CN110148946B - Island microgrid load flow calculation method based on two-step solution of auxiliary factors - Google Patents

Island microgrid load flow calculation method based on two-step solution of auxiliary factors Download PDF

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CN110148946B
CN110148946B CN201910441049.3A CN201910441049A CN110148946B CN 110148946 B CN110148946 B CN 110148946B CN 201910441049 A CN201910441049 A CN 201910441049A CN 110148946 B CN110148946 B CN 110148946B
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auxiliary factors
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CN110148946A (en
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林立亨
董树锋
朱承治
唐坤杰
宋永华
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Zhejiang University ZJU
State Grid Zhejiang Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H02J3/382—
    • H02J3/383—
    • H02J3/386—
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/388—Islanding, i.e. disconnection of local power supply from the network
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects

Abstract

The invention discloses an island microgrid load flow calculation method based on two-step solution of auxiliary factors, which comprises the following steps: rewriting an original power flow equation, moving all constant terms to the right side of the equation, reserving the PV node voltage amplitude, and replacing the voltage term and the system frequency omega by a logarithmic form; and introducing auxiliary factors y and u, converting a power flow calculation equation into a relation function among a group of underdetermined equations, a group of overdetermined equations and a group of auxiliary factors, setting an initial power flow value, and solving the converted equation through a two-step method, wherein the converted equation is converted into a least square problem in the first step to find a linearization point closer to a real solution, the robustness of the algorithm on the initial value is improved, and the next iteration step variable is directly solved in the second step to reduce the calculated amount. The method of the invention can effectively improve the convergence and the robustness.

Description

Island microgrid load flow calculation method based on two-step solution of auxiliary factors
Technical Field
The invention relates to the technical field of power systems, in particular to the field of island micro-grid load flow calculation, and provides an island micro-grid load flow calculation method based on two-step solution of auxiliary factors.
Background
The micro-grid load flow calculation is used as a basis for micro-grid stability analysis and optimal configuration, and is an important research field. When the micro-grid is in grid-connected operation, the load flow calculation is similar to that of a power distribution network. Under the peer-to-peer control of the micro-grid operating in the island, no balance node exists in the system, a DG controlled by droop exists, and the system frequency needs to be solved, so that the traditional load flow calculation method is not applicable any more, and an algorithm more suitable for load flow calculation of the micro-grid operating in the island needs to be researched.
From the current island microgrid power flow calculation research result, part of methods adopt an optimization idea to solve a power flow equation, such as a BFGS confidence domain algorithm, a Levenberg-Marquardt (LM) algorithm and the like, but the algorithms have the problems of excessive parameters and complex parameter adjustment, and the LM algorithm has a tail effect and is difficult to adapt to the calculation with high precision requirements. The other idea is to decompose the original power flow problem into two sub-problems of traditional power flow calculation and droop node updating, but the convergence speed is slow. Therefore, an island microgrid power flow calculation method based on two-step solution of auxiliary factors is needed, an original nonlinear power flow equation is decomposed into a set of underdetermined linear equations, a set of overdetermined linear equations and a set of relation functions among auxiliary vectors by introducing the two auxiliary factors, and the transformed equations are subjected to iterative solution in two steps. Through comparison and verification of an example, the algorithm has the characteristics of high convergence speed, strong robustness and short calculation time.
Disclosure of Invention
The invention aims to solve the technical problem of perfecting and improving the prior technical scheme and provides an island microgrid power flow calculation method based on two-step solution of auxiliary factors so as to improve the convergence speed and robustness of calculation.
In order to solve the technical problems, the invention adopts the following technical scheme:
the method comprises the following steps:
1. rewriting the equation of load flow calculation
The two-step solution algorithm of the auxiliary factors has certain requirements on the form of the power flow equation, and the original power flow equation needs to be rewritten.
The island microgrid power flow equation can be abstractly expressed as:
F(x)＝0 x∈Rn
the system has n nodes, nPQPQ node, nPVA PV node and nDA droop node, the formula (1) is an integer containing n + nPQ+nDN + n of individual position variablesPQ+nDA dimensional equation;
by moving all constant terms in the above equation to the right of the equation and retaining the PV node voltage magnitude, it is rewritten as follows:
F1(x)＝p
in the formula:
Figure BDA0002072026780000021
p0for the vector composed of constant terms in the power flow equation and for the convenience of subsequent calculation, the voltage amplitude of the PV node is preserved in p, expressed by its square form,
Figure BDA0002072026780000022
for vector x, where the voltage term and the system frequency ω are replaced by a logarithmic form:
x＝[δ2,…,δn,a1,…,an,w]T
in the formula: deltaiIs the phase angle of node i, ai＝lnVi＝2lnUi，w＝lnω。
2. Introduction of cofactor
The introduction of the co-factors y, u,
Figure BDA0002072026780000031
in the formula: second to last term UD,iFor the amplitude of the voltage at the droop node, nDAn item; alpha and beta are active and reactive load indexes, and for nodes i and j at two ends of each branch, let Kij＝UiUj cosδij、Lij＝UiUj sinδijWherein δij＝δi-δj；
Figure BDA0002072026780000032
In the formula: a isij＝ai+aj，δij＝δi-δj；
Converting the load flow calculation equation into a set of underdetermined equations, a set of overdetermined equations and a set of relationship functions among the auxiliary factors, namely:
Figure BDA0002072026780000033
in the formula: f (-) is a non-linear transformation reversible between cofactors with y ═ f inverse-1The specific form (u) is as follows:
Figure BDA0002072026780000041
3. tidal current initial value setting
Setting an initial value x of a tidal current state variable0Setting the convergence accuracy epsilon and the maximum iteration number k as 0maxFrequency of system omega0Voltage amplitude U0And the initial value delta of the phase angle0Get y0＝f-1(Cx0)。
4. Two-step method for solving equation
The transformed equation is solved through a two-step method, wherein the transformed equation is transformed into a least square problem to find a linearization point closer to a real solution in the first step, the robustness of the algorithm to an initial value is improved, and a next iteration step variable is directly solved in the second step to reduce the calculated amount.
Step 1:
1) solving the following equation to obtain a vector λ:
(EET)λ＝p-Eyk
2) computing
Figure BDA0002072026780000042
Figure BDA0002072026780000043
3)
Figure BDA0002072026780000044
And calculating the Jacobian matrix
Figure BDA0002072026780000045
Step 2:
1) solving the following formula to obtain xk+1：
Figure BDA0002072026780000051
2) Updating yk+1＝f-1(Cxk+1)；
3) If | | | p-Eyk+1||∞If the value is less than epsilon, convergence is carried out, otherwise k is equal to k +1, and the iteration is continued by returning to the step 1.
The beneficial results of the invention are as follows: solving the equation by introducing auxiliary factors and adopting a two-step method, and obtaining the initial value x0Classical newton's method tends to fail to converge or converge slowly when far from the true solution of the equation. The invention can effectively improve the convergence and the robustness by constructing a least square problem and searching for a linearization point which is as close to a real solution as possible under the condition of meeting the constraint.
Drawings
FIG. 1 is a diagram of an embodiment of the present invention: the microgrid algorithm graph comprises 115 node island micro-grid.
Fig. 2 is a flow chart of the island micro-grid load flow calculation method based on two-step solution of the auxiliary factor.
FIG. 3 is a graph comparing the convergence times of the present invention with Newton's method (N-R), single-step adaptive LM algorithm (A-LM), and three-step LM algorithm (MTLM) at different accuracies.
Detailed Description
The method and steps of the present invention are described in detail in the following with reference to the accompanying drawings and specific embodiments, it is to be understood that these embodiments are merely illustrative of the present invention and are not intended to limit the scope of the invention, which is defined by the appended claims, and various equivalent modifications thereof will occur to those skilled in the art after reading this disclosure.
In this embodiment, a specific method of the present invention is described by taking an example of a node of a large-scale microgrid 115. The example has 115 nodes, 118 branches, 3 wind turbines, 2 photovoltaic cells and 8 gas turbines, as shown in fig. 1.
1. Rewriting the equation of load flow calculation
The island microgrid power flow equation can be abstractly expressed as:
F(x)＝0 x∈Rn (12)
the system has n nodes, nPQPQ node, nPVA PV node and nDA droop node, the formula (1) is an integer containing n + nPQ+nDN + n of individual position variablesPQ+nDAnd (4) dimensional equations.
By moving all constant terms in equation (1) to the right of the equation and preserving the PV node voltage magnitude, equation (1) can be rewritten as follows:
F1(x)＝p (13)
in the formula:
p＝[p0,V1,…,VnPV]T (14)
p0for the vector composed of constant terms in the power flow equation and for the convenience of subsequent calculation, the voltage amplitude of the PV node is preserved in p, expressed by its square form,
Figure BDA0002072026780000061
for vector x, where the voltage term and system frequency are replaced by logarithmic form:
x＝[δ2,…,δn,a1,…,an,w]T (15)
in the formula: deltaiIs the phase angle of node i, ai＝ln Vi＝2 ln Ui，w＝lnω。
2. Introduction of cofactor
Introducing a cofactor y:
Figure BDA0002072026780000062
in the formula: second to last term UD,iFor the amplitude of the voltage at the droop node, nDAn item; alpha and beta are active and reactive load indexes, and for nodes i and j at two ends of each branch, let Kij＝UiUj cosδij、Lij＝UiUj sinδijWherein δij＝δi-δj。
Introduction of a cofactor u:
Figure BDA0002072026780000071
in the formula: the second last term is the same as equation (2) and represents a droop node; a isij＝ai+aj，δij＝δi-δj。
With the aid of the auxiliary factors, the original power flow equation can be changed into the following form:
Figure BDA0002072026780000072
in the formula: f (-) is a non-linear transformation reversible between cofactors with y ═ f inverse-1The specific form (u) is as follows:
Figure BDA0002072026780000073
3. tidal current initial value setting
Setting an initial value x of a tidal current state variable0Setting the convergence accuracy epsilon and the maximum iteration number k as 0maxFrequency of system omega0Voltage amplitude U0And the initial value delta of the phase angle0Get y0＝f-1(Cx0)。
4. Two-step method for solving equation
After the conversion of the power flow equation is completed, the converted equation can be solved by adopting a two-step method, and the specific steps are as follows:
step 1:
1) solving the following equation to obtain a vector λ:
(EET)λ＝p-Eyk (20)
2) computing
Figure BDA0002072026780000081
Figure BDA0002072026780000082
3)
Figure BDA0002072026780000083
And calculates the Jacobian matrix of equation (8)
Figure BDA0002072026780000084
Step 2:
1) solving the following formula to obtain xk+1：
Figure BDA0002072026780000085
2) Updating yk+1＝f-1(Cxk+1)。
3) If | | | p-Eyk+1||∞If the value is less than epsilon, convergence is carried out, otherwise k is equal to k +1, and the iteration is continued by returning to the step 1.
After the method is applied to a 115-node large-scale micro-grid, the method is compared with a Newton method (N-R), a single-step self-adaptive LM algorithm (A-LM) and a three-step LM method (MTLM), and the non-convergence times of different algorithms are recorded under the change of initial values and are shown in the table 1 (the running times are 100):
TABLE 1 comparison of 4 algorithm convergence conditions under initial value change
Figure BDA0002072026780000086
Meanwhile, comparing 4 algorithms, the time spent in 1000 Monte Carlo simulations is shown in Table 2:
TABLE 2 Monte Carlo simulation elapsed time
Figure BDA0002072026780000091

Claims (3)

1. An island microgrid load flow calculation method based on two-step solution of auxiliary factors is characterized by comprising the following steps:
1) rewriting a load flow calculation equation; the method specifically comprises the following steps:
the island microgrid power flow equation can be abstractly expressed as:
F(x)＝0 x∈Rn (1)
the system has n nodes, nPQPQ node, nPVA PV node and nDA droop node, the formula (1) is an integer containing n + nPQ+nDN + n of individual position variablesPQ+nDA dimensional equation;
by moving all constant terms in equation (1) to the right of the equation and preserving the PV node voltage magnitude, equation (1) can be rewritten as follows:
F1(x)＝p (2)
in the formula:
Figure FDA0003400569320000011
p0for the vector composed of constant terms in the power flow equation and for the convenience of subsequent calculation, the voltage amplitude of the PV node is preserved in p, expressed by its square form,
Figure FDA0003400569320000012
for vector x, where the voltage term and the system frequency ω are replaced by a logarithmic form:
x＝[δ2,…,δn,a1,…,an,w]T (4)
in the formula: deltaiIs the phase angle of node i, ai＝lnVi＝2lnUi，w＝lnω；
2) Introducing auxiliary factors, and converting a load flow calculation equation into a set of underdetermined equations, a set of overdetermined equations and a set of relation functions among the auxiliary factors; the method specifically comprises the following steps:
introducing a cofactor y:
Figure FDA0003400569320000021
in the formula: second to last term UD,iFor the amplitude of the voltage at the droop node, nDAn item; alpha and beta are active and reactive load indexes, and for nodes i and j at two ends of each branch, let Kij＝UiUjcosδij、Lij＝UiUjsinδijWherein δij＝δi-δj；
Introduction of a cofactor u:
Figure FDA0003400569320000022
in the formula: a isij＝ai+aj，δij＝δi-δj；
With the aid of the auxiliary factors, the original power flow equation can be changed into the following form:
Figure FDA0003400569320000023
in the formula: f (-) is a non-linear transformation reversible between cofactors with y ═ f inverse-1The specific form (u) is as follows:
Figure FDA0003400569320000024
3) setting a tidal current initial value;
4) solving the equation by a two-step method: and solving the transformed equation, wherein the transformed equation is transformed into a least square problem in the first step, and the next iteration step variable is directly solved in the second step.
2. The island microgrid power flow calculation method based on two-step solution of auxiliary factors as claimed in claim 1, characterized in that a power flow state variable initial value x is set0Setting the convergence accuracy epsilon and the maximum iteration number k as 0maxFrequency of system omega0Voltage amplitude U0And the initial value delta of the phase angle0Get y0＝f-1(Cx0)。
3. The island microgrid power flow calculation method based on two-step solution of auxiliary factors as claimed in claim 2 is characterized in that after the conversion of a power flow equation is completed, the converted equation is solved by adopting a two-step method, and the specific steps are as follows:
step 1:
1) solving the following equation to obtain a vector λ:
(EET)λ＝p-Eyk (9)
2) computing
Figure FDA0003400569320000031
Figure FDA0003400569320000032
3)
Figure FDA0003400569320000033
And calculates the Jacobian matrix of equation (8)
Figure FDA0003400569320000034
Step 2:
1) solving the following formula to obtain xk+1：
Figure FDA0003400569320000035
2) Updating yk+1＝f-1(Cxk+1)；
3) If | | | p-Eyk+1||∞If the value is less than epsilon, convergence is carried out, otherwise k is equal to k +1, and the iteration is continued by returning to the step 1.
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