CN107123983A - A kind of transformer station's access scheme aided assessment method based on security domain - Google Patents
A kind of transformer station's access scheme aided assessment method based on security domain Download PDFInfo
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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
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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Abstract
The invention discloses a kind of transformer station's access scheme aided assessment method based on security domain, including：The status information obtained by Load flow calculation under the current method of operation generates the admittance matrix under the grid structure；Obtain node and inject the expression matrix form of equation, and decision parameters space is determined by the control variable of system, so as to build corresponding Static Voltage Security domain border；Stability margin analysis is carried out to power system, the minimum border of stability margin under the current method of operation of power system is found, obtains the corresponding parameter information in the border, it is determined that input transformer station selection indicators；The transformer station newly put into transformer station's priority access point access on the legacy network architecture basics of power system, and the PQ nodes at access point are converted into PV node；In the case where input Substation parameters are consistent, security domain structure is re-started to the power system corresponding to transformer station's access scheme, is analyzed by stability margin, relatively more different access schemes are good and bad, are defined as final scheme.
Description
Technical field
The invention belongs to Electric Power Network Planning field, more particularly to substation operation planning field.
Background technology
Intelligent substation will pass through the whole process of intelligent grid construction as the physical basis of intelligent grid.With society
Can and it is economical continuing to develop with improving, the power consumers of all trades and professions to the basic demand of power system warp-wise it is safer,
More reliable, more economical transformation, transformer station is born as transmission of electricity and controller switching equipment as a ring particularly important in power system
In most important energy transfer point responsibility, whether its planning and designing reasonable, if can adapt to the big ups and downs of load, meets
Load growth requirement in forthcoming years, is extremely important, therefore, to the optimization A+E of transformer station's access system
Technology is one of important content in Operation of Electric Systems project study.
Design method is accessed with traditional transformer station --- compared with " point by point method ", the security domain quickly grown in recent years
(Security Region, SR) method can effectively overcome the defect of " point by point method ".SR and the network of system are one-to-one,
Running status independent of system；After SR border is calculated, it is possible to by judge the injection of system currently whether position
In carrying out security related verification in SR.Meanwhile, SR can provide relative position of the current point of operation in domain, be to characterize
The security margin for entirety of uniting.
The out-of-limit problem of node voltage in power system merits attention, existing research node voltage amplitude constraint at present
Security domain only has idle Steady State Security Region.Variable in the decision space of idle Steady State Security Region be node reactive power inject to
Amount, it gives higher dimensional space based on the mapping relations in solution lotus root power flow equation between expression voltage vector and reactive power vector
The idle security domain of upper hyperpolyhedron form.Required idle Steady State Security Region is made up of multipair approximately parallel hyperplane,
It is very concise.It is completely unrelated with the method for operation and the domain is corresponded with network topology, so can above be counted offline in application
Calculate, online practical, superiority is very prominent.But, because it is, based on solution lotus root trend, to have ignored active injection to voltage
Influence, so error is larger sometimes, it is impossible to meet safety on line monitoring, the requirement of defence and control.
In recent years, to Static Voltage Security domain (Static Voltage Security Region, SVSR) and its related
Using having been carried out substantial amounts of research.Research found in the range of engineering care, and SVSR border can be with one or more
Hyperplane is indicated.In the past about in SVSR research, being never applied in transformer station's access scheme evaluation problem.How to adopt
With the method for security domain, aid decision is provided for transformer station's access system plan, needs further exploration.
The content of the invention
The present invention is on the basis of idle Steady State Security Region, based on AC Ioad flow model, research meter and node voltage constraint
Static Voltage Security domain there is provided a kind of transformer station's access scheme aided assessment method based on security domain, try hard to obtain energy
The approximate analysis expression formula on the Static Voltage Security domain border of practical implementation needs is enough met, and then is connect for different substation
Enter scheme, system node voltage problem is analyzed, aid decision is provided for substation operation planning.In order to solve above-mentioned technology
Problem, The present invention gives a kind of transformer station's access scheme aided assessment method based on security domain, comprises the following steps：
Step 1: by electric power system data, the status information (V, θ) under the current method of operation is obtained by Load flow calculation,
Generate the admittance matrix under the grid structure；Wherein, V is node voltage amplitude, and θ is node voltage phase angle；
Step 2: the admittance matrix drawn using step one obtains the expression matrix form that node injects equation, and by electricity
The control variable of Force system determines decision parameters spaceSo as to build corresponding Static Voltage Security domain border；
Step 3: the Static Voltage Security domain obtained according to step 2, stability margin analysis is carried out to power system；Find
The minimum border of stability margin, obtains the corresponding parameter information in the border under the current method of operation of power system, it is determined that input becomes
Power station selection indicators, input transformer station selection indicators refer to：The corresponding coefficient of active parameter and there is the absolute of work value product
The sum of value coefficient corresponding with idle parameter and the absolute value without work value product；Input transformer station selection indicators are carried out
Sequence, it is transformer station's priority access point to take out the big node of N number of input transformer station selection indicators numerical value, and N value is 2~10；
Step 4: the legacy network structure of power system is set as scenario A, in the legacy network architecture basics of power system
On scene after the transformer station that the transformer station priority access point access that step 3 is determined newly is put into be scenario B, at access point
PQ nodes be converted to PV node；
Step 5: in the case where input Substation parameters are consistent, the method provided using step 2 is to the N number of of scenario B
Power system corresponding to transformer station's access scheme re-starts security domain structure, is analyzed by stability margin, to N number of transformer station
The stability margin value of the power system of access scheme and the power system of scenario A is compared, if stability margin value maximum
Power system is transformer station's access scheme in scenario B, then most the program is defined as transformer station's access scheme at last, no
Then, do not consider to access transformer station in the power system.
Further, in step 2, Static Voltage Security domain structuring approach is specifically included：
If：Power system has n-1 node and nb bar branch roads, and its interior joint 0 is slack bus, there is g+1 generator section
Point；Generator node in addition to slack bus, the set of power transformation tiny node are represented with S；The set of load bus is represented with L；
In Operation of Electric Systems point V=1, the small neighbourhood of θ=0, cos θ are utilizedij=1, sin θij=θi-θjTo exchange side
Cheng Jinhang processing obtains formula (2), shown in exchange equation such as formula (1)：
In formula (1), Pij、QijThe active power and reactive power transmitted for circuit ij；Vi、VjRespectively node i, j electricity
Pressure amplitude value；θi、θjRespectively node i, j voltage phase angle, θij=θi-θj；Gij、BijFor the corresponding element of admittance matrix；
Node i application Kirchhoff's theorem is obtained：
In formula (3), Pi、QiFor the active power injection and reactive power injection of node i；
Being write formula (3) as matrix form is：
In formula (4), G, B is respectively n × n rank matrixes, wherein, G is the real part of admittance matrix, and B is the imaginary part of admittance matrix,
And be all constant；In Load flow calculation, active power injection P and reactive power inject the node that Q is all specified rate, referred to as PQ sections
Point, the active power injection P and node voltage amplitude V of node is all the node of specified rate, referred to as PV node；
It is many-to-one mapping from V- θ spaces to P-Q spaces, Operation of Electric Systems is in point (near V=1, θ=0), at this
In the small neighbourhood of operating point, there are one by one mapping relations of the V- θ spaces to P-Q spaces, therefore formula (4) is transformed to matrix form such as
Under：
In formula (5), PV nodes and PQ nodes are separated, A, B, C, D, E, F, G, H and I are matrix in block form, and exponent number is respectively n
× n, n × (n-g), n × g, (n-g) × n, (n-g) × (n-g), (n-g) × g, g × n, g × (n-g), g × g；
Drawn by formula (5)：
△VG=G △ P+H △ QL+I·△QG (6)
△VL=D △ P+E △ QL+F·△QG (7)
Drawn by formula (6)：
△QG=I-1·△VG-I-1·G·△P-I-1·H·△QL (8)
Wushu (7) brings formula (8) into, obtains：
△VL=(D-FI-1·G)·△P+(E-F·I-1·H)·△QL+F·I-1·△VG (9)
IfFor the load bus i voltage magnitude upper limit,For load bus i current voltage, P0, Q0And VG 0Difference table
Show the value of the respective amount under current operating conditions, matrix (D-FIs of the row vector s by node i voltage magnitude in formula (9)-1·G)、(E-F·I-1) and FI H-1In corresponding row vector composition；Then have：
Formula (10) is finally arranged：
In formula (11), α, β and λ are Steady State Security Region border coefficient；
Then, the Steady State Security Region of load bus i upper voltage limits is defined as：
It can similarly obtain, the Steady State Security Region of load bus i lower voltage limits：
The Static Voltage Security domain of whole power system be all nodes the constraint of voltage bound be all met it is quiet
The common factor of state Voltage Security Region in Node, i.e.,：
In step 3, the computational methods of power system stability margin value are：
The security domain boundaries coefficient obtained by step 2, calculate node stability margin is as follows：
In formula (15), srmjNumerical value represents that current power system is safe to be positive, and numerical value is bigger to represent current power system
The stability margin for the method for operation of uniting is bigger, and node j belongs to load bus；
The stability margin value of power system is the corresponding nargin minimum value in all borders；The stability margin value of power system
SRM calculation formula：
SRM=min (srmj)(j∈L) (16)
In step 3, the calculation formula of input transformer station selection indicators is as follows：
OISA=| αiPi|+|βiQi|(i∈L) (17)
Compared with prior art, the beneficial effects of the invention are as follows：
Currently, existing transformer station's access scheme appraisal procedure, belongs to the category of " point by point method ", it is difficult to provide the planning side
Influence of the case to power network overall operation level of security.The present invention can effectively solve above-mentioned defect, using the side of security domain
Method, weak node of the identification power network under a certain method of operation, provides transformer station's access system plan.Contrast different substation connects
Enter improvement situation of the scheme to system SVSR nargin, obtain preferably transformer station's access scheme.
Brief description of the drawings
Fig. 1 is transformer station's access system aided assessment method flow that the present invention is provided；
Fig. 2 is the 118 node system wiring diagrams that the present invention is provided；
Fig. 3 is the SVSR on the dimension space of system 2 that the present invention is provided；
Fig. 4 is the contrast for the nargin information that the present invention is provided.
Embodiment
Technical solution of the present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings, described is specific
Only the present invention is explained for embodiment, is not intended to limit the invention.
As shown in figure 1, a kind of proposed by the present invention 1. transformer station's access scheme aided assessment methods based on security domain, bag
Include following steps：
Step 1: by electric power system data, the status information (V, θ) under the current method of operation is obtained by Load flow calculation,
Generate the admittance matrix under the grid structure；Wherein, V is node voltage amplitude, and θ is node voltage phase angle；The present invention with
Exemplified by IEEE118 node systems, as shown in Figure 2.
Step 2: the admittance matrix drawn using step one obtains the expression matrix form that node injects equation, and by electricity
The control variable of Force system determines decision parameters spaceSo as to build corresponding Static Voltage Security domain border；Tool
Hold in vivo as follows：
If：Power system has n-1 node and nb bar branch roads, and its interior joint 0 is slack bus, there is g+1 generator section
Point；Generator node in addition to slack bus, the set of power transformation tiny node are represented with S；The set of load bus is represented with L；
In Operation of Electric Systems point V=1, the small neighbourhood of θ=0, cos θ are utilizedij=1, sin θij=θi-θjTo exchange side
Cheng Jinhang processing obtains formula (2), shown in exchange equation such as formula (1)：
In formula (1), Pij、QijThe active power and reactive power transmitted for circuit ij；Vi、VjRespectively node i, j electricity
Pressure amplitude value；θi、θjRespectively node i, j voltage phase angle, θij=θi-θj；Gij、BijFor the corresponding element of admittance matrix；
Node i application Kirchhoff's theorem is obtained：
In formula (3), Pi、QiFor the active power injection and reactive power injection of node i；
Being write formula (3) as matrix form is：
In formula (4), G, B is respectively n × n rank matrixes, wherein, G is the real part of admittance matrix, and B is the imaginary part of admittance matrix,
And be all constant；In Load flow calculation, active power injection P and reactive power inject the node that Q is all specified rate, referred to as PQ sections
Point, the active power injection P and node voltage amplitude V of node is all the node of specified rate, referred to as PV node；
It is many-to-one mapping from V- θ spaces to P-Q spaces, Operation of Electric Systems is in point (near V=1, θ=0), at this
In the small neighbourhood of operating point, there are one by one mapping relations of the V- θ spaces to P-Q spaces, therefore formula (4) is transformed to matrix form such as
Under：
In formula (5), PV nodes and PQ nodes are separated, A, B, C, D, E, F, G, H and I are matrix in block form, and exponent number is respectively n
× n, n × (n-g), n × g, (n-g) × n, (n-g) × (n-g), (n-g) × g, g × n, g × (n-g), g × g；
Drawn by formula (5)：
△VG=G △ P+H △ QL+I·△QG (6)
△VL=D △ P+E △ QL+F·△QG (7)
Drawn by formula (6)：
△QG=I-1·△VG-I-1·G·△P-I-1·H·△QL (8)
Wushu (7) brings formula (8) into, obtains：
△VL=(D-FI-1·G)·△P+(E-F·I-1·H)·△QL+F·I-1·△VG (9)
IfFor the load bus i voltage magnitude upper limit,For load bus i current voltage, P0, Q0And VG 0Difference table
Show the value of the respective amount under current operating conditions, matrix (D-FIs of the row vector s by node i voltage magnitude in formula (9)-1·G)、(E-F·I-1) and FI H-1In corresponding row vector composition；Then have：
Formula (10) is finally arranged：
In formula (11), α, β and λ are Steady State Security Region border coefficient；
Then, the Steady State Security Region of load bus i upper voltage limits is defined as：
It can similarly obtain, the Steady State Security Region of load bus i lower voltage limits：
The Static Voltage Security domain of whole power system be all nodes the constraint of voltage bound be all met it is quiet
The common factor of state Voltage Security Region in Node, i.e.,：
The control parameter space of system is determined according to current power system element model parameter and network topology data, is asked for
System corresponding Static Voltage Security domain coefficient under a certain method of operation, partial surface data information is as shown in table 2.In order to just
SVSR in the displaying of result, 2 dimension spaces of selection, i.e. sections of the SVSR on specific 2 dimension space, as shown in Figure 3.Choose negative
Bidimensional sectional view of the security domain boundaries on P11, Q11 corresponding to lotus node 9.
Step 3: the Static Voltage Security domain obtained according to step 2, stability margin analysis is carried out to power system, i.e., by
The security domain boundaries coefficient that step 2 is obtained, then according to formula (15) calculate node stability margin：
In formula (15), srmjNumerical value represents that current power system is safe to be positive, and numerical value is bigger to represent current power system
The stability margin for the method for operation of uniting is bigger, and node j belongs to load bus；
The minimum border of stability margin under the current method of operation of power system is found, the stability margin value of power system is institute
There is the corresponding nargin minimum value in border；The stability margin value SRM calculation formula of power system：
SRM=min (srmj)(j∈L) (16)。
The methods of operation of practical power systems can be because the maintenance of power system be extended, different seasons, and one day not
The same period, change.For the ease of the displaying of result, choose different load level and analyzed, analysis result such as table 1
It is shown.Being analyzed by table 1 to obtain, and the increase of system loading amount causes the stability margin reduction of system.Due to the installed capacity of system
The standby abundances of 9966.2MW, the amplitude that system stability margin is reduced after load increase is smaller.Current point of operation is apart from load section
Point BUS 9 security domain boundaries are most short.
Table 1
| Current amount | After increase | |
| System total load (MW) | 4242.0 | 4666.2 |
| Stability margin | 0.047 | 0.0466 |
| Margin value corresponding load node serial number | BUS 9 | BUS 9 |
According to resulting Steady State Security Region border coefficient α and β, it is determined that input transformer station selection indicators (optimized
Index of substation access, OISA), input transformer station selection indicators refer to：The corresponding system of active parameter
Count and have the absolute value coefficient corresponding with idle parameter of work value product and the sum of the absolute value without work value product, i.e.,：
OISA=| αiPi|+|βiQi|(i∈L) (17)
Input transformer station selection indicators are ranked up, the section of N number of input transformer station selection indicators numerical value greatly is taken out
Point is transformer station's priority access point, and during N value is 2~10, the present embodiment, N value is 2, that is, have chosen 2 transformer stations and connect
Enter scheme, as scheme 1 and scheme 2.
Step 4: the legacy network structure of power system is set as scenario A, in the legacy network architecture basics of power system
On scene after the transformer station that the transformer station priority access point access that step 3 is determined newly is put into be scenario B, at access point
PQ nodes be converted to PV node.
It can be obtained by step 3, the current method of operation is most short apart from the corresponding frontier distances of BUS 9.From input, transformer station improves
Static system voltage security level is set out, and the coefficient corresponding to the borders of BUS 9 is analyzed, partial data is as shown in table 2.It is right
OISA is ranked up, and it is transformer station's priority access point to take the big node of OISA numerical value；It must can be paid the utmost attention in the He of node 11 by table 2
Transformer station is put at node 13.Scheme 1：Transformer station is put into load bus 11；Scheme 2：Transformer station is put into load bus 13.
Table 2
Step 5: in the case where input Substation parameters are consistent, the method provided using step 2 is to the N number of of scenario B
Power system corresponding to transformer station's access scheme re-starts security domain structure, is analyzed by stability margin, to N number of transformer station
The stability margin value of the power system of access scheme and the power system of scenario A is compared, if stability margin value maximum
Power system is transformer station's access scheme in scenario B, then most the program is defined as transformer station's access scheme at last, no
Then, do not consider to access transformer station in the power system.
In the present embodiment, scheme 1 and scheme 2 and system stability margin pair corresponding to the power system of transformer station is not accessed
Than as shown in Figure 4.Being analyzed by table 1 to obtain, and be improved in the stability margin of BUS 11 and BUS 13 access transformer substation systems.
It is larger that the amplitude that nargin is lifted after transformer station is accessed compared to BUS 11.Therefore it is more reasonable in the scheme that BUS 11 accesses transformer station.
Although above in conjunction with accompanying drawing, invention has been described, and the invention is not limited in above-mentioned specific implementation
Mode, above-mentioned embodiment is only schematical, rather than restricted, and one of ordinary skill in the art is at this
Under the enlightenment of invention, without deviating from the spirit of the invention, many variations can also be made, these belong to the present invention's
Within protection.
Claims (4)
1. a kind of transformer station's access scheme aided assessment method based on security domain, it is characterised in that comprise the following steps：
Step 1: by electric power system data, the status information (V, θ) under the current method of operation is obtained by Load flow calculation, generate
Admittance matrix under the grid structure；Wherein, V is node voltage amplitude, and θ is node voltage phase angle；
Step 2: the admittance matrix drawn using step one obtains the expression matrix form that node injects equation, and by power train
The control variable of system determines decision parameters spaceSo as to build corresponding Static Voltage Security domain border；
Step 3: the Static Voltage Security domain obtained according to step 2, stability margin analysis is carried out to power system；Find electric power
The minimum border of stability margin, obtains the corresponding parameter information in the border under the current method of operation of system, it is determined that input transformer station
Selection indicators, input transformer station selection indicators refer to：The corresponding coefficient of active parameter and have the absolute value of work value product with
The sum of the corresponding coefficient of idle parameter and the absolute value without work value product；Input transformer station selection indicators are arranged
Sequence, it is transformer station's priority access point to take out the big node of N number of input transformer station selection indicators numerical value, and N value is 2~10；
Step 4: set the legacy network structure of power system as scenario A, on the legacy network architecture basics of power system
Scene after the transformer station that transformer station's priority access point access that step 3 is determined newly is put into is scenario B, by the PQ at access point
Node is converted to PV node；
Step 5: in the case where input Substation parameters are consistent, N number of power transformation of the method provided using step 2 to scenario B
The power system corresponding to access scheme of standing re-starts security domain structure, is analyzed by stability margin, and N number of transformer station is accessed
The stability margin value of the power system of scheme and the power system of scenario A is compared, if the maximum electric power of stability margin value
System is transformer station's access scheme in scenario B, then most the program is defined as transformer station's access scheme at last, otherwise, no
Consideration accesses transformer station in the power system.
2. transformer station's access scheme aided assessment method based on security domain according to claim 1, wherein, step 2 it is quiet
State voltage security domain structuring approach, is specifically included：
If：Power system has n-1 node and nb bar branch roads, and its interior joint 0 is slack bus, there is g+1 generator node；With
S represents generator node in addition to slack bus, the set of power transformation tiny node；The set of load bus is represented with L；
In Operation of Electric Systems point V=1, the small neighbourhood of θ=0, cos θ are utilizedij=1, sin θij=θi-θjExchange equation is entered
Row processing obtains formula (2), shown in exchange equation such as formula (1)：
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In formula (1), Pij、QijThe active power and reactive power transmitted for circuit ij；Vi、VjRespectively node i, j voltage amplitude
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<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>Q</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Node i application Kirchhoff's theorem is obtained：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>&Element;</mo>
<mi>i</mi>
</mrow>
</munder>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>&Element;</mo>
<mi>i</mi>
</mrow>
</munder>
<mo>&lsqb;</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>&Element;</mo>
<mi>i</mi>
</mrow>
</munder>
<msub>
<mi>Q</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>&Element;</mo>
<mi>i</mi>
</mrow>
</munder>
<mo>&lsqb;</mo>
<mo>-</mo>
<msub>
<mi>B</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (3), Pi、QiFor the active power injection and reactive power injection of node i；
Being write formula (3) as matrix form is：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>P</mi>
<mo>=</mo>
<mo>-</mo>
<mi>G</mi>
<mi>V</mi>
<mo>+</mo>
<mi>B</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>Q</mi>
<mo>=</mo>
<mi>B</mi>
<mi>V</mi>
<mo>+</mo>
<mi>G</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (4), G, B is respectively n × n rank matrixes, wherein, G is the real part of admittance matrix, and B is the imaginary part of admittance matrix, and all
For constant；In Load flow calculation, active power injection P and reactive power inject the node that Q is all specified rate, referred to as PQ nodes,
The active power injection P and node voltage amplitude V of node is all the node of specified rate, referred to as PV node；
It is many-to-one mapping from V- θ spaces to P-Q spaces, Operation of Electric Systems is in point (near V=1, θ=0), in the operation
In the small neighbourhood of point, there are one by one mapping relations of the V- θ spaces to P-Q spaces, therefore it is as follows that formula (4) is transformed into matrix form：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>&Delta;</mi>
<mi>&theta;</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>&Delta;</mi>
<msub>
<mi>V</mi>
<mi>L</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;V</mi>
<mi>G</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>A</mi>
</mtd>
<mtd>
<mi>B</mi>
</mtd>
<mtd>
<mi>C</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>D</mi>
</mtd>
<mtd>
<mi>E</mi>
</mtd>
<mtd>
<mi>F</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>G</mi>
</mtd>
<mtd>
<mi>H</mi>
</mtd>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>&Delta;</mi>
<mi>P</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>&Delta;</mi>
<msub>
<mi>Q</mi>
<mi>L</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;Q</mi>
<mi>G</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (5), PV nodes and PQ nodes are separated, A, B, C, D, E, F, G, H and I be matrix in block form, exponent number be respectively n × n,
N × (n-g), n × g, (n-g) × n, (n-g) × (n-g), (n-g) × g, g × n, g × (n-g), g × g；
Drawn by formula (5)：
△VG=G △ P+H △ QL+I·△QG (6)
△VL=D △ P+E △ QL+F·△QG (7)
Drawn by formula (6)：
△QG=I-1·△VG-I-1·G·△P-I-1·H·△QL (8)
Wushu (7) brings formula (8) into, obtains：
△VL=(D-FI-1·G)·△P+(E-F·I-1·H)·△QL+F·I-1·△VG (9)
IfFor the load bus i voltage magnitude upper limit,For load bus i current voltage, P0, Q0And VG 0It is illustrated respectively in
The value of respective amount under current operating conditions, matrix (D-FIs of the row vector s by node i voltage magnitude in formula (9)-1·G)、
(E-F·I-1) and FI H-1In corresponding row vector composition；Then have：
<mrow>
<msubsup>
<mi>u</mi>
<mi>i</mi>
<mrow>
<mi>u</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>u</mi>
<mi>i</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<mi>s</mi>
<mo>&CenterDot;</mo>
<mo>&lsqb;</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>P</mi>
<mo>-</mo>
<msup>
<mi>P</mi>
<mn>0</mn>
</msup>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>,</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>Q</mi>
<mo>-</mo>
<msup>
<mi>Q</mi>
<mn>0</mn>
</msup>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>,</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>V</mi>
<mi>G</mi>
</msub>
<mo>-</mo>
<msubsup>
<mi>V</mi>
<mi>G</mi>
<mn>0</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Formula (10) is finally arranged：
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
<mo>&cup;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
</mrow>
</munder>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (11), α, β and λ are Steady State Security Region border coefficient；
Then, the Steady State Security Region of load bus i upper voltage limits is defined as：
<mrow>
<msubsup>
<mi>&Omega;</mi>
<mrow>
<mi>V</mi>
<mo>,</mo>
<mi>i</mi>
</mrow>
<mrow>
<mi>u</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>:</mo>
<mo>=</mo>
<mo>{</mo>
<mfenced open = "(" close = ")">
<mtable>
<mtr>
<mtd>
<msup>
<mi>P</mi>
<mi>T</mi>
</msup>
</mtd>
<mtd>
<msup>
<mi>Q</mi>
<mi>T</mi>
</msup>
</mtd>
<mtd>
<msubsup>
<mi>V</mi>
<mi>G</mi>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>|</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
<mo>&cup;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
</mrow>
</munder>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>&le;</mo>
<mn>1</mn>
<mo>}</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
It can similarly obtain, the Steady State Security Region of load bus i lower voltage limits：
<mrow>
<msubsup>
<mi>&Omega;</mi>
<mrow>
<mi>V</mi>
<mo>,</mo>
<mi>i</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>o</mi>
<mi>w</mi>
<mi>m</mi>
</mrow>
</msubsup>
<mo>:</mo>
<mo>=</mo>
<mo>{</mo>
<mfenced open = "(" close = ")">
<mtable>
<mtr>
<mtd>
<msup>
<mi>P</mi>
<mi>T</mi>
</msup>
</mtd>
<mtd>
<msup>
<mi>Q</mi>
<mi>T</mi>
</msup>
</mtd>
<mtd>
<msubsup>
<mi>V</mi>
<mi>G</mi>
<mi>T</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>|</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
<mo>&cup;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
</mrow>
</munder>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>&GreaterEqual;</mo>
<mn>1</mn>
<mo>}</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
The Static Voltage Security domain of whole power system is that the voltage bound of all nodes constrains the Static Electro being all met
The common factor of security domain is pressed, i.e.,：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Omega;</mi>
<mi>V</mi>
</msub>
<mo>:</mo>
<mo>=</mo>
<msubsup>
<mi>&Omega;</mi>
<mrow>
<mi>V</mi>
<mo>,</mo>
<mi>i</mi>
</mrow>
<mrow>
<mi>u</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>&cap;</mo>
<msubsup>
<mi>&Omega;</mi>
<mrow>
<mi>V</mi>
<mo>,</mo>
<mi>i</mi>
</mrow>
<mrow>
<mi>d</mi>
<mi>o</mi>
<mi>w</mi>
<mi>n</mi>
</mrow>
</msubsup>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>&Element;</mo>
<mi>L</mi>
<mo>&cup;</mo>
<mi>S</mi>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
3. transformer station's access scheme aided assessment method based on security domain according to claim 2, wherein, in step 3,
The computational methods of power system stability margin value are：
The security domain boundaries coefficient obtained by step 2, calculate node stability margin is as follows：
<mrow>
<msub>
<mi>srm</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mrow>
<mo>(</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
<mo>&cup;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>L</mi>
</mrow>
</munder>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>Q</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>&Element;</mo>
<mi>S</mi>
</mrow>
</munder>
<msub>
<mi>&lambda;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>&Element;</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (15), srmjNumerical value represents that current power system is safe to be positive, and numerical value is bigger to represent current power system operation
The stability margin of mode is bigger, and node j belongs to load bus；
The stability margin value of power system is the corresponding nargin minimum value in all borders；The stability margin value SRM meters of power system
Calculate formula：
SRM=min (srmj)(j∈L) (16)。
4. transformer station's access scheme aided assessment method based on security domain according to claim 2, wherein, in step 3,
The calculation formula for putting into transformer station's selection indicators is as follows：
OISA=| αiPi|+|βiQi|(i∈L) (17)。
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107732904A (en) * | 2017-10-17 | 2018-02-23 | 武汉大学 | A kind of Steady-State Real Power Security Region construction method of meter and single TCSC equivalent reactances parameter |
| CN109149636A (en) * | 2018-09-10 | 2019-01-04 | 国网天津市电力公司 | Wind power integration point transient stability based on Dynamic Security Region influences research method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107732904A (en) * | 2017-10-17 | 2018-02-23 | 武汉大学 | A kind of Steady-State Real Power Security Region construction method of meter and single TCSC equivalent reactances parameter |
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| CN109687434B (en) * | 2018-12-11 | 2022-05-10 | 天津大学 | Power supply path search-based power distribution network static voltage security domain calculation method |
| CN110148935A (en) * | 2019-05-10 | 2019-08-20 | 东北电力大学 | A kind of power grid static security nargin appraisal procedure based on shot and long term Memory Neural Networks |
| CN110148935B (en) * | 2019-05-10 | 2021-12-28 | 东北电力大学 | Power grid static safety margin evaluation method based on long-term and short-term memory neural network |
| CN111525548A (en) * | 2020-04-02 | 2020-08-11 | 中国电力科学研究院有限公司 | Method and system for evaluating static voltage stability margin of power grid based on information driving |
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