CN107947192B - Reactive power optimization configuration method for droop control type island microgrid - Google Patents

Reactive power optimization configuration method for droop control type island microgrid Download PDF

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CN107947192B
CN107947192B CN201711354355.0A CN201711354355A CN107947192B CN 107947192 B CN107947192 B CN 107947192B CN 201711354355 A CN201711354355 A CN 201711354355A CN 107947192 B CN107947192 B CN 107947192B
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scene
power
reactive power
compensation
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CN107947192A (en
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潘忠美
陈鲁鹏
王飞
王家梁
何宏伟
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Xian University of Technology
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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
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
    • 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
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • 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
    • 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
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

Abstract

The invention discloses a reactive power optimization configuration method of a droop control type island microgrid, which comprises the steps of sampling a droop control type island microgrid by adopting a Monte Carlo method according to the probability distribution of wind speed or illumination intensity to obtain a sample set of output of Ns wind turbine generators or photovoltaic power generation units, and performing scene reduction on the sampled sample based on a backward reduction technology to obtain Ns scene samples; then, an IMG power flow model of the droop control type DG networking is established and solved, singular value decomposition is carried out on a Jacobian matrix when an IMG power flow equation converges to obtain a minimum singular value and a left singular vector and a right singular vector corresponding to the minimum singular value, then a system reactive compensation node is obtained, a compensation capacity optimization configuration model is established, an IPOPT optimization tool package is called to carry out optimization solution to obtain an optimization configuration scheme, and the problem that optimization planning of a reactive compensation device for an island micro-grid containing a droop control type distributed power supply in the prior art is difficult to implement is solved.

Description

Reactive power optimization configuration method for droop control type island microgrid
Technical Field
The invention belongs to the technical field of optimization planning of power systems, and particularly relates to a reactive power optimization configuration method of a droop control type island micro-grid.
Background
The installation of reactive power compensation devices is advantageous for improving the quality of the distribution voltage and reducing the network loss, so that the problem of optimal planning of reactive power compensation devices has long been the subject of much attention. With the large access of intermittent Distributed Generation (DG) such as wind power Generation, photovoltaic and the like, the installation of the reactive compensation device can reduce the adverse effect of the random fluctuation of the DG output on the voltage on one hand, and can also improve the utilization rate of clean energy by matching and adjusting the reactive compensation device and the DG power factor on the other hand.
The micro-grid is used as a form for flexibly and efficiently utilizing distributed energy, and has two forms of grid connection and isolated island operation. The Islanded Microgrid (IMG) is small in scale, the impact of intermittent power supply output and load fluctuation on the Islanded Microgrid is relatively large, and reactive compensation on the Islanded Microgrid can improve the voltage quality and the voltage stability. The IMG has two structures of master-slave control and peer-to-peer control. A main power supply in a microgrid of a master-slave control structure provides voltage frequency support, the operation mechanism of the microgrid is similar to that of a traditional power grid, in a peer-to-peer control structure, a plurality of controllable distributed power supplies jointly participate in voltage and frequency regulation and control, the DGs usually adopt a droop control method, and the operation mechanism of a system is obviously different from that of the traditional power grid. Therefore, there is a need to study the reactive optimization planning problem of such IMG in combination with the characteristics of droop control.
Regarding the reactive power optimization planning problem, scholars at home and abroad respectively make researches on the optimization planning of parallel capacitors on a distribution line, the reactive power compensation optimization planning of a low-voltage side of a distribution network, the reactive power compensation optimization configuration of a medium-voltage distribution line and the low-voltage side of the distribution network, the reactive power compensation optimization configuration of a rural distribution network, the reactive power optimization of an alternating current and direct current system, the reactive power optimization configuration of the distribution network containing DGs such as photovoltaic or wind generating sets and the like, and establish an optimization planning model; and solving methods such as a nonlinear programming method, an intelligent optimization algorithm, robust optimization and the like are provided. However, no research on reactive power optimization planning of an island micro-grid of a droop control type micro-source networking exists at present.
Disclosure of Invention
The invention aims to provide a reactive power optimization configuration method for a droop control type island microgrid, and solves the problem that optimization planning of a reactive power compensation device for the island microgrid with a droop control type distributed power supply is difficult to implement in the prior art.
The invention adopts the technical scheme that a reactive power optimization configuration method of a droop control type island microgrid is implemented according to the following steps:
step 1, sampling the wind speed or illumination intensity probability distribution by adopting a Monte Carlo method to obtain a sample set of the output of Ns wind turbine generators or photovoltaic power generation units, and performing scene reduction on the sampled samples based on a backward reduction technology to obtain Ns scene samples;
step 2, establishing an IMG power flow model of a droop control type DG networking;
step 3, solving the IMG power flow model by adopting a Newton-Raphson method;
step 4, performing singular value decomposition on the Jacobian matrix during IMG tidal current equation convergence to obtain a minimum singular value and left and right singular vectors corresponding to the minimum singular value, and further obtain a system reactive power compensation node;
step 5, establishing a compensation capacity optimization configuration model;
and 6, calling an IPOPT optimization tool package to carry out optimization solution to obtain an optimized configuration scheme.
The present invention is also characterized in that,
in step 1, an initial scene set of the sample is set as omega, a target scene set after reduction is set as omega, and a scene reduction algorithm is as follows:
step 1.1, calculating scene distance KD of any two scenes in the initial scene set, establishing a scene distance matrix, and marking as KDM;
step 1.2, aiming at any scene xiiFinding the scene xi closest to itjAnd is denoted by min { KD (ξ)i,ξj) And marking the scene in a KDM matrix;
step 1.3, for each pair of scenes in step 1.2, P is calculatedKDi＝min{KD(ξi,ξj)}×P(ξi) Wherein P (ξ)i) For the probability of the evaluated scene, P of all scene pairs in KDM is then foundKDMinimum value of (1), denoted as PKDsTo PKDsCorresponding scene pair, will xiiAnd xijOne of the two is closer to other scenes and has smaller probability, such as subtracting xii；
Step 1.4, cut down xiiThen, a new KDM is constructed, and the scene probability P (xi) is updatedj)＝P(ξi)+P(ξj)；
And 1.5, repeating the steps 1.2-1.4 until the target scene number is reduced.
Step 2, establishing an IMG power flow model of the droop control type DG networking, which is shown as the following formula:
Figure BDA0001510834230000031
wherein, PGi、QGiThe power active power and the reactive power of the power supply are respectively; pLi、QLiRespectively the active power and the reactive power of the load; u shapeiAnd UkThe voltages of node i and node k, respectively; y isikAnd thetaikThe amplitude and the phase angle of the element of the node admittance matrix are respectively; deltaiAnd deltakVoltage phase angles of the node i and the node k respectively; b is a set of all nodes;
active power P of loadLiAnd reactive power QLiThe calculation is shown below:
Figure BDA0001510834230000032
in the formula, PLi0And QLi0Respectively the active power and the reactive power of the initial load of the node i; u shapei0Is the initial value of the voltage at node i; omega is the angular frequency of the system, omega0Is the initial value of angular frequency; a. thepi、BpiAnd CpiRespectively, the static voltage characteristic coefficient of the active power of the load, Aqi、BqiAnd CqiRespectively, the load reactive power static voltage characteristic coefficient, kPfiAnd kQfiStatic frequency characteristic coefficients of load active power and reactive power respectively;
active and reactive power P for the power supplyGi、QGiIn other words, it is calculated by the following equation:
Figure BDA0001510834230000041
in the formula, PDroopiAnd QDroopiActive power and reactive power P of droop control type micro-source accessed by node iWTGiAnd QWTGiActive power and reactive power P of the wind generating set respectively connected to the node iPViAnd QPViRespectively the active power and the reactive power of the photovoltaic unit accessed by the node i;
if wind turbine generator or photovoltaic unit is connected, PWTGiOr PPViSubstituting according to the actual active power, otherwise, taking the value as zero;
if constant power factor control, then QWTGiOr QPViSubstituting according to actual reactive power;
if the control is constant voltage control, i is a PV node, the reactive power of the PV node is an unknown quantity, and a corresponding balance equation is not temporarily listed in a power flow equation set;
if there is no droop control type micro source access, PDroopiAnd QDroopiValues are all zero; for nodes with Droop-controlled micro-sources, commonly referred to as Droop nodes, then PDroopiAnd QDroopiCalculated as follows:
Figure BDA0001510834230000042
wherein m ispi、nqiDroop coefficients of active power and reactive power of the droop control micro source of the node i are respectively; omega0Is an initial value of angular frequency, U0Is the initial value of the voltage; b isDroopIs a collection of drop nodes.
The step 3 is as follows:
solving the IMG power flow model by adopting a Newton-Raphson method, wherein the modified equation form is as follows:
Figure BDA0001510834230000053
wherein, the delta P and the delta Q are the unbalance amount of the active power and the reactive power of the node respectively; delta theta and delta U are respectively voltage phase angle and amplitude correction; Δ ω is a correction amount of the frequency; j is a Jacobian matrix.
The step 4 is as follows:
the Jacobian matrix J when the IMG tide equation converges is subjected to singular value decomposition as shown in the following formula to obtain a minimum singular value delta2n-mAnd its corresponding left and right singular vectors M2n-mAnd N2n-m：
Figure BDA0001510834230000051
Wherein M isiAnd NiRespectively are left and right singular vectors of a system singular value; sigma is a diagonal matrix taking positive real singular values arranged from large to small as diagonal elements; m is the number of PV nodes, and n is the total number of nodes of the microgrid;
the maximum element of the right singular vector of the minimum singular value indicates the most sensitive node voltage, so that a few large index values in the right singular vector are selected as the reactive compensation nodes of the system:
Figure BDA0001510834230000052
wherein, Δ θ and Δ U are correction values of voltage phase angle and amplitude respectively; Δ ω is the correction amount of the frequency.
The step 5 is as follows:
for the reduced scene set, with the expectation of economic targets in all scenes as an objective function and the trend equation and the safety inequality in each scene as constraints, establishing a compensation capacity optimization configuration model, which is specifically as follows:
step 5.1, setting a target function:
the method is characterized in that a capacitor is used as reactive compensation equipment of the micro-grid, the randomness of the output of a wind turbine generator in the micro-grid is considered, the economic benefit brought by the capacitor is maximized into a target function of reactive planning, the economic benefit brought by the compensation capacitor installed on the micro-grid is evaluated by adopting a net present value criterion, and the target function is expressed as
Figure BDA0001510834230000061
In the formula, d is the discount rate; l is the engineering period; cIInvestment cost for adding compensation capacitors; cOAnd C'ORespectively representing the annual average cost of active loss of the micro-grid before and after the compensation capacitor is added, wherein,
Figure BDA0001510834230000062
Figure BDA0001510834230000063
in the formula, σEIs the price of electricity;
Figure BDA0001510834230000064
and
Figure BDA0001510834230000065
respectively obtaining the expected values of the network loss of the s th scene of the microgrid before and after reactive power optimization; rhosProbability of the s-th scene of the microgrid;
the investment cost of the compensation capacitor is
Figure BDA0001510834230000066
In the formula, nCCompensating the point number for the capacitor; qCjMounting capacity for the capacitor at the jth compensation point; p is a radical ofCjA unit price of a capacitor installed for the jth compensation point;
and 5.2, setting constraint conditions:
step 5.2.1, power flow equation constraint:
according to the formulas (1) to (4), the power flow equation constraint of the IMG having the droop control type DG networking is expressed as follows, corresponding to any scene s, s is 1,2 … ns:
Figure BDA0001510834230000067
Figure BDA0001510834230000071
in the formula (I), the compound is shown in the specification,
Figure BDA0001510834230000072
and
Figure BDA0001510834230000073
voltage amplitudes and phase angle differences of the node i and the node j in the s-th scene are respectively; omegasThe angular frequency of the system under the s-th scene;
Figure BDA0001510834230000074
and
Figure BDA0001510834230000075
the active power and the load active power of the wind turbine generator and the photovoltaic connected with the node i in the s-th scene are respectively;
Figure BDA0001510834230000076
and
Figure BDA0001510834230000077
the reactive power of the wind turbine generator and the photovoltaic of the node i in the s-th scene, the reactive power of the reactive compensation capacitor bank and the load reactive power are respectively;
step 5.2.2, setting droop control type micro-source capacity inequality constraint:
the power of the DG for droop control of access node i needs to meet the capacity limit inequality constraint:
Figure BDA0001510834230000078
wherein the content of the first and second substances,
Figure BDA0001510834230000079
and
Figure BDA00015108342300000710
controlling the active power and the reactive power of a DG (distributed generation) for the droop connected with the node i in the s-th scene respectively;
Figure BDA00015108342300000711
and
Figure BDA00015108342300000712
the upper and lower limit values of the capacity of the droop control type DG are respectively;
for a reactive compensation capacitor bank:
0≤QCi≤QCimax (14)
wherein Q isCiFor capacitor mounting capacity at i-th compensation point, QCimaxMaximum allowable mounting capacity for the access capacitor at the ith compensation point;
and 5.2.3, setting system safe operation inequality constraints:
in order to ensure the normal operation of the system, the safety limit constraint of the node voltage and the safety constraint of the branch power need to be met, in addition, the system frequency is also one of the variables, and the safety constraint of the system also needs to be considered in the optimization process:
Figure BDA00015108342300000713
in the formula (I), the compound is shown in the specification,
Figure BDA00015108342300000714
and
Figure BDA00015108342300000715
respectively an upper voltage amplitude limit and a lower voltage amplitude limit of the node i;
Figure BDA00015108342300000716
an upper limit value of the amplitude of the current allowed to flow for the branch ij; omegamaxAnd ωminAre respectively provided withThe upper and lower limits of the angular frequency of the system;
Figure BDA00015108342300000717
the current amplitude of branch ij under the s-th scenario is shown.
The optimization solving method in the step 6 can be replaced by an interior point method, a genetic algorithm and a particle swarm optimization algorithm.
The reactive power optimization configuration method has the advantages that the reactive power optimization configuration method for the droop control type island micro-grid is suitable for optimizing and planning the reactive power compensation device for the island micro-grid of the droop control type distributed power supply networking; the mounting position of the reactive power compensation device is determined through a singular value decomposition method, so that the solution efficiency of the optimization problem is improved on one hand, and the stability of the static voltage of the system is improved on the other hand.
Drawings
Fig. 1 is a flow chart of a reactive power optimization configuration method of a droop control type island micro-grid according to the invention;
fig. 2 is a node average voltage curve before and after compensation in schemes 1-3 in the reactive power optimization configuration method for a droop control type island microgrid of the present invention;
fig. 3 is a right singular vector element diagram of corresponding node voltages in different scenes in the reactive power optimization configuration method of the droop control island microgrid of the present invention;
fig. 4 is a node voltage diagram before and after compensation in the reactive power optimization configuration method of the droop control island microgrid of the invention;
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a reactive power optimization configuration method of a droop control type island microgrid, which is implemented according to the following steps as shown in a flow chart shown in figure 1:
step 1, sampling the samples by adopting a Monte Carlo method according to the probability distribution of wind speed or illumination intensity to obtain a sample set of output of Ns wind turbine generators or photovoltaic power generation units, carrying out scene reduction on the sampled samples based on a backward reduction technology to obtain Ns scene samples, setting an initial scene set of the samples as omega, and setting a target scene set after reduction as omega, wherein a scene reduction algorithm is as follows:
step 1.1, calculating scene distance KD of any two scenes in the initial scene set, establishing a scene distance matrix, and marking as KDM;
step 1.2, aiming at any scene xiiFinding the scene xi closest to itjAnd is denoted by min { KD (ξ)i,ξj) And marking the scene in a KDM matrix;
step 1.3, for each pair of scenes in step 1.2, P is calculatedKDi＝min{KD(ξi,ξj)}×P(ξi) Wherein P (ξ)i) For the probability of the evaluated scene, P of all scene pairs in KDM is then foundKDMinimum value of (1), denoted as PKDsTo PKDsCorresponding scene pair, will xiiAnd xijOne of the two is closer to other scenes and has smaller probability, such as subtracting xii；
Step 1.4, cut down xiiThen, a new KDM is constructed, and the scene probability P (xi) is updatedj)＝P(ξi)+P(ξj)；
Step 1.5, repeating the step 1.2 to the step 1.4 until the target scene number is reduced;
step 2, establishing an IMG power flow model of the droop control type DG networking, which is shown as the following formula:
Figure BDA0001510834230000091
wherein, PGi、QGiThe power active power and the reactive power of the power supply are respectively; pLi、QLiRespectively the active power and the reactive power of the load; u shapeiAnd UkThe voltages of node i and node k, respectively; y isikAnd thetaikThe amplitude and the phase angle of the element of the node admittance matrix are respectively; deltaiAnd deltakVoltage phase angles of the node i and the node k respectively; b is a set of all nodes;
active power P of loadLiAnd reactive power QLiThe calculation is shown below:
Figure BDA0001510834230000092
in the formula, PLi0And QLi0Respectively the active power and the reactive power of the initial load of the node i; u shapei0Is the initial value of the voltage at node i; omega is the angular frequency of the system, omega0Is the initial value of angular frequency; a. thepi、BpiAnd CpiRespectively, the static voltage characteristic coefficient of the active power of the load, Aqi、BqiAnd CqiRespectively, the load reactive power static voltage characteristic coefficient, kPfiAnd kQfiStatic frequency characteristic coefficients of load active power and reactive power respectively;
active and reactive power P for the power supplyGi、QGiIn other words, it is calculated by the following equation:
Figure BDA0001510834230000101
in the formula, PDroopiAnd QDroopiActive power and reactive power P of droop control type micro-source accessed by node iWTGiAnd QWTGiActive power and reactive power P of the wind generating set respectively connected to the node iPViAnd QPViRespectively the active power and the reactive power of the photovoltaic unit accessed by the node i;
if wind turbine generator or photovoltaic unit is connected, PWTGiOr PPViSubstituting according to the actual active power, otherwise, taking the value as zero;
if constant power factor control, then QWTGiOr QPViSubstituting according to actual reactive power;
if the control is constant voltage control, i is a PV node, the reactive power of the PV node is an unknown quantity, and a corresponding balance equation is not temporarily listed in a power flow equation set;
if there is no droop control type micro source access, PDroopiAnd QDroopiValues are all zero; for nodes with Droop-controlled micro-sources, commonly referred to as Droop nodes, then PDroopiAnd QDroopiCalculated as follows:
Figure BDA0001510834230000102
wherein m ispi、nqiDroop coefficients of active power and reactive power of the droop control micro source of the node i are respectively; omega0Is an initial value of angular frequency, U0Is the initial value of the voltage; b isDroopA set of Droop nodes;
step 3, solving the IMG power flow model by adopting a Newton-Raphson method, which comprises the following steps:
solving the IMG power flow model by adopting a Newton-Raphson method, wherein the modified equation form is as follows:
Figure BDA0001510834230000111
wherein, the delta P and the delta Q are the unbalance amount of the active power and the reactive power of the node respectively; delta theta and delta U are respectively voltage phase angle and amplitude correction; Δ ω is a correction amount of the frequency; j is a Jacobian matrix;
step 4, singular value decomposition is carried out on the Jacobian matrix during IMG tidal current equation convergence to obtain a minimum singular value and left and right singular vectors corresponding to the minimum singular value, and then a system reactive compensation node is obtained, wherein the method specifically comprises the following steps:
the Jacobian matrix J when the IMG tide equation converges is subjected to singular value decomposition as shown in the following formula to obtain a minimum singular value delta2n-mAnd its corresponding left and right singular vectors M2n-mAnd N2n-m：
Figure BDA0001510834230000112
Wherein M isiAnd NiRespectively are left and right singular vectors of a system singular value; Σ is so as to press from large toThe small-arranged positive real singular values are diagonal matrixes of diagonal elements; m is the number of PV nodes, and n is the total number of nodes of the microgrid;
the maximum element of the right singular vector of the minimum singular value indicates the most sensitive node voltage, so that a few large index values in the right singular vector are selected as the reactive compensation nodes of the system:
Figure BDA0001510834230000113
wherein, Δ θ and Δ U are correction values of voltage phase angle and amplitude respectively; Δ ω is a correction amount of the frequency;
step 5, establishing a compensation capacity optimization configuration model, which specifically comprises the following steps:
for the reduced scene set, with the expectation of economic targets in all scenes as an objective function and the trend equation and the safety inequality in each scene as constraints, establishing a compensation capacity optimization configuration model, which is specifically as follows:
step 5.1, setting a target function:
the method is characterized in that a capacitor is used as reactive compensation equipment of the micro-grid, the randomness of the output of a wind turbine generator in the micro-grid is considered, the economic benefit brought by the capacitor is maximized into a target function of reactive planning, the economic benefit brought by the compensation capacitor installed on the micro-grid is evaluated by adopting a net present value criterion, and the target function is expressed as
Figure BDA0001510834230000121
In the formula, d is the discount rate; l is the engineering period; cIInvestment cost for adding compensation capacitors; cOAnd C'ORespectively representing the annual average cost of active loss of the micro-grid before and after the compensation capacitor is added, wherein,
Figure BDA0001510834230000122
Figure BDA0001510834230000123
in the formula, σEIs the price of electricity;
Figure BDA0001510834230000124
and
Figure BDA0001510834230000125
respectively obtaining the expected values of the network loss of the s th scene of the microgrid before and after reactive power optimization; rhosProbability of the s-th scene of the microgrid;
the investment cost of the compensation capacitor is
Figure BDA0001510834230000126
In the formula, nCCompensating the point number for the capacitor; qCjMounting capacity for the capacitor at the jth compensation point; p is a radical ofCjA unit price of a capacitor installed for the jth compensation point;
and 5.2, setting constraint conditions:
step 5.2.1, power flow equation constraint:
according to the formulas (1) to (4), the power flow equation constraint of the IMG having the droop control type DG networking is expressed as follows, corresponding to any scene s, s is 1,2 … ns:
Figure BDA0001510834230000131
in the formula (I), the compound is shown in the specification,
Figure BDA0001510834230000132
and
Figure BDA0001510834230000133
voltage amplitudes and phase angle differences of the node i and the node j in the s-th scene are respectively; omegasThe angular frequency of the system under the s-th scene;
Figure BDA0001510834230000134
and
Figure BDA0001510834230000135
the active power and the load active power of the wind turbine generator and the photovoltaic connected with the node i in the s-th scene are respectively;
Figure BDA0001510834230000136
and
Figure BDA0001510834230000137
the reactive power of the wind turbine generator and the photovoltaic of the node i in the s-th scene, the reactive power of the reactive compensation capacitor bank and the load reactive power are respectively;
step 5.2.2, setting droop control type micro-source capacity inequality constraint:
the power of the DG for droop control of access node i needs to meet the capacity limit inequality constraint:
Figure BDA0001510834230000138
wherein the content of the first and second substances,
Figure BDA0001510834230000139
and
Figure BDA00015108342300001310
controlling the active power and the reactive power of a DG (distributed generation) for the droop connected with the node i in the s-th scene respectively;
Figure BDA00015108342300001311
and
Figure BDA00015108342300001312
the upper and lower limit values of the capacity of the droop control type DG are respectively;
for a reactive compensation capacitor bank:
0≤QCi≤QCimax (14)
wherein Q isCiFor electricity at the i-th compensation pointContainer mounting capacity, QCimaxMaximum allowable mounting capacity for the access capacitor at the ith compensation point;
and 5.2.3, setting system safe operation inequality constraints:
in order to ensure the normal operation of the system, the safety limit constraint of the node voltage and the safety constraint of the branch power need to be met, in addition, the system frequency is also one of the variables, and the safety constraint of the system also needs to be considered in the optimization process:
Figure BDA00015108342300001313
in the formula (I), the compound is shown in the specification,
Figure BDA0001510834230000141
and
Figure BDA0001510834230000142
respectively an upper voltage amplitude limit and a lower voltage amplitude limit of the node i;
Figure BDA0001510834230000143
an upper limit value of the amplitude of the current allowed to flow for the branch ij; omegamaxAnd ωminRespectively the upper and lower limits of the angular frequency of the system;
Figure BDA0001510834230000144
the current amplitude of the branch ij under the s-th scene;
and 6, calling an IPOPT optimization tool kit to carry out optimization solution to obtain an optimization configuration scheme, wherein the optimization solution method can be replaced by an interior point method, a genetic algorithm and a particle swarm optimization algorithm.
Examples
Referring to fig. 2, the micro-source is configured by an IEEE33 node system and operates in an island.
Step 1, setting A in a load modelpi＝Aqi＝0.3，Bpi＝Bqi＝0.3，Cpi＝Cqi0.4; coefficient of static frequency characteristic of load, kLpi＝2、kLqiForming a micro-source access system with three droop controls as-2The network is disconnected from the main network and operates as an island, a load of 0.06+ j0.03, the access position of each micro source and a per unit value (rated capacity S) are connected to the node 1B1MVA) as shown in table 1:
TABLE 1 controllable micro-Source Access locations and parameters
DG# Node point Rated capacity U0 ω0 mpi nqi
1 4 3.0 1.05 1.004 0.0033 0.0667
2 22 1.5 1.05 1.004 0.0067 0.1333
3 25 1.0 1.05 1.004 0.0100 0.2000
Step 2, connecting the same wind generating set to the node 3 and the node 16 respectively, wherein the parameters are as follows: the cut-in wind speed, the rated wind speed and the cut-out wind speed are respectively 3m/s, 14m/s and 25m/s, the maximum output power is 0.8MW, and the power factor is 0.95. Calculating by adopting wind speed data acquired by accessing a certain dispersion in northwest China to a wind power plant, and firstly obtaining Weibull distribution parameters of input wind speeds of two distributed wind generating sets by utilizing maximum likelihood estimation, wherein k is [ 6.7578; 6.6702]Scale parameter c ═ 1.7828; 1.8100]. Wind speed is randomly sampled 3000 times, 10 typical scenes are obtained by scene reduction respectively, and the output P of the wind turbine generator under each sceneWTG3、PWTG16And probability ρsAs shown in table 2:
TABLE 2 typical scenes after cut
Scene s PWTG3 PWTG16 ρs
1 0.0000 0.0000 0.297
2 0.0657 0.0117 0.065
3 0.1229 0.0780 0.074
4 0.1889 0.1444 0.150
5 0.2469 0.2295 0.055
6 0.2933 0.2658 0.080
7 0.3810 0.3708 0.105
8 0.4546 0.4628 0.076
9 0.6352 0.7046 0.054
10 0.7427 0.8000 0.044
Step 3, establishing an IMG power flow model according to the formulas (1) to (4), and solving by adopting a Newton-Raphson method to obtain a Jacobian matrix J during power flow convergence;
step 4, performing singular value decomposition on the Jacobian matrix J according to a formula (6), and respectively calculating right singular vectors N under 10 scenes2n-mFor convenience of display, fig. 3 shows curves of elements corresponding to voltages of nodes in odd-numbered scenes (respectively denoted as S1, S3, S5, S7, and S9), and it can be seen that relative size laws of elements corresponding to right singular vectors of voltages of nodes in the scenes are substantially consistent;
and determining a compensation point according to the right singular vector, and selecting a node set {12, 17, 30 and 32} with larger right singular vector elements as the compensation point in consideration of the fact that the number of parallel capacitors installed on the same line is not too large. For comparison, the effectiveness of selecting compensation points according to the size of the right singular vector is illustrated, secondary sets {9, 14, 26 and 29} and smaller nodes {1, 18, 21 and 24} are simultaneously selected as compensation points to be selected, and are respectively marked as a scheme 1, a scheme 2 and a scheme 3, and optimization planning is respectively carried out;
step 5, establishing a planning model according to the formulas (8) to (15), solving by adopting an IPOPT tool kit, obtaining compensation planning results of each scheme as shown in table 3, analyzing economic benefits as shown in table 4, and giving node average voltage curves before and after compensation of the schemes 1 to 3 in fig. 2:
TABLE 3 Compensation results under the respective scenarios
Figure BDA0001510834230000151
Figure BDA0001510834230000161
TABLE 4 analysis of economic benefits of different reactive compensation schemes
Figure BDA0001510834230000162
Step 6, analyzing the effectiveness of algorithm efficiency: as can be seen from tables 3, 4 and 4, the total number of groups of the compensation capacitors in the scheme 1 is 25, the scheme 2 is 28, the scheme 3 is 15, and the scheme 3 has low installation cost, but the loss reduction effect of the scheme 3 is obviously poor as can be seen from table 4, the improvement effect on the voltage level is also obviously poor as can be seen from fig. 4, the voltage level of the IMG is obviously low when no compensation is performed, and the compensation of the scheme 3 still has partial node voltage lower than 0.93, so that the compensation effect of the scheme 3 is not ideal; for the case of the scheme 1 and the scheme 2, the scheme 1 is better than the scheme 2, the loss reduction effect scheme 1 is slightly better than the scheme 2, so the total economic benefit is better than the scheme 1, and as can be seen from fig. 4, the voltage after compensation of the two schemes is more than 0.93, and the two schemes have satisfactory improvement effect on the voltage level. Therefore, the search space in the reactive power optimization planning can be reduced by determining the compensation points according to the sizes of the elements corresponding to the right singular vectors, and the calculation efficiency of the optimization planning is improved.

Claims (1)

1. A reactive power optimization configuration method for a droop control type island microgrid is characterized by being implemented according to the following steps:
step 1, sampling the wind speed or illumination intensity probability distribution by adopting a Monte Carlo method to obtain a sample set of the output of Ns wind turbine generators or photovoltaic power generation units, and performing scene reduction on the sampled samples based on a backward reduction technology to obtain Ns scene samples;
step 2, establishing an IMG power flow model of a droop control type DG networking, wherein the IMG is an island micro-grid;
step 3, solving the IMG power flow model by adopting a Newton-Raphson method;
step 4, performing singular value decomposition on the Jacobian matrix during IMG tidal current equation convergence to obtain a minimum singular value and left and right singular vectors corresponding to the minimum singular value, and further obtain a system reactive power compensation node;
step 5, establishing a compensation capacity optimization configuration model;
step 6, calling an IPOPT optimization toolkit to carry out optimization solution to obtain an optimization configuration scheme;
in the step 1, the initial scene set of the sample is set to be ω, the reduced target scene set is set to be ω, and the scene reduction algorithm is as follows:
step 1.1, calculating scene distance KD of any two scenes in the initial scene set, establishing a scene distance matrix, and marking as KDM;
step 1.2, aiming at any scene xiiFinding the scene xi closest to itjAnd is denoted by min { KD (ξ)i,ξj) And marking the scene in a KDM matrix;
step 1.3, for each pair of scenes in step 1.2, P is calculatedKDi＝min{KD(ξi,ξj)}×P(ξi) Wherein P (ξ)i) For the probability of the evaluated scene, P of all scene pairs in KDM is then foundKDMinimum value of (1), denoted as PKDsTo PKDsCorresponding scene pair, will xiiAnd xijOne of the two is closer to other scenes and has smaller probability, such as subtracting xii；
Step 1.4, cut down xiiThen, a new KDM is constructed, and scene probability is updated
P(ξj)＝P(ξi)+P(ξj)；
Step 1.5, repeating the step 1.2 to the step 1.4 until the target scene number is reduced;
step 2, establishing an IMG power flow model of the droop control type DG networking, as shown in the following formula:
Figure FDA0003233711380000021
wherein, PGi、QGiRespectively the active power and the reactive power of the power supply; pLi、QLiRespectively the active power and the reactive power of the load; u shapeiAnd UkThe voltages of node i and node k, respectively; y isikAnd thetaikThe amplitude and the phase angle of the element of the node admittance matrix are respectively; deltaiAnd deltakVoltage phase angles of the node i and the node k respectively; b is a set of all nodes;
active power P of loadLiAnd reactive power QLiThe calculation is shown below:
Figure FDA0003233711380000022
in the formula, PLi0And QLi0Respectively the active power and the reactive power of the initial load of the node i; u shapei0Is the initial value of the voltage at node i; omega is the angular frequency of the system, omega0Is the initial value of angular frequency; a. thepi、BpiAnd CpiRespectively, the static voltage characteristic coefficient of the active power of the load, Aqi、BqiAnd CqiRespectively, the load reactive power static voltage characteristic coefficient, kPfiAnd kQfiStatic frequency characteristic coefficients of load active power and reactive power respectively;
active and reactive power P for the power supplyGi、QGiIn other words, it is calculated by the following equation:
Figure FDA0003233711380000023
in the formula, PDroopiAnd QDroopiActive power and reactive power P of droop control type micro-source accessed by node iWTGiAnd QWTGiActive power and reactive power P of the wind generating set respectively connected to the node iPViAnd QPViRespectively the active power and the reactive power of the photovoltaic unit accessed by the node i;
if wind turbine generator or photovoltaic unit is connected, PWTGiOr PPViSubstituting according to the actual active power, otherwise, taking the value as zero;
if constant power factor control, then QWTGiOr QPViSubstituting according to actual reactive power;
if the control is constant voltage control, i is a PV node, the reactive power of the PV node is an unknown quantity, and a corresponding balance equation is not temporarily listed in a power flow equation set;
if there is no droop control type micro source access, PDroopiAnd QDroopiValues are all zero; for the node connected with the Droop control type micro source, called Droop node, P isDroopiAnd QDroopiCalculated as follows:
Figure FDA0003233711380000031
wherein m ispi、nqiDroop coefficients of active power and reactive power of the droop control micro source of the node i are respectively; omega0Is an initial value of angular frequency, U0Is the initial value of the voltage; b isDroopA set of Droop nodes;
the step 3 is specifically as follows:
solving the IMG power flow model by adopting a Newton-Raphson method, wherein the modified equation form is as follows:
Figure FDA0003233711380000032
wherein, the delta P and the delta Q are the unbalance amount of the active power and the reactive power of the node respectively; delta theta and delta U are respectively voltage phase angle and amplitude correction; Δ ω is a correction amount of the frequency; j is a Jacobian matrix;
the step 4 is specifically as follows:
the Jacobian matrix J when the IMG tide equation converges is subjected to singular value decomposition as shown in the following formula to obtain a minimum singular value delta2n-mAnd its corresponding left and right singular vectors M2n-mAnd N2n-m：
Figure FDA0003233711380000041
Wherein M isiAnd NiRespectively are left and right singular vectors of a system singular value; sigma is a diagonal matrix taking positive real singular values arranged from large to small as diagonal elements; m is the number of PV nodes, and n is the total number of nodes of the microgrid;
the maximum element of the right singular vector of the minimum singular value indicates the most sensitive node voltage, so that a few large index values in the right singular vector are selected as the reactive compensation nodes of the system:
Figure FDA0003233711380000042
wherein, Δ θ and Δ U are correction values of voltage phase angle and amplitude respectively; Δ ω is a correction amount of the frequency;
the step 5 is specifically as follows:
for the reduced scene set, with the expectation of economic targets in all scenes as an objective function and the trend equation and the safety inequality in each scene as constraints, establishing a compensation capacity optimization configuration model, which is specifically as follows:
step 5.1, setting a target function:
the method is characterized in that a capacitor is used as reactive compensation equipment of the micro-grid, the randomness of the output of a wind turbine generator in the micro-grid is considered, the economic benefit brought by the capacitor is maximized into a target function of reactive planning, the economic benefit brought by the compensation capacitor installed on the micro-grid is evaluated by adopting a net present value criterion, and the target function is expressed as
Figure FDA0003233711380000043
In the formula, d is the discount rate; l is the engineering period; cIInvestment cost for adding compensation capacitors; cOAnd C'ORespectively representing the annual average cost of active loss of the micro-grid before and after the compensation capacitor is added, wherein,
Figure FDA0003233711380000051
Figure FDA0003233711380000052
in the formula, σEIs the price of electricity;
Figure FDA0003233711380000053
and
Figure FDA0003233711380000054
respectively obtaining the expected values of the network loss of the s th scene of the microgrid before and after reactive power optimization; rhosProbability of the s-th scene of the microgrid;
the investment cost of the compensation capacitor is
Figure FDA0003233711380000055
In the formula, nCCompensating the point number for the capacitor; qCjMounting capacity for the capacitor at the jth compensation point; p is a radical ofCjA unit price of a capacitor installed for the jth compensation point;
and 5.2, setting constraint conditions:
step 5.2.1, power flow equation constraint:
according to the formulas (1) to (4), the power flow equation constraint of the IMG having the droop control type DG networking is expressed as follows, corresponding to any scene s, s is 1,2 … ns:
Figure FDA0003233711380000056
in the formula (I), the compound is shown in the specification,
Figure FDA0003233711380000057
and
Figure FDA0003233711380000058
voltage amplitudes and phase angle differences of the node i and the node j in the s-th scene are respectively; omegasThe angular frequency of the system under the s-th scene;
Figure FDA0003233711380000059
and
Figure FDA00032337113800000510
the active power and the load active power of the wind turbine generator and the photovoltaic connected with the node i in the s-th scene are respectively;
Figure FDA00032337113800000511
and
Figure FDA00032337113800000512
the reactive power of the wind turbine generator and the photovoltaic of the node i in the s-th scene, the reactive power of the reactive compensation capacitor bank and the load reactive power are respectively;
step 5.2.2, setting droop control type micro-source capacity inequality constraint:
the power of the DG for droop control of access node i needs to meet the capacity limit inequality constraint:
Figure FDA0003233711380000061
wherein the content of the first and second substances,
Figure FDA0003233711380000062
and
Figure FDA0003233711380000063
controlling the active power and the reactive power of a DG (distributed generation) for the droop connected with the node i in the s-th scene respectively;
Figure FDA0003233711380000064
and
Figure FDA0003233711380000065
the upper and lower limit values of the capacity of the droop control type DG are respectively;
for a reactive compensation capacitor bank:
0≤QCi≤QCimax (14)
wherein Q isCiFor capacitor mounting capacity at i-th compensation point, QCimaxMaximum allowable mounting capacity for the access capacitor at the ith compensation point;
and 5.2.3, setting system safe operation inequality constraints:
in order to ensure the normal operation of the system, the safety limit constraint of the node voltage and the safety constraint of the branch power need to be met, in addition, the system frequency is also one of the variables, and the safety constraint of the system also needs to be considered in the optimization process:
Figure FDA0003233711380000066
in the formula (I), the compound is shown in the specification,
Figure FDA0003233711380000067
and
Figure FDA0003233711380000068
respectively an upper voltage amplitude limit and a lower voltage amplitude limit of the node i;
Figure FDA0003233711380000069
an upper limit value of the amplitude of the current allowed to flow for the branch ij; omegamaxAnd ωminRespectively the upper and lower limits of the angular frequency of the system;
Figure FDA00032337113800000610
the current amplitude of branch ij under the s-th scenario is shown.
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