sureshchandra B. Patel
Original assignee: Individual
Current assignee: Individual
Priority date: 1993-11-09
Filing date: 1993-11-09
Publication date: 2011-07-05
Anticipated expiration: 2013-11-09
Also published as: CA2107388A1

Abstract

The loadflow computation method of the present invention called Fast Super Decoupled Loadflow (FSDL) is characterized by the use of 1) the slack-start whereby the same voltage magnitude and angle as those of the slack-node are used for all the other nodes as an initial guess solution, and thereby reducing almost all effort of mismatch calculation in the first P-.theta. iteration, and PV-nodes voltage magnitudes are assigned their known values while updating voltage angles after P-.theta. iteration, 2) the restricted rotation angles to the maximum of -36 degrees for improved convergence in the situations of low voltage solution, 3) the gain matrices [Y.theta.], and [YV] whose elements are defined independent of rotation angle, 4) the same indexing and addressing information for storing both the constant gain matrices [Y.theta.], and [YV]
factorized using the same ordering regardless of node types as they are of the same dimension and sparsity structure.

In addition, the FSDL method is characterized in the modification of the real power mismatch at PV-nodes by a factor K p= Absolute (B pp/Y.theta.pp) such that RP
p = .DELTA.P p /(K p V p) in order to correct the Super Decoupled Loadflow model at PV-nodes in P-.theta. sub-problem thereby achieving improved convergence and consequent processing acceleration to a great extent. Also while solving for [.DELTA.V] in Q-V sub-problem, all the rows and columns corresponding to PV-nodes in factorized gain matrix [YV] are skipped from calculation.

In addition to listed four characteristics in the beginning, an alternate Novel Fast Super Decoupled Loadflow (NFSDL) method is characterized in that it employs overlap update of the voltage angle corrections at PV-nodes. It involves calculation of angle corrections at PV-nodes along with voltage magnitude corrections at PQ-nodes in Q-V sub-problem in addition to regular angle corrections in P-.theta. sub-problem as illustrated in Fig.4. This improves convergence and achieves consequent processing acceleration of the same order as that of the FSDL method.

Description

METHOD OF FAST SUPER DECOUPLED 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 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.

[005] 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.

[006] 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 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 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 modern 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 Loadflow, 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 + jBpq : (p-q) th element of nodal admittance matrix without shunts Ypp = Gpp + jBpp : p-th diagonal element of nodal admittance matrix without shunts yp = gp + jbp : total shunt admittance at any node-p VP = ep + jfp = VpZOp : complex voltage of any node-p AOP, AVP : voltage angle, magnitude corrections Aep, Afp : real, imaginary components of voltage corrections Pp + jQP : net nodal injected power calculated APP + jAQp : nodal power residue or mismatch RPP + jRQp : modified nodal power residue or mismatch (DP rotation or transformation angle [RP] : vector of modified real power residue or mismatch [RQ] : vector of modified reactive power residue or mismatch [YO] : gain matrix of the P-0 loadflow sub-problem defined by eqn. (1) [YV] : gain matrix of the Q-V loadflow sub-problem defined by eqn. (2) in : number of PQ-nodes k : number of PV-nodes n=m+k+1 : total number of nodes q>p : q is the node adjacent to node-p excluding the case of q=p [ I : indicates enclosed variable symbol to be a vector or a matrix LRA : Limiting Rotation Angle, -90 for prior art, -36 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 Ypq' = Gpq' + jBpq': rotated (p-q) th element of nodal admittance matrix without shunts YPP' = GPP' + jBPP': rotated p-th diagonal element of nodal admittance matrix without shunts APP'= APPCos(DP + AQpSin(Dp: rotated or transformed real power mismatch AQp'= AQpCos(Dp - APpSinq)p: rotated or transformed reactive power mismatch 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.

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 (SDL) Models, Fast Super Decoupled Loadflow (FSDL) Model, and Novel Fast Super Decoupled Loadflow (NFSDL) 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 (SDL) Methods, Fast Super Decoupled Loadflow (FSDL) Method, and Novel Fast Super Decoupled Loadflow (NFSDL) Method. All decoupled loadflow methods described in this application use successive (10, 1V) iteration scheme, defined in the following.

[011] Loadflow computation of the kind carried out as step-30 in Fig. 5, include a class of methods known as decoupled loadflow. This class consists of decouled loadflow and super decoupled loadflow methods, both prior art and invented. However, functional forms of different elements of the prior art Super Decoupled Loadflow: XB, and BX versions, SDLXB
and SDLBX

.CA 02107388 2011-01-10 models defined by system of equations (1) and (2) will be given below before description of steps of the prior art loadflow computation methods. The prior art loadflow models are inaccurate causing the prior art loadflow computation methods to take more iterations to converge to a solution, and therefore required increased calculation time.

[012] The aforesaid class of Decoupled Loadflow models involves a system of equations for the separate calculation of voltage angle and voltage magnitude corrections. Each decoupled model comprises a system of equations (1) and (2) differing in the definition of elements of [RP], [RQ], [Y0] and [YV].

[RP] _ [Y0] [AO] (1) [RQ] _ [YV] [AV] (2) [013] Equations (1) and (2) are referred to as P-0 sub-problem and Q-V sub-problem respectively. A decoupled loadflow computation method involves solution of a decoupled loadflow model comprising system of equations (1) and (2) in an iterative manner. Commonly, successive (10, 1V) iteration scheme is used for solving system of equations (1) and (2) alternately with intermediate updating. Each iteration involves one calculation of [RP] and [AO] to update [0] and then one calculation of [RQ] and [AV] to update [V]. The sequence of equations (3) to (6) depicts the scheme.

[A0] = [YO] -' [RP] (3) [0] = [0] + [A0] (4) [AV] = [YV] -' [RQ] (5) [V] = [V] + [AV] (6) [014] The elements of [RP] and [RQ] for PQ-nodes are given by equations (7) to (10).

RPp = (APpCos(Dp + AQpSin(Dp)/Vp = APp'/Vp (7) RQp = (-APpSin(Dp + AQpCos(Dp)/Vp = AQp'/Vp (8) Cos(Dp = Absolute (Bpp / v(Gpp2 + Bpp2)) (9) Sinop = - Absolute (Gpp / v(Gpp2 + Bpp2)) (10) [015] A description of Super Decoupling principle is given in "A new decoupled model for state estimation of power systems", IFAC symposium on Theory and application of Digital Control, Vol.2, pp.7-11, 5-7 January 1982, New Delhi, India. The prior art Super Decoupled Loadflow models are herein SDLXB and SDLBX. The Super Decoupled Loadflow model SDLXB is described in "Super Decoupled Loadflow with distributed slack bus, IEEE
Transactions, PAS-104, pp. 104-113, 1985". The other SDLBX is obvious from the description in "A
general-purpose version of the Fast Decoupled Loadflow, IEEE Transactions, PWRS-4, pp.760-770, 1989".

[016] The Super Decoupled Loadflow: XB-version: SDLXB model consists of equations (3) to (14).

RPp = APp/Vp - For PV-nodes (11) Y6pq = -1/Xpq' and YVpq = -Bpq' (12) Y9pp = Y-Y9pq and YVpp = -2bp + I-YVpq (13) q>p q>p bp' = bpCos(Dp or bp' = by (14) Where Xpq' is the transformed branch reactance defined by equation (21) and Bpq' is the corresponding transformed branch susceptance defined in equation (19).

[017] The Super Decoupled Loadflow: BX-version: SDLBX model differs from the SDLXB
version only in equation (12) as given by (15). Therefore, the model SDLBX
comprises the equations (3) to (11), (15), (13), and (14).

Y9pq = -Bpq' and YVpq= 1/Xpq' (15) [018] The following steps give the procedure for determining transformed/rotated branch admittance necessary in forming symmetrical gain matrices [YO] and [YV] of the SDLXB and SDLBX models.

1. Compute: Op = arctan (Gpp)`Bpp) and (Dq = arctan (Gqq/Bqq) (16) 2. Compute the average of rotations at the terminal nodes p and q of a branch:

(Dav = (I + (Dq)/2 (17) 3. Compare (Dav with the Limiting Rotation Angle (LRA) and let tav to be the smaller of the two:
(k, = minimum (I av, LRA) (18) 4. Compute transformed pq-th element of the admittance matrix:

Ypq' = Gpq' + jBpq' = (Cos (Da,, + jSin (bay,) (Gpq + jBpq) (19) Ypp' = Gpp' + jBpp' = E-(Gpq +jBpq) (20) q>p 5. Note that the transformed branch reactance is:

Xpq' = Bpq'/(Gpq'2 + Bpq'2) (21) Similarly, Xpp' = Bpp'/(Gpp'2 + Bpp'2) (22) [019] In super decoupled loadflow models [YO] and [YV] are real, sparse, symmetrical and built only from network elements. Since they are constant, they need to be factorized once only at the start of the solution. Equations (1) and (2) are to be solved repeatedly by forward and backward substitutions. [Y6] and [YV] are of the same dimensions (m+k) x (m+k) when only a row/column of the slack-node or reference-node is excluded and both are triangularized using the same ordering regardless of the node-types. For a row/column corresponding to a PV-node excluded in [YV], use a large diagonal to mask out the effects of the off-diagonal terms. When the PV-node is switched to the PQ-type, removing the large diagonal reactivates the row/column corresponding to a switched PV-node to PQ-node type.. This technique is especially useful in the treatment of PV-nodes in the gain matrix [YV 1.

[020] The steps of loadflow computation methods SDLXB and SDLBX 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. It can be seen that the loadflow computation methods SDLXB and SDLBX differ only in step-c defining gain matrices.

a. Read system data and assign an initial approximate solution. If better solution estimate is not available, set specified voltage magnitude at PV-nodes and 1.0 p.u.
voltage magnitude at PQ-nodes. Set all the node angles equal to that of the slack-node angle.
This is referred to as the flat-start.

b. Form nodal admittance matrix, and Initialize iteration count ITRP = ITRQ= r = 0 c. Form (m+k) x (m+k) size gain matrices [YO] and [YV] of (1) and (2) respectively each in a compact storage exploiting sparsity 1) In case of SDLXB-model, the gain matrices are formed using equations (12), (13), and (14) 2) In case of SDLBX-model, the gain matrices are formed using equations (15), (13), and (14) In gain matrix [YV], replace diagonal elements corresponding to PV-nodes by very large value say, (10.0)10. In case the [YV] is of dimension (m x m), this is not required to be performed. Factorize gain matrices [YO] and [YV] using the same ordering of nodes regardless of node-types. In case [YV] is of dimension (m x m), it is factorized using different ordering than that of [Y0].
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-m. Otherwise follow the next step.
e. Compute the vector of modified residues [RP] using (7) for PQ-nodes and using (11) for PV-nodes.
f. Solve (3) for [A0] and update voltage angles using, [0] = [0] + [A0].
g. Increment the iteration count ITRP=ITRP+1 and r=(ITRP+ITRQ)/2.
h. Compute residues [AP] at PQ- and PV-nodes, and [AQ] at PQ-nodes only. If all are less than the tolerance (c), proceed to step-m. Otherwise follow the next step.
i. Compute the vector of modified residues [RQ] using (8) for only PQ-nodes.
j. Solve (5) for [AV] and update PQ-node magnitudes using, [V] = [V] + [AV].
k. 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 described in "LTC Transformers and MVAR
violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9, PP.

3332, September 1982".

1. Increment the iteration count ITRQ=ITRQ+l and r=(ITRP+ITRQ)/2, and Proceed to step-d.
in. 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.

[021] In using either Super Decoupled Loadflow model for loadflow computation, rotation or transformation operators are applied to the complex node injections, and the corresponding admittance values that relate them to the system state variables, transform the network equations such that branch, or alternatively transmission line or transformer, admittance appear to be almost entirely reactive. Better decoupling is thus realized. However, transformation as given by equations (7) and (8) in the Super Decoupled Loadflow models can be applied only at PQ-nodes, because reactive power having not been specified/scheduled/assigned/set/known for PV-nodes, it is not possible to calculate AQp at PV-nodes. The corresponding transformation applied to branch, or alternatively transmission line or transformer, admittance as determined in the above in equations (16 ) to (22) leads to the definition of the elements of symmetrical gain matrices [YO], and [YV] of loadflow models. This means rotation gets applied to the elements in the rows corresponding to PV-nodes of the gain matrix [Y0], but rotation angle is not possible to be applied to PV-nodes injection mismatch equations as in equation (11). Stated alternatively, one side of the sub-set of equations corresponding to PV-nodes in equation (1) gets transformed or rotated, whereas the other side not. Therefore, the prior art loadflow models SDLXB and SDLBX are inaccurate in respect of PV-nodes causing the prior art super decoupled loadflow computation methods to take more iterations to converge to a solution, and therefore require increased calculation time. Moreover, these prior art loadflow computation method fail to converge to a solution, or alternatively diverge, in the presence of large Resistance(R)/Reactance(X) ratio branches and under severe power network operating conditions, because of the said inaccuracy in the prior art loadflow models. It is this breakthrough revelation that led to the development of the inventive Fast Super Decoupled Loadflow models with substantial acceleration of loadflow computation particularly in the presence of large Resistance(R)/Reactance(X) ratio branches in the network..

SUMMARY OF THE INVENTION

[022] It is a primary object of the present invention to improve convergence and efficiency of super decoupled loadflow computation methods 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.

[023] The above and other objects are achieved, according to the present invention, with a system of Fast Super Decoupled Loadflow (FSDL) computation for Electrical Power System. In context of voltage control, the inventive system of FSDL computation for Electrical Power system 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 one of the super decoupled loadflow models of the power network characterized by inventive FSDL or inventive NFSDL model for providing an indication of the quantity of reactive power to be supplied by each generator including the slack/reference 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.

[024] 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.

[025] The inventive system of Fast Super Decoupled Loadflow (FSDL) or Novel Fast Super Decoupled Loadflow (NFSDL) 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 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.

[026] For voltage control, either system of FSDL or NFSDL 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.

[027] The present inventive system of loadflow computation for Electrical Power System consists of, a Fast Super Decoupled Loadflow (FSDL) method characterized in that 1) the slack-start is used as the initial guess solution, 2) elements of gain matrices [Y0]
and [YV] are defined independent of rotation angles, 3) transformation angles are restricted to maximum of -36 , and 4) modified real power mismatches at PV-nodes are determined as RPp =
APp/(KpVp) in order to keep gain matrix [Y8] symmetrical. If the value of factor Kp=l, the gain matrix [Y0] becomes unsymmetrical in that elements in the rows corresponding to PV-nodes are defined without transformation or rotation applied, as YOpq= -Bpq, 5) Also while solving for [AV] in Q-V
subproblem, all the rows and columns corresponding to PV-nodes in factorized gain matrix [YV]
are skipped from calculation leading to some more processing acceleration.
These inventive loadflow computation steps together yield significant processing acceleration and consequent efficiency gains, and are each individually inventive.

[028] An alternate inventive system of loadflow computation for Electrical Power System consists of, a Novel Fast Super Decoupled Loadflow (NFSDL) method characterized in that 1) the slack-start is used as the initial guess solution, 2) elements of gain matrices [Y0] and [YV] are defined independent of rotation angles, 3) transformation angles are restricted to maximum of -36 , and 4) overlap correction calculation of PV-nodes voltage angles in Q-V
sub-problem in addition to regular calculation in P-0 sub-problem is used as illustrated in Fig. 4.

[029] It is also disclosed that both the FSDL and NFSDL calculating systems use the same indexing and addressing information for forming and storing both the constant gain matrices [Y0], and [YV] factorized using the same ordering regardless of node types leading to about 35%
saving in computer storage/memory or alternatively calculating volume requirements. The. FSDL

and NFSDL models are the simplest, easiest to implement and overall best in performance in terms of efficiency of calculations, reliability of convergence, and least computer memory requirements among many of their simple variants with almost similar performance.

BRIEF DESCRIPTION OF DRAWINGS

[030] Fig. 1 is a flow-chart of prior art loadflow computation methods [031] Fig. 2 is a flow-chart embodiment of the invented Fast Super Decoupled Loadflow computation method [032] Fig. 3 is a flow-chart embodiment of the invented Novel Fast Super Decoupled Loadflow computation method [033] Fig. 4 is an explanatory illustration of overlap correction calculation of PV-nodes angles in Q-V sub-problem defined by equation (2), in addition to regular in P-A sub-problem defined by equation (1), in Novel Fast Super Decoupled Loadflow method using exemplary 6-node power system of Fig. 7 where 3-PQ-nodes are numbered 1 to 3, nodes are numbered 4 and 5, and the slack-node is numbered 6 [034] 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 or 3 [035] 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 [036] Fig. 7 is a one-line diagram of an exemplary 6-node power network having a slack/swing/reference node, two PV-nodes, and three PQ-nodes DESCRIPTION OF A PREFERED EMBODYMENT

[037] 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.

[038] 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, forth 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.

[039] Node-6 is a reference-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 more circuit breakers modify the configuration of the network. The arrows extending certain nodes represent loads.

[040] 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 60 and 62.

[041] 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 [Y0] and [YV], and replacing steps of "Exercise Newton-Raphson Algorithm" by steps of "Exercise Fast Super Decoupled Loadflow 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-60 and -62 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.

[042] In Fig. 6, function step 10 provides stored impedance values of each network component in the system. This data is modified in a function step 12, which contains stored information about the open or close status of each circuit breaker. For each breaker that is open, the function step 12 assigns very high impedance to the associated line or transformer. The resulting data is than employed in a function step 14 to establish an admittance matrix for the power network. The data provided by function step 10 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.

[043] Each of the transformers TI 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 20.

[044] The indications provided by function steps 14, and 20 are supplied to a function step 60 in which constant gain matrices [Y0] and [YV] of any of the invented super decoupled loadflow models are constructed, factorized and stored. The gain matrices [Y0] and [YV]
are conventional tools employed for solving Super Decoupled Loadflow model defined by equations (1) and (2) for a power system.

[045] Indications of initial reactive power, or Q on each node, based on initial calculations or measurements, are provided by a function step 30 and these indications are used in function step 32, 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.

[046] An indication of measured real power, P, on each node is supplied by function step 40.
Indications of assigned/specified/scheduled/set generating plant loads that are constituted by known program are provided by function step 42, 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 40 and 42 are supplied to function step 44 which adjusts the P distribution on the various plant nodes accordingly. Function step 50 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.

[047] The indications provided by function steps 32, 44, 50 and 60 are supplied to function step 62 where inventive Fast Super Decoupled Loadflow computation or Novel Fast Super Decoupled Loadflow computation is carried out, the results of which appear in function step 64. The loadflow computation yields voltage magnitudes and voltage angles at PQ-nodes, real and reactive power generation by the slack/swing/reference 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 62 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 64. The indications provided in step 64 actuate machine excitation control and transformer tap position control. Both the loadflow computation methods using FSDL and NFSDL models can be used to effect efficient and reliable voltage control in power systems as in the process flow diagram of Fig. 6.

[048] Particular inventive loadflow computation steps of the FSDL and NFSDL
methods are described followed by inventive FSDL and NFSDL models in terms of equations for determining elements of vectors [RP], [RQ], and elements of gain matrices [Y0], and [YV]
of equations (1) and (2), further followed by detailed steps of inventive loadflow computation methods.

[049] The slack-start is to use the same voltage magnitude and angle as those of the slack/swing/reference 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-0 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.

[050] The same indexing and addressing information can be used for the storage of both the gain matrices [Y0] and [YV] as they are of the same dimension and sparsity structure as explained herein. This is achieved for both the inventive FSDL and NFSDL models. Voltage magnitude is specified/scheduled/set for PV-nodes where generators are connected, which each maintains/controls specified voltage magnitude at its node by changing its reactive power generation. Therefore, corrections in voltage magnitudes at PV-nodes are not required to be calculated as they do not change, and Q-V subproblem of equation (2) need to be solved only for PQ-nodes voltage corrections. However, matrix [YV] is formed of dimension (m+k) x (m+k) including PV-nodes, and large diagonal value say, 10.010 is used for diagonal elements corresponding to PV-nodes to mask out the effect of off diagonal terms in the factorization process that normalizes the elements of a row in the matrix by its diagonal term. This process makes rows of PV-nodes in the gain matrix [YV] numerically absent despite physical presence, which process need not be carried out in case of the NFSDL model as PV-nodes are also active because of the overlap calculation of PV-node voltage angle corrections in Q-V
sub problem along with voltage magnitude corrections. Because gain matrices [Y0] and [YV]
are of the same power network, they are of the same dimension and sparsity structure.
Therefore, they can be stored using the same indexing and addressing information leading to about 35%
saving in computer memory or calculating volume requirements. Detailed description of the factorization process and storage schemes for sparse matrix is given by K.Zollenkopf, "Bi-factorization - Basic Computational Algorithm and Programming Techniques", Large Sparse Sets of Linear Equations:
Proceedings of Oxford conference of the Institute of Mathematics and its Application held in April 1970, edited by J.K.Reid.

[051] The efficiency of inventive FSDL method is increased by skipping all PV-nodes and factor elements with indices corresponding to PV-nodes while solving (5) for [AV]. In other words efficiency can be realized by skipping operations on rows/columns corresponding to PV-nodes in the forward-backward solution of (5). This is possible because rows and columns corresponding to PV-nodes are made numerically inactive by putting large value in diagonal terms of [YV]. This has been implemented and time saving of about 4% of the total solution time, including the time of input/output, could be realized.

[052] Elements of gain matrices [Y8], and [YV] are possible to be defined independent of rotation or transformation angle in both the inventive FSDL and NFSDL models as explained herein. In super decoupling or transformation approach, rotation operators are applied to the complex node injections and the corresponding admittance values that relate them to the system state variables, transform the network equations such that branch or alternatively transmission line or transformer admittance appear to be almost entirely reactive. Better decoupling is thus realized. When rotated the complex branch admittance Ypq = Gpq + jBpq gets transformed into Ypq' = Gpq' + jBpq' , which is almost entirely reactive meaning Gpq' is almost of zero value. That means almost I Ypq' I _ I Bpq' I. Therefore, by using I Ypq' I with the same algebraic sign as of Bpq' applied, in place of Bpq' in the definition of elements of gain matrices given by equations (24), (25), (26), (29), (30), and (31), the gain matrices IY8], and [YVI are defined independent of rotation angles. This simplifies FSDL and NFSDL models such that they are easy to program and implement, do not require performing steps involved in equations (16) to (22), and achieve improved acceleration in the loadflow computation.

[053] Rotation or transformation angle restriction to maximum of -36 in case of invented loadflow models for use in equations (7) and (8) is arrived at experimentally.
The factor 0.9 in equations (24), (25), and (29) is also determined experimentally. These said values of rotation angle -36 and the factor 0.9 are determined experimentally such that best possible convergence of loadflow computation is obtained under network operating condition that result in low voltage solution.

[054] Said inaccuracy in prior art loadflow models SDLXB and SDLBX in respect of sub-set of equations corresponding to PV-nodes in system of equation (1), is corrected by a factor Kp given by equation (28) as used in equation (23) in case of inventive FSDL model leading to improved convergence of the FSDL method in the presence of large R/X ratio branches in the power network, and consequent efficiency gain and increased reliability of obtaining converged loadflow computation over wide range of network parameters and operating conditions. It is determined experimentally that the factor Kp be restricted to minimum value of 0.75 for improved convergence, and it is independent of size of a6 system.

[055] Said inaccuracy in prior art loadflow models SDLXB and SDLBX in respect of sub-set of equations corresponding to PV-nodes in system of equation (1), is corrected by overlap calculation and updating of PV-nodes voltage angles in Q-V subproblem in addition to regular calculation and updating in P-0 subproblem, leading to improved convergence of the NFSDL
method in the presence of large R/X ratio branches in the power network, and consequent efficiency gain and increased reliability of obtaining converged solution over wide range of network parameters and operating conditions.

[056] Fast Super Decoupled Loadflow (FSDL) model consists of equations (3) to (10), and (23) to (28).

RPp = APP / (KpVp) (23) YOpq = -Ypq -for branch r/x ratio <_ 2.0 -(Bpq + 0.9(Ypq Bpq)) -for branch r/x ratio > 2.0 -Bpq -for branches connected between two PV-nodes or a PV-node and the slack-node (24) YVpq = rypq -for branch r/x ratio <_ 2.0 Bpq + 0.9(Ypq-Bpq)) -for branch r/x ratio > 2.0 (25) YOpp = Y--YOpq and YVpp = -2bp + Y--YVpq (26) q>p q>p bp' = b0Cos(Dp or bp' = by (27) Kp = Absolute (Bpp/YOpp) (28) [057] Branch admittance magnitude in (24) and (25) is of the same algebraic sign as its susceptance. Elements of the two gain matrices differ in that diagonal elements of [YV]
additionally contain the b' values given by equation (27) and in respect of elements corresponding to branches connected between two PV-nodes or a PV-node and the slack-node. In two simple variations of the FSDL model, one is to make YVpq=YOpq and the other is to make YOpq=YVpq.

[058] The steps of loadflow computation method FSDL 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. Double lettered steps indicate the inventive characteristic steps of the FSDL method. The words "Read system data" in Step-aa correspond to step-10 and step-20 in Fig. 5, and step-14, step-20, step-32, step-44, step-50 in Fig. 6. All other steps in the following correspond to step-30 in Fig.5, and step-60, step-62, and step-64 in Fig. 6.

aa. Read system data and assign an initial approximate solution. If better solution estimate is not available, set all the nodes voltage magnitudes and angles equal to those of the slack-node. This is referred to as the slack-start.
b. Form nodal admittance matrix, and Initialize iteration count ITRP = ITRQ= r = 0.
bc. Compute sine and cosine of rotation angles using equations (9) and (10), and store them.
If Cos(Dp < Cos (-36 ), set CosD0 = Cos (-36 ) and SinDp = Sin (-36 ).
cc. Form (m+k) x (m+k) size gain matrices [YO] and IYV I of (1) and (2) respectively each in a compact storage exploiting sparsity, using equations (24) to (27). In [YV]
matrix, replace diagonal elements corresponding to PV-nodes by very large value, say, 10.010.
Factorize [Y0] and [YVI using the same ordering of nodes regardless of node-types and store them using the same indexing and addressing information.
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-m. Otherwise follow the next step.

ee. Compute the vector of modified residues [RP] using (7) for PQ-nodes, and using (23) and (28) for PV-nodes.

f. Solve (3) for [A0] and update voltage angles using, [0] = [0] + [A0].
fg. Set voltage magnitudes of PV-nodes equal to the specified values.

g. Increment the iteration count ITRP=ITRP+1 and r=(ITRP+ITRQ)/2.
h. Compute residues [AP] at PQ- and PV-nodes and [AQ] at PQ-nodes only. If all are less than the tolerance (s), proceed to step-m. Otherwise follow the next step.
i. Compute the vector of modified residues [RQ] using (8) for only PQ-nodes.
jj. Solve (5) for [AV] and update PQ-node magnitudes using [V] = [V] + [AV].
While solving equation (5), skip all the rows and columns corresponding to PV-nodes, or stated alternatively, rows and columns corresponding to PV-nodes in factorized gain matrix [YV] are skipped from processing while calculating [AV] in Q-V sub-problem.
k. 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 described in "LTC Transformers and MVAR
violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9, PP.

3332, September 1982".
1. Increment the iteration count ITRQ=ITRQ+1 and r=(ITRP+ITRQ)/2, and Proceed to step-d.
in. 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.

[059] Novel Fast Super Decoupled Loadflow (NFSDL) Model consists of equations (3) to (11) with RQp calculated by equation (8) negated as seen from Fig. 4c, (29) to (31) and (27). Branch admittance magnitude in (29) is of the same sign as its susceptance.

YOpq = -Ypq -for branch r/x ratio <_ 2.0 -(Bpq + 0.9(Ypq Bpq)) -for branch r/x ratio > 2.0 -Bpq -for branches connected between two PV-nodes or a PV-node and the slack-node (29) YVpq = Gpq -for branches connected to a PQ-node & a PV-node -YOpq -for branches connecting PQ-nodes -Bpq -for branches connecting two PV-nodes or a PV-node and the slack-node (30) YOpp = r-YOpq and YVpp = 2bp' - YOpp -for PQ-nodes [bp'-q>p -for PV-nodes (31) [060] The steps of loadflow computation method NFSDL are shown in the flowchart of Fig. 3.
Referring to the flowchart of Fig.3, different steps are elaborated in steps marked with similar letters in the following. Triple lettered steps indicate the inventive characteristic steps of the NFSDL method. The words "Read system data" in Step-aa correspond to step-10 and step-20 in Fig. 5, and step-14, step-20, step-32, step-44, step-50 in Fig. 6. All other steps in the following correspond to step-30 in Fig.5, and step-60, step-62, and step-64 in Fig. 6.

aa. Read system data and assign an initial approximate solution. If better solution estimate is not available, set all the nodal voltage magnitudes and angles equal to those of the slack-node. This is referred to as the slack-start.
b. Form nodal admittance matrix, and Initialize iteration count ITRP = ITRQ= r = 0 be. Compute sine and cosine of rotation angles using equations (9) and (10), and store them.
If Cos(Dp < Cos (-36 ), set Cos(Dp = Cos (-36 ) and Sinop = Sin (-36 ).
ccc. Form (m+k) x (m+k) size gain matrices [YO] and [YV] of (1) and (2) respectively each in a compact storage exploiting sparsity using equations (29) to (31), and (27) Factorize [YO] and [YV] using the same ordering of nodes regardless of node-types and store them using the same indexing and addressing information.
d. Compute residues [AP] at PQ- and PV-nodes, and [AQ] at only PQ-nodes. If all are less than the tolerance (E), proceed to step-m. Otherwise follow the next step.
e. Compute the vector of modified residues [RP] using (7) for PQ-nodes and using (11) for PV-nodes.
f. Solve (3) for [AO] and update voltage angles using, [0] = [0] + [AO].
fg. Set voltage magnitudes of PV-nodes equal to the specified values.

g. Increment the iteration count ITRP=ITRP+1 and r=(ITRP+ITRQ)/2.

h. Compute residues [AP] at PQ- and PV-nodes, and IAQ] at PQ-nodes only. If all are less than the tolerance (E), proceed to step-m. Otherwise follow the next step.
iii. Compute the vector of modified residues [RQ] using (8) for PQ-nodes with each element negated, and using (11) for PV-nodes.
jjj. Solve (5) for [AV at PQ-nodes, AO at PV-nodes] and update PQ-node magnitudes using [V] = [V] + [AV] and PV-node angles using [0] = [0] + [A0]. While solving equation (5), skip all the columns corresponding to PV-nodes in back substitution part of the calculation of correction sub-vector [AV].
k. 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 described in "LTC Transformers and MVAR
violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9, PP.

3332, September 1982".
Increment the iteration count ITRQ=ITRQ+1 and r=(ITRP+ITRQ)/2, and Proceed to step-d.
in. 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.

[061] The illustration of Fig.4 and particularly that of Fig.4c helps understand the characteristic triple lettered steps-ccc, iii, and jjj in calculation steps for the solution of NFSDL model, which is characterized in calculation of voltage angle corrections at PV-nodes along with voltage magnitude corrections at PQ-nodes in Q-V sub-problem in addition to regular voltage angle corrections in P-0 sub-problem. It should be noted that -B's in Fig.4b and B's in Fig.4c are not the actual transformed quantities of gain matrices [YO] and [YV] defined in step-ccc, but they are retained from Fig.4a. It should also be noted that double-lettered steps are the characteristic of calculation steps for the solution of FSDL model.

[062] It is a further inventive step that all the loadflow models described in the above can be organized to produce corrections to the initial approximate/guess solution or global corrections by storing modified real and reactive power mismatch vectors [RP] and [RQ] of the current iteration and adding them to the vectors [RP] and [RQ] of the next iteration. Such inventive step involves storage of the vectors of modified residues and replacing the equations (7), (8), (11), (23), (4) and (6) respectively by (32), (33), (34), (35), (36) and (37). Superscript `0' in equations (36) and (37) indicates the initial solution estimate.

RPpr = (APprCos(Dp + AQpr Sin(Dp)/Vpr + RPpr r 1 ) (32) RQpr = (-APpFSin(Dp + AQpr Cos(Dp)/Vpr + RQp~ r-I) (33) RPPr = APpr /Vpr + RPp( r-I) (34) RPpr = APpr /(KpVpr) + RPpr-1) (35) Apr=Op +A6pr (36) Vpr = V p + AV pr (37) [063] The inventive FSDL and NFSDL models can be restated from polar coordinates to rectangular coordinates. This involves following changes in the equations describing the loadflow models formulated in polar coordinates.

(i) Replace 0 and AO respectively by f and Af in equations (1), (3), (4) and (36) (ii) Replace V and AV respectively by e and Ae in equations (2), (5), (6) and (37) (iii) Replace VP by ep or es in equations (7), (8), (11), (23), (32), (33), (34) and (35). The subscript 's' indicates the slack-node variable.

(iv) After calculation of corrections to the imaginary part of complex voltage (Af) of PV-nodes and updating the imaginary component (f) of PV-nodes, calculate real component by:

ep = VSp2 - fp2 (38) [064] 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.

[065] 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.

REFERENCES
Foreign Patent Document 1. US Patent Number: 4868410 dated September 19, 1989: "System of Load Flow Calculation for Electric Power System"
2. US Patent Number: 5081591 dated January 14, 1992: "Optimizing Reactive Power Distribution in an Industrial Power Network"

Other Publications 3. R.N.Allan and C.Arruda, "LTC Transformers and MVAR violations in the Fast Decoupled Load Flow", IEEE Trans., PAS-101, No.9, PP. 3328-3332, September 1982.
4. N.R.Rao and G.M.Krishna, "A new decoupled model for state estimation of power systems", IFAC Symposium on Theory and Application of Digital Control,vol.2, 5-January 1982, New Delhi, India.
5. P.H.Haley and M.Ayres, "Super Decoupled Loadflow with distributed slack bus", IEEE
Trans., Vol.PAS-104, pp.104-113, January 1985.
6. Robert A.M. Van Amerongen, "A general-purpose version of the Fast Decoupled Loadflow", IEEE Transactions, PWRS-4, pp.760-770, May 1989.
7. S.B.Patel, "Fast Super Decoupled Loadflow", IEE proceedings Part-C, Vol.139, No.1, pp.
13-20, January 1992.
8. P.E.Crouch, D.J.Tylavsky, H.chen, L.Jarriel, and R.Adapa, "Critically coupled algorithms for solving the Power Flow equation", IEEE Trans., Vol.PWRS-7, pp.451-457, February 1992.

Claims

1. A method of forming/defining and solving a loadflow computation model of a power network to affect control of voltages and power flows in a power system, comprising the steps of:
obtaining on-line or 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, 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, initiating loadflow computation with initial approximate/guess solution of the same voltage magnitude and angle as those of the reference/slack node for all the PQ-nodes and the PV-nodes, and said initial approximate/guess solution is referred to as a slack-start, forming and storing factorized gain matrices [Y.theta.] and [YV] using the same indexing and addressing information for both as they are of the same dimension and sparsity structure, wherein said [Y.theta.] relate vector of modified real power mismatches [RP]
to angle corrections vector [.DELTA..theta.] in equation [RP] =[Y.theta.]
[.DELTA..theta.] referred to as P-.theta.
sub-problem, and said ¦YV] relate vector of modified reactive power mismatches [RQ] to voltage magnitude corrections vector [.DELTA.V] in equation [RQ] =[YV]
[.DELTA.V]
referred to as Q-V sub-problem, restricting transformation/rotation angle .PHI.P at node-p to maximum -36° in determining transformed real power mismatch as .DELTA.P p'= .DELTA.P p Cos.PHI.p +
.DELTA.Q p Sin.PHI.p, and transformed reactive power mismatch as .DELTA.Q p'= .DELTA.Q p Cos.PHI.p-.DELTA.P p Sin.PHI.p wherein .DELTA.P p is real power mismatch at node-p and .DELTA.Q p is reactive power mismatch at node-p, calculating modified real power mismatch at node-p as RP p= .DELTA.P p'/V p and modified reactive power mismatch at node-p as RQ p= .DELTA.Q p'/V p for PQ-nodes, and calculating modified real power mismatch at node-p as RP p= .DELTA.P p/V p for PV-nodes;
wherein V p is voltage magnitude at node-p, performing loadflow computation by solving a super decoupled loadflow model of the power network defined by set of equations [RP] =[Y.theta.] [.DELTA..theta.]
and [RQ] =[YV] [.DELTA.V]
employing successive (1.theta., 1V) iteration scheme, wherein each iteration involves one calculation of [RP] and [.DELTA..theta.] to update voltage angle vector [.theta.] and then one calculation of [RQ] and [.DELTA.V] to update voltage magnitude vector [V], to calculate values of the voltage angle and the voltage magnitude at PQ-nodes, voltage angle and reactive power generation at PV-nodes, and turns ratio of tap-changing transformers in dependence the set of said obtained-online readings, or given/scheduled/specified/set values of controlled variables/parameters and physical limits of operation of the power network components, evaluating loadflow computation for any over loaded components of the power network and for under/over voltage at any of the nodes of the power network, correcting one or more controlled variables/parameters and repeating the performing loadflow computation by decomposing, initializing, solving, adding, counting, storing, evaluating, and correcting steps until evaluating step finds no over loaded components and no under/over voltages in the power network, and affecting a change in power flow through components 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 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.

2. A method as defined in claim-1 wherein loadflow computation is referred to as involving formation and solution of Fast Super Decoupled Loadflow model when characterized in calculating modified real power mismatch at a node-p which is a PV-node by RP p = .DELTA.P p I (K p V p) (23) Where, K p = Absolute (B pp/Y.theta.pp) (28) and wherein B pp is the imaginary part of a diagonal element of the nodal admittance matrix without network shunts and Y.theta.pp is a corresponding diagonal element of the gain matrix [Y.theta.].

3. A method as defined in claim-1 wherein loadflow computation involving formation and solution of said Super Decoupled Loadflow model or in claim-2 wherein loadflow computation involving formation and solution of said Fast Super Decoupled Loadflow model is further characterized in that rows and columns corresponding to PV-nodes in factorized gain matrix [YV] are skipped from processing while calculating [.DELTA.V] in Q-V
sub-problem.

4. A method as defined in claim-1 wherein loadflow computation is referred to as formation and solution of Novel Fast Super Decoupled Loadflow model when characterized in calculation of the voltage angle corrections at PV-nodes along with voltage magnitude corrections at PQ-nodes in Q-V sub-problem in addition to regular voltage angle corrections in P-.theta. sub-problem.

5. A method as defined in claim-1, or claim-2, or claim-3, or claim-4 wherein loadflow computation is further characterized in producing corrections to initial approximate/guess solution or alternatively global corrections in all iterations by storing modified real and reactive power mismatch vectors [RP] and [RQ] of the current iteration and adding them to the vectors [RP] and [RQ] of the next iteration.