A method for calculating available transmission capacity based on AQ nodes

Abstract

The present invention proposes a method for calculating available transmission capacity based on AQ nodes, which includes: 1) obtaining basic power grid flow parameters; 2) initializing power grid flow parameters; 3) setting the load type to constant power factor load, and setting the system node N to AQ node; 4) setting the growth mode of the generator and the load; 5) increasing the load active power, performing flow calculation by Newton-Raphson method, and judging whether the flow calculation iteration converges; 6) converting the flow calculation mode from Newton-Raphson method to AQ node method; 7) obtaining the active power P after the node N increases. N ; 8) Active power P after growth by node N N Update the active power of other load nodes and generator nodes, and solve the power flow again; 9) Increase the phase difference between node N and the balance node, and repeat steps 6), 7), and 8) until the active power P of node N increases. N Until the limit is exceeded; 10) Output power flow solution; 11) Output available transmission capacity.

Description

Technical Field

[0001] The present invention relates to the technical field of power transmission and distribution of electric power systems, and in particular to a method for calculating available power transmission capacity based on an AQ node. Background Art

[0002] In the modern power market environment, available transfer capability (ATC) is not only an influencing factor of transmission system management, but also a technical indicator for dispatchers to maintain safe and stable operation of the system. At the same time, it also serves as a market signal and is a reference for market participants to conduct related commercial activities. Therefore, how to solve ATC more accurately has become an important part of power market research.

[0003] At present, the ATC calculation considering voltage stability constraints usually adopts the continuation power flow (CPF) method, which can continuously change the transmission power from the generator group to the load group in the power flow equation. By adding continuous parameters to the conventional power flow equation, the ill-conditioned problem of the Jacobian matrix of the conventional power flow equation when the parameters are close to the limit value is overcome; however, CPF includes two steps, prediction and correction, so it is necessary to solve the nonlinear equation group once more, and in the correction step, CPF still needs to solve the problem of the Jacobian matrix being poor near the maximum load point; when the generator constraint is taken into account, the conventional calculation method converts the node where the over-limit generator is located from a PV node to a PQ node after the reactive power exceeds the limit, and the reactive power of the generator is kept constant at the limit value, but this processing method is usually not practical, because, when the generator is converted from a PV node to a PQ node, as the system load increases, the terminal voltage is no longer constant, which is bound to bring about changes in the reactive power of the generator. Summary of the invention

[0004] The present invention proposes a method for calculating available transmission capacity based on AQ nodes, which aims to solve the problem that when the available transmission capacity is calculated based on the existing CPF method, the correction step needs to solve an additional set of nonlinear equations and the Jacobian matrix near the maximum load point is poor.

[0005] The technical solution of the present invention is a method for calculating the available power transmission capacity based on the AQ node, the method comprising the following steps:

[0006] (1) Obtain basic power grid flow parameters of the power system;

[0007] (2) Initialization of power grid flow parameters;

[0008] (3) Set the load type to constant power factor load and set the system node N to AQ node;

[0009] (4) Starting from the initial operating point of the power system, set the growth pattern of generators and loads;

[0010] (5) Increase the load active power, take into account the constraints of the excitation current and the armature current, jump into the node switching judgment subroutine, perform power flow calculation by the Newton-Raphson method, and determine whether the power flow calculation iteration converges; if the power flow calculation iteration converges, continue to run step (5); if the power flow calculation iteration does not converge, run step (6);

[0011] (6) The power flow calculation method is changed from the Newton-Raphson method to the AQ node method;

[0012] (7) Increase the phase angle difference between node N (AQ node) and the balance node, and obtain the active power P after the increase of node N (AQ node) N ;

[0013] (8) The active power P after the increase of node N (AQ node) in step 7) N Update the active power of other load nodes and generator nodes, take into account the constraints of excitation current and armature current, jump into the node switching judgment subroutine, and use the updated node data to solve the power flow again;

[0014] (9) Determine the active power P after the increase of node N (AQ node) N Is it over the limit? If so, jump to step (10); otherwise, repeat steps (6), (7), and (8) until the active power P of node N (AQ node) increases to N Until the limit is exceeded;

[0015] (10) Output power flow solution;

[0016] (11) Available power transmission capacity under stable output voltage conditions.

[0017] Furthermore, the power grid flow parameters in step (1) include the voltage amplitude and phase angle of each node, the active power and reactive power of the generator of each node, the active power and reactive power of the load of each node, the admittance matrix of the node, and the active power and reactive power of the transmission line.

[0018] Furthermore, the initialization of the power grid flow parameters in step (2) specifically includes: setting the control variables (including the voltage amplitude and phase angle of each node), state variables (generator active power and reactive power, load active power and reactive power), upper and lower limits of generator active power and reactive power, upper and lower limits of load node active power and reactive power, maximum transmission capacity of the line, and upper and lower limits of the voltage amplitude of each node.

[0019] Furthermore, in step (3), the load type is set to a constant power factor load, as shown in formula (1):

[0020]

[0021] In the formula, Q l is the reactive power of node l, is the power factor angle, l is the constant power load node number, N p is the initial number of the constant power load node, N is the total number of grid nodes, P l It is the active power of the load in the power receiving area.

[0022] Furthermore, in step (4), starting from the initial operation point of the power system, the growth mode of the generator and the load is set, wherein the active power P of the load in the power receiving area (except the node N) l Active power P passing through node N (AQ node) N To grow, as shown in formula (2):

[0023]

[0024] In the formula, α l is the proportional coefficient of load growth, P l 0 and are the initial active power of load l and node N (AQ node), respectively, where the active power of node N (AQ node) is P N The growth of can be achieved by continuously increasing the phase angle difference between node N (AQ node) and the balance node until the voltage stability critical point is reached, l is the constant power load node number, N p is the initial number of the constant power load node, and N is the total number of grid nodes;

[0025] The increased load is met by increasing the transmission area generator node 1 to node N G The active output of the generator in the transmission area is balanced, and the growth mode of the active output of the generator in the transmission area is shown in formula (3):

[0026]

[0027] Where P1 is the active power of the balancing node, β k is the proportional coefficient of generator growth, and P1 0 are the initial active output of generator k and the balancing node, P k is the active output of generator k, k is the generator number in the transmission area, N G is the total number of generators in the power transmission area.

[0028] Furthermore, in step (5), the load active power is increased, and the power flow calculation is performed by the Newton-Raphson method, specifically as follows: Assuming that the number of generator nodes in the power system is NG, the total number of power grid nodes is N, and the order is that nodes 1 to NG are all generator nodes in the power transmission area, and nodes NG+1 to N are all load nodes in the power receiving area (including AQ nodes). Assuming that node 1 is a balance node, the active power and reactive power balance equations of the power system are as shown in equations (4) and (5):

[0029] △P i =P i -f Pi (θ,V)=0 i=2,...,N (4);

[0030] △Q i =Q i -f Qi (θ,V)=0 i=N G +1,...,N (5);

[0031] Where: i is the node number, P i and Q i are the active power and reactive power given to node i, respectively, and f Pi (θ, V) and f Qi (θ, V) are the active power equation and reactive power equation of node i, θ and V are the voltage phase angle and amplitude of the node, △P i and △Q i are the active power error and reactive power error of node i respectively;

[0032] Solving with Newton's method, we can obtain the modified equation (6):

[0033]

[0034] Where:

[0035]

[0036] θ=[θ2,...,θ N ] T (8);

[0037]

[0038] △θ and △V are the correction values ​​of θ and V.

[0039] Furthermore, the power flow calculation method in step (6) is changed from the Newton-Raphson method to the AQ node method, specifically:

[0040] If the Newton-Raphson method does not converge in the iteration of the power flow calculation in step (5), the Newton-Raphson method is converted into the power flow calculation method based on the AQ node. The specific method is as follows: the phase angle of the node N (AQ node) is changed from the control variable to the given value θ N ,θ N The initial value is The reactive power of node N is a given value Q N , then the correction equation changes to:

[0041]

[0042] Where:

[0043]

[0044] θ C =[θ2,...,θ N-1 ] T (12);

[0045] Since the node phase angle and reactive power of node N (AQ node) remain constant, the active power P N It is no longer given, and its power balance equation only has the reactive power balance equation. Therefore, equation (10) only contains the active power balance equation from node 2 to node N-1.

[0046] Furthermore, in step (7), the active power P of node N (AQ node) after growth is obtained. N , specifically according to the active power equation f PN (θ, V) to obtain the active power P of node N (AQ node) N .

[0047] Furthermore, in step (8), the active power P increased by the node N (AQ node) in step (7) is N Update the active power of other load nodes and generator nodes, and use the updated node data to solve the power flow again; specifically: the active power P of node N (AQ node) in step (7) N Substitute the active power of other load nodes and generator nodes into equations (2) and (3) to update them, and substitute the updated node data into equations (10), (11), and (12) to solve the power flow again.

[0048] Furthermore, after taking into account the constraints of the excitation current and the armature current in step (5) and step (8), a node switching determination subroutine needs to be embedded in step (5) and step (8); the node switching determination subroutine is specifically as follows:

[0049] 1) According to the node's P gi , Qgi and V i , solve the generator no-load electromotive force E of the PV node according to formula (13): qi :

[0050]

[0051] 2) Determine whether the reactive power of the generator node exceeds the limit. If The no-load electromotive force E qi Maintain at upper limit Constant;

[0052] 3) The generator node type is converted from PV node to PI f Node, the reactive power model is the constant excitation model, E qi Keep upper limit Constant, solve the generator power angle δ i , calculate Q under over-limit according to formula (14) gi ,

[0053]

[0054]

[0055]

[0056] The Jacobian matrix and reactive power balance equation are modified according to equations (15) and (16), where P g and Q g are the active power and reactive power of the generator, E q is the no-load electromotive force of the generator, δ is the generator power angle, V is the terminal voltage, X d and X q They are direct-axis reactance and quadrature-axis reactance respectively. For hidden-pole machines, there are X d =X q ;

[0057] 4) According to the node's P gi , Q gi and V i , solve the generator node armature current I according to formula (17): ai :

[0058]

[0059] 5) Determine whether the generator armature current exceeds the limit. If Then I ai Keep at upper limit If constant, execute step 6), otherwise, exit the inner loop;

[0060] 6) Convert the generator node type to PIa The reactive power model is a constant armature current model. The Q under over-limit is calculated according to formula (17): gi , and according to equations (18) and (19) the Jacobian matrix and reactive power balance equation are modified:

[0061]

[0062]

[0063] Beneficial effects of the present invention:

[0064] 1) By increasing the phase angle difference between the AQ node and the balance node, the node active load is increased until the voltage stability critical point is reached, which has better stability and calculation speed;

[0065] 2) Through further optimization, considering the influence of excitation current and armature current on the reactive power of the generator, the node where the over-limit generator is located is converted into PI f Node or Pi a Nodes are more consistent with the actual system operation status, and the ATC results are closer to reality;

[0066] 3) For different reactive power models, in the solution process, it is only necessary to correct the partial derivative of the reactive power with respect to the voltage in the Jacobian matrix without considering the correction of the partial derivative vector of the load parameter, which reduces the derivation of the formula and is of great significance for ATC calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Attached Figure 1 The main flow chart of the available transmission capacity calculation method based on AQ nodes.

[0068] Attached Figure 2 This is a flow chart of the system initialization subroutine in the main flow chart of the method of the present invention.

[0069] Attached Figure 3 The main flow chart of the method of the present invention is converted into a flow chart of a subroutine for power flow calculation based on the AQ node method.

[0070] Attached Figure 4 This is a flowchart of a node switching determination subroutine in the main flowchart of the method of the present invention.

[0071] Attached Figure 5 PV curves of node 16 under four conditions in Example 1.

[0072] Attached Figure 6 ] are the AP curves of node 16 in four cases in Example 1.

[0073] Attached Figure 7 It is the AQ curve of the generator node in the power generation area under Case 1 in Example 1.

[0074] Attached Figure 8 It is the AQ curve of the generator node in the power generation area under Case 2 in Example 1.

[0075] Attached Fig. 9 It is the AQ curve of the generator node in the power generation area under Case 3 in Example 1.

[0076] Attached Fig.10 It is the AQ curve of the generator node in the power generation area under Case 4 in Example 1.

[0077] Attached Fig.11 ] are AQ curves of the generator node 35 under four conditions in Example 1.

[0078] Attached Fig.12 This is the IEEE-39 node system diagram in Example 1. DETAILED DESCRIPTION

[0079] The technical solution of the present invention is described in detail below in conjunction with specific implementation methods.

[0080] Assume that the number of generator nodes in the power system is N G , the total number of nodes is N, and the order is node 1 to node N G All are generator nodes, node N G +1 to node N are all load nodes (including AQ node). If node 1 is a balance node, the active power and reactive power balance equations of the power system are as follows:

[0081] △P i =P i -f Pi (θ,V)=0 i=2,...,N (20);

[0082] △Q i =Q i -f Qi (θ,V)=0 i=N G +1,...,N (21);

[0083] Where: P i and Q i is the active and reactive power given to node i, f Pi (θ, V) and f Qi (θ, V) is the active power and reactive power equation of node i, θ and V are the voltage phase angle and amplitude of the node respectively, △P i and △Q i is the power error of node i.

[0084] Solving with Newton's method, we can get the corrected equation:

[0085]

[0086] Where:

[0087]

[0088] θ=[θ2,...,θ N ] T (twenty four);

[0089]

[0090] △θ and △V are the correction values ​​of θ and V.

[0091] Fixed node N (AQ node) phase angle The node reactive power is a given value Q N , then the correction equation changes to:

[0092]

[0093] Where:

[0094]

[0095] θ C =[θ2,...,θ N-1 ] T (28);

[0096] Since the node phase angle and reactive power of node N (AQ node) remain constant, the active power P N No longer given, it can be obtained through the active power equation f PN (θ, V) is obtained, and its power balance equation only contains the reactive power balance equation. Therefore, equation (7) only contains the active power balance equation from node 2 to node N-1.

[0097] CPF forms an extended power flow equation by adding a continuous parameter λ. The Jacobian matrix of the extended power flow equation has one more row and one more column than the Jacobian matrix of the conventional power flow equation, which overcomes the ill-conditioned problem of the Jacobian matrix of the conventional power flow equation when the parameters are close to the limit values. Different from it, the AQ node method reduces the number of active balance equations by setting AQ nodes, so that the new Jacobian matrix has one less row and one column, which solves the problem of the singularity of the Jacobian matrix at the critical point of voltage stability.

[0098] The essence of ATC calculation is to increase the generator output of the power transmission area S and the active load of the power receiving area R while ensuring that the basic power flow in the non-power transmission and non-power receiving areas remains unchanged, until the maximum value of the available transmission capacity between the given areas S and R is achieved when the safe and stable operation of the system is no longer met.

[0099] For constant power factor load node Np To node N, its power factor angle is Then the reactive power of node l is Different from the continuous power flow method, the load P in the receiving area l It is no longer increased by the load parameter λ, but by the active power P of node N (AQ node) N To grow:

[0100]

[0101] In the formula, α l is the proportional coefficient of load growth, P l 0 and are the initial active power of load l and AQ node respectively, and P N The growth of can be achieved by continuously increasing the phase angle difference between node N (AQ node) and the balance node until the voltage stability critical point is reached.

[0102] The increased load can be balanced by increasing the active output of the generator from node 1 to node q in the transmission area, and the growth pattern is:

[0103]

[0104] Where P1 is the active power of the balancing node, β k is the proportional coefficient of generator growth, and P1 0 are the initial active outputs of generator k and the balancing node respectively.

[0105] Without considering the transmission reliability margin and capacity efficiency margin, it is believed that when the power generation output and load growth reach the limit value respectively, the obtained transmission capacity is the ATC value that satisfies the static voltage stability constraint.

[0106] The important factors affecting the reactive power output of the generator are mainly the stator heating limit, the rotor heating limit, the generator magnetic circuit saturation, and the leading phase operation mode of the generator. When the generator magnetic circuit is saturated, the synchronous reactance values ​​of its direct axis and quadrature axis will change. The calculation of the saturated synchronous reactance is relatively complicated and is not considered. Similarly, the leading phase operation mode of the generator is not considered. Only the influence of the excitation current and armature current under the stator heating limit and rotor heating limit is considered.

[0107] According to the theory of electrical machinery, for salient pole machines, ignoring the stator side resistance, the steady-state power equation of the generator can be expressed as:

[0108]

[0109] Where: P g and Q gare the active power and reactive power of the generator respectively; E q is the no-load electromotive force of the generator; δ is the generator power angle; V is the terminal voltage; X d and X q They are direct-axis reactance and quadrature-axis reactance respectively. For hidden-pole machines, there are X d =X q .

[0110] In actual operation, in order to prevent the generator excitation winding from overheating, an integral controlled overexcitation limiter is usually used to limit the excitation current. Under steady-state conditions, when the excitation current reaches the upper limit, that is, When the unsaturated electromotive force E q Keep at a constant value:

[0111]

[0112] Where: is the upper limit of the no-load electromotive force of the generator; ω0 is the synchronous angular velocity; L ad is the mutual inductance between the excitation winding and the direct axis.

[0113] Under the per-unit value, equation (32) can be expressed as:

[0114]

[0115] At this time, the generator reactive power can be expressed as:

[0116]

[0117] The generator power angle can be expressed as a function of the generator active output and terminal voltage at the steady state moment:

[0118] δ=f(P g ,V) (35);

[0119] In case of voltage emergency in the power system, in order to prevent the generator stator winding from overheating, an armature current limiter is usually used to limit the armature current. When the armature current reaches the upper limit, that is, When , the reactive power of the generator is:

[0120]

[0121] In the conventional power flow calculation process, the generator nodes without reactive power exceeding the limit are set as PV nodes. This calculation method takes into account the constraints of excitation current and armature current. When the corresponding parameters exceed the limit, the generator node type will be converted and its mathematical model will also change. Under the constraint of excitation current, the generator node type is converted to PI f The mathematical model is changed to a constant excitation model. Under the armature current constraint, the node type is converted to PI. aNode, the mathematical model is the constant armature current model.

[0122] In the constant excitation model, the no-load electromotive force E of the generator node is q Maintain at upper limit At this time, the node voltage V i and generator power angle δ i is an unknown quantity, δ i It can be expressed as P gi and V i Therefore, when solving the Jacobian matrix, we need to consider correction.

[0123] From formula (34), we can get:

[0124]

[0125] For the unknown quantity δ i , can be obtained from the generator active power equation in equation (31) by the first-order Newton method, and the initial value is It can converge stably.

[0126] The diagonal elements of the modified Jacobian matrix are On the basis of the original Item, then formula (21) is corrected to:

[0127]

[0128] In the constant armature current model, the armature current reaches an upper limit, i.e. Formula (29) for V i Find the partial derivative:

[0129]

[0130] Similarly, the Jacobian matrix is ​​corrected, and formula (21) is corrected to:

[0131]

[0132] In summary, the steps of the method for calculating the available power transmission capacity based on the AQ node described in the specific implementation manner of the present invention are as follows:

[0133] (1) Obtaining basic power grid flow parameters of the power system: including the voltage amplitude and phase angle of each node, the active power and reactive power of the generator at each node, the active power and reactive power of the load at each node, the admittance matrix of the node, and the active power and reactive power of the transmission line;

[0134] (2) Grid power flow parameter initialization: including the setting of control variables, state variables, upper and lower limits of generator active power and reactive power, upper and lower limits of load node active power and reactive power, maximum transmission capacity of the line, and related parameters;

[0135] (3) Set the load type to constant power factor load and set the system node N to AQ node;

[0136] (4) Starting from the initial operating point of the power system, set the growth pattern of generators and loads;

[0137] (5) Increase the load active power, take into account the constraints of the excitation current and the armature current, jump into the node switching judgment subroutine, perform power flow calculation by the Newton-Raphson method, and determine whether the power flow calculation iteration converges; if the power flow calculation iteration converges, continue to run step (5); if the power flow calculation iteration does not converge, run step (6);

[0138] (6) The power flow calculation method is changed from the Newton-Raphson method to the AQ node method;

[0139] (7) Increase the phase angle difference between node N (AQ node) and the balance node, and obtain the active power P after the increase of node N (AQ node) N ;

[0140] (8) The active power P after the increase of node N (AQ node) in step 7) N Update the active power of other load nodes and generator nodes, take into account the constraints of excitation current and armature current, jump into the node switching judgment subroutine, and use the updated node data to solve the power flow again;

[0141] (9) Determine the active power P after the increase of node N (AQ node) N Is it over the limit? If so, jump to step (10); otherwise, repeat steps 6), 7), and 8) until the active power P of node N (AQ node) increases. N Until the limit is exceeded;

[0142] (10) Output power flow solution;

[0143] (11) Available power transmission capacity under stable output voltage conditions.

[0144] After considering the constraints of excitation current and armature current, the embedded node determination subroutine steps are as follows:

[0145] 1) According to the node's P gi , Q gi and V i , solve the generator no-load electromotive force E at the PV node qi ;

[0146] 2) Determine whether the reactive power of the generator node exceeds the limit. If The no-load electromotive force E qi Maintain the upper limit Constant;

[0147] 3) The generator node type is converted from PV node to PI f Node, the reactive power model is the constant excitation model, E qi Keep upper limit Constant, solve the generator power angle δ i , calculate Q under the limit gi , and correct the Jacobian matrix and reactive power balance equation;

[0148] 4) According to the node's P gi , Q gi and V i , solve the armature current I of the generator node ai ;

[0149] 5) Determine whether the generator armature current exceeds the limit. If Then I ai Keep at upper limit If constant, execute step 6), otherwise, exit the inner loop;

[0150] 6) Convert the generator node type to PI a Node, the reactive power model is the constant armature current model, and the Q under the limit is calculated gi , and correct the Jacobian matrix and reactive power balance equation.

[0151] The present invention proposes an ATC calculation model based on AQ nodes and taking into account the operation constraints of generators. The active load of the node is increased by increasing the phase difference between the AQ node and the balance node until the voltage stability critical point, which has better stability and calculation speed. At the same time, the influence of excitation current and armature current on the reactive power of the generator is considered, and the node where the over-limit generator is located is converted into PI f Node or Pi a The node is more in line with the actual system operation state, and the obtained ATC result is closer to reality. Moreover, for different reactive power models, it is only necessary to correct the partial derivative of the reactive power to voltage in the Jacobian matrix during the solution process, without considering the correction of the partial derivative vector of the load parameter, which reduces the derivation of the formula and is of great significance for ATC calculation.

[0152] Since the present invention does not add the load parameter λ, for different reactive power models, it is only necessary to modify the Jacobian matrix, which reduces the derivation of the formula and simplifies the calculation process. At the same time, the present invention considers the influence of the excitation current and the armature current on the reactive power of the generator, embeds the node switching judgment, and converts the node where the over-limit generator is located into PI f Node or Pi a The nodes are more in line with the actual operating conditions, and the available transmission capacity obtained is more practical.

[0153] Example 1

[0154] The New England 10-machine 39-node (IEEE 39) system was selected for verification. Fig.12 It is the IEEE 39-node system partition diagram, Area 1 is the power transmission area, Area 2 is the power receiving area, nodes 31 to 36 in Area 1 are generator nodes for balanced load growth, and nodes 3, 15 to 18, 21, 25 to 29 in Area 2 are load growth nodes, among which node 31 is a balancing node and node 16 is an AQ node. The proportional coefficients of the relevant nodes are shown in Table 1. Table A1 is the IEEE-39-node system generator parameter table.

[0155]

[0156] Table 1

[0157]

[0158] Table A1

[0159] Note: All units are in per unit, and the power reference value is 100MVA.

[0160] Consider the following four cases: Case 1, no processing is performed on reactive power exceeding the limit; Case 2, considering the change of node type after reactive power exceeding the limit, the generator exceeding the limit is converted into a PQ node, and the reactive power of the generator is kept constant; Case 3, considering the excitation current constraint, the generator node exceeding the limit is converted into a PI node. f Node; Case 4, taking into account the armature current constraint, the over-limit generator node is converted into PI a Node,generator data are shown in Table A1.

[0161]

[0162] Table 2

[0163] Figure 5 , 6 The PV curve and AP curve of node 16 are given in four cases. Table 2 gives the calculation results in the four cases. Figure 7-10The AQ curves under four constraints of each generator node in the power generation area are given; from the above curves and Table 2, it can be seen that in case 1, the reactive power of the generator in the power generation area continues to increase with the increase of the angle difference between the AQ node and the balance node, until the maximum load point, the reactive power of some generators has exceeded the limit, and the obtained ATC value is too large, which is 1641.55MW; case 2 adopts the constant reactive power limit method to keep the reactive power of the over-limit generator constant, and the node where it is located is converted from a PV node to a PQ node. Although the reactive power limit of the generator is taken into account, its ATC value is reduced compared with case 1, which is 1144.89MW. However, this case does not take into account that the reactive power of the generator will decrease with the increase of active power in actual conditions, and the result is still too large; while cases 3 and 4 take into account the constraints of the generator excitation current and armature current, consider the transformation of the node type and the reactive power model of the generator after the relevant parameters exceed the limit, and convert the node where the over-limit generator is located from a PV node to a PI node. f or PI a After the node, with the increase of load active power, the AQ curve decreases, and the reactive power of the generator also decreases significantly, until the reactive power at the critical point of voltage stability has dropped to a lower level; in summary, case 1 does not consider the constraint of the reactive upper limit, and the reactive value continues to increase with the increase of active power. As a result, the reactive power of the generator at the maximum load point exceeds the limit. Case 2 does not consider that the reactive power of the generator will decrease with the increase of active power after reaching the reactive upper limit. Obviously, these two cases deviate from reality; compared with the above two cases, cases 3 and 4 consider the change of the reactive power of the generator with the active power after the relevant generator parameters exceed the limit, which is more in line with the actual system operation state. Therefore, the ATC value under this condition is also the closest to the actual value, which is 1102.00MW and 1030.00MW respectively.

[0164] Taking the node 35 (generator node 6) that first crossed the limit as an example, the AQ curves of this node in the four cases are as follows: Fig.11 shown; combined Figure 5It can be seen that before point A, the curves in the four cases are consistent. When running to point A, case 2 first determines that the generator reactive power exceeds the limit. After exceeding the limit, the generator reactive power is constant at the upper limit value. In cases 3 and 4, the generator reactive power continues to increase, and exceeds the limit at points B and C respectively. After exceeding the limit, the reactive power of the generator begins to decrease, and its corresponding AQ curve also decreases rapidly. When it is near the critical point of voltage stability, its reactive power has dropped to a very low level. Correspondingly, the PV curve of the load also drops rapidly after exceeding the limit. At the critical point of voltage stability, the voltage has dropped to a very low level. The reason is that in case 2, the constant reactive upper limit model underestimates the reactive capacity of the system when the generator is lightly loaded, and generates less reactive power than cases 3 and 4, which is conservative. However, it overestimates the reactive capacity of the generator when it is heavily loaded, and its reactive curve remains constant above cases 3 and 4 without decreasing. Between point A and point C, cases 3 and 4 do not exceed the limit, and the curves remain consistent. When it reaches point C, the armature current of the generator exceeds the limit, which is earlier than the excitation current exceeding the limit point B. This shows that when the generator meets the excitation current limit, it cannot guarantee that the armature current of the generator will not exceed the limit, and according to Figure 5 It can be seen that the reactive power curve of case 4 is always smaller than that of case 3, which means that with the increase of active power, it is not ruled out that it is always affected by a single restriction, but the ATC value under the armature current restriction is smaller; after point B, in case 1, since the node conversion under the reactive power constraint is not considered, the reactive power of the generator always shows an increasing trend, which is obviously not in line with reality.

[0165] This embodiment proposes a method for calculating the available transmission capacity based on the AQ node. According to the operating characteristics of the synchronous generator, the influence of the excitation current and the armature current on the reactive power of the generator is considered, and the node where the over-limit generator is located is converted into the PI f Node or Pi a For nodes, since the load parameter λ is not added, for different reactive power models, only the Jacobian matrix needs to be corrected, which reduces the derivation of the formula. The feasibility of the model and algorithm is verified through simulation calculation of the IEEE 39-bus system.

[0166] As mentioned above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself, and various changes in form and details may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for calculating available transmission capacity based on AQ nodes, characterized in that The method comprises the following steps: (1) Obtain basic power grid flow parameters of the power system; (2) Initialization of power grid flow parameters; (3) Set the load type to constant power factor load and set the system node N to AQ node; (4) Starting from the initial operating point of the power system, set the growth pattern of generators and loads; (5) Increase the load active power, take into account the constraints of excitation current and armature current, jump into the node switching judgment subroutine, and convert the node where the over-limit generator is located into PI f Node or Pi a Node, perform power flow calculation using the Newton-Raphson method, and determine whether the power flow calculation iteration converges; if the power flow calculation iteration converges, continue to run step (5); if the power flow calculation iteration does not converge, run step (6); (6) The power flow calculation method is changed from the Newton-Raphson method to the AQ node method; (7) Increase the phase angle difference between node N and the balance node to obtain the active power P after node N increases. N ; (8) The active power P after the node N increases from step 7) N Update the active power of other load nodes and generator nodes, take into account the constraints of excitation current and armature current, jump into the node switching judgment subroutine, and use the updated node data to solve the power flow again; (9) Determine the active power P after node N increases N Is it over the limit? If so, jump to step (10); otherwise, repeat steps (6), (7), and (8) until the active power P of node N increases. N Until the limit is exceeded; (10) Output power flow solution; (11) Available power transmission capacity under stable output voltage conditions.

2. The method for calculating the available power transmission capacity based on the AQ node according to claim 1, characterized in that The basic power grid flow parameters in step (1) include the voltage amplitude of each node, the voltage phase angle of each node, the active power of the generator of each node, the reactive power of the generator of each node, the active power of the load of each node, the reactive power of the load of each node, the admittance matrix of the node, the active power of the transmission line, and the reactive power of the transmission line.

3. The method for calculating the available power transmission capacity based on the AQ node according to claim 1, characterized in that The grid power flow parameter initialization in step (2) specifically includes: defining control variables, defining state variables, setting upper and lower limits of generator active power, generator reactive power, load node active power, load node reactive power, and voltage amplitude of each node, and setting the maximum transmission capacity of the line; the definition of control variables includes defining the voltage amplitude of each node and the voltage phase angle of each node as control variables; the definition of state variables includes defining the generator active power, generator reactive power, load active power, and load reactive power as state variables.

4. The method for calculating the available power transmission capacity based on the AQ node according to claim 1, characterized in that In step (3), the load type is set to a constant power factor load, as shown in formula (1): In the formula, Q l is the reactive power of node l, is the power factor angle, l is the constant power load node number, N p is the initial number of the constant power load node, N is the total number of grid nodes, P l It is the active power of the load in the power receiving area.

5. The method for calculating the available power transmission capacity based on the AQ node according to claim 1, characterized in that In step (4), starting from the initial operation point of the power system, the growth mode of the generator and the load is set, wherein the active power P of the load in the receiving area is l Active power P passing through node N N The load in the receiving area does not include node N, as shown in formula (2): In the formula, α l is the proportional coefficient of load growth, P l 0 and are the initial active power of load l and node N respectively, where the active power of node N is P N The growth of is achieved by continuously increasing the phase angle difference between node N and the balance node until the voltage stability critical point is reached, l is the constant power load node number, N p is the initial number of the constant power load node, and N is the total number of grid nodes; The increased load is met by increasing the transmission area generator node 1 to node N G The active output of the generator in the transmission area is balanced, and the growth mode of the active output of the generator in the transmission area is shown in formula (3): Where P1 is the active power of the balancing node, β k is the proportional coefficient of generator growth, and P1 0 are the initial active output of generator k and the balancing node, P k is the active output of generator k, k is the generator number in the transmission area, N G is the total number of generators in the power transmission area.

6. The method for calculating the available power transmission capacity based on the AQ node according to claim 1, characterized in that In step (5), the load active power is increased, and after taking into account the constraints of the excitation current and the armature current, the node switching determination subroutine is entered, and the power flow calculation is performed by the Newton-Raphson method, as follows: Assuming that the number of generator nodes in the power system is N G The total number of nodes in the power grid is N, and the order is node 1 to node N. G All are power transmission area generator nodes, node N G +1 to node N are all load nodes in the power receiving area. Assuming node 1 is a balance node, the active power and reactive power balance equations of the power system are as follows: ΔP i =P i -f Pi (θ,V)=0 i=2,...,N (4); ΔQ i =Q i -f Qi (θ,V)=0 i=N G +1,...,N (5); Where: i is the node number, P i and Q i are the active power and reactive power given to node i, respectively, and f Pi (θ, V) and f Qi (θ, V) are the active power equation and reactive power equation of node i, θ and V are the voltage phase angle and amplitude of the node, ΔP i and ΔQ i are the active power error and reactive power error of node i respectively; Solving with Newton's method, we can obtain the modified equation (6): Where: θ=[θ2,...,θ N ] T (8); Δθ and ΔV are the correction amounts of θ and V.

7. The method for calculating the available power transmission capacity based on the AQ node according to claim 1, characterized in that In step (6), the power flow calculation method is changed from the Newton-Raphson method to the AQ node method, specifically: If the Newton-Raphson method does not converge in the iteration of the power flow calculation in step (5), the power flow calculation based on the Newton-Raphson method is transformed into the power flow calculation method based on the AQ node. The specific method is as follows: the node N phase angle is changed from the control variable to the given value θ N ,θ N The initial value is The reactive power of node N is a given value Q N , then the correction equation changes to: Where: i C =[θ2,...,θ N-1 ] T (12); Since the node phase angle and reactive power of node N remain constant, the active power P N It is no longer given, and its power balance equation only has the reactive power balance equation. Therefore, equation (10) only contains the active power balance equation from node 2 to node N-1.

8. The method for calculating available power transmission capacity based on AQ nodes according to claim 5, characterized in that In step (7), the active power P of node N after growth is obtained N , specifically according to the active power equation f PN (θ, V) to obtain the active power P of node N N ; In step (8), the active power P after the node N increases in step (7) N Update the active power of other load nodes and generator nodes, specifically: the active power P of the node in step (7) N Substitute into equations (2) and (3) to update the active power of other load nodes and generator nodes.

9. The method for calculating the available power transmission capacity based on the AQ node according to claim 7, characterized in that In step (8), the updated node data is used to solve the power flow again. Specifically, the updated node data is substituted into equations (10), (11), and (12) to solve the power flow again.

10. A method for calculating available power transmission capacity based on an AQ node according to any one of claims 1 to 9, characterized in that After taking into account the excitation current and armature current constraints in step (5) and step (8), a node switching determination subroutine needs to be embedded in step (5) and step (8); the node switching determination subroutine is specifically as follows: 1) According to the node's P gi , Q gi and V i , solve the generator no-load electromotive force E of the PV node according to formula (13): qi : 2) Determine whether the reactive power of the generator node exceeds the limit. If The no-load electromotive force E qi Maintain at upper limit Constant; 3) The generator node type is converted from PV node to PI f Node, the reactive power model is the constant excitation model, E qi Keep upper limit Constant, solve the generator power angle δ i , calculate Q under over-limit according to formula (14) gi , The Jacobian matrix and reactive power balance equation are modified according to equations (15) and (16), where P g and Q g are the active power and reactive power of the generator, E q is the no-load electromotive force of the generator, δ is the generator power angle, V is the terminal voltage, X d and X q They are direct-axis reactance and quadrature-axis reactance respectively. For hidden-pole machines, there are X d =X q ; 4) According to the node's P gi , Q gi and V i , solve the generator node armature current I according to formula (17): ai : 5) Determine whether the generator armature current exceeds the limit. If Then I ai Keep at upper limit If constant, execute step 6), otherwise, exit the inner loop; 6) Convert the generator node type to PI a The reactive power model is a constant armature current model. The Q under over-limit is calculated according to formula (17): gi , and according to equations (18) and (19) the Jacobian matrix and reactive power balance equation are modified: Among them, f Qi (θ,V) is the reactive power equation of node i.

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