CN109840717A - A kind of linear tidal current computing method of power distribution network containing distributed generation resource - Google Patents
A kind of linear tidal current computing method of power distribution network containing distributed generation resource Download PDFInfo
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Abstract
A kind of linear tidal current computing method of power distribution network containing distributed generation resource, it include: that Taylor's formula expansion is carried out to the nonlinear terms in basic power flow equation, casts out quadratic term and more high-order term using Taylor series expansion technology, to obtain its linear forms, it is denoted as linear approximation model；Non- PV type distributed generation resource power flow algorithm is subjected to Taylor's formula expansion, casts out cubic term and more high-order term, to obtain non-PV type distributed generation resource simplified model；Based on linear approximation model and non-PV type distributed generation resource simplified model, nonlinear basic power flow equation is simplified, finally obtains a kind of linear power flow algorithm of the power distribution network containing distributed generation resource.Compared with existing linear power flow algorithm, the present invention not only calculating computational accuracy with higher applies also for the power distribution network containing various distributed generation resources, versatility with higher.The present invention is suitable for power distribution network Quick tidal current calculation.
Description
Technical field
The invention belongs to distribution power system load flow calculation analysis fields.
Background technique
With the rapid development of power distribution network, in more and more distributed generation resource access power distribution networks, and distributed generation resource
Access produces tremendous influence to the network structure of power distribution network, voltage's distribiuting and Load flow calculation.Conventional electrical distribution net is generally containing only PQ
Node and reference mode, but with the addition of distributed generation resource, such as PV node, PI node and PQ (V) are increased in power distribution network
Node.System interior joint type increases, and conventional electrical distribution net tidal current computing method is made to be difficult to be suitable for matching containing distributed generation resource
Power grid.Currently, academia is more to the Power Flow Calculation Methods For Distribution Network research containing distributed generation resource, but these algorithms are with iterative calculation
Based on, complicated, especially more and larger in solution distributed generation resource network is calculated, iterative process is greatly lowered
Computational efficiency, or even there is the phenomenon that not restraining.In addition, the work such as the planning of power distribution network, optimization and network reconfiguration are also because non-
The addition of linear power flow equation, which makes to solve, becomes complicated.In recent years, to the research relative maturity of the linear algorithm of distribution power flow,
The it is proposed of linear power flow algorithm, significantly improves Load flow calculation efficiency.Up to the present, most of linear power flow algorithms are only examined
Consider PQ type distributed generation resource, and type containing PV, PI type, the linear tidal current computing method of PQ (V) type distributed generation resource are relatively fewer, make
Its scope of application is limited.
Summary of the invention
It is an object of the invention to low for the linear power flow algorithm versatility of existing power distribution network, computational accuracy is not high
Defect proposes a kind of linear tidal current computing method of the power distribution network containing distributed generation resource.The model is applicable not only to containing various types
The power distribution network of distributed generation resource also maintains higher computational accuracy, can effectively solve the problems, such as power distribution network Quick tidal current calculation.
The present invention is achieved by the following technical solutions.
The linear tidal current computing method of a kind of power distribution network containing distributed generation resource of the present invention, comprising: using Taylor's grade
Number expansion technique carries out Taylor's formula expansion to the nonlinear terms (inverse and trigonometric function of voltage) in basic power flow equation,
And cast out quadratic term and more high-order term, it obtains its linear forms, is denoted as linear approximation model；Equally use Taylor series expansion skill
Non- PV type distributed generation resource power flow algorithm is carried out Taylor's formula expansion, and casts out cubic term and more high-order term by art, thus
Obtain non-PV type distributed generation resource simplified model；Based on linear approximation model and non-PV type distributed generation resource simplified model, to base
This power flow equation is linearized, and a kind of linear power flow algorithm of the power distribution network containing distributed generation resource is finally obtained.
Nonlinear terms in basic power flow equation of the present invention are linearized, linear approximation model are as follows:
In formula: i, j indicate the node serial number in power distribution network；ViFor the voltage magnitude of node i；δijFor node i and node j it
Between phase difference of voltage.
The simplified mathematical model of non-PV type distributed generation resource of the present invention are as follows:
In formula: PGi, QGiThe respectively active power and reactive power of distributed generation resource sending；ViFor node i voltage magnitude；WithIt is constant, for different types of distributed generation resource, value is different.
The linear power flow algorithm of power distribution network of the present invention containing distributed generation resource are as follows:
In formula: PLi, QLiThe respectively active power and reactive power of node i load；Gij, BijRespectively admittance matrix
Real and imaginary parts；PGi, QGiThe respectively active power and reactive power of distributed generation resource sending；Vi, VjRespectively node i and j
Voltage magnitude；WithIt is constant.
Compared with prior art, the beneficial effects of the present invention are: using Taylor series expansion technology and power distribution network
Typical characteristics simplify the computation model of basic power flow equation and distributed generation resource, finally obtain a kind of containing distributed electrical
The linear power flow algorithm of the power distribution network in source.The model applies also for while keeping higher computational accuracy containing various types
The power distribution network of distributed generation resource, versatility with higher can effectively solve the Quick tidal current calculation problem of power distribution network.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 is that node voltage of the embodiment of the present invention in the case where testing 3 system situations calculates error amount distribution map.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with attached drawing to the present invention into
Row is described in detail.It should be appreciated that specific example described herein is only used to explain the present invention, it is not used to limit this hair
It is bright.
Fig. 1 is the linear power flow algorithm flow chart of the power distribution network containing distributed generation resource of one embodiment of the present invention,
Include:
A kind of linear power flow algorithm of power distribution network containing distributed generation resource, comprising: Taylor series expansion technology is used, it is right
Nonlinear terms (inverse and trigonometric function of voltage) in basic power flow equation carry out Taylor's formula expansion, and cast out quadratic term and
More high-order term is denoted as linear approximation model to obtain its linear forms；Taylor series expansion technology is equally used, by non-PV
The power flow algorithm of type distributed generation resource carries out Taylor's formula expansion, and casts out cubic term and more high-order term, to obtain non-
PV type distributed generation resource simplified model；Based on linear approximation model and non-PV type distributed generation resource simplified model, to basic trend
Equation is linearized, and a kind of linear power flow algorithm of the power distribution network containing distributed generation resource is finally obtained.
Specifically, the principle of the linear power flow algorithm of power distribution network containing distributed generation resource are as follows:
The basic power flow equation of power distribution network is writeable are as follows:
In formula: (i, j=1,2,3 ... n) for the node serial number in i, j expression power distribution network；PGi, QGiThe respectively power supply of node i
The active power and reactive power of sending；PLi, QLiThe respectively active power and reactive power of node i load；Pi, QiRespectively
The active power always injected and reactive power of node i；ViFor the voltage magnitude of node i；δijBetween node i and node j
Phase difference of voltage；Gij, BijThe respectively real and imaginary parts of admittance matrix.
Contain two kinds of nonlinear terms (1/V and trigonometric function) in basic power flow equation, therefore it need to be carried out linearly
Change.
When carrying out Load flow calculation, the voltage magnitude for usually defining reference mode is 1.0p.u., voltage phase angle 0.According to
The characteristics of power distribution network, is it is found that node voltage amplitude Vi≈ 1.0p.u., voltage phase angle δi≈0；Voltage phase between any two node
Angular difference δij≈0。
Definition voltage magnitude is Vi=1+ Δ Vi, it takes it reciprocal and carries out Taylor's formula expansion, can obtain:
Cast out quadratic term and more high-order term, can obtain:
Δ Vi=1-ViSubstitution can obtain:
According to the typical characteristics of power distribution network, equally to trigonometric function cos δijWith sin δijTaylor's formula expansion is carried out, and is given up
Quadratic term and more high-order term are removed, then trigonometric function cos δijWith sin δijAvailable linearization are as follows:
The type of distributed generation resource is divided into two major classes by the present invention: PV type distributed generation resource and non-PV type distributed generation resource.
PV type distributed generation resource is not made to simplify, the present invention only simplifies non-PV type distributed generation resource.Define non-PV type distribution
The reactive power that formula power supply issues expresses formula are as follows:
QG=k2·V2+k1·V+k0+y(V) (10)
In formula: k2, k1And k0It is constant；Y (V) is the function (not including quadratic term, first order and constant term) about V.
By taking PI type distributed generation resource as an example, output reactive power expression formula isThen formula
(10) the constant k in2, k1And k0It is zero, QGIt is writeable are as follows:
In formula: V is node voltage；IGFor the electric current of distributed generation resource；PGThe active power issued for distributed generation resource.
Since node voltage amplitude V is close to 1.0p.u., y (V) is nearby subjected to Taylor expansion at V=1.0p.u.,
It can obtain:
In formula: yn(V) n order derivative of the representative function y (V) about V；Δ V is the amount of being slightly variable of V and there are 1+ Δ V=V.By
It is smaller in Δ V, formula (12) retention constant item, first order and quadratic term, and Δ V=V-1 is substituted into, it can show that PI type is distributed
Power supply issues the One- place 2-th Order expression formula of reactive power, i.e.,
Same method can also obtain the One- place 2-th Order expression formula for the reactive power that PQ (V) type distributed generation resource issues.Therefore
Non- PV type distributed generation resource power flow algorithm can simplify are as follows:
In formula: PGi, QGiThe respectively active power and reactive power of distributed generation resource sending；ViFor node i voltage magnitude；WithIt is constant, for different types of distributed generation resource, value is different.
Distributed generation resource simplified model (15) are substituted into basic power flow equation (5), and according to linear approximation model (8),
The left side of basic power flow equation equal sign can turn to:
Linear approximation model (9) are substituted into basic power flow equation (5), the left side of basic power flow equation equal sign can turn to:
Due to the admittance very little over the ground of distribution line, it is usually closer to zero.In the feelings for the admittance over the ground for ignoring distribution line
Under condition, the self-admittance element of a certain node is equal to the sum of each branch admittance being connected with the node, i.e. admittance in admittance matrix
Every row element of matrix, which is added, is equal to zero.Therefore, exist in formula (18):
Wushu (19) substitutes into formula (18), and according to the node voltage of power distribution network close to the characteristic of 1.0p.u., formula (18)
It can be organized into:
Convolution (16), formula (17) and formula (20) can obtain a kind of linear Load flow calculation mould of the power distribution network containing distributed generation resource
Type, i.e.,
Scheme in order to better illustrate the present invention has done in detail embodiments of the present invention using typical distribution system
It describes in detail bright.
Embodiment 1.
Using IEEE33 as test macro, the specific data and network topology structure of system are shown in Goswami S K, Basu S
K.A new algorithm for the reconfiguration of distribution feeders for loss
Minimization [J] .IEEE Transactions on Power Delivery, 1992,7 (3): 1484-1491.
Using the present invention with existing linear power flow algorithm to IEEE33 test macro carry out Load flow calculation, and devise as
It sows test.
Test 1: distributed generation resource is free of.Trend is carried out to IEEE33 Node power distribution system using 3 kinds of linear power flow algorithms
It calculates, and carries out application condition.
Test 2: the distributed generation resource of type containing PV and PQ type distributed generation resource.4 are accessed in IEEE33 Node power distribution system
Distributed generation resource, number are respectively distributed generation resource 1, distributed generation resource 2, distributed generation resource 3, distributed generation resource 4, constitute one
Test macro containing PV node, the specific on-position of distributed generation resource and given parameters are shown in Table 1.And use 2 kinds of linear trends
Algorithm carries out Load flow calculation to test macro, and carries out application condition.
Test 3: the distributed generation resource containing 4 seed types.On the basis of testing 2, then access distributed generation resource 5 and distribution
Power supply 6 (by taking no adjustment of field excitation ability synchronous generator as an example) constitutes the survey for containing PV node, PI node and PQ (V) node
Test system.And Load flow calculation is carried out to test macro using the present invention.
For convenience of explanation, existing linear power flow algorithm 1 is derived from Garces A.A linear three-phase load
Flow for power distribution systems [J] .IEEE Transactions on Power Systems,
2016,31 (1): 827-828. is denoted as LPF_XV；Existing linear power flow algorithm 2 is derived from Yi Wang, Ning Zhang, Hai Li,
et al.Linear Three-Phase Power Flow for Unbalanced Active Distribution
Networks with PV Nodes [J] .CSEE Journal of Power and Energy Systems, 2017,3 (3):
321-324. is denoted as LPF_V.
The physical resource of 1 distributed generation resource of table
The calculating error amount (test 1) of 2 three kinds of table linear power flow algorithms
The error amount (test 2) of 3 two kinds of table linear power flow algorithms
Table 2 gives the calculating error amount of the node voltage of test 1, shown in error calculation formula such as formula (22).It can by table
Find out, worst error of the invention and mean error are respectively 6.11 × 10-4P.u. with 3.37 × 10-4P.u., worst error value
The order of magnitude be 10-4.Compared with LPF_XV, computational accuracy is slightly lower, but is not much different, the worst error difference of two kinds of linear methods
8.1×10-5P.u., mean error difference 5.0 × 10-5p.u.；Compared with LPF_V, computational accuracy is obviously improved.
Δ=| XLPF-XPF| (22)
In formula: XLPFFor linear calculation of tidal current；XPFFor traditional Newton method calculation of tidal current, convergence precision takes 10-5。
Table 3 gives the calculating error amount of the node voltage in the case of test 2, since LPF_XV cannot handle the distribution of PV type
Formula power supply only provides the node voltage error amount of 2 kinds of linear power flow algorithms in table.Compared with LPF_V, worst error of the invention
By 2.95 × 10-3P.u. 8.57 × 10 are reduced to-4P.u., mean error is by 1.23 × 10-3P.u. 4.43 × 10 are reduced to- 4p.u..As it can be seen that its computational accuracy is apparently higher than LPF_V, cause this phenomenon most important the reason is that: Thailand employed herein
It strangles formula expansion technique and considerably reduces power flow equation brought error during simplification.
It tests in 3 systems and can not containing PI type distributed generation resource and PQ (V) type distributed generation resource, LPF_XV and LPF_V
Load flow calculation is carried out to the test macro, Fig. 2 only gives voltage error Distribution value of the invention.Fig. 2 shows the maximum of node
Voltage error value appears in node 10, and value is 6.41 × 10-4P.u., mean error is 3.37 × 10-4P.u., worst error
The order of magnitude of value and mean error remains at 10-4。
By above 3 kinds tests it is found that LPF_XV computational accuracy with higher, but non-PQ type distributed electrical can not be handled
Source, versatility are lower；LPF_V is although it is contemplated that PV type distributed generation resource, but computational accuracy is not high, and can not handle the distribution of PI type
Formula power supply and PQ (V) type distributed generation resource.For computational accuracy, the computational accuracy of the present invention and LPF_XV are almost the same,
Computational accuracy with higher；For versatility, the present invention can handle the distributed generation resource of all types, with higher
Versatility.
The 5 Load flow calculation time of table
Table 5 gives 3 kinds of linear power flow algorithms and traditional Newton method calculates the time used.IEEE16 and PG& in example
The specific data of E69 test macro visible Civanlar S, Grainger J J, Yin H, et al.Distribution
feeder reconfiguration for loss reduction[J].IEEE Transactions on Power
Delivery, 1988,3 (3): 1217-1223. and Baran M E, Wu F F.Optimal capacitor placement
On radial distribution systems [J] .IEEE Transactions on Power Delivery, 1989,4
(1): as seen from table, it is almost the same that 3 kinds of linear power flow algorithms calculate the time to 725-734., this is because using Matlab software
When carrying out Load flow calculation, the order of this 3 kinds linear power flow algorithm matrix operations is the same, therefore it is about the same to calculate the time.
Compared with traditional Newton method, the present invention successively reduces by 54.3%, 53.1% and to the Load flow calculation time of 3 test macros
56.0%, computational efficiency significantly improves.
The above analysis, present invention dramatically reduces the Load flow calculation time, computational efficiency promotes 50%~60% or so；
Compared with existing linear power flow algorithm, the present invention not only has higher computational accuracy, it is also contemplated that various types of distributions
Power supply has stronger versatility.In addition to this, the present invention carries out being not necessarily to iteration when Load flow calculation, non-so as to avoid tradition
Computational efficiency occur low or the phenomenon that do not restrain because distributed generation resource is excessive for linear tidal current computing method.Therefore, of the invention
It can be used as a kind of analysis of power distribution network rapid tidal current, the method that Real-Time Scheduling calculates analysis.
Claims (4)
1. a kind of linear tidal current computing method of power distribution network containing distributed generation resource characterized by comprising use Taylor series exhibition
Technology is opened, Taylor's formula expansion is carried out to the nonlinear terms in basic power flow equation, and cast out quadratic term and more high-order term, obtained
Its linear forms, is denoted as linear approximation model；Non- PV type distributed generation resource power flow algorithm is subjected to Taylor's formula expansion, and
Cast out cubic term and more high-order term, to obtain non-PV type distributed generation resource simplified model；Based on linear approximation model and distribution
Formula power supply simplified model carries out abbreviation to nonlinear basic power flow equation, to obtain the distribution cable containing distributed generation resource
Property power flow algorithm.
2. the linear tidal current computing method of a kind of power distribution network containing distributed generation resource according to claim 1, which is characterized in that
The linear approximation model are as follows:
In formula: i, j indicate the node serial number in power distribution network；ViFor the voltage magnitude of node i；δijBetween node i and node j
Phase difference of voltage.
3. the linear tidal current computing method of a kind of power distribution network containing distributed generation resource according to claim 1, which is characterized in that
The simplified model of the non-PV type distributed generation resource are as follows:
In formula: PGi, QGiThe respectively active power and reactive power of distributed generation resource sending；ViFor node i voltage magnitude；WithIt is constant.
4. the linear tidal current computing method of a kind of power distribution network containing distributed generation resource according to claim 1, which is characterized in that
The linear power flow algorithm containing distributed generation resource are as follows:
In formula: PLi, QLiThe respectively active power and reactive power of node i load；Gij, BijThe respectively real part of admittance matrix
And imaginary part；PGi, QGiThe respectively active power and reactive power of distributed generation resource sending；Vi, VjRespectively node i and j voltage
Amplitude；WithIt is constant.
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