CA2661753A1 - Method of loadflow computation for electrical power system - Google Patents
Method of loadflow computation for electrical power system Download PDFInfo
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- CA2661753A1 CA2661753A1 CA002661753A CA2661753A CA2661753A1 CA 2661753 A1 CA2661753 A1 CA 2661753A1 CA 002661753 A CA002661753 A CA 002661753A CA 2661753 A CA2661753 A CA 2661753A CA 2661753 A1 CA2661753 A1 CA 2661753A1
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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- Y02E40/30—Reactive power compensation
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Abstract
A method of performing loadflow calculations for controlling voltages and power flow in a power network by reading on-line data of given/specified/scheduled/set network variables/parameters and using control means, so that no component of the power network is overloaded as well as there is no over/under voltage at any nodes in the network following a small or large disturbances. A loadflow calculation method could be any method including invented Patel Decoupled Loadflow (PDL) method, and Decoupled Gauss-Seidel-Patel Loadflow (DGSPL) method. The invented Patel Decoupled Loadflow (PDL) calculation method is characterized in 1) the use of the same coefficient matrix [GB] for both the p-f and q-e sub-problems of the loadflow calculation; 2) almost no effort in the modified mismatch calculations in the iteration process; and 3) all the nodes in both the sub-problems being active, no refactorization of [GB] required for implementation of Q-limit violations. These features make the invented PDL method computationally almost two times more efficient than the current state-of-the-art Super Super Decoupled Loadflow (SSDL) method. It is also possible to organize the RP-f, and RQ-e sub-problems for solution by Gauss-Seidel iterations. The invented DGSPL calculation method is characterized in decoupling the calculation of real and imaginary components of complex node voltage leading to increased stability and efficiency of the DGSPL calculation method.
Claims (8)
1. A method of forming/defining and solving a model of the power network to effect control of voltages and power flows in a power system, comprising the steps of:
obtaining on-line/simulated data of open/close status of switches and circuit breakers in the power network, and reading data of operating limits of the network components including PV-node, a generator-node where Real-Power-P and Voltage-Magnitude-V are scheduled/specified/set, generators maximum and minimum reactive power generation capability limits and transformers tap position limits, obtaining on-line readings of scheduled/specified/set real and reactive power at PQ-nodes, the load-nodes where Real-Power-P and Reactive-Power-Q are scheduled/specified/set, real power and voltage magnitude at PV-nodes, voltage magnitude and angle at the reference/slack node, and transformer turns ratios, which are the controlled variables/parameters, defining loadflow calculation method as Patel Decoupled Loadflow (PDL) when loadflow caculation model is characterized by equations, [RP] = [GB] [f] (51) [RQ] = [GB] [e] (52) wherein, each component of [RP], [RQ], and [GB] are defined by, RP p = [(I1p PSH p + I2p QSH p)/f p] - [I1p(G pp+g p) - I2p(B pp+b p)]e p2/f p - (e p/f p) .SIGMA. (I lp G pq - I2p B pq)e q + (e p/f p) .SIGMA. (I2p G pq +
I lp B pq)f q - .SIGMA. (I2p G pq + I lp B pq)e q (53) q>p q>p q>p RQ p = [(I lp PSH p + I2p QSH p)/e p] - [I lp(G pp+g p) - I2p(B pp+b p)]f p2/e p - (f p/e p) .SIGMA. (I lp G pq - I2p B pq)f q - (f p/e p) .SIGMA. (I2p G pq +
I lp B pq)e q + .SIGMA. (I2p G pq + I lp B pq)f q (54) q>p q>p q>p GB pq = I lp G pq - I2p B pg (55) GB pp = [I lp(G pp + g p) - I2p(B pp + b p)] (56) wherein, equations (51) and (52), which represent decoupled sub-problems of the loadflow problem, can be written for solving each linearized sub-problem by Guass-Seidel method as equations (57) and (58) respectively, wherein, e p and f p are the real and imaginary parts of the complex voltage V
p of node-p, PSH p and QSH p are scheduled/specified/set values, except that QSH p at a PV-node is calculated value using specified voltage magnitude constrained by upper and lower reactive power generation capability limits of a PV-node generator, G pq, G pp, and B pq , B pq are off-diagonal and diagonal elements of real and imaginary parts of the complex admittance matrix of the network respectively, and g p, b p are real and imaginary components of network admittance shunts, q>p indicates node-q is the node adjacent directly connected to node-p excluding the case of q=p, n is the number of nodes in network, superscript 'r' indicates the iteration count, and factors I1p & I2p can take any values from -.infin., ..., -2, -1, 0, 1, 2, ..., .infin..
performing load-flow calculation by initiating it with approximate/guess solution to calculate complex voltages or its real and imaginary components or voltage magnitude corrections and voltage angle corrections at the power network nodes providing for the calculation of power flowing through different network components, and reactive power generation and transformer tap-position indications, evaluating loadflow calculation for any of the over loaded power network components and for under/over voltage at any of the network nodes, correcting one or more controlled parameters and repeating the performing loadflow calculation by decomposing, initializing, and evaluating, and correcting steps until evaluating step finds no over loaded components and no under/over voltages in the power network, and effecting a change in the power flowing through network components 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 alternatively a power network without any overloaded components and under/over voltages, which finally obtained controlled variables/parameters however are stored in case of simulation for acting upon fast in case the simulated event actually occurs.
obtaining on-line/simulated data of open/close status of switches and circuit breakers in the power network, and reading data of operating limits of the network components including PV-node, a generator-node where Real-Power-P and Voltage-Magnitude-V are scheduled/specified/set, generators maximum and minimum reactive power generation capability limits and transformers tap position limits, obtaining on-line readings of scheduled/specified/set real and reactive power at PQ-nodes, the load-nodes where Real-Power-P and Reactive-Power-Q are scheduled/specified/set, real power and voltage magnitude at PV-nodes, voltage magnitude and angle at the reference/slack node, and transformer turns ratios, which are the controlled variables/parameters, defining loadflow calculation method as Patel Decoupled Loadflow (PDL) when loadflow caculation model is characterized by equations, [RP] = [GB] [f] (51) [RQ] = [GB] [e] (52) wherein, each component of [RP], [RQ], and [GB] are defined by, RP p = [(I1p PSH p + I2p QSH p)/f p] - [I1p(G pp+g p) - I2p(B pp+b p)]e p2/f p - (e p/f p) .SIGMA. (I lp G pq - I2p B pq)e q + (e p/f p) .SIGMA. (I2p G pq +
I lp B pq)f q - .SIGMA. (I2p G pq + I lp B pq)e q (53) q>p q>p q>p RQ p = [(I lp PSH p + I2p QSH p)/e p] - [I lp(G pp+g p) - I2p(B pp+b p)]f p2/e p - (f p/e p) .SIGMA. (I lp G pq - I2p B pq)f q - (f p/e p) .SIGMA. (I2p G pq +
I lp B pq)e q + .SIGMA. (I2p G pq + I lp B pq)f q (54) q>p q>p q>p GB pq = I lp G pq - I2p B pg (55) GB pp = [I lp(G pp + g p) - I2p(B pp + b p)] (56) wherein, equations (51) and (52), which represent decoupled sub-problems of the loadflow problem, can be written for solving each linearized sub-problem by Guass-Seidel method as equations (57) and (58) respectively, wherein, e p and f p are the real and imaginary parts of the complex voltage V
p of node-p, PSH p and QSH p are scheduled/specified/set values, except that QSH p at a PV-node is calculated value using specified voltage magnitude constrained by upper and lower reactive power generation capability limits of a PV-node generator, G pq, G pp, and B pq , B pq are off-diagonal and diagonal elements of real and imaginary parts of the complex admittance matrix of the network respectively, and g p, b p are real and imaginary components of network admittance shunts, q>p indicates node-q is the node adjacent directly connected to node-p excluding the case of q=p, n is the number of nodes in network, superscript 'r' indicates the iteration count, and factors I1p & I2p can take any values from -.infin., ..., -2, -1, 0, 1, 2, ..., .infin..
performing load-flow calculation by initiating it with approximate/guess solution to calculate complex voltages or its real and imaginary components or voltage magnitude corrections and voltage angle corrections at the power network nodes providing for the calculation of power flowing through different network components, and reactive power generation and transformer tap-position indications, evaluating loadflow calculation for any of the over loaded power network components and for under/over voltage at any of the network nodes, correcting one or more controlled parameters and repeating the performing loadflow calculation by decomposing, initializing, and evaluating, and correcting steps until evaluating step finds no over loaded components and no under/over voltages in the power network, and effecting a change in the power flowing through network components 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 alternatively a power network without any overloaded components and under/over voltages, which finally obtained controlled variables/parameters however are stored in case of simulation for acting upon fast in case the simulated event actually occurs.
2. A loadflow calculation as defined in claim-1 is referred to as Decoupled Gauss-Seidel-Patel Loadflow (DGSPL) calculation method, when the DGSPL calculation model is characterized by following set of equations, which represents similar complex simultaneous equations appearing in other subject areas whose real and imaginary components added as in equation (32) and then decoupled for simultaneous or successive solution, I1p PSH p+I2p QSH p = A p(e p2+f p2) + e p.SIGMA.(I1p BB1p I2p BB2p) + f p.SIGMA.(I2p BB1p+I1p BB2p) (32) q>p q>p Where, A p = I1p (G pp + g p) - I2p (B pp + b p) (33) BB1p = (e q G pq - f q B pq) (34) BB2p = (f q G pq + e q B pq) (35) now, equation (32) can be decoupled into two quadratic equations as, A1p e p2 + B1p e p + C1p = 0 (36) A2p f p2 + B2p f p + C2p = 0 (37) Where, A1p = A2p = A p (38) B lp = .SIGMA. (I1p BB1p - I2p BB2p) (39) q >p B2p = .SIGMA. (I2p BB1p + I1p BB2p) (40) q >p C lp = A2p f p2 + B2p f p - (I1p PSH p + I2p QSH p) (41) C2p = A lp e p2 + B lp e p - (I1p PSH p + I2p QSH p) (42) where, PSH p and QSH p are scheduled or specified values, except that QSH p at a PV-node is calculated value using specified voltage magnitude constrained by upper and lower reactive power generation capability limits of a PV-node generator, and equations (36) and (37) can be iterated incorporating self-iteration for solution as, (e p(sr+1))(r+1) = [{-C1p / ((e p)sr) r } - (B lp)r) / A lp (43) (f p(sr+1))(r+1) = [{-C2p / ((f p)sr) r } - (B2p)r~] / A2p (44) and also equations (36) and (37), which are quadratic in e p and f p, can also be iterated without incorporating self-iteration for solution as, e p(r+1) = (-B1p r + SQRT ((B1p r)2 - 4A lp C lp)) / 2A l (45) f p(r+l) = (-B2p r + SQRT ((B2p r)2 - 4A2p C2p)) / 2A2 (46) wherein, the words SQRT means take square root of the expression enclosed in parenthesis immediately following words SQRT, equations (36), (43) or (45) and (37), (44) or (46) can be solved simultaneously or successively, and successive mode either first (36), (43) or (45) and, then (37), (44) or (46) or first (37), (44) or (46) and, then (36), (43) or (45) are solved alternately, and further e p(r+1) and f p(r+1) values calculated by (43) or (45) and (44) or (46) are modified as, e p (r+l) = e P (r+l) + .beta. .about.e p(r+l) (47) f p(r+l) = f p(r+l) + .beta. .about.f p(r+l) (48) Where, .about.e p(r+l) = e p(r+l) - e p r (49) .about.f p(r+l) = f p(r+l) - f p r (50) and .beta. is an acceleration factor used to speed-up the convergence, and .about.e p(r+l) and .about.f p(r+l) are the corrections in the real and imaginary parts of the voltage at node-p in the (r+l)th iteration, and wherein, e p and f p are real and imaginary parts of complex voltage at node-p, G pq, G pp, and B pq, B pp are off-diagonal and diagonal elements of real and imaginary parts of the complex admittance matrix of the network respectively, and g p, b p are real and imaginary components of network admittance shunts, r is iteration count, and factors I1p & I2p can take any values from -.infin., ..., -2, -1, 0, 1, 2, ..., .infin..
3. A simple system for controlling generator and transformer voltages in an electrical power utility containing 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 Decoupled Loadflow calculation models of the power network characterized in claim-1 and claim-2 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 set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and physical limits of operation of the network components, machine control means connected to the said means defining and solving one of the decoupled loadflow calculation models of the power network characterized in claim-1 and claim-2 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 one of the Decoupled Loadflow calculation models of the power network in dependence on the set of obtained-online readings or scheduled/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 one of the Decoupled Loadflow calculation models of the power network characterized in claim-1 and claim-2 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 Decoupled Loadflow calculation model of the power network in dependence on the set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and operating limits of the tap-changing elements.
means defining and solving one of the Decoupled Loadflow calculation models of the power network characterized in claim-1 and claim-2 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 set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and physical limits of operation of the network components, machine control means connected to the said means defining and solving one of the decoupled loadflow calculation models of the power network characterized in claim-1 and claim-2 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 one of the Decoupled Loadflow calculation models of the power network in dependence on the set of obtained-online readings or scheduled/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 one of the Decoupled Loadflow calculation models of the power network characterized in claim-1 and claim-2 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 Decoupled Loadflow calculation model of the power network in dependence on the set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and operating limits of the tap-changing elements.
4. A system as defined in claim-3 wherein the power network includes a plurality of nodes each connected to at least one of: a slack/reference generator; a rotating machine;
and an electrical load, and the said means defining and solving one of the Decoupled Loadflow calculation models of the power network receives representations of selected values of the real and reactive power flow from each machine and to each load, and the model is operative for producing calculated values for the reactive power quantity to be produced or absorbed by each machine.
and an electrical load, and the said means defining and solving one of the Decoupled Loadflow calculation models of the power network receives representations of selected values of the real and reactive power flow from each machine and to each load, and the model is operative for producing calculated values for the reactive power quantity to be produced or absorbed by each machine.
5. A system as defined in claim-4 wherein the power network further has at least one transformer having an adjustable transformer turns ratio, and the said means defining and solving Decoupled Loadflow calculation models of the power network is further operative for producing a calculated value of the transformer transformation/turns ratio.
6. A system as defined in claim-3 wherein said machine control means are connected to said excitation element of each machine for controlling the operation of the excitation element of each machine, and wherein said transformer turns ratio control means are connected to said transformer tap changing element of each transformer for controlling the operation of the tap changing element of each transformer.
7. A method for controlling generator and transformer voltages in an electrical power utility containing plurality of electromechanical rotating machines, transformers and electrical loads connected in a network, each machine having a reactive power characteristic and excitation element which is controllable for adjusting the reactive power generated or absorbed by the machine, and some of the transformers each having tap changing element which is controllable for adjusting turns ratio or alternatively terminal voltage of the transformer, said method comprising:
creating and solving any of the said Decoupled Loadflow calculation models of the power network as characterized in claim-1 and claim-2 for providing an indication of turns ratio of each of the tap-changing transformers and the quantity of reactive power to be supplied by each generator in dependence on the set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and physical limits of operation of the network components, controlling the operation of the excitation elements of machines to produce or absorb the amount of reactive power, and controlling tap changing elements of transformers to adjust transformer turns ratio indicated by means creating/forming/defining and solving any of the said Decoupled Loadflow calculation models as characterized in claim-1 and claim-2 in dependence on the set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and physical limits of operation of the network components.
creating and solving any of the said Decoupled Loadflow calculation models of the power network as characterized in claim-1 and claim-2 for providing an indication of turns ratio of each of the tap-changing transformers and the quantity of reactive power to be supplied by each generator in dependence on the set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and physical limits of operation of the network components, controlling the operation of the excitation elements of machines to produce or absorb the amount of reactive power, and controlling tap changing elements of transformers to adjust transformer turns ratio indicated by means creating/forming/defining and solving any of the said Decoupled Loadflow calculation models as characterized in claim-1 and claim-2 in dependence on the set of obtained-online readings or scheduled/specified/set controlled network variables/parameters, and physical limits of operation of the network components.
8. A method as defined in claim-9 wherein said step of controlling is carried out to control the excitation element of each machine and a said step of controlling is carried out to control the tap-changing element of each controllable transformer.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA2661753A CA2661753C (en) | 2006-08-26 | 2007-08-27 | Method of loadflow computation for electrical power system |
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| Application Number | Priority Date | Filing Date | Title |
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| CANONE | 2006-11-30 | ||
| CA2661753A CA2661753C (en) | 2006-08-26 | 2007-08-27 | Method of loadflow computation for electrical power system |
| PCT/CA2007/001537 WO2008025162A1 (en) | 2007-08-27 | 2007-08-27 | System and method of loadflow calculation for electrical power system |
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| CA2661753A1 true CA2661753A1 (en) | 2008-03-06 |
| CA2661753C CA2661753C (en) | 2011-10-11 |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103198205A (en) * | 2013-02-25 | 2013-07-10 | 中国电力科学研究院 | Initial value calculation method suitable for large-scale data load flow calculation |
| CN112417363A (en) * | 2020-11-11 | 2021-02-26 | 深圳供电局有限公司 | Load analysis method and system for transformer substation |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US11853384B2 (en) | 2014-09-22 | 2023-12-26 | Sureshchandra B. Patel | Methods of patel loadflow computation for electrical power system |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103198205A (en) * | 2013-02-25 | 2013-07-10 | 中国电力科学研究院 | Initial value calculation method suitable for large-scale data load flow calculation |
| CN112417363A (en) * | 2020-11-11 | 2021-02-26 | 深圳供电局有限公司 | Load analysis method and system for transformer substation |
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