CN109494746B - Island alternating current-direct current series-parallel micro-grid load flow calculation method based on improved adaptive droop control - Google Patents

Island alternating current-direct current series-parallel micro-grid load flow calculation method based on improved adaptive droop control Download PDF

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CN109494746B
CN109494746B CN201811326708.0A CN201811326708A CN109494746B CN 109494746 B CN109494746 B CN 109494746B CN 201811326708 A CN201811326708 A CN 201811326708A CN 109494746 B CN109494746 B CN 109494746B
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CN109494746A (en
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唐俊杰
杨勇
舒铜
林星宇
刘福潮
秦睿
杨云
郑晶晶
梁福波
张建华
彭晶
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STATE GRID GASU ELECTRIC POWER RESEARCH INSTITUTE
Chongqing University
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Chongqing 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
    • 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
    • H02J3/381—Dispersed generators
    • 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 an island alternating current-direct current series-parallel micro-grid load flow calculation method based on improved adaptive droop control, which mainly comprises the following steps of: 1) and establishing an alternating current-direct current hybrid micro-grid control model. 2) And establishing an island alternating current-direct current parallel-serial microgrid tide model. 3) And establishing a trust domain-based LMTR solving algorithm. 4) Carrying out load flow calculation on an AC/DC hybrid system of an island microgrid by using an alternating iteration method, wherein the convergence judgment condition is
Figure DDA0001858923810000011
If so, go to step 5. If not, continuing the iteration until convergence. 5) And outputting a load flow calculation result, changing the active load, updating a droop control coefficient by adopting an improved self-adaptive droop control strategy, and performing load flow calculation again. The invention can maintain the stability of frequency and voltage, ensure that all distributed power supplies output according to the power capacity ratio when power disturbance occurs in the system, avoid the out-of-range condition of single power supply output when overload occurs, and is beneficial to maintaining the safe, stable, reliable and efficient operation of the system.

Description

Island alternating current-direct current series-parallel micro-grid load flow calculation method based on improved adaptive droop control
Technical Field
The invention relates to the field of new energy grid connection, in particular to an island alternating current and direct current series-parallel connection microgrid load flow calculation method based on improved adaptive droop control.
Background
Under the current large background of energy shortage and environmental deterioration, micro-grids are more and more accepted and developed by scholars at home and abroad. The micro-grid is a small-sized power generation and distribution system which is formed by collecting a distributed power supply, an energy storage device, an energy conversion device, a load, a monitoring and protecting system and the like, and can realize an autonomous system with self-control, protection and management. The micro-grid can not only solve the flexible access and the efficient operation of a large-scale distributed power supply and supply power to users in remote areas, islands and deserts, but also is an important way for realizing self-healing, user-side interaction and demand response of the intelligent power distribution network in the future.
The micro-grid is characterized in that a power source is close to a load, long-distance transmission is not needed, the impedance characteristic of a power transmission line is similar to that of a traditional power distribution network, and meanwhile, the access of a distributed power source, the diversity of a distributed power source control mode and the flexible diversity of a micro-grid operation mode enable the load flow distribution and calculation of the micro-grid to be different from that of the traditional power distribution network in diversity. In addition, the randomness of the output of the intermittent distributed power supply in the microgrid, the random faults of the circuits and the distributed power supply, and uncertain factors of system load fluctuation can cause serious influence on the electric energy quality of the system, and the safe, stable and reliable operation of the system is not facilitated.
The power flow calculation is one of the most basic calculations in the analysis of the power system and is the basis for the analysis and control of the steady-state operation of the power system. The conventional power flow calculation of the micro-grid is an important field of micro-grid technology research and is the basis of micro-grid safety analysis, electromechanical transient stability analysis and electromagnetic transient analysis, wherein the electromagnetic transient analysis and the electromechanical transient stability analysis firstly need to give an initial state, and the conventional power flow calculation needs to be carried out when the initial state is given; meanwhile, the method is also an important basis for the operation reliability of the micro-grid island. Therefore, the model and the algorithm for researching the conventional power flow of the micro-grid are used for obtaining the rapid, accurate and practical deterministic power flow result, and the method is the basis of the steady-state analysis of the micro-grid and has important research significance and application value.
In an island alternating current-direct current hybrid micro-grid system, each distributed power supply usually adopts equivalent droop control, a plurality of balance nodes exist in the system, the plurality of balance nodes bear unbalanced power together, the resistance of a circuit in the micro-grid system cannot be far smaller than reactance, and the factors can cause singularity of a Jacobian matrix. In an island micro-grid system, after the island micro-grid system is separated from an alternating current main grid support, the frequency is easy to deviate from a rated value, and when the system is disturbed, a more advanced control mode needs to be adopted to maintain the stability of the frequency and the voltage. Meanwhile, in order to enable the load flow calculation result to be more accurate, the frequency/voltage characteristics of the load need to be considered, and an alternating-current and direct-current series-parallel system is solved by adopting an alternating iteration method. In addition, all the distributed power supplies are not communicated with each other, and in order to ensure that all the distributed power supplies output power according to the power capacity ratio and ensure the same power margin, the condition that the output power of a single power supply exceeds the threshold when overload occurs does not occur, an effective droop coefficient selection method needs to be provided.
Disclosure of Invention
The present invention is directed to solving the problems of the prior art.
The technical scheme adopted for achieving the purpose of the invention is that the island alternating current and direct current series-parallel connection microgrid load flow calculation method based on improved self-adaptive droop control mainly comprises the following steps:
1) and constructing an alternating current-direct current series-parallel micro-grid.
2) The method comprises the steps of establishing an alternating current-direct current hybrid micro-grid control model, wherein the alternating current-direct current hybrid micro-grid control model mainly comprises an alternating current distributed power supply droop control model, a direct current distributed power supply droop control model, a connecting converter control model, a load model considering frequency/voltage characteristics and an improved self-adaptive droop control model.
The droop control model of the alternating-current distributed power supply is as follows:
Figure BDA0001858923790000021
in the formula, ωi、Uaci、PGiAnd QGiThe actual frequency, the machine terminal voltage amplitude, the output active power and the output reactive power of the ith alternating current distributed power supply are respectively. Omega0And Uac0Respectively, the no-load frequency and the no-load machine terminal voltage amplitude. KPiAnd KQiRespectively an active droop coefficient and a reactive droop coefficient.
Active droop coefficient KPiEquation 2 is satisfied, i.e.:
KP1PN1＝KP2PN2＝KP3PN3＝···＝KPnPNn＝ωmax-ωmin。 (2)
wherein n is the total number of the AC distributed power sources. PNiThe active power of the power supply is distributed for the ith alternating current.
Reactive sag coefficient KQiEquation 3 is satisfied, i.e.:
KQ1QN1＝KQ2QN2＝KQ3QN3＝···＝KQnQNn＝Uac.imax-Uac.imin。 (3)
in the formula, QNiThe reactive power of the ith AC distribution power supply. U shapeac.imaxThe maximum voltage of the ith ac distribution power supply. U shapeac.iminThe minimum voltage of the ith ac distribution power supply.
The droop control model of the direct-current distributed power supply is as follows:
Udi＝Ud0-KdciPGdci。 (4)
in the formula of Udi、Ud0And PGdciThe actual direct current voltage amplitude, the no-load direct current voltage amplitude and the output active power are respectively. KdciIs the droop coefficient of the direct current distributed power supply.
Droop coefficient K of direct-current distributed power supplydciEquation 5 is satisfied, i.e.:
Kdc1PdN1＝Kdc2PdN2＝···＝KdcnPdNn＝Udc.max-Udc.min。 (5)
in the formula, PdNnAnd outputting active power for the direct-current distributed power supply. U shapedc.maxThe maximum voltage of the direct current distributed power supply. U shapedc.minThe minimum voltage of the direct current distributed power supply.
The connection converter control model is as follows:
using formula 6 to couple frequency omega of converter and DC voltage UILCdcNormalizing to connect the frequency omega of the converterpuAnd a DC voltage UILC.puWithin the same unit range.
Figure BDA0001858923790000031
In the formula, ωmaxAnd ωminRespectively, the maximum frequency and the minimum frequency allowed by the ac subsystem. U shapeILCdc,maxAnd UILCdc,minRespectively, the maximum voltage and the minimum voltage allowed by the dc subsystem. U shapeILCdcIs the dc subsystem voltage.
After normalization, ωpu＝[-1,1]And U isILC.pu＝[-1,1]。
The power control equation for the connected converter is as follows:
Figure BDA0001858923790000032
in the formula of UILCac0And UILCacRespectively, no-load AC voltage amplitude and actual AC voltage amplitude。KPILCAnd KQILCThe active and reactive control coefficients of the connecting converter are respectively. PILCdcThe active power of the converter direct current subsystem is connected. QILCacFor connecting the reactive power of the converter AC subsystem. PILCacFor connecting the active power of the converter ac subsystem.
The load model taking into account the frequency/voltage characteristics is as follows:
Figure BDA0001858923790000041
wherein when the frequency and voltage of the system are respectively fL0iAnd UL0iWhen is, PL0iAnd QL0iRespectively corresponding real active power and reactive power. When the frequency and voltage are equal to f and U, respectivelyiWhen is, PLiAnd QLiThe actual active power and the reactive power corresponding to the load are respectively. KPfiAnd KQfiThe static frequency characteristic coefficients of the load are respectively. KPViAnd KQViLoad active power index and reactive power index respectively.
The main steps for establishing the improved self-adaptive droop control model are as follows:
I) and obtaining an initial droop coefficient according to a formula 2 and a formula 3, and calculating an initial power flow.
II) the improved adaptive droop control model is shown in equation 9 and equation 10, respectively:
Figure BDA0001858923790000042
Figure BDA0001858923790000043
in the formula, ωNAnd UacNRespectively, the rated frequency and the rated voltage of the alternating current distributed power supply.
Figure BDA0001858923790000044
And
Figure BDA0001858923790000045
the actual active power output and the reactive power output of the distributed power supply at the moment t-1 before the load change are respectively. U'aciThe terminal voltage amplitude of the ith alternating current distributed power supply is improved. Omega'iIs the actual frequency of the modified ith ac distributed power source.
Actual active power of distributed power supply at t-1 moment before load change
Figure BDA0001858923790000046
Satisfies the following formula:
Figure BDA0001858923790000047
in the formula, PminThe minimum active power output of the distributed power supply at the moment t-1 before the load changes. PmaxThe maximum value of the active power output of the distributed power supply at the moment t-1 before the load changes.
Figure BDA0001858923790000048
In the formula, QminAnd the minimum reactive power output of the distributed power supply at the moment t-1 before the load is changed. QmaxThe maximum reactive power output of the distributed power supply at the moment t-1 before the load is changed.
3) And establishing an island alternating current-direct current parallel-serial microgrid tide model.
The method mainly comprises the following steps of establishing an island alternating current-direct current series-parallel micro-grid power flow model:
and 3.1) establishing an island AC/DC parallel-serial micro-grid. The alternating current nodes are divided into 4 types: PQ node, PV node, droop node, and ILC-AC node. The direct current nodes are divided into 3 types: a constant P node, a droop node, and an ILC-DC node.
3.2) establishing a power flow model of the AC subsystem.
The power balance equation for any ith node in the ac subsystem is as follows:
Figure BDA0001858923790000051
in the formula, xacIs the state variable of the AC subsystem. PGiAnd QGiThe active output and the reactive output of the generator of the ith node are respectively. PLiAnd QLiRespectively the active power and the reactive power of the load of the ith node. PILCaciAnd QILCaciActive and reactive power are injected for connecting the converter ILC, respectively. SPQ、SPV、SDr-ac、SILC-acThe PQ node, the PV node, the droop node and the ILC-AC node are respectively set. PiAnd QiActive power and reactive power are injected into the nodes respectively.
Node injection active power PiAnd node injection reactive power QiRespectively as follows:
Figure BDA0001858923790000052
in the formula, N is the total number of nodes. U shapeiIs the ith node voltage. U shapejIs the jth node voltage. DeltaijIs a voltage UiSum voltage UjPhase angle difference of (2). GijIs the conductance between node i and node j. B isijIs the susceptance between node i and node j.
FPmis.ac.i(xac) And FQmis.ac.i(xac) Respectively the active and reactive unbalanced power of the ith node. State variable x of four node typesac＝[xPQi,xPVi,xDr-aci,xILC-aci]TRespectively as follows:
Figure BDA0001858923790000053
δiis the ithThe voltage phase angle of the node.
3.3) establishing a power flow model of the direct current subsystem
The power balance equation of any ith' node in the dc subsystem is as follows:
Fdci'(xdc)＝PGdci'-PLdci'-Pdci'-PILCdc＝0。 (16)
in the formula, xdcIs a direct current subsystem state variable. PGdci'、PLdci'And PILCdcAnd respectively injecting active power for the direct current distributed power supply, active power for the load and active power for the connection converter. PdciAnd injecting power for the direct current subsystem node.
Direct current subsystem node injection power Pdci'As follows:
Figure BDA0001858923790000061
in the formula, N' is the number of nodes of the direct current subsystem. U shapedcj'Is the voltage of the jth node of the DC subsystem. U shapedci'Is the voltage of the ith' node of the DC subsystem. Y isi'j'Is the admittance between the ith' node and the jth node of the direct current subsystem.
State variable x of DC subsystemdc＝[xP-dci',xDr-dci',xILC-dci']TSpecifically, the following are shown:
Figure BDA0001858923790000062
in the formula, SP-dcAnd the constant P node set is a direct current subsystem. SDr-dcAnd the method is a droop node set of the direct current subsystem. SILC-dcThe system is a direct current subsystem ILC-DC node set.
4) And establishing a trust domain-based LMTR solving algorithm.
5) Carrying out load flow calculation and convergence judgment on the load flow model of the island AC/DC series-parallel micro-grid by using an alternating iteration method and an LMTR solution algorithmThe other condition being the merit function ψ (x)k) Result of vector differentiation of
Figure BDA0001858923790000063
ε1The convergence accuracy of the load flow calculation is obtained. If so, go to step 6. If not, continuing the iteration until convergence.
The method mainly comprises the following steps of establishing a trust domain-based LMTR solving algorithm:
5.1) eliminating Jacobian matrix J by using a trust domain method based on unit step lengthkThe singularity of (a), namely:
Figure BDA0001858923790000064
in the formula, Fk＝F(xk)。Jk＝J(xk)。dLMKFor the current operating point xkThe direction of iteration of (1). x is the number ofk+1Is the value of the next iteration point. I is a unit vector. FkRepresenting active and reactive imbalance equations, F in convergencekTending to 0.
According to equation 19, when μkWhen approaching 0, dLMKTends to Gauss-Newton step when mu iskWhen approaching infinity, dLMKTending to the steepest descending step.
5.2) calculating the current operation point x according to the load flow based LMTR methodkDirection of iteration dLMKUpdating is carried out, namely:
Figure BDA0001858923790000071
in the formula, theta is a constant, and theta is more than or equal to 0 and less than or equal to 1. Parameter betakUpdating by using a trusted domain method.
5.3) defining the merit function ψ (x)k)＝0.5||F(xk)||2Then the ratio r of the actual drop to the estimated dropkComprises the following steps:
Figure BDA0001858923790000072
then after k iterations, point x is runk+1As follows:
Figure BDA0001858923790000073
in the formula eta1For iterative successful discrimination coefficient, η1Is greater than 0. Wherein x isk+1＝xk+dLMkIndicates the success of the iteration, xk+1＝xkIndicating that the iteration failed. r iskIs an operating point xkThe iterative decision parameter of (1).
Parameter betakThe update is as follows:
Figure BDA0001858923790000074
in the formula eta2For iterative successful discrimination coefficients, 0 < eta1＜η2＜1。γ1And gamma2Is betakCorrection coefficient of gamma1> 1 and 0 < gamma2＜1。βminIs betakIs measured. If rk＞η2Then the iteration is very successful, at which time βk+1＝max(γ2βk,βmin). If eta1＜γk＜η2Then the iteration is successful, at which time betak+1＝βk. If gamma isk＜η1Then the iteration fails, in which case βk+1＝γ1。γkIs betakThe iterative decision parameter of (1).
6) And outputting a load flow calculation result, changing the active load, updating a droop control coefficient by adopting an improved self-adaptive droop control strategy, and performing load flow calculation again until the output of the distributed power supply exceeds the limit.
The technical effect of the present invention is undoubted. The basic idea of the invention is: the frequency and the voltage of the island alternating current and direct current series-parallel micro-grid are stabilized by adaptively changing the droop control coefficient of the distributed power supply, and meanwhile, a more precise load model and an advanced solving algorithm are adopted to obtain a more accurate and rapid tide result. The invention solves the problem that the Jacobian matrix in an island AC/DC hybrid micro-grid is possible to be singular, can maintain the stability of frequency and voltage, and simultaneously ensures that all distributed power supplies output according to the power capacity ratio when power disturbance occurs in the system, so that the out-of-range condition of single power supply output during overload can not occur, thereby being beneficial to maintaining the safe, stable, reliable and efficient operation of the system.
Drawings
FIG. 1 is a flow chart of island alternating current and direct current series-parallel connection micro-grid load flow calculation based on improved adaptive droop control;
FIG. 2 is an isolated island AC/DC hybrid micro-grid system node network formed by an IEEE-33 node power distribution system and a Benchmark low-voltage micro-grid after modification;
FIG. 3 is a DC bus voltage profile;
FIG. 4 is a graph of system frequency with varying load;
FIG. 5 is a schematic diagram of the output of all the AC DGs at varying loads;
fig. 6 is a dc No. 11 bus voltage distribution diagram when the load changes.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
as shown in fig. 1 to 2, the island alternating current/direct current hybrid microgrid power flow calculation method based on the improved adaptive droop control mainly includes the following steps:
1) and constructing an alternating current-direct current series-parallel micro-grid. An IEEE-33 node power distribution system and a Benchmark low-voltage micro-grid are slightly modified to form an island alternating current and direct current hybrid micro-grid system, and the system is shown in figure 1.
2) The method comprises the steps of establishing an alternating current-direct current hybrid micro-grid control model, wherein the alternating current-direct current hybrid micro-grid control model mainly comprises an alternating current distributed power supply droop control model, a direct current distributed power supply droop control model, a connecting converter control model, a load model considering frequency/voltage characteristics and an improved self-adaptive droop control model.
When the alternating current sub-network adopts a peer-to-peer control strategy, the alternating current distributed power supply generally adopts a P-f/Q-U droop control characteristic, and the droop control model of the alternating current distributed power supply is as follows:
Figure BDA0001858923790000081
in the formula, ωi、Uaci、PGiAnd QGiThe actual frequency, the machine terminal voltage amplitude, the output active power and the output reactive power of the ith alternating current distributed power supply are respectively. Omega0And Uac0Respectively, the no-load frequency and the no-load machine terminal voltage amplitude. KPiAnd KQiRespectively an active droop coefficient and a reactive droop coefficient.
Active droop coefficient KPiEquation 2 is satisfied, i.e.:
KP1PN1＝KP2PN2＝KP3PN3＝···＝KPiPNi＝···＝KPnPNn＝ωmax-ωmin。 (2)
wherein n is the total number of the AC distributed power sources. PNiThe active power of the power supply is distributed for the ith alternating current.
Reactive sag coefficient KQiSatisfy formula 3, i.e.
KQ1QN1＝KQ2QN2＝KQ3QN3＝···＝KQiQNi＝···＝KQnQNn＝Uac.imax-Uac.imin (3)
In the formula, QNiThe reactive power of the ith AC distribution power supply. U shapeac.imaxThe maximum voltage of the ith ac distribution power supply. U shapeac.iminThe minimum voltage of the ith ac distribution power supply.
Taking two power sources in an alternating current power grid as an example to analyze the output condition of the alternating current distributed power source, substituting the expression (2) into the expression (1) to obtain the following result:
Figure BDA0001858923790000091
Figure BDA0001858923790000092
because two power supplies are connected to the same AC power grid, they have the same frequency omega1＝ω2Formula (5) may be combined to obtain formula (6):
Figure BDA0001858923790000093
it can be seen from equation (6) that all distributed power supplies output according to the power capacity ratio, and all distributed power supplies are ensured to have the same power margin, and single power supply boundary crossing cannot occur due to overload.
The droop control model of the direct-current distributed power supply is as follows:
Udi＝Ud0-KdciPGdci。 (7)
in the formula of Udi、Ud0And PGdciThe actual direct current voltage amplitude, the no-load direct current voltage amplitude and the output active power are respectively. KdciIs the droop coefficient of the direct current distributed power supply.
Droop coefficient K of direct-current distributed power supplydciEquation 8 is satisfied, i.e.:
Kdc1PdN1＝Kdc2PdN2＝···＝KdcnPdNn＝Udc.max-Udc.min。 (8)
in the formula, PdNnAnd outputting active power for the direct current power supply. U shapedc.maxFor maximum voltage of DC distributed power supply。Udc.minThe minimum voltage of the direct current distributed power supply.
The connecting converter (ILC) control model is as follows:
the droop characteristics of the active power of alternating current and direct current are different, the ordinate of the characteristic curve respectively represents the frequency and the direct current voltage, and the unit is inconsistent. Therefore, it is necessary to adjust the frequency ω and the DC voltage UILCdcThe normalization processing of equation (9) is performed. Frequency omega of connecting current transformerpuAnd a DC voltage UILC.puWithin the same unit range.
Figure BDA0001858923790000101
In the formula, ωmaxAnd ωminRespectively, the maximum frequency and the minimum frequency allowed by the ac subsystem. U shapeILCdc,maxAnd UILCdc,minRespectively, the maximum voltage and the minimum voltage allowed by the dc subsystem. U shapeILCdcIs the dc subsystem voltage.
After normalization, ωpu＝[-1,1]And U isILC.pu＝[-1,1]。
The power control equation for the connected converter is as follows:
Figure BDA0001858923790000102
in the formula of UILCac0And UILCacRespectively, the no-load alternating voltage amplitude and the actual alternating voltage amplitude. KPILCAnd KQILCThe active and reactive control coefficients of the connecting converter are respectively. PILCdcThe active power of the converter direct current subsystem is connected. QILCacFor connecting the reactive power of the converter AC subsystem. PILCacFor connecting the active power of the converter ac subsystem.
In an islanded ac/dc microgrid, the frequency is not always equal to the nominal frequency. Therefore, the frequency/voltage characteristics of the load need to be considered in power flow modeling. The exact load model can be expressed as follows:
Figure BDA0001858923790000103
wherein when the frequency and voltage of the system are respectively fL0iAnd UL0iWhen is, PL0iAnd QL0iRespectively corresponding real active power and reactive power. When the frequency and voltage are equal to f and U, respectivelyiWhen is, PLiAnd QLiThe actual active power and the reactive power corresponding to the load are respectively. KPfiAnd KQfiThe static frequency characteristic coefficients of the load are respectively. KPViAnd KQViLoad active power index and reactive power index respectively.
TABLE 1 selection rule table for static parameters of load
Figure BDA0001858923790000111
The main steps for establishing the improved self-adaptive droop control model are as follows:
I) and obtaining an initial droop coefficient according to a formula 2 and a formula 3, and calculating an initial power flow.
II) the improved adaptive droop control model is shown in equation 12 and equation 13, respectively:
Figure BDA0001858923790000112
Figure BDA0001858923790000113
in the formula, ωNAnd UacNRespectively, the rated frequency and the rated voltage of the alternating current distributed power supply.
Figure BDA0001858923790000114
And
Figure BDA0001858923790000115
the actual active power output and the reactive power output of the distributed power supply at the moment t-1 before the load change are respectively. U'aciThe terminal voltage amplitude of the ith alternating current distributed power supply is improved. Omega'iIs the actual frequency of the modified ith ac distributed power source.
Actual active power of distributed power supply at t-1 moment before load change
Figure BDA0001858923790000116
Satisfies the following formula:
Figure BDA0001858923790000117
in the formula, PminThe minimum active power output of the distributed power supply at the moment t-1 before the load changes. PmaxThe maximum value of the active power output of the distributed power supply at the moment t-1 before the load changes.
Figure BDA0001858923790000118
In the formula, QminAnd the minimum reactive power output of the distributed power supply at the moment t-1 before the load is changed. QmaxThe maximum reactive power output of the distributed power supply at the moment t-1 before the load is changed.
3) And establishing an island alternating current-direct current parallel-serial microgrid tide model.
The method mainly comprises the following steps of establishing an island alternating current-direct current series-parallel micro-grid power flow model:
and 3.1) establishing an island AC/DC parallel-serial micro-grid. The alternating current nodes are divided into 4 types: PQ node, PV node, droop node, and ILC-AC node. The direct current nodes are divided into 3 types: a constant P node, a droop node, and an ILC-DC node. The PV node is known active power P, voltage amplitude V, and is generally a generator node; the PQ node is known active power P, reactive power Q, and is generally a load node.
3.2) establishing a power flow model of the AC subsystem.
The power balance equation for any ith node in the ac subsystem is as follows:
Figure BDA0001858923790000121
in the formula, xacIs the state variable of the AC subsystem. PGiAnd QGiThe active output and the reactive output of the generator of the ith node are respectively. PLiAnd QLiRespectively the active power and the reactive power of the load of the ith node. PILCaciAnd QILCaciActive and reactive power are injected for connecting the converter ILC, respectively. SPQ、SPV、SDr-ac、SILC-acThe PQ node, the PV node, the droop node and the ILC-AC node are respectively set. PiAnd QiActive power and reactive power are injected into the nodes respectively.
Node injection active power PiAnd node injection reactive power QiRespectively as follows:
Figure BDA0001858923790000122
in the formula, N is the total number of nodes; u shapeiIs the ith node voltage; u shapejIs the jth node voltage; deltaijIs a voltage UiSum voltage UjThe phase angle difference of (a); gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j;
FPmis.ac.i(xac) And FQmis.ac.i(xac) Respectively the active and reactive unbalanced power of the ith node. State variable x of four node typesac＝[xPQi,xPVi,xDr-aci,xILC-aci]TRespectively as follows:
Figure BDA0001858923790000123
δiis the voltage phase angle of the ith node.
Wherein x isPQiIndicating the corresponding state variable when node i is a PQ node. x is the number ofPViRepresenting the corresponding state variable when node i is the PV node. x is the number ofDr-aciAnd representing the corresponding state variable when the node i is the droop node. x is the number ofILC-aciAnd representing the corresponding state variable when the node i is an ILC-AC node.
3.3) establishing a power flow model of the direct current subsystem
The power balance equation of any ith' node in the dc subsystem is as follows:
Fdci'(xdc)＝PGdci'-PLdci'-Pdci'-PILCdc＝0。 (19)
in the formula, xdcIs a direct current subsystem state variable. PGdci'、PLdci'And PILCdcAnd respectively injecting active power for the direct current distributed power supply, active power for the load and active power for the connection converter. PdciAnd injecting power for the direct current subsystem node.
Direct current subsystem node injection power Pdci'As follows:
Figure BDA0001858923790000131
state variable x of DC subsystemdc＝[xP-dci',xDr-dci',xILC-dci']TSpecifically, the following are shown:
Figure BDA0001858923790000132
in the formula, SP-dcAnd the constant P node set is a direct current subsystem. SDr-dcAnd the method is a droop node set of the direct current subsystem. SILC-dcThe system is a direct current subsystem ILC-DC node set.
xP-dci'Representing the corresponding state variable when node i' is a constant P node. x is the number ofDr-dci'Indicating the corresponding state variable when node i' is a droop node. x is the number ofILC-dci'Representing the corresponding state variables when node i' is the ILC-DC node.
4) A trust domain-based Levenberg Marquardt method with trust region technical solving algorithm, namely an LMTR solving algorithm, is established. Under an equivalent droop control strategy, no balance node exists in the island alternating current-direct current series-parallel micro-grid system. Furthermore, the line resistance cannot be much smaller than the reactance in a microgrid. These features will all likely result in the singularity of the jacobian matrix. Therefore, a trust domain method based on unit step size is used to solve this problem.
5) Carrying out load flow calculation on the island alternating current and direct current series-parallel micro-grid load flow model by using an alternating iteration method and an LMTR (Linear minimum mean square root) solution algorithm, wherein the convergence judgment condition is a value function psi (x)k) Result of vector differentiation of
Figure BDA0001858923790000133
In this example
Figure BDA0001858923790000134
As a merit function ψ (x)k) Of the gradient of (c). Epsilon1The convergence accuracy of the load flow calculation is obtained. If so, go to step 6. If not, continuing the iteration until convergence.
The method mainly comprises the following steps of establishing a trust domain-based LMTR solving algorithm:
5.1) eliminating Jacobian matrix J by using a trust domain method based on unit step lengthkThe singularity of (a), namely:
Figure BDA0001858923790000141
in the formula, Fk＝F(xk)。Jk＝J(xk)。dLMKFor the current operating point xkThe direction of iteration of (1). x is the number ofk+1Is the value of the next iteration point. I is a unit vector.
According to equation 19, when μkWhen approaching 0, dLMKTends to Gauss-Newton-Newton) step, when μkWhen approaching infinity, dLMKTending to the steepest descending step.
5.2) calculating the current operation point x according to the load flow based LMTR methodkDirection of iteration dLMKUpdating is carried out, namely:
Figure BDA0001858923790000142
in the formula, theta is a constant, and theta is more than or equal to 0 and less than or equal to 1. Parameter betakUpdating by using a trusted domain method. FkRepresenting active and reactive imbalance equations, F in convergencekTending to 0.
5.3) defining the merit function ψ (x)k)＝0.5||F(xk)||2Then the ratio r of the actual drop to the estimated dropkComprises the following steps:
Figure BDA0001858923790000143
then after k iterations, point x is runk+1As follows:
Figure BDA0001858923790000144
in the formula eta1For iterative successful discrimination coefficient, η1Is greater than 0. Wherein x isk+1＝xk+dLMkIndicates the success of the iteration, xk+1＝xkIndicating that the iteration failed. r iskIs an operating point xkThe iterative decision parameter of (1).
Parameter betakThe update is as follows:
Figure BDA0001858923790000145
in the formula eta2For iterative successful discrimination coefficients, 0 < eta1＜η2＜1。γ1And gamma2Is betakCorrection coefficient of gamma1> 1 and 0 < gamma2＜1。βminIs betakIs measured. If rk＞η2Then the iteration is very successful, at which time βk+1＝max(γ2βk,βmin). If eta1＜γk＜η2Then the iteration is successful, at which time betak+1＝βk. If gamma isk＜η1Then the iteration fails, in which case βk+1＝γ1。γkIs betakThe iterative decision parameter of (1).
6) After the LMTR algorithm is adopted to solve the power flow of the direct current subsystem, the judgment is carried out
Figure BDA0001858923790000151
Whether the current is established or not is judged, if so, the current result x of the direct current subsystem is obtaineddckAnd PILCdcThe subscript dc denotes the dc subsystem. And P isILCdc＝PILCacAnd (4) carrying the load flow equation into the alternating current subsystem, and solving the load flow of the alternating current subsystem by adopting an LMTR algorithm. And if not, updating the frequency omega and carrying out load flow calculation again.
After the power flow of the AC subsystem is solved, judgment is carried out
Figure BDA0001858923790000152
And if so, obtaining a power flow result of the direct current subsystem, wherein the subscript ac represents the direct current subsystem, and turning to the step 7. And if not, updating the frequency omega and carrying out load flow calculation again.
7) And outputting information such as system frequency, alternating current/direct current bus voltage, branch power, converter exchange power and the like, changing load active power, updating a droop control coefficient by adopting an improved self-adaptive droop control strategy, and performing load flow calculation again until all load parameters are subjected to load flow calculation.
According to the island alternating current and direct current hybrid micro-grid frequency and voltage stabilizing method, the frequency and voltage of the island alternating current and direct current hybrid micro-grid are stabilized by adaptively changing the droop control coefficient of the distributed power supply, and meanwhile, a more precise load model and an advanced solving algorithm are adopted to obtain a more accurate and rapid tide result. Fig. 6 is a process of alternating iteration of island alternating current and direct current series-parallel micro-grid load flow calculation based on adaptive droop control.
Example 2:
an experiment for verifying an island alternating current-direct current parallel-serial microgrid load flow calculation method based on improved adaptive droop control mainly comprises the following steps:
1) setting the experimental parameters of the island AC/DC series-parallel micro-grid, namely: eta1＝0.25、η2＝0.75、γ1＝4、γ2＝0.25、θ＝0.5、β0＝0.005、βmin＝10-8. All droop control DG devices contain reactive compensation equipment, the amplitude of the no-load voltage is 1.06pu, and the frequency of the no-load voltage of the alternating current P-f/Q-U droop control DG device is 1.004 pu. The droop DG device parameters are mainly shown in table 2.
Setting communication subsystem parameters: the system reference power is 1MVA, the reference frequency is 50Hz, and the steady-state frequency range is [0.996, 1.004%]pu, the phase angle of the voltage at node 39 is the reference phase angle. The reference power of the direct current subsystem is 100 kVA. ILC device parameter setting: u shapeILCdc.max、UILCdc.minAre respectively 1.06pu and 0.94pu, omegamax、ωminRespectively 1.004pu and 0.996pu, KPILC＝8，KQILC5. Setting eMWhen the frequency of the alternating current subsystem, the amplitude of the unknown alternating current node voltage and the phase angle are 0.05pu, the initial values of the frequency, the amplitude of the unknown alternating current node voltage and the phase angle of the alternating current subsystem are respectively 1pu, 1pu and 0rad, and the initial value of the unknown node voltage of the direct current subsystem is 1 pu.
TABLE 2 droop DG device parameters
Figure BDA0001858923790000161
2) And calculating the isolated island alternating current and direct current parallel-serial micro-grid fundamental power flow, and the result is shown in tables 3 and 4.
Table 3 island ac/dc series-parallel micro-grid load flow calculation result
Node number Ui/pu δi/(°) Node number Ui/pu δi/(°)
1 0.9846 0.0700 21 1.0021 0.4559
2 0.9845 0.0827 22 1.0100 0.7033
3 0.9811 0.1383 23 0.9793 0.1072
4 0.9803 0.1933 24 0.9762 0.0333
5 0.9798 0.2483 25 0.9762 0.0030
6 0.9784 0.3727 26 0.9786 0.4153
7 0.9785 0.3253 27 0.9788 0.4754
8 0.9788 0.2826 28 0.9795 0.7624
9 0.9778 0.2304 29 0.9804 0.9880
10 0.9772 0.1867 30 0.9819 1.0963
11 0.9772 0.1815 31 0.9886 1.2675
12 0.9772 0.1697 32 0.9912 1.3491
13 0.9785 0.1280 33 0.9953 1.5107
14 0.9796 0.1267 34 0.9865 0.3746
15 0.9812 0.1211 35 0.9962 0.4172
16 0.9833 0.1132 36 1.0155 0.8207
17 0.9889 0.2084 37 0.9841 0.0896
18 0.9937 0.3859 38 1.0169 1.9991
19 0.9857 0.1092 39 0.9857 0
20 0.9981 0.3461
Table 4 other information for load flow calculation
Figure BDA0001858923790000171
The alternative iteration method is very effective as can be seen from the ground state power flow result, all parameters are in a normal range, and the LMTR solving algorithm has high convergence and calculation rapidity as can be seen from the experimental result. In addition, the algorithm can also calculate the steady-state frequency of the power system to be 0.9991 Hz.
2) Effect comparison for improved adaptive droop control
As shown in fig. 3 to 6, the improved adaptive droop control can keep the frequency stable well, and has strong robustness when the load fluctuates. Meanwhile, when the load fluctuates, all DGs can still output power according to respective capacity ratios, so that the fault caused by the fact that a single DG in an island micro-grid is out of limit is avoided, and meanwhile, through coordination of all DGs and power on the AC-DC side, the control method also has certain help on the stability of the DC voltage.

Claims (4)

1. An island alternating current-direct current series-parallel micro-grid load flow calculation method based on improved adaptive droop control is characterized by mainly comprising the following steps of:
1) building the alternating current-direct current series-parallel micro-grid;
2) establishing an alternating current-direct current hybrid micro-grid control model; the method mainly comprises an alternating current distributed power supply droop control model, a direct current distributed power supply droop control model, a connecting converter control model, a load model considering frequency/voltage characteristics and an improved self-adaptive droop control model;
3) establishing an island alternating current-direct current parallel-serial microgrid tide model;
4) establishing a trust domain-based LMTR solving algorithm;
5) carrying out load flow calculation on the island alternating current and direct current series-parallel micro-grid load flow model by using an alternating iteration method and an LMTR (Linear minimum mean square root) solution algorithm, wherein the convergence judgment condition is a value function psi (x)k) Vector differential result of ++ (x)k) Satisfy the requirement of
Figure FDA0003228159880000011
ε1Calculating convergence accuracy for the load flow; if yes, turning to step 6; if not, continuing the iteration until convergence; j. the design is a squarekIs a Jacobian matrix; fk＝F(xk)；FkAn imbalance equation representing active power and reactive power;
6) and outputting a load flow calculation result, changing the active load, updating a droop control coefficient by adopting an improved self-adaptive droop control strategy, and performing load flow calculation again until the output of the distributed power supply exceeds the limit.
2. The island alternating current-direct current hybrid micro-grid power flow calculation method based on the improved adaptive droop control according to claim 1, characterized by comprising the following steps of:
the droop control model of the alternating-current distributed power supply is as follows:
Figure FDA0003228159880000012
in the formula, ωi、Uaci、PGiAnd QGiThe actual frequency, the machine terminal voltage amplitude, the output active power and the output reactive power of the ith alternating current distributed power supply are respectively; omega0And Uac0Respectively is a no-load frequency and a no-load machine terminal voltage amplitude; kPiAnd KQiRespectively, active droop coefficientAnd a reactive droop coefficient;
active droop coefficient KPiEquation 2 is satisfied, i.e.:
KP1PN1＝KP2PN2＝KP3PN3＝···＝KPnPNn＝ωmax-ωmin； (2)
in the formula, n is the total number of the alternating current distributed power supplies; pNiDistributing the active power of the power supply for the ith alternating current; omegamaxAnd ωminMaximum frequency and minimum frequency allowed by the AC subsystem respectively;
reactive sag coefficient KQiEquation 3 is satisfied, i.e.:
KQ1QN1＝KQ2QN2＝KQ3QN3＝···＝KQnQNn＝Uac.imax-Uac.imin； (3)
in the formula, QNiDistributing the reactive power of the power supply for the ith alternating current; u shapeac.imaxThe maximum voltage of the ith alternating current distributed power supply; u shapeac.iminThe minimum voltage of the ith alternating current distributed power supply;
the droop control model of the direct-current distributed power supply is as follows:
Udi＝Ud0-KdciPGdci； (4)
in the formula of Udi、Ud0And PGdciThe actual direct current voltage amplitude, the no-load direct current voltage amplitude and the output active power are respectively; kdciThe droop coefficient of the direct current distributed power supply is obtained;
droop coefficient K of direct-current distributed power supplydciEquation 5 is satisfied, i.e.:
Kdc1PdN1＝Kdc2PdN2＝···＝KdcnPdNn＝Udc.max-Udc.min； (5)
in the formula, PdNiOutputting active power for the direct-current distributed power supply; u shapedc.maxThe maximum voltage is the maximum voltage of the direct current distributed power supply; u shapedc.minThe minimum voltage is the minimum voltage of the direct current distributed power supply;
the connection converter control model is as follows:
using formula 6 to couple converter frequency ω and dc subsystem voltage UILCdcNormalizing to connect the frequency omega of the converterpuAnd a DC voltage UILC.puWithin the same unit range;
Figure FDA0003228159880000021
in the formula of UILCdc,maxAnd UILCdc,minMaximum voltage and minimum voltage allowed by the direct current subsystem respectively; u shapeILCdcIs the DC subsystem voltage;
after normalization, ωpu＝[-1,1]And U isILC.pu＝[-1,1]；
The power control equation for the connected converter is as follows:
Figure FDA0003228159880000022
in the formula of UILCac0And UILCacRespectively is a no-load alternating voltage amplitude and an actual alternating voltage amplitude; kPILCAnd KQILCActive and reactive control coefficients of the connecting converter are respectively; pILCdcConnecting the active power of a converter direct current subsystem; qILCacThe reactive power is connected with the converter AC subsystem; pILCacFor connecting the active power of the converter AC subsystem;
the load model taking into account the frequency/voltage characteristics is as follows:
Figure FDA0003228159880000031
wherein when the frequency and voltage of the system are respectively fL0iAnd UL0iWhen is, PL0iAnd QL0iRespectively corresponding actual active power sumReactive power; when the frequency and voltage are equal to f and U, respectivelyiWhen is, PLiAnd QLiActual active power and reactive power corresponding to the load respectively; kPfiAnd KQfiStatic frequency characteristic coefficients of the load are respectively; kPViAnd KQViRespectively a load active power index and a reactive power index;
the main steps for establishing the improved self-adaptive droop control model are as follows:
I) obtaining an initial droop coefficient according to a formula 2 and a formula 3, and calculating an initial power flow;
II) the improved adaptive droop control model is shown in equation 9 and equation 10, respectively:
Figure FDA0003228159880000032
Figure FDA0003228159880000033
in the formula, ωNAnd UacNRated frequency and rated voltage of the alternating current distributed power supply are respectively;
Figure FDA0003228159880000034
and
Figure FDA0003228159880000035
actual active power output and reactive power output of the distributed power supply at the moment t-1 before the load is changed are respectively obtained; u'aciThe terminal voltage amplitude of the ith alternating current distributed power supply is improved; omega'iThe actual frequency of the improved ith alternating current distributed power supply;
actual active power output of distributed power supply at t-1 moment before load change
Figure FDA0003228159880000036
Satisfies the following formula:
Figure FDA0003228159880000037
in the formula, PminThe minimum value of the active power output of the distributed power supply at the moment t-1 before the load is changed; pmaxThe maximum value of the active output of the distributed power supply at the moment t-1 before the load is changed;
Figure FDA0003228159880000038
in the formula, QminThe minimum reactive power output of the distributed power supply at the t-1 moment before the load is changed; qmaxThe maximum reactive power output of the distributed power supply at the moment t-1 before the load is changed.
3. The island alternating current and direct current hybrid micro-grid power flow calculation method based on the improved adaptive droop control according to claim 1 or 2, characterized in that the island alternating current and direct current hybrid micro-grid power flow model is established through the following main steps:
1) establishing an island AC/DC series-parallel micro-grid; the alternating current nodes are divided into 4 types: PQ node, PV node, droop node and ILC-AC node; the direct current nodes are divided into 3 types: a constant P node, a droop node and an ILC-DC node;
2) establishing a power flow model of the alternating current subsystem;
the power balance equation for any ith node in the ac subsystem is as follows:
Figure FDA0003228159880000041
in the formula, xacIs the state variable of the AC subsystem; pGiAnd QGiActive output and reactive output of the generator of the ith node are respectively; pLiAnd QLiRespectively the active power and the reactive power of the ith node load; pILCaciAnd QILCaciAre respectively provided withInjecting active and reactive power for connecting the converter ILC; sPQ、SPV、SDr-ac、SILC-acRespectively a set of PQ node, PV node, droop node, ILC-AC node; piAnd QiRespectively injecting active power and reactive power into the nodes;
node injection active power PiAnd node injection reactive power QiRespectively as follows:
Figure FDA0003228159880000042
in the formula, N is the total number of nodes; u shapeiIs the ith node voltage; u shapejIs the jth node voltage; deltaijIs a voltage UiSum voltage UjThe phase angle difference of (a); gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j;
FPmis.ac.i(xac) And FQmis.ac.i(xac) The active unbalanced power and the reactive unbalanced power of the ith node are respectively; state variable x of four node typesac＝[xPQi,xPVi,xDr-aci,xILC-aci]TRespectively as follows:
Figure FDA0003228159880000043
δiis the voltage phase angle of the ith node; u shapeILCdcIs the DC subsystem voltage;
2) establishing a power flow model of a direct current subsystem
The power balance equation of any ith' node in the dc subsystem is as follows:
PGdci'-PLdci'-Pdci'-PILCdc＝0； (16)
in the formula, xdcIs a state variable of the direct current subsystem; pGdci'、PLdci'And PILCdcAre respectively direct currentThe distributed power supply has active output, load active power and active power injected by the connecting converter; pdci'Injecting power into the direct current subsystem node;
direct current subsystem node injection power Pdci'As follows:
Figure FDA0003228159880000051
in the formula, N' is the number of nodes of the direct current subsystem; u shapedcj'The voltage of the jth node of the direct current subsystem; u shapedci'The voltage of the ith node of the direct current subsystem; y isi'j'Is the admittance between the ith' node and the jth node of the direct current subsystem;
state variable x of DC subsystemdc＝[xP-dci',xDr-dci',xILC-dci']TSpecifically, the following are shown:
Figure FDA0003228159880000052
in the formula, SP-dcA constant P node set of the direct current subsystem; sDr-dcA droop node set of the direct current subsystem is provided; sILC-dcThe system is a direct current subsystem ILC-DC node set.
4. The island alternating current-direct current hybrid micro-grid power flow calculation method based on the improved adaptive droop control according to claim 1 or 2, characterized in that the main steps of establishing the trust domain-based LMTR solving algorithm are as follows:
1) elimination of Jacobian matrix J using unit step length based trust domain methodkThe singularity of (a), namely:
Figure FDA0003228159880000053
in the formula, Fk＝F(xk)；Jk＝J(xk)；FkEquation of unbalance representing active and reactive power, F at convergencekTends to 0; dLMKFor the current operating point xkThe direction of iteration of; x is the number ofk+1Is the value of the next iteration point; i is a unit vector;
according to equation 19, when μkWhen approaching 0, dLMKTends to Gauss-Newton step when mu iskWhen approaching infinity, dLMKThe step of descending at the fastest speed;
2) according to the LMTR method based on load flow calculation, the current operation point x is processedkDirection of iteration dLMKUpdating is carried out, namely:
Figure FDA0003228159880000061
in the formula, theta is a constant and is more than or equal to 0 and less than or equal to 1; parameter betakUpdating by using a trusted domain method;
3) defining a merit function psi (x)k)＝0.5||F(xk)||2Then the ratio r of the actual drop to the estimated dropkComprises the following steps:
Figure FDA0003228159880000062
then after k iterations, point x is runk+1As follows:
Figure FDA0003228159880000063
in the formula eta1For iterative successful discrimination coefficient, η1Is greater than 0; wherein x isk+1＝xk+dLMkIndicates the success of the iteration, xk+1＝xkIndicating an iteration failure; r iskIs an operating point xkThe iterative discrimination parameters of (1);
parameter betakThe update is as follows:
Figure FDA0003228159880000064
in the formula eta2For iterative successful discrimination coefficients, 0 < eta1＜η2＜1；γ1And gamma2Is betakCorrection coefficient of gamma1> 1 and 0 < gamma2＜1；βminIs betakMinimum value of (d); if rk＞η2Then the iteration is very successful, at which time βk+1＝max(γ2βk,βmin) (ii) a If eta1＜γk＜η2Then the iteration is successful, at which time betak+1＝βk(ii) a If gamma isk＜η1Then the iteration fails, in which case βk+1＝γ1；γkIs betakThe iterative decision parameter of (1).
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