CN113363990B - HELM power flow calculation method considering PI nodes - Google Patents

HELM power flow calculation method considering PI nodes Download PDF

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CN113363990B
CN113363990B CN202110691838.XA CN202110691838A CN113363990B CN 113363990 B CN113363990 B CN 113363990B CN 202110691838 A CN202110691838 A CN 202110691838A CN 113363990 B CN113363990 B CN 113363990B
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高慧敏
钟毅
赵嘉敏
黄卓
罗平
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Hangzhou Dianzi University
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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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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 discloses a method for HELM power flow calculation considering PI nodes. The method comprises the steps of firstly establishing a mathematical model of the power distribution network containing PQ and PI nodes, then constructing a pure function corresponding to the PI node according to an HELM method, and finally deducing a PI node pure function recursion formula according to a recursion method to calculate the power flow of the power distribution network containing the PI node. According to the method, a PI node mathematical model is considered by using a HELM method, a PI node full-pure function recursion formula is deduced, the power flow of the power distribution network containing PI nodes can be calculated, and the method can be used for power flow calculation and voltage analysis control of the power distribution network containing PI distributed power supplies.

Description

HELM power flow calculation method considering PI nodes
Technical Field
The invention belongs to the technical field of electric power information, and particularly relates to a method for HELM power flow calculation considering PI nodes.
Background
With the development of new energy technology in the field of power distribution networks, Distributed Generation (DG) is gradually connected in large quantities. The distributed power supply is a small generator set which utilizes renewable energy sources and generates power below 50MW, is placed near a user to carry out short-distance power supply work, and is connected to a power distribution network nearby to meet the power demand of the user. Distributed power sources typically include photovoltaic power generation systems, micro gas turbines, fuel cells, wind turbines, and the like. The traditional PQ decomposition method and the forward-backward substitution method can solve the load flow containing PQ and PV nodes in the process of solving the power grid load flow, but one of the differences between the power distribution network load flow calculation containing DG and the common load flow calculation is that the DG load flow calculation model is inconsistent with the traditional generator set calculation model. The traditional generator node is generally taken as a PQ node, a PV node or a balance node in load flow calculation, and DG has particularity, wherein the double-fed induction machine and the synchronous fan can correspondingly adjust and control power through a conversion signal of a frequency conversion control system, and the double-fed induction machine and the synchronous fan are generally regarded as the PQ node; micro gas turbines, fuel cells, voltage controlled photovoltaic power generation systems are generally considered PV nodes; if the photovoltaic power generation system adopts a current control inverter strategy, the power generation system is considered as a PI node, and outputs active power and current to be injected into a power distribution network. The grid power flow including the DG may also be processed by solving the power flow including the PQ and PV nodes by a PQ decomposition method and a forward-backward substitution method, and iteratively converting the PI node into the PQ node.
In recent two years, a load flow calculation method based on Holomorphic Embedding (HELM) is provided, the load flow method completely subverts the traditional cow pulling method, and whether a load flow solution exists can be determined without depending on a node initial value. The method can completely solve the problems of load flow calculation, reactive power optimization, voltage stability analysis and the like of the traditional power system. Currently, the HELM can solve the power flow containing PQ and PV nodes, but no relevant literature research exists at present on how to calculate the power grid power flow containing PI nodes by using the HELM. Since the HELM method is a recursive algorithm and not an iterative algorithm, it cannot be handled by a conventional method of converting a PI node into a PQ node in an iteration.
Disclosure of Invention
Aiming at the defects of the prior art of the HELM power flow calculation, the invention provides the HELM power flow calculation method considering the PI nodes, which can be used for the power flow calculation of the distributed power supply comprising the PI nodes and the voltage stabilization prevention control of the power distribution network comprising the distributed power supply, and has the advantages of high calculation speed, simple calculation and higher theoretical significance and application value.
The technical scheme of the invention is as follows:
a power grid HELM power flow calculation method considering PI nodes comprises the following steps:
step one, establishing a mathematical model of a power grid, and establishing the mathematical model of the power grid comprising PI nodes:
if the node is a PI node, the node power equation:
Figure BDA0003127085730000021
Figure BDA0003127085730000022
where P is the set of PI nodes, PiRepresenting injected active power of the I-node, IiRepresents the injection current of the I node, | IiThe absolute value of which is expressed in,
Figure BDA0003127085730000023
representing the magnitude of the current, V, at the i-nodei、VkThe voltages of node i and node k, respectively; y isikThe upper mark represents the conjugate relation for the admittance between the node i and the node k; n is the total number of the nodes of the power grid; re (·) represents the real part of the complex phasor.
Step two, constructing an embedded pure imaginary function of the PI node by using an HELM method:
Figure BDA0003127085730000024
wherein Vi[n]Nth voltage component, s, representing i-node voltage in HELM power flow calculationnAn n-th term representing a frequency domain operator s;
if the node is a PI node, the formula (4) is substituted into the formula (2) and a corresponding pure function is constructed to obtain:
Figure BDA0003127085730000025
in the formula PiInjecting active power, Q, for the i-nodei(s) injected reactive power Q for i nodei(s)＝Qi[0]+Qi[1]s+Qi[2]s2+…+Qi[n]sn，
Figure BDA0003127085730000026
YiiSelf-admittance of an i-node in a node admittance matrix; y isikThe mutual admittance between the i and k nodes in the node admittance matrix is obtained; y isi,shuntIs the ground admittance of the i-node.
Constraint by PI node:
Figure BDA0003127085730000027
the formula (4) may be substituted for the formula (7):
Figure BDA0003127085730000031
is unfolded into
Figure BDA0003127085730000032
The coefficients according to the s-order are equal by equation (12):
Figure BDA0003127085730000033
Figure BDA0003127085730000034
Figure BDA0003127085730000035
if the node is a PI node, taking the formula (4) into the formula (6) to obtain:
Figure BDA0003127085730000036
and then substituting formula (8) for formula (19) to obtain:
Figure BDA0003127085730000037
the coefficients according to the s-order are equal by equation (20):
Figure BDA0003127085730000038
by
Figure BDA0003127085730000041
The coefficients according to the s series are equal, so that:
Figure BDA0003127085730000042
step three, recursively calculating the load flow according to the constructed all-pure-function load flow calculation model;
1) first, V is obtained from the equation (10)k[i](i.ltoreq.n-1), and d is determined from the formula (23)k[i](i.ltoreq.n-1), and Q is obtained from equations (13) to (15) for the PI nodek[i](i≤n-1)；
2) Solving V by using the recursive equation of equation (21)k[n]；
Repeating the steps 1) and 2) to obtain all Vk[n]、Qi[n],i∈p。
Thereby, it is possible to obtain:
Figure BDA0003127085730000043
when s is 1, a solution to the trend can be obtained.
The invention has the following beneficial effects: the method can be used for load flow calculation, voltage sensitivity calculation, voltage stability analysis and voltage control of a power distribution network comprising the PI node distributed power supply, the voltage analysis control problem of the power distribution network comprising the distributed power supply, the access of new energy, the voltage stability analysis and control and the like, so that the selection of a reactive compensation point is more reasonable, the economy of a compensation scheme is better, the network loss is further reduced, the voltage level and the power factor are improved, and the method has higher theoretical significance and application value on reactive optimization and voltage stability analysis control of the power grid.
Drawings
Fig. 1 is a mathematical model for establishing a 33-node power grid for raw data in a specific application example.
FIG. 2 is a flow chart illustrating flow results in an exemplary embodiment;
FIG. 3 is a schematic diagram of the results of a flow including the HELM process and the Newton's method.
Detailed Description
The embodiment of the invention provides a method for HELM power flow calculation considering PI nodes, which comprises the following steps:
step one, establishing a mathematical model of a power grid comprising a PQ node and a PI node.
The root node is a balance node, and in addition, a PQ node and a PI node are arranged:
if the node is a PQ node, the power equation of the node is as follows:
Figure BDA0003127085730000051
in the formula, m is a PQ node set, and i and k are node numbers; vi、VkThe voltages of node i and node k, respectively; y isikIs the admittance between node i and node k; siInjection power for node i; n is the total number of nodes; superscript denotes conjugation;
if the node is a PI node, the node power equation:
Figure BDA0003127085730000052
Figure BDA0003127085730000053
where P is the set of PI nodes, PiRepresenting injected active power of the I-node, IiRepresents the injection current of the I node, | IiThe absolute value of which is expressed in,
Figure BDA0003127085730000054
representing the magnitude of the current, V, at the i-nodei、VkThe voltages of node i and node k, respectively; y isikThe upper mark represents the conjugate relation for the admittance between the node i and the node k; n is the total number of the nodes of the power grid; re (·) represents the real part of the complex phasor.
And step two, constructing a pure function mathematical model by using an HELM method.
Because the node voltage is related to the node injection power and the like, the injection power comprises active power and reactive power and is usually expressed by complex numbers, and the holomorphic function is a complex analysis method, an embedded pure imaginary function can be constructed according to the embedded holomorphic function method:
Figure BDA0003127085730000055
in the formula, s is an embedded parameter factor; vi(s) is the s-series expansion of the inode; n is the order of s series; vi[n]Is the coefficient of the s-order and n-order terms of the voltage of the i node. snRepresenting the n-th order of the frequency domain operator s.
If the node is PQ node, formula (4) is substituted into formula (1) and corresponding pure function is constructed to obtain:
Figure BDA0003127085730000061
in the formula:
Figure BDA0003127085730000062
Yiiself-admittance of an i-node in a node admittance matrix; y isikThe mutual admittance between the i and k nodes in the node admittance matrix is obtained; y isi,shuntIs the ground admittance of the i-node.
If the node is a PI node, the formula (4) is substituted into the formula (2) and a corresponding pure function is constructed to obtain:
Figure BDA0003127085730000063
in the formula PiInjecting active power, Q, for the i-nodei(s) injected reactive power Q for i nodei(s)＝Qi[0]+Qi[1]s+Qi[2]s2+…+Qi[n]sn。
Constraint by PI node:
Figure BDA0003127085730000064
suppose that:
Figure BDA0003127085730000065
when s is 0, the following formula (5) or (6) can be obtained:
Figure BDA0003127085730000066
solving for V of all nodes by equation (9)i[0]
Vi[0]＝1 (10)
The formula (4) may be substituted for the formula (7):
Figure BDA0003127085730000067
is unfolded into
Figure BDA0003127085730000071
The coefficients according to the s-order are equal by equation (12):
Figure BDA0003127085730000072
Figure BDA0003127085730000073
Figure BDA0003127085730000074
if the node is a PQ node, taking the formula (4) into the formula (5) to obtain:
Figure BDA0003127085730000075
and substituting formula (8) for formula (16) to obtain:
Figure BDA0003127085730000076
the coefficients according to the s-order are equal by equation (17):
Figure BDA0003127085730000077
if the node is a PI node, taking the formula (4) into the formula (6) to obtain:
Figure BDA0003127085730000078
and then substituting formula (8) for formula (19) to obtain:
Figure BDA0003127085730000081
the coefficients according to the s-order are equal by equation (20):
Figure BDA0003127085730000082
by
Figure BDA0003127085730000083
The coefficients according to the s series are equal, so that:
Figure BDA0003127085730000084
and thirdly, recursively calculating the load flow according to the constructed all-pure-function load flow calculation model.
1) First, V is obtained from the equation (10)k[i](i.ltoreq.n-1), and d is determined from the formula (23)k[i](i.ltoreq.n-1), and Q is obtained from equations (13) to (15) for the PI nodek[i](i≤n-1)；
2) Solving V by using the recursion equations of the equations (18) and (21)k[n]；
Repeating the steps 1) and 2) to obtain all Vk[n]、Qi[n],i∈p。
Thereby, it is possible to obtain:
Figure BDA0003127085730000085
when s is 1, a solution to the trend can be obtained.
The HELM power flow solution is not set by an initial value, the HELM can clearly inform whether the power flow solution exists or not, and a voltage collapse point can be predicted.
The following is a further description of a specific application example in conjunction with the accompanying drawings.
a. A mathematical model of the grid was built from the raw data of fig. 1, which are shown in table 1. The grid includes both PQ nodes and PI nodes, where 1 node is a balanced node, 16 nodes are PI nodes (a distributed power source with P being 300KW and I being 50A is added), and the other nodes are PQ nodes.
If the node is PQ node, the power equation of the node is calculated
Figure BDA0003127085730000091
In the formula: m is a PQ node set, i and k are node numbers; vi、VkThe voltages of node i and node k, respectively; y isikIs the admittance between node i and node k; siInjection power for node i; n is the total number of nodes; superscript denotes the conjugate relationship.
If the node is a PI node, the node power equation:
Figure BDA0003127085730000092
Figure BDA0003127085730000093
where P is the set of PI nodes, PiRepresenting the real part of the injected power,
Figure BDA0003127085730000094
representing the current magnitude of the i-node;
b. and constructing a pure function mathematical model by using an HELM method.
c. The load flow is calculated recursively according to the constructed pure function load flow calculation model, and the results of calculating the power grid load flow including the PI nodes by the HELM method and the Newton-Czochralski method are shown in FIG. 2. The error of the results of the HELM method and the Czochralski method are shown in FIG. 3.
As can be seen from fig. 2 and 3, the power distribution network hell power flow calculation result is basically consistent with the cow-pulling power flow calculation result, which shows that the method for calculating the power grid power flow including the PI node by using the hell method of the present invention is correct and feasible.
Grid system standard data of table 133 node
Figure BDA0003127085730000095
Figure BDA0003127085730000101

Claims (1)

1. The HELM power flow calculation method considering the PI nodes is characterized by comprising the following steps: the method specifically comprises the following steps:
step one, establishing a mathematical model of a power grid, and establishing the mathematical model of the power grid comprising PI nodes:
if the node is a PQ node, the power equation of the node is as follows:
Figure FDA0003523604500000011
in the formula, m is a PQ node set, and i and k are node numbers; vi、VkThe voltages of node i and node k, respectively; y isikIs the admittance between node i and node k; siInjection power for node i; n is the total number of nodes; superscript denotes conjugation;
if the node is a PI node, the node power equation:
Figure FDA0003523604500000012
Figure FDA0003523604500000013
where P is the set of PI nodes, PiRepresenting injected active power of the I-node, IiRepresents the injection current of the I node, | IiThe absolute value of which is expressed in,
Figure FDA0003523604500000014
representing the magnitude of the current, V, at the i-nodei、VkThe voltages of node i and node k, respectively; y isikThe upper mark represents the conjugate relation for the admittance between the node i and the node k; n is the total number of the nodes of the power grid; re (·) represents the real part of the complex phasor;
step two, constructing an embedded pure imaginary function of the PI node by using an HELM method:
Figure FDA0003523604500000015
wherein Vi[n]Nth voltage component, s, representing i-node voltage in HELM power flow calculationnAn n-th term representing a frequency domain operator s;
if the node is a PQ node, substituting the formula (4) into the formula (1) and constructing a corresponding holomorphic function to obtain:
Figure FDA0003523604500000016
in the formula:
Figure FDA0003523604500000017
Yiiself-admittance of an i-node in a node admittance matrix; y isikThe mutual admittance between the i and k nodes in the node admittance matrix is obtained; y isi，shuntA ground admittance for the i-node;
if the node is a PI node, the formula (4) is substituted into the formula (2) and a corresponding holomorphic function is constructed to obtain:
Figure FDA0003523604500000021
in the formula PiInjecting active power, Q, for the i-nodei(s) injected reactive power Q for i nodei(s)＝Qi[0]+Qi[1]s+Qi[2]s2+…Qi[n]sn；
Constraint by PI node:
Figure FDA0003523604500000022
suppose that:
Figure FDA0003523604500000023
when s is 0, the formula (5) or (6) gives:
Figure FDA0003523604500000024
solving for V of all nodes by equation (9)i[0]
Vi[0]＝1 (10)
Substituting formula (4) for formula (7) to obtain:
Figure FDA0003523604500000025
is unfolded into
Figure FDA0003523604500000026
The coefficients according to the s-order are equal by equation (12):
Figure FDA0003523604500000027
Figure FDA0003523604500000031
Figure FDA0003523604500000032
if the node is a PI node, the formula (4) is substituted into the formula (6) to obtain:
Figure FDA0003523604500000033
and then substituting formula (8) for formula (19) to obtain:
Figure FDA0003523604500000034
the coefficients according to the s-order are equal by equation (20):
Figure FDA0003523604500000035
by
Figure FDA0003523604500000036
And obtaining the following coefficients according to the equality of the coefficients of the s series:
Figure FDA0003523604500000041
step three, recursively calculating the load flow according to the constructed all-pure-function load flow calculation model;
1) first, V is obtained from the equation (10)k[i](i.ltoreq.n-1), and d is determined from the formula (23)k[i](i.ltoreq.n-1), and Q is obtained from equations (13) to (15) for the PI nodek[i](i≤n-1)；
2) Solving V by using the recursive equation of equation (21)k[n]；
Repeating the steps 1) and 2) to obtain all Vk[n]、Qi[n]，i∈p，
Thereby obtaining:
Figure FDA0003523604500000042
when s is 1, a solution of the trend is obtained.
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