CN113489013A - AQ node-based available transmission capacity calculation method - Google Patents

AQ node-based available transmission capacity calculation method Download PDF

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CN113489013A
CN113489013A CN202110794168.4A CN202110794168A CN113489013A CN 113489013 A CN113489013 A CN 113489013A CN 202110794168 A CN202110794168 A CN 202110794168A CN 113489013 A CN113489013 A CN 113489013A
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node
power
load
generator
nodes
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任宾
周建平
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State Grid Jiangsu Electric Power Co Ltd
Maintenance Branch of State Grid Jiangsu Electric Power Co Ltd
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State Grid Jiangsu Electric Power Co Ltd
Maintenance Branch of State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention provides an available transmission capacity calculation method based on AQ nodes, which comprises the following steps: 1) obtaining a basic power grid flow parameter; 2) initializing power grid flow parameters; 3) setting a load type as a constant power factor load, and setting a system node N as an AQ node; 4) setting the increasing modes of the generator and the load; 5) increasing the load active power, performing load flow calculation by a Newton-Raphson method, and judging whether the load flow calculation iteration is converged; 6) the load flow calculation mode is changed from a Newton-Raphson method to an AQ node-based method; 7) obtaining the increased active power P of the node NN(ii) a 8) Active power P increased by node NNUpdating active power of other load nodes and generator nodes, and performing load flow solving again; 9) increasing the phase angle difference between the node N and the balance node, and repeating the steps 6), 7) and 8) until the node is connectedN increased active power PNUntil the limit is out of limit; 10) outputting a tide solution; 11) and outputting the available transmission capacity.

Description

AQ node-based available transmission capacity calculation method
Technical Field
The invention relates to the technical field of power transmission and distribution of a power system, in particular to an available transmission capacity calculation method based on AQ nodes.
Background
Under the modern electric power market environment, Available Transmission Capacity (ATC) is not only an influencing factor of transmission system management, but also a technical index for a dispatcher to maintain the safe and stable operation of the system, and meanwhile, the ATC has the function of a market signal and is a reference for market participants to perform related commercial activities; therefore, how to solve the ATC more accurately has become an important part of the electric power market research.
At present, the ATC calculation considering the voltage stability constraint usually adopts a Continuous Power Flow (CPF) method, the method can continuously change the transmission power from a generator group to a load group in a power flow equation, and the sick problem of a Jacobian matrix when the parameter of the conventional power flow equation is close to a limit value is solved by adding continuous parameters to the conventional power flow equation; however, the CPF includes two steps of prediction and correction, so that an additional solution to a nonlinear equation system is required, and in the correction step, the CPF still needs to solve the problem of the yagar ratio matrix groove cake near the maximum load point; when generator constraint is taken into consideration, the conventional calculation method converts the node where the out-of-limit generator is located into a PQ node from a PV node after the reactive power is out of limit, and the reactive power of the generator keeps the limit value constant.
Disclosure of Invention
The invention provides an available transmission capacity calculation method based on AQ nodes, and aims to solve the problems that when available transmission capacity is calculated based on a CPF method, a primary nonlinear equation system needs to be solved additionally in a correction step, and a Jacobian matrix channel cake near a maximum load point needs to be solved.
The technical solution of the invention is as follows: an available transmission capacity calculation method based on an AQ node comprises the following steps:
(1) obtaining a basic power grid flow parameter of a power system;
(2) initializing power grid flow parameters;
(3) setting a load type as a constant power factor load, and setting a system node N as an AQ node;
(4) setting the increasing modes of a generator and a load from the initial operation point of the power system;
(5) increasing the load active power, jumping into a node switching judgment stator program after considering the constraint of exciting current and armature current, carrying out load flow calculation by a Newton-Raphson method, and judging whether the iteration of the load flow calculation is converged; if the iteration of the power flow calculation is converged, continuing to operate the step (5), and if the iteration of the power flow calculation is not converged, operating the step (6);
(6) the load flow calculation mode is changed from a Newton-Raphson method to an AQ node-based method;
(7) increasing the phase angle difference between the node N (AQ node) and the balance node to obtain the active power P after the node N (AQ node) is increasedN；
(8) The active power P increased by the node N (AQ node) in the step 7)NUpdating active power of other load nodes and generator nodes, jumping into a node switching judgment subprogram after considering the constraint of exciting current and armature current, and carrying out load flow solution again by using updated node data;
(9) determining active power P of node N (AQ node) after increaseNWhether the limit is out of limit or not, if so, jumping to the step (10); otherwise, repeating the steps (6), (7) and (8) until the active power P after the node N (AQ node) is increasedNUntil the limit is out of limit;
(10) outputting a tide solution;
(11) available power transmission capacity under stable output voltage conditions.
Further, the power flow parameters of the power grid in the step (1) include voltage amplitude and phase angle of each node, active power and reactive power of a generator of each node, load active power and reactive power of each node, admittance matrix of the node, and active power and reactive power of a transmission line.
Further, the initializing of the power grid flow parameter in the step (2) specifically includes: setting control variables (including voltage amplitude and phase angle of each node), state variables (active power and reactive power of a generator, load active power and reactive power), upper and lower limits of the active power and reactive power of the generator, upper and lower limits of the active power and reactive power of load nodes, maximum transmission capacity of a line and upper and lower limits of the voltage amplitude of each node.
Further, the load type is set to be a constant power factor load in the step (3), specifically as shown in formula (1):
Figure BDA0003162237180000031
in the formula, QlIs the reactive power of the node i and,
Figure BDA0003162237180000032
is the power factor angle, l is the constant power load node number, NpThe nodes are initially numbered for constant power load, N is the total number of the nodes of the power grid, PlAnd loading active power for the power receiving area.
Further, in the step (4), starting from the initial operation point of the power system, the increase modes of the generator and the load are set, wherein the active power P of the load (except the node N) in the power receiving area islActive power P through node N (AQ node)NThe growth is carried out, specifically shown in formula (2):
Figure BDA0003162237180000033
in the formula, alphalProportional coefficient for load increase, Pl 0And
Figure BDA0003162237180000041
initial active power of load l and node N (AQ node), respectively, wherein active power P of node N (AQ node)NThe increase of (2) can be realized by continuously increasing the phase angle difference value between the node N (AQ node) and the balance node until reaching the voltage stabilization critical point, wherein l is the constant power load node number, and N is the constant power load node numberpThe nodes are initially numbered for constant power load nodes, and N is the total number of the nodes of the power grid;
increased load through increased transmission area generator node 1 to node NGThe active output of the generator in the power transmission region is balanced, and the active output of the generator in the power transmission region increases in a manner shown in formula (3):
Figure BDA0003162237180000042
in the formula, P1To balance the active power of the nodes, betakFor the scaling factor of the generator to increase,
Figure BDA0003162237180000043
and P1 0Initial active power output, P, of generator k and balance node, respectivelykIs the active power output of a generator k, k is the generator number of a power transmission area, NGThe total number of generators in the power transmission area.
Further, in the step (5), the load active power is increased, and the load flow calculation is performed by a newton-raphson method, which specifically includes: assuming that the number of generator nodes of the power system is NG, the total number of nodes of the power grid is N, the nodes 1 to the NG are all power transmission region generator nodes in the sequence, the nodes NG +1 to the nodes N are all power receiving region load nodes (including AQ nodes), and the node 1 is a balance node, then the active power and reactive power balance equation of the power system is as shown in formula (4) and formula (5):
△Pi＝Pi-fPi(θ,V)＝0 i＝2,...,N (4)；
△Qi＝Qi-fQi(θ,V)＝0 i＝NG+1,...,N (5)；
in the formula: i is the node number, PiAnd QiRespectively given active and reactive power, f, for node iPi(theta, V) and fQi(theta, V) are an active power equation and a reactive power equation of the node i, respectively, theta and V are a voltage phase angle and an amplitude of the node, respectively, and Delta PiAnd Δ QiRespectively an active power error quantity and a reactive power error quantity of a node i;
the solution is carried out by using a Newton method, and a correction equation (6) can be obtained:
Figure BDA0003162237180000051
in the formula:
Figure BDA0003162237180000052
θ＝[θ2,...,θN]T (8)；
Figure BDA0003162237180000056
Δ θ and Δ V are correction amounts of θ and V.
Further, the load flow calculation mode in the step (6) is changed from a newton-raphson method to an AQ node-based method, and specifically includes:
if the iteration of the power flow calculation is not converged by the Newton-Raphson method in the step (5), the power flow calculation performed by the Newton-Raphson method is converted into a power flow calculation method based on AQ nodes for power flow calculation, and the specific method is as follows: the phase angle of the node N (AQ node) is changed from a control variable to a given value thetaN，θNInitial value is
Figure BDA0003162237180000053
Node N reactive power is given value QNThen the correction equation changes to:
Figure BDA0003162237180000054
in the formula:
Figure BDA0003162237180000055
θC＝[θ2,...,θN-1]T (12)；
since the node phase angle and the reactive power of the node N (AQ node) are kept constant, the active power PNNo longer given, only the reactive power balance equation exists in the power balance equation, and therefore, only the active power balance equation from node 2 to node N-1 is included in equation (10).
Further, in the step (7), the active power P after the node N (AQ node) is increased is obtainedNIn particular according to the active power equation fPN(theta, V) obtaining active power P of node N (AQ node)N。
Further, the active power P increased by the node N (AQ node) in the step (7) in the step (8) isNUpdating active power of other load nodes and generator nodes, and performing load flow solution again by using the updated node data; the method specifically comprises the following steps: the active power P of the node N (AQ node) in the step (7)NAnd (3) updating the active power of other load nodes and generator nodes in the equations (2) and (3), and replacing the equations (10), (11) and (12) with the updated node data to perform the power flow solution again.
Further, after the excitation current and the armature current are regulated in the step (5) and the step (8), a node switching determination subroutine needs to be embedded in the step (5) and the step (8); the node switching judgment subprogram specifically comprises the following steps:
1) according to P of nodegi、QgiAnd ViSolving the generator no-load electromotive force E of the PV node according to the formula (13)qi：
Figure BDA0003162237180000061
2) Judging whether the reactive power of the generator node exceeds the limit, if so
Figure BDA0003162237180000062
Then no-load electromotive force EqiIs maintained at the upper limit value
Figure BDA0003162237180000063
Constant;
3) generator node type conversion from PV node to PIfThe node, the reactive power model is a constant excitation model, EqiMaintaining the upper limit value
Figure BDA0003162237180000064
Constancy, solving for the generator power angle deltaiCalculating the out-of-limit Q according to equation (14)gi，
Figure BDA0003162237180000071
Figure BDA0003162237180000072
Figure BDA0003162237180000073
And modifying the Jacobian matrix and the reactive balance equation according to equations (15), (16), where PgAnd QgActive and reactive power, respectively, of the generator, EqIs generator no-load electromotive force, delta is generator power angle, V is generator terminal voltage, and XdAnd XqRespectively a direct-axis reactance and a quadrature-axis reactance, and has an X for a non-salient pole machined＝Xq；
4) According to P of nodegi、QgiAnd ViSolving for the armature current I at the generator node according to equation (17)ai：
Figure BDA0003162237180000074
5) Determining whether the armature current of the generator is out of limit, if so
Figure BDA0003162237180000075
Then IaiIs maintained at the upper limit value
Figure BDA0003162237180000076
If the constant value is constant, executing the step 6), otherwise, jumping out of the inner loop;
6) generator node type conversion to PIaThe node and the reactive power model are constant armature current models, and the out-of-limit Q is calculated according to the formula (17)giAnd modifying the Jacobian matrix and the reactive balance equation according to the equations (18) and (19):
Figure BDA0003162237180000077
Figure BDA0003162237180000078
the invention has the beneficial effects that:
1) the active load of the node is increased by increasing the phase angle difference between the AQ node and the balance node until the voltage stabilization critical point, so that the stability and the calculation speed are better;
2) by further optimization, the influence of exciting current and armature current on the reactive power of the generator is considered, and the node where the out-of-limit generator is located is converted into PIfNode or PIaThe node is more in line with the actual system running state, and the obtained ATC result is closer to the actual result;
3) aiming at different reactive power models, only the reactive voltage partial derivative in the Jacobian matrix needs to be corrected in the solving process, the correction of the load parameter partial derivative vector does not need to be considered, the derivation of a formula is reduced, and the method has important significance for ATC calculation.
Drawings
Fig. 1 is a main flow chart of a method for calculating available transmission capacity based on AQ nodes.
FIG. 2 is a flow chart of a system initialization subroutine in the main flow chart of the method of the present invention.
Fig. 3 is a flow chart of a flow calculation subroutine converted based on the AQ node method in the main flow chart of the method of the present invention.
FIG. 4 is a flowchart of a node switch determination subroutine in the main flowchart of the method of the present invention.
FIG. 5 is a P-V curve of node 16 for 4 cases in example 1.
FIG. 6 is an A-P curve of node 16 for 4 cases in example 1.
Fig. 7 is an a-Q curve of a power generation region generator node in case 1 in embodiment 1.
Fig. 8 is an a-Q curve of a power generation region generator node in case 2 of embodiment 1.
Fig. 9 is an a-Q curve of a power generation region generator node in case 3 in embodiment 1.
Fig. 10 is an a-Q curve of a power generation region generator node in case 4 in embodiment 1.
Fig. 11 is a graph of the a-Q curves of the generator node 35 in 4 cases in example 1.
FIG. 12 is a system diagram of an IEEE-39 node in embodiment 1.
Detailed Description
The technical solution of the present invention will be described in detail with reference to the specific embodiments.
Suppose the number of generator nodes of the power system is NGThe total number of nodes is N, and the nodes from 1 to N are arranged in sequenceGAll being generator nodes, node NGAll the +1 to the node N are load nodes (including AQ nodes), and the node 1 is a balance node, then the active power and reactive power balance equation of the power system is as follows:
△Pi＝Pi-fPi(θ,V)＝0 i＝2,...,N (20)；
△Qi＝Qi-fQi(θ,V)＝0 i＝NG+1,...,N (21)；
in the formula: piAnd QiGiving active and reactive power, f, to node iPi(theta, V) and fQi(theta, V) are the active and reactive power equations for node i, theta and V are the voltage phase angle and amplitude, respectively, of the node, and DeltaPiAnd Δ QiIs the amount of power error at node i.
The solution is carried out by using a Newton method, and a correction equation can be obtained:
Figure BDA0003162237180000091
in the formula:
Figure BDA0003162237180000092
θ＝[θ2,...,θN]T (24)；
Figure BDA0003162237180000093
Δ θ and Δ V are correction amounts of θ and V.
Fixed node N (AQ node) phase angle
Figure BDA0003162237180000094
The node reactive power being given value QNThen the correction equation changes to:
Figure BDA0003162237180000095
in the formula:
Figure BDA0003162237180000101
θC＝[θ2,...,θN-1]T (28)；
the node phase angle and the reactive power of the node N (AQ node) are kept constant, and the active powerRate PNIs not given any more, can pass the active power equation fPN(θ, V) to obtain, the power balance equation only has reactive balance equation, therefore, equation (7) only includes the active balance equation from node 2 to node N-1.
The CPF forms an extended power flow equation by adding continuous parameters lambda, a Jacobian matrix of the extended power flow equation is added with one line and one column compared with a Jacobian matrix of a conventional power flow equation, and the morbid problem of a Jacobian matrix of the conventional power flow equation when the parameters are close to a limit value is solved.
The essence of the ATC calculation is that under the condition of ensuring that the basic power flows of the non-power transmission region and the non-power receiving region are not changed, the output of the generator of the power transmission region S and the active load of the power receiving region R are simultaneously increased until the maximum value of the available transmission capacity between the given regions S and R is not met during the safe and stable operation of the system.
For constant power factor load node NpTo node N, with a power factor angle of
Figure BDA0003162237180000102
Then the reactive power of node l
Figure BDA0003162237180000103
Unlike the continuous power flow method, the load P of the power receiving arealNo longer increased by the load parameter λ, but by the active power P of the node N (AQ node)NAnd (3) growing:
Figure BDA0003162237180000104
in the formula, alphalProportional coefficient for load increase, Pl 0And
Figure BDA0003162237180000105
is the initial of load l and AQ node respectivelyInitially active, and PNThis increase can be achieved by continuously increasing the phase angle difference between node N (AQ node) and the balance node until the voltage stability threshold is reached.
The increased load can be balanced by increasing the active output of the generator node 1 to the node q in the power transmission region by:
Figure BDA0003162237180000111
in the formula, P1To balance the active power of the nodes, betakFor the scaling factor of the generator to increase,
Figure BDA0003162237180000112
and P1 0The initial active output of the generator k and the balance node respectively.
Considering that the transmission reliability margin and the capacity benefit margin are not considered, when the generated output and the load increase correspondingly reach the limit values, the obtained transmission capacity is the ATC value meeting the static voltage stability constraint.
The important factors influencing the reactive power output of the generator mainly include the stator heating limit, the rotor heating limit, the saturation of the generator magnetic circuit and the phase advance operation mode of the generator, and because the synchronous reactance values of the direct axis and the quadrature axis of the generator magnetic circuit can change when the generator magnetic circuit is saturated, the calculation of the saturated synchronous reactance is complex and is not considered, the phase advance operation mode of the generator is also not considered, and only the influence of the exciting current and the armature current under the stator heating limit and the rotor heating limit is considered.
According to the theory of electromechanics, for a salient pole machine, neglecting the resistance at the stator side, the steady state power equation of the generator can be expressed as:
Figure BDA0003162237180000113
in the formula: pgAnd QgActive power and reactive power of the generator are respectively; eqIs the no-load electromotive force of the generator; delta is the power angle of the generator; v is terminal voltage; xdAnd XqRespectively a direct-axis reactance and a quadrature-axis reactance, and has an X for a non-salient pole machined＝Xq。
In actual operation, in order to prevent the field winding of the generator from overheating, an integrally controlled over-excitation limiter is usually used to limit the field current, and under steady-state conditions, when the field current reaches an upper limit, i.e. the field current reaches the upper limit
Figure BDA0003162237180000121
Time, unsaturated electromotive force EqHeld at a constant value:
Figure BDA0003162237180000122
in the formula:
Figure BDA0003162237180000123
the upper limit of the no-load electromotive force of the generator; omega0Is the synchronous angular velocity; l isadThe excitation winding is mutually inducted with the straight shaft.
At a per unit value, equation (32) can be expressed as:
Figure BDA0003162237180000124
at this time, the reactive power of the generator can be expressed as:
Figure BDA0003162237180000125
the generator power angle can be expressed as a function of the generator active power output and the generator terminal voltage at the steady state moment:
δ＝f(Pg,V) (35)；
in order to prevent overheating of the generator stator winding in an emergency of the power system voltage, an armature current limiter is usually used to limit the armature current when the armature current reaches an upper limit, i.e. when the armature current reaches the upper limit
Figure BDA0003162237180000126
And the reactive power of the generator is as follows:
Figure BDA0003162237180000127
in the conventional load flow calculation process, a generator node without a reactive power out-of-limit is set as a PV node, the calculation method takes the constraint of exciting current and armature current into consideration, when corresponding parameters are out-of-limit, the type of the generator node is converted, and a mathematical model of the generator node is changed; under the constraint of exciting current, the generator node type is converted into PIfThe node and the mathematical model are changed into a constant excitation model, and the node type is converted into PI under the constraint of armature currentaAnd the node and the mathematical model are constant armature current models.
No-load electromotive force E of generator node in constant excitation modelqIs maintained at the upper limit value
Figure BDA0003162237180000131
At this time, the node voltage ViAnd power angle delta of generatoriIs an unknown quantity, δiCan be expressed as PgiAnd ViAnd therefore need to be considered when solving the Jacobian matrix
Figure BDA0003162237180000132
And (4) correcting.
From formula (34):
Figure BDA0003162237180000133
for unknown quantity delta in the formulaiThe power equation of the generator in the formula (31) can be obtained by a first-order Czochralski method, and the initial value is taken
Figure BDA0003162237180000134
Convergence can be stabilized.
The Jacobian matrix diagonal elements after the correction
Figure BDA0003162237180000135
On the original basis add
Figure BDA0003162237180000136
Term, in this case equation (21) is modified as:
Figure BDA0003162237180000137
in the constant armature current model, the armature current reaches an upper limit, i.e.
Figure BDA0003162237180000138
Formula (29) to ViCalculating a partial derivative:
Figure BDA0003162237180000139
similarly, the Jacobian matrix is modified, and then the formula (21) is modified as follows:
Figure BDA00031622371800001310
in summary, the method for calculating available transmission capacity based on AQ nodes according to the specific embodiment of the present invention includes the following steps:
(1) obtaining basic power grid flow parameters of a power system: the method comprises the steps of obtaining the voltage amplitude and the phase angle of each node, the active power and the reactive power of a generator of each node, the load active power and the reactive power of each node, the admittance matrix of the nodes, and the active power and the reactive power of a transmission line;
(2) initializing power grid flow parameters: setting control variables, state variables, upper and lower limits of active power and reactive power of a generator, upper and lower limits of active power and reactive power of a load node, maximum transmission capacity of a line and related parameters;
(3) setting a load type as a constant power factor load, and setting a system node N as an AQ node;
(4) setting the increasing modes of a generator and a load from the initial operation point of the power system;
(5) increasing the load active power, jumping into a node switching judgment stator program after considering the constraint of exciting current and armature current, carrying out load flow calculation by a Newton-Raphson method, and judging whether the iteration of the load flow calculation is converged; if the iteration of the power flow calculation is converged, continuing to operate the step (5), and if the iteration of the power flow calculation is not converged, operating the step (6);
(6) the load flow calculation mode is changed from a Newton-Raphson method to an AQ node-based method;
(7) increasing the phase angle difference between the node N (AQ node) and the balance node to obtain the active power P after the node N (AQ node) is increasedN；
(8) The active power P increased by the node N (AQ node) in the step 7)NUpdating active power of other load nodes and generator nodes, jumping into a node switching judgment subprogram after considering the constraint of exciting current and armature current, and carrying out load flow solution again by using updated node data;
(9) determining active power P of node N (AQ node) after increaseNWhether the limit is out of limit or not, if so, jumping to the step (10); otherwise, repeating the steps 6), 7) and 8) until the active power P after the node N (AQ node) is increasedNUntil the limit is out of limit;
(10) outputting a tide solution;
(11) available power transmission capacity under stable output voltage conditions.
After considering the constraint of the exciting current and the armature current, the embedded node stator judging program comprises the following steps:
1) according to P of nodegi、QgiAnd ViAnd solving the generator no-load electromotive force E of the PV nodeqi；
2) Judging whether the reactive power of the generator node exceeds the limit, if so
Figure BDA0003162237180000151
Then is unloadedElectromotive force EqiMaintained at the upper limit value
Figure BDA0003162237180000152
Constant;
3) generator node type conversion from PV node to PIfThe node, the reactive power model is a constant excitation model, EqiMaintaining the upper limit value
Figure BDA0003162237180000153
Constancy, solving for the generator power angle deltaiCalculating out of limit QgiCorrecting the Jacobian matrix and the reactive power balance equation;
4) according to P of nodegi、QgiAnd ViSolving the armature current I of the generator nodeai；
5) Determining whether the armature current of the generator is out of limit, if so
Figure BDA0003162237180000154
Then IaiIs maintained at the upper limit value
Figure BDA0003162237180000155
If the constant value is constant, executing the step 6), otherwise, jumping out of the inner loop;
6) generator node type conversion to PIaThe node and the reactive power model are constant armature current models, and the Q under the out-of-limit is calculatedgiAnd correcting the Jacobian matrix and the reactive balance equation.
The invention provides an ATC calculation model considering the operation constraint of a generator based on AQ nodes, which increases the active load of the nodes by increasing the phase angle difference between the AQ nodes and a balance node until a voltage stabilization critical point, and has better stability and calculation speed; meanwhile, the influence of exciting current and armature current on the reactive power of the generator is considered, and the node where the out-of-limit generator is located is converted into PIfNode or PIaThe node is more in line with the actual system running state, and the obtained ATC result is closer to the actual result; and aiming at different reactive power models, only the partial derivatives of the reactive power to the voltage in the Jacobian matrix need to be corrected in the solving processTherefore, the correction of the load parameter partial derivative vector is not considered, the derivation of a formula is reduced, and the method has important significance for ATC calculation.
Because no load parameter lambda is added, aiming at different reactive power models, the invention only needs to correct the Jacobian matrix, reduces the derivation of formulas and simplifies the calculation process, and simultaneously, the invention considers the influence of exciting current and armature current on the reactive power of the generator, embeds node switching judgment and converts the node where the out-of-limit generator is positioned into PIfNode or PIaThe node is more in line with the actual operation condition, and the obtained available transmission capacity is more practical.
Example 1
A new England 10 machine 39 node (IEEE 39) system is selected for verification, an IEEE 39 node system partition diagram is shown in figure 12, Area 1 is a power transmission Area, Area 2 is a power receiving Area, nodes 31-36 in the Area 1 are generator nodes for balancing load growth, nodes 3, 15-18, 21 and 25-29 in the Area 2 are load growth nodes, the node 31 is a balancing node, the node 16 is an AQ node, the proportional coefficient of related nodes is shown in a table 1, and a table A1 is an IEEE-39 node system generator parameter table.
Figure BDA0003162237180000161
TABLE 1
Figure BDA0003162237180000171
TABLE A1
Note: the unit is per unit system, and the power reference value is 100 MVA.
Consider the following 4 cases: in case 1, the reactive violation is not handled; in case 2, the type of node is changed after the reactive power exceeds the limit, the out-of-limit generator is converted into a PQ node, and the reactive power of the generator keeps the limit constant; case 3, taking into account the excitation current constraints, convert the out-of-limit generator node into PIfA node; case 4, accounting for armature current constraints, will overrun generator sectionsPoint transformation of PIaThe node, generator data are shown in table a 1.
Figure BDA0003162237180000172
TABLE 2
FIGS. 5 and 6 show P-V curves and A-P curves of the node 16 in 4 cases, Table 2 shows the calculation results in 4 cases, and FIGS. 7 to 10 show A-Q curves of each generator node in a power generation region under 4 constraint conditions; it can be seen by a connection of the above curves to table 2: in the case 1, the reactive power of the generator in the power generation area continuously increases along with the increase of the angle difference between the AQ node and the balance node until the reactive power of part of the generator is out of limit at the maximum load point, and the ATC value is larger and is 1641.55 MW; in case 2, a constant reactive power limit method is adopted, the reactive power maintaining limit of the out-of-limit generator is constant, the node where the limit is located is converted into a PQ node from a PV node, although the reactive power limit value of the generator is considered, the ATC value of the generator is reduced to 1144.89MW compared with the case 1, but the situation does not consider that the reactive power capability of the generator is reduced along with the increase of the active power in the actual situation, and the result is still larger; and cases 3 and 4 take the excitation current and armature current constraints of the generator into consideration, and the PV node of the node where the out-of-limit generator is located is converted into the PI node by considering the node type after related parameters are out-of-limit and the conversion of the reactive power model of the generatorfOr PIaAfter the node, along with the increase of the active power of the load, the A-Q curve is reduced, and the reactive power of the generator is greatly reduced until the reactive power at the voltage stabilization critical point is reduced to a lower level; in summary, in case 1, the constraint of the upper limit of reactive power is not considered, the reactive power value continuously increases with the increase of active power, and the result is that the reactive power of the generator at the maximum load point exceeds the limit, and in case 2, the reactive power of the generator decreases with the increase of active power after the upper limit of reactive power is not considered, and obviously, the 2 cases deviate from the reality; compared with the 2 cases, the cases 3 and 4 consider the reactive power change of the generator with the active power after the relevant generator parameters are out of limit, and are relatively consistent with the running state of the actual system, so the ATC value under the condition is also closest to the actual value, namely 1102.00MW and 1030.00 MW.
Taking the first out-of-limit node 35 (generator node No. 6) as an example, the a-Q curve of this node in 4 cases is shown in fig. 11; as can be seen in connection with fig. 5: before the point A, the curves under 4 conditions are consistent, when the operation reaches the point A, the condition 2 firstly judges that the reactive power of the generator is out of limit, the reactive power of the generator is invariable at an upper limit value after the out of limit, the reactive power of the generator is continuously increased in the conditions 3 and 4, the out of limit occurs at the point B and the point C respectively, after the out of limit, the reactive power of the generator begins to decline, the corresponding A-Q curve also rapidly declines, when the reactive power of the generator is close to a voltage stabilization critical point, the reactive power of the generator already declines to a very low level, correspondingly, the P-V curve of the load also rapidly declines after the out of limit, and at the voltage stabilization critical point, the voltage already declines to a very low level; the reason is that in case 2, the constant reactive upper limit model underestimates the reactive capability of the system when the generator is lightly loaded, generates less partial reactive power than cases 3 and 4, is conservative, overestimates the reactive capability of the generator when the generator is heavily loaded, and the reactive curve is kept constant above cases 3 and 4 without reduction; between the point A and the point C, the conditions 3 and 4 do not exceed the limit, the curves are kept consistent, when the point C is operated, the generator has armature current exceeding, which is earlier than the excitation current exceeding point B, and the situation that the generator meets the excitation current limit cannot ensure that the armature current of the generator does not exceed the limit is shown, and according to the graph shown in the figure 5, the reactive curve of the condition 4 is always smaller than the reactive curve of the condition 3, which shows that the influence of single limit is not eliminated along with the increase of active power, but the ATC value under the condition of meeting the armature current limit is smaller; after point B, case 1 is obviously not practical because the reactive power of the generator always tends to increase due to the node conversion without considering reactive power constraint.
In the available transmission capacity calculation method based on the AQ node provided in this embodiment, according to the operation characteristics of the synchronous generator, the influence of the exciting current and the armature current on the reactive power of the generator is considered, and the node where the out-of-limit generator is located is converted into the PIfNode or PIaThe nodes do not add the load parameter lambda, and only need to correct the Jacobian matrix aiming at different reactive power models, so that the derivation of the formula is reduced, and the IEEE is performedAnd (4) performing simulation calculation on the 39-node system to verify the feasibility of the model and the algorithm.
While the invention has been particularly shown and described with reference to a particular preferred embodiment, it is not to be construed as limited to the invention itself, as various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. An available transmission capacity calculation method based on an AQ node is characterized by comprising the following steps:
(1) obtaining a basic power grid flow parameter of a power system;
(2) initializing power grid flow parameters;
(3) setting a load type as a constant power factor load, and setting a system node N as an AQ node;
(4) setting the increasing modes of a generator and a load from the initial operation point of the power system;
(5) increasing the load active power, jumping into a node switching judgment stator program after considering the constraint of exciting current and armature current, carrying out load flow calculation by a Newton-Raphson method, and judging whether the iteration of the load flow calculation is converged; if the iteration of the power flow calculation is converged, continuing to operate the step (5), and if the iteration of the power flow calculation is not converged, operating the step (6);
(6) the load flow calculation mode is changed from a Newton-Raphson method to an AQ node-based method;
(7) increasing the phase angle difference between the node N and the balance node to obtain the active power P after the node N is increasedN；
(8) The active power P increased by the node N in the step 7)NUpdating active power of other load nodes and generator nodes, jumping into a node switching judgment subprogram after considering the constraint of exciting current and armature current, and carrying out load flow solution again by using updated node data;
(9) determining the increased active power P of the node NNWhether the threshold is out of limit; if the limit is out of limit, jumping to the step (10); otherwise, repeating the steps (6), (7) and (8) until the active power P after the node N is increasedNUntil the limit is out of limit;
(10) outputting a tide solution;
(11) available power transmission capacity under stable output voltage conditions.
2. The method according to claim 1, wherein the basic grid power flow parameters in step (1) include voltage amplitude of each node, voltage phase angle of each node, active power of each node generator, reactive power of each node generator, active power of each node load, reactive power of each node load, admittance matrix of nodes, active power of transmission line, and reactive power of transmission line.
3. The method for calculating the available transmission capacity based on the AQ nodes as claimed in claim 1, wherein the initializing of the power flow parameters in the step (2) specifically comprises: defining control variables, defining state variables, setting respective upper and lower limits of active power of a generator, reactive power of the generator, active power of load nodes, reactive power of the load nodes and voltage amplitudes of all the nodes, and setting the maximum transmission capacity of a line; defining the control variables comprises defining the voltage amplitude of each node and the voltage phase angle of each node as the control variables; the defining the state variables comprises defining generator active power, generator reactive power, load active power and load reactive power as the state variables.
4. The method according to claim 1, wherein the load type is set to be a constant power factor load in step (3), specifically as shown in formula (1):
Figure FDA0003162237170000021
in the formula, QlIs the reactive power of the node i and,
Figure FDA0003162237170000022
is the power factor angle, l is the constant power load node number, NpThe nodes are initially numbered for constant power load, N is the total number of the nodes of the power grid, PlAnd loading active power for the power receiving area.
5. The method for calculating available transmission capacity based on AQ nodes as claimed in claim 1, wherein in said step (4), starting from the initial operation point of the power system, the increase mode of the generator and the load is set, wherein the active power P of the load in the power receiving region islActive power P through node NNAnd (3) increasing, wherein the load of the power receiving area does not comprise a node N, and the specific formula is as follows (2):
Figure FDA0003162237170000031
in the formula, alphalProportional coefficient for load increase, Pl 0And
Figure FDA0003162237170000032
initial active power of load l and node N, respectively, wherein active power P of node NNThe increase of (1) is realized by continuously increasing the phase angle difference value between the node N and the balance node until reaching the voltage stabilization critical point, wherein l is the constant power load node number, and N is the constant power load node numberpThe nodes are initially numbered for constant power load nodes, and N is the total number of the nodes of the power grid;
increased load through increased transmission area generator node 1 to node NGThe active output of the generator in the power transmission region is balanced, and the active output of the generator in the power transmission region increases in a manner shown in formula (3):
Figure FDA0003162237170000033
in the formula, P1To balance the active power of the nodes, betakFor the scaling factor of the generator to increase,
Figure FDA0003162237170000034
and P1 0Initial active power output, P, of generator k and balance node, respectivelykIs the active power output of a generator k, k is the generator number of a power transmission area, NGThe total number of generators in the power transmission area.
6. The method for calculating available transmission capacity based on AQ nodes as claimed in claim 1, wherein in step (5), load active power is increased, and after excitation current and armature current constraints are taken into account, a node switching decision sub-program is skipped, and power flow calculation is performed by a newton-raphson method, specifically as follows: suppose the number of generator nodes of the power system is NGThe total number of nodes of the power grid is N, and the nodes from 1 to N are arranged in sequenceGAll being power transmission region generator node, node NGAnd all the +1 to the node N are load nodes in the power receiving area, and the node 1 is a balance node, so that the active power and reactive power balance equation of the power system is as shown in the formula (4) and the formula (5):
△Pi＝Pi-fPi(θ,V)＝0 i＝2,...,N (4)；
△Qi＝Qi-fQi(θ,V)＝0 i＝NG+1,...,N (5)；
in the formula: i is the node number, PiAnd QiRespectively given active and reactive power, f, for node iPi(theta, V) and fQi(theta, V) are an active power equation and a reactive power equation of the node i, respectively, theta and V are a voltage phase angle and an amplitude of the node, respectively, and Delta PiAnd Δ QiRespectively an active power error quantity and a reactive power error quantity of a node i;
the solution is carried out by using a Newton method, and a correction equation (6) can be obtained:
Figure FDA0003162237170000041
in the formula:
Figure FDA0003162237170000042
θ＝[θ2,...,θN]T (8)；
Figure FDA0003162237170000043
Δ θ and Δ V are correction amounts of θ and V.
7. The method for calculating available transmission capacity based on the AQ nodes as claimed in claim 1, wherein the power flow calculation mode in the step (6) is changed from a newton-raphson method to an AQ node-based method, specifically:
if the iteration of the power flow calculation is not converged by the Newton-Raphson method in the step (5), the power flow calculation performed by the Newton-Raphson method is converted into a power flow calculation method based on AQ nodes for power flow calculation, and the specific method is as follows: the phase angle of the node N is changed from a control variable to a given value thetaN，θNInitial value is
Figure FDA0003162237170000044
Node N reactive power is given value QNThen the correction equation changes to:
Figure FDA0003162237170000045
in the formula:
Figure FDA0003162237170000051
θC＝[θ2,...,θN-1]T (12)；
since the node phase angle and the reactive power of the node N are kept constant, the active power PNNo longer given, only the reactive power balance equation exists in the power balance equation, and therefore, only the active power balance equation from node 2 to node N-1 is included in equation (10).
8. The method according to claim 5, wherein the step (7) of calculating the active power P of the node N after increasing is to calculate the available transmission capacity based on the AQ nodeNIn particular according to the active power equation fPN(theta, V) determining the active power P of the node NN(ii) a The active power P increased by the node N in the step (7) in the step (8)NUpdating the active power of other load nodes and generator nodes, specifically: the active power P of the node in the step (7)NAnd (4) updating the active power of other load nodes and generator nodes in equations (2) and (3).
9. The method according to claim 7, wherein the flow solution is performed again in step (8) by using the updated node data, and specifically comprises: the updated node data is substituted for equations (10), (11), and (12) to perform the power flow solution again.
10. The method for calculating the available transmission capacity based on the AQ nodes as claimed in any one of claims 1 to 9, wherein after the excitation current and the armature current are constrained in step (5) and step (8), a node switching judgment subroutine is embedded in step (5) and step (8); the node switching judgment subprogram specifically comprises the following steps:
1) according to P of nodegi、QgiAnd ViSolving the generator no-load electromotive force E of the PV node according to the formula (13)qi：
Figure FDA0003162237170000061
2) Judging whether the reactive power of the generator node exceeds the limit, if so
Figure FDA0003162237170000062
Then no-load electromotive force EqiIs maintained at the upper limit value
Figure FDA0003162237170000063
Constant;
3) generator node type conversion from PV node to PIfThe node, the reactive power model is a constant excitation model, EqiMaintaining the upper limit value
Figure FDA0003162237170000064
Constancy, solving for the generator power angle deltaiCalculating the out-of-limit Q according to equation (14)gi，
Figure FDA0003162237170000065
Figure FDA0003162237170000066
Figure FDA0003162237170000067
And modifying the Jacobian matrix and the reactive balance equation according to equations (15), (16), where PgAnd QgActive and reactive power, respectively, of the generator, EqIs generator no-load electromotive force, delta is generator power angle, V is generator terminal voltage, and XdAnd XqRespectively a direct-axis reactance and a quadrature-axis reactance, and has an X for a non-salient pole machined＝Xq；
4) According to P of nodegi、QgiAnd ViSolving for the armature current I at the generator node according to equation (17)ai：
Figure FDA0003162237170000068
5) Determining whether the armature current of the generator is out of limit, if so
Figure FDA0003162237170000069
Then IaiIs maintained at the upper limit value
Figure FDA00031622371700000610
If the constant value is constant, executing the step 6), otherwise, jumping out of the inner loop;
6) generator node type conversion to PIaThe node and the reactive power model are constant armature current models, and the out-of-limit Q is calculated according to the formula (17)giAnd modifying the Jacobian matrix and the reactive balance equation according to the equations (18) and (19):
Figure FDA0003162237170000071
Figure FDA0003162237170000072
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Publication number Priority date Publication date Assignee Title
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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