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CN108462200B - Power distribution network reactive voltage robust control method considering photovoltaic and load uncertainty - Google Patents

Power distribution network reactive voltage robust control method considering photovoltaic and load uncertainty Download PDF

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CN108462200B
CN108462200B CN201810087877.7A CN201810087877A CN108462200B CN 108462200 B CN108462200 B CN 108462200B CN 201810087877 A CN201810087877 A CN 201810087877A CN 108462200 B CN108462200 B CN 108462200B
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voltage
photovoltaic
control
vector
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CN108462200A (en
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袁晓冬
柳丹
葛浦东
窦晓波
顾伟
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Southeast University
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
State Grid Corp of China SGCC
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Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
State Grid Corp of China SGCC
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    • H02J3/383—
    • 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
    • H02J3/12—Circuit arrangements for AC mains or AC distribution networks for adjusting voltage in AC networks by changing a characteristic of the network load
    • 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
    • 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]
    • 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

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Abstract

本发明公开了一种计及光伏和负荷不确定性的配电网无功电压鲁棒控制方法，属于配电网运行控制领域，该方法能够应用于高比例分布式电源接入配电网的运行控制，保证在负荷和分布式电源出力不确定的情况下配电网电压的安全稳定运行，提高配电网运行的可靠性。本发明通过考虑配电网层次控制过程中可能存在的通信延迟，将不确定性时滞转化为确定性时滞，简化了控制模型和控制器设计。利用多胞体模型将分布式光伏和负荷出力的不确定性考虑在系统模型中，方便采用LMI的优化方法求解控制参数。采用

Figure 48123DEST_PATH_IMAGE001
鲁棒控制原理设计电压控制参数，达到对配电网中的多个分布式电源的功率控制，解决电压越限问题。

Figure 201810087877

The invention discloses a robust control method for reactive power and voltage of a distribution network that takes into account photovoltaic and load uncertainty, belonging to the field of distribution network operation control. Operation control ensures the safe and stable operation of distribution network voltage under the condition of uncertain load and distributed power output, and improves the reliability of distribution network operation. The invention converts the uncertain time delay into a deterministic time delay by considering the communication delay that may exist in the control process of the distribution network level, and simplifies the control model and the controller design. The uncertainty of distributed photovoltaic and load output is considered in the system model by using the multicellular model, which is convenient to use the LMI optimization method to solve the control parameters. use

Figure 48123DEST_PATH_IMAGE001
The robust control principle designs voltage control parameters to achieve power control of multiple distributed power sources in the distribution network and solve the problem of voltage overrun.

Figure 201810087877

Description

Power distribution network reactive voltage robust control method considering photovoltaic and load uncertainty
Technical Field
The invention relates to the technical field of operation control of a power distribution network, in particular to a power distribution network reactive voltage Lubang control method considering photovoltaic and load uncertainty.
Background
For the power distribution network with high photovoltaic ratio access, the reactive power regulation capacity brought by the high photovoltaic ratio access can provide voltage support for the power distribution network, and the problem that the voltage of the power distribution network is out of limit is solved. However, due to the fluctuation and uncertainty of the photovoltaic output and the load, if the actual active photovoltaic output operating in the Maximum Power Point Tracking (MPPT) mode is large and the actual load power is small, the system voltage may be unsafe, especially the local overvoltage at the photovoltaic node.
Disclosure of Invention
The invention aims to provide a power distribution network reactive voltage robust control method considering photovoltaic and load uncertainty, which can reduce the influence of uncertain power fluctuation and communication delay of a power distribution network on voltage control, improve the quality of voltage waveform and ensure the safety and stability of the voltage of the power distribution network under the condition of distributed photovoltaic high-proportion access.
The technical scheme adopted by the invention is as follows: a power distribution network reactive voltage robust control method considering photovoltaic and load uncertainty comprises the following steps:
s1, converting the uncertain time lag caused by the communication delay into the confirmed time lag, and establishing a discrete control system model of the controlled node of the power distribution network;
s2, based on the discrete control system model established in S1, the load and the photovoltaic accessed by the node are used as uncertain quantities, and a multi-cell model describing the dynamic characteristics of the voltage control system of the power distribution network is established, so that various values of the uncertain quantities are constrained in the multi-cell model and correspond to each vertex of the multi-cell;
s3, using H∞Robust control principle for converting gain of node voltage disturbance to output into H∞Solving the problem of norm boundary by using a linear matrix inequality optimization method to solve the problem with the gain minimization as the target to obtain a discrete system H which enables all vertexes in the multicellular model to meet the linear matrix inequality∞Control parameters of the robust voltage controller;
s4, collecting voltage vectors of controlled nodes of the power distribution network, and calculating to obtain node voltage deviation as H∞An input quantity of the robust voltage controller; discrete system H determined by using control parameters obtained in S3∞And the robust voltage controller obtains the reactive power regulating quantity corresponding to each photovoltaic access point in the controlled node, and performs reactive voltage control on the distributed photovoltaic accessed by the node according to the reactive power regulating quantity.
Further, discrete system H∞The robust voltage controller comprises a state feedback controller u which minimizes the gain of the disturbance on the outputk＝Kxk(ii) a In S3, the discrete system H obtained by the solution∞The control parameter of the robust voltage controller is a control parameter matrix K of the state feedback controller.
Preferably, in S1, the uncertain time lag is converted into a determined time lag which is the control period T of the robust voltage controller, i.e. the control quantity u at the time k-1k-1As a disturbance to the k-th time, namely a discrete control system model:
xk+1＝Axk+Buuk+Buuk-1+Bwwk
zk＝Cxk (1)
to convert to:
Figure GDA0002952256560000021
zk＝Cxk (2)
wherein x iskA state vector of the control system at the moment k comprises a voltage deviation vector delta V of each photovoltaic grid-connected point; u. ofkControl vectors of a control system at the moment k comprise reactive power regulation vectors delta Q of all the photovoltaic cells; z is a radical ofkThe control output quantity of the controlled node at the moment k is obtained; w is akRepresenting interference items of the voltage of each photovoltaic grid-connected point at the kth moment, namely voltage fluctuation caused by load and photovoltaic active output fluctuation; a is I, C is I, I is an identity matrix; b isuA voltage sensitivity matrix representing the relation between photovoltaic grid-connected point voltage and photovoltaic reactive, BwA voltage sensitivity matrix representing the relation between the photovoltaic grid-connected point voltage and the photovoltaic active power output and load;
order to
Figure GDA0002952256560000022
The discrete control system model is simplified to:
xk+1＝Axk+Buuk+Bw'wk'
zk＝Cxk (3)。
preferably, S2 includes:
the photovoltaic active power is output by PpvLoad active power PloadLoaded reactive QloadAs the indeterminate quantity, the definition vector P ═ (P)pv,Pload,Qload) Constrained within a multicellular model;
considering the changes of the load and the photovoltaic output, setting the control vector as u ═ Δ Q and the state vector as x ═ Δ V, and then forming a system multilocular body model by the dynamic characteristics of the control system as follows:
Figure GDA0002952256560000031
in the formula, coefficient matrix Bu(p)、Bw' (P) by an indeterminate quantity Ppv、PloadAnd QloadDetermining that the uncertainty is contained in a vector P, and Ppv,Pload,QloadConstrained within an interval between respective maximum and minimum values:
Figure GDA0002952256560000032
defining respective uncertainty Ppv,Pload,QloadAre respectively equal to 2NEach vertex { v1,...,vLIn the convex polyhedron, N is the number of groups of uncertain quantity, and each vertex viCorresponding to a vector P ═ P (P)pv,Pload,Qload) Value of (a) piI.e. a matrix [ B ]u(pi),Bw′(pi)]Is taken from the value of
Figure GDA0002952256560000033
Is the apex of the asperity, then:
Figure GDA0002952256560000034
preferably, S3 includes:
s31, converting the gain of the disturbance to the output into H∞Problem of norm bound: defining the transfer function of disturbance signal w to output signal z as G (z), corresponding to H∞The norm of (a) is:
Figure GDA0002952256560000035
wherein | · | purple sweet∞And | · | non-conducting phosphor2Respectively, infinite norm and 2 norm, for a given scalar γ > 0, if | | G (z) | non-conducting phosphor∞If < gamma, the system is said to have H∞Performance γ;
s32, establishing a linear matrix inequality with the gain minimization as a target:
Figure GDA0002952256560000041
where ρ represents the minimum disturbance suppression degree
Figure GDA0002952256560000042
Square of (d), superscript T represents the transpose of the matrix;
suppose that for a discrete control system, there is one H∞State feedback controller uk＝Kxk(ii) a If and only if the positive matrix X ∈ Rn*n，Y∈Rn*nIf there is a feasible solution Y*,X*If the linear matrix inequality in the expression (9) is satisfied and all the vertices of the multicellular model satisfy the expression (i) in the expression (9), u isk＝Y*(X*)-1xkIs a state feedback H of a discrete control system∞A controller, wherein K ═ Y*(X*)-1Namely a control parameter matrix K of the state feedback controller.
I.e. access to all vertices in the multicellular model of load and distributed photovoltaics for nodes of corresponding uncertainty
Figure GDA0002952256560000043
When the control parameter matrix is solved, the stability problem of different steady-state working points of the system can be solved only by enabling all vertexes of the multilocular body model to satisfy the formula (i) in the formula (9).
The invention also discloses a power distribution network reactive voltage robust control system considering the uncertainty of the photovoltaic and the load, which comprises the following steps:
the discrete control system model building module is used for converting uncertain time lag brought by communication delay into determined time lag and building a discrete control system model of a controlled node of the power distribution network;
the multi-cell model building module is used for building a multi-cell model for describing the dynamic characteristics of the voltage control system of the power distribution network by taking the load and the photovoltaic accessed by the node as uncertain quantities based on the discrete control system model built in the S1, so that various values of the uncertain quantities are constrained in the multi-cell model and correspond to each vertex of the multi-cell;
H∞control parameter solving module of robust voltage controller using H∞Robust control principle for converting gain of node voltage disturbance to output into H∞Solving the problem of norm boundary by using a linear matrix inequality optimization method to solve the problem with the gain minimization as the target to obtain a discrete system H which enables all vertexes in the multicellular model to meet the linear matrix inequality∞Control parameters of the robust voltage controller;
H∞an application module of the robust voltage controller collects voltage vectors of controlled nodes of the power distribution network, and calculates to obtain node voltage deviation as H∞An input quantity of the robust voltage controller; discrete system H determined by using control parameters obtained in S3∞And the robust voltage controller obtains the reactive power regulating quantity corresponding to each photovoltaic access point in the controlled node, and performs reactive voltage control on the distributed photovoltaic accessed by the node according to the reactive power regulating quantity.
Advantageous effects
Compared with the prior art, the invention has the following advantages and progresses:
(1) communication delay possibly existing in the power distribution network level control process is considered, uncertainty time lag is converted into certainty time lag, the control model and the controller design are simplified, effective response of the controller is facilitated, and influence caused by control instantaneity brought by the communication delay is reduced;
(2) by converting the uncertain time lag into the confirmed time lag, the influence of uncertain power change (photovoltaic and load) and uncertain time lag of the power distribution network on voltage control can be reduced, the quality of voltage waveform is improved, and the safety and stability of the voltage of the power distribution network under the condition of distributed photovoltaic high-proportion access are ensured;
(3) the method comprises the steps of considering the changes of load and photovoltaic output, namely the changes of reactive voltage sensitivity, into a system model, establishing the system model by using a multicell model in a convex optimization theory so as to conveniently solve control parameters by adopting an optimization method of a Linear Matrix Inequality (LMI), wherein the method can ensure the stability and the optimal anti-interference capability of the system under different operating conditions;
(4) by means of H∞The voltage control parameter is designed according to the robust control principle, and the gain of the disturbance on the output is converted into H∞The problem of norm boundary is solved by using an optimization method of a Linear Matrix Inequality (LMI), the solving process of the control parameters is simplified, the design process of multiple control parameters can be simplified, and engineering realization is facilitated.
In conclusion, the invention considers the uncertainty of the power distribution network system, simplifies the design of voltage control parameters, is suitable for the power distribution network with distributed photovoltaic multipoint access, can effectively inhibit the fluctuation of the voltage of the power distribution network, and improves the operation safety of the power distribution network.
Drawings
FIG. 1 is a schematic diagram of the control principle architecture of the present invention;
FIG. 2 is a schematic diagram of a voltage control system implementation;
fig. 3 is a schematic diagram illustrating the feedback control principle of the voltage controller.
Detailed Description
The following further description is made in conjunction with the accompanying drawings and the specific embodiments.
Example 1
A power distribution network reactive voltage robust control method considering photovoltaic and load uncertainty comprises the following steps:
s1, converting the uncertain time lag caused by the communication delay into the confirmed time lag, and establishing a discrete control system model of the controlled node of the power distribution network;
s2, based on the discrete control system model established in S1, the load and the photovoltaic accessed by the node are used as uncertain quantities, and a multi-cell model describing the dynamic characteristics of the voltage control system of the power distribution network is established, so that various values of the uncertain quantities are constrained in the multi-cell model and correspond to each vertex of the multi-cell;
s3, using H∞Robust control principle for converting gain of node voltage disturbance to output into H∞Solving the problem of norm boundary by using a linear matrix inequality optimization method to solve the problem with the gain minimization as the target to obtain a discrete system H which enables all vertexes in the multicellular model to meet the linear matrix inequality∞Control parameters of the robust voltage controller;
s4, collecting voltage vectors of controlled nodes of the power distribution network, and calculating to obtain node voltage deviation as H∞An input quantity of the robust voltage controller; discrete system H determined by using control parameters obtained in S3∞And the robust voltage controller obtains the reactive power regulating quantity corresponding to each photovoltaic access point in the controlled node, and performs reactive voltage control on the distributed photovoltaic accessed by the node according to the reactive power regulating quantity.
In S1, the determined time lag converted from the uncertain time lag is the control period T of the robust voltage controller, namely the control quantity u at the k-1 momentk-1As a disturbance to the k-th time, namely a discrete control system model:
xk+1＝Axk+Buuk+Buuk-1+Bwwk
zk＝Cxk (1)
to convert to:
Figure GDA0002952256560000061
zk＝Cxk (2)
wherein x iskA state vector of the control system at the moment k comprises a voltage deviation vector delta V of each photovoltaic grid-connected point; u. ofkControl vectors of a control system at the moment k comprise reactive power regulation vectors delta Q of all the photovoltaic cells; z is a radical ofkThe control output quantity of the controlled node at the moment k is obtained; w is akRepresenting interference items of the voltage of each photovoltaic grid-connected point at the kth moment, namely voltage fluctuation caused by load and photovoltaic active output fluctuation; a is I, C is I, I is an identity matrix; b isuA voltage sensitivity matrix representing the relation between photovoltaic grid-connected point voltage and photovoltaic reactive, BwRepresenting photovoltaic grid-connected point electricityA voltage sensitivity matrix of the relation between the voltage and the photovoltaic active power output and the load;
order to
Figure GDA0002952256560000071
The discrete control system model is simplified to:
xk+1＝Axk+Buuk+Bw'wk'
zk＝Cxk (3)。
s2 includes:
the photovoltaic active power is output by PpvLoad active power PloadLoaded reactive QloadAs the indeterminate quantity, the definition vector P ═ (P)pv,Pload,Qload) Constrained within a multicellular model;
considering the changes of the load and the photovoltaic output, setting the control vector as u ═ Δ Q and the state vector as x ═ Δ V, and then forming a system multilocular body model by the dynamic characteristics of the control system as follows:
Figure GDA0002952256560000072
in the formula, coefficient matrix Bu(p)、Bw' (P) by an indeterminate quantity Ppv、PloadAnd QloadDetermining that the uncertainty is contained in a vector P, and Ppv,Pload,QloadConstrained within an interval between respective maximum and minimum values:
Figure GDA0002952256560000073
defining respective uncertainty Ppv,Pload,QloadAre respectively equal to 2NEach vertex { v1,...,vLIn the convex polyhedron, N is the number of groups of uncertain quantity, and each vertex viCorresponding to a vector P ═ P (P)pv,Pload,Qload) Value of (a) piI.e. a matrix [ B ]u(pi),Bw′(pi)]Is taken from the value of
Figure GDA0002952256560000074
Is the apex of the asperity, then:
Figure GDA0002952256560000075
in the present invention, the discrete system H∞The robust voltage controller comprises a state feedback controller u which minimizes the gain of the disturbance on the outputk＝Kxk(ii) a In S3, the discrete system H obtained by the solution∞The control parameter of the robust voltage controller is a control parameter matrix K of the state feedback controller.
Specifically, S3 includes the steps of:
s31, converting the gain of the disturbance to the output into H∞Problem of norm bound: defining the transfer function of disturbance signal w to output signal z as G (z), corresponding to H∞The norm of (a) is:
Figure GDA0002952256560000081
wherein | · | purple sweet∞And | · | non-conducting phosphor2Respectively, infinite norm and 2 norm, for a given scalar γ > 0, if | | G (z) | non-conducting phosphor∞If < gamma, the system is said to have H∞Performance γ;
s32, establishing a linear matrix inequality with the gain minimization as a target:
Figure GDA0002952256560000082
where ρ represents the minimum disturbance suppression degree
Figure GDA0002952256560000083
Square of (d), superscript T represents the transpose of the matrix;
hypothesis pairIn a discrete control system, there is one H∞State feedback controller uk＝Kxk(ii) a If and only if the positive matrix X ∈ Rn*n，Y∈Rn*nIf there is a feasible solution Y*,X*If the linear matrix inequality in the expression (9) is satisfied and all the vertices of the multicellular model satisfy the expression (i) in the expression (9), u isk＝Y*(X*)-1xkIs a state feedback H of a discrete control system∞A controller, wherein K ═ Y*(X*)-1Namely a control parameter matrix K of the state feedback controller.
I.e. access to all vertices in the multicellular model of load and distributed photovoltaics for nodes of corresponding uncertainty
Figure GDA0002952256560000084
When the control parameter matrix is solved, the stability problem of different steady-state working points of the system can be solved only by enabling all vertexes of the multilocular body model to satisfy the formula (i) in the formula (9).
Example 2
The embodiment specifically describes a power distribution network reactive voltage robust control method considering photovoltaic and load uncertainty, and the method comprises the following steps:
(1) referring to fig. 1 and 2, the control system acquires voltage data of each photovoltaic grid-connected point from the sensors to obtain voltage vectors V of multiple photovoltaics and voltage reference vectors VrefThe input quantity delta V of the voltage robust controller is obtained through comparison, namely the voltage deviation vector of each photovoltaic grid-connected point, and as a period of time is required from the acquisition of voltage data to the completion of the tracking of each photovoltaic control command to the completion of the voltage control, the control hysteresis problem is brought, so that the uncertainty time lag needs to be converted into the certainty time lag for simplifying the control model and the controller design;
(2) the reactive voltage sensitivity changes along with the change of the power flow due to nonlinearity in the power system, namely the reactive voltage sensitivity changes along with the change of the load and the photovoltaic output, is not a fixed value, and causes certain errors on the control of the system. Therefore, the system model is established by using the multilocular body model in the convex optimization theory, so that the control parameters can be conveniently solved by adopting an optimization method of a Linear Matrix Inequality (LMI), and the method can ensure the stability and the optimal anti-interference capability of the system under different operating conditions;
(3) the invention adopts H∞The robust control principle solves a voltage controller feedback control matrix K by utilizing an optimization method of a Linear Matrix Inequality (LMI), and converts the gain of the disturbance on the output into H∞And in the problem of norm boundary, the voltage deviation vector delta V of each photovoltaic grid-connected point is subjected to robust controller to obtain the output quantity delta Q of the controller, namely the reactive power regulation vector photovoltaic of each photovoltaic, so that the power control of a plurality of distributed photovoltaics in the power distribution network is achieved, the problem of voltage out-of-limit is solved, and the engineering realization is facilitated.
Transition with regard to indeterminate skew:
referring to the voltage control system implementation structure diagram shown in fig. 2, a sensor acquires a distribution network node voltage vector V and a voltage reference vector VrefAfter comparison, the control instruction Q, tau is obtained by a voltage controllers k cRepresenting the time delay, τ, of the sensor to the controllerc k aThe time delay from the controller to the actuator is shown, and the problem of voltage control lag is brought by communication delay, so the invention converts the uncertain time lag into the deterministic time lag, and the specific form is as follows:
referring to fig. 3, due to the existence of the time lag, the control command at the time k-1 may not be completely executed at the time k, and therefore, the discrete control system model may be represented as:
Figure GDA0002952256560000091
in the formula: x is the number ofkControlling the state quantity of the system at the moment k, and taking the state quantity as a voltage deviation vector delta V of each photovoltaic grid-connected point; u. ofkControlling the control quantity of the system at the moment k, and obtaining a reactive power regulation vector delta Q of each photovoltaic; z is a radical ofkThe output quantity controlled at the moment k; w is akIndicates the k-th timeAnd interference items of the voltage of each photovoltaic grid-connected point, namely voltage fluctuation caused by load and photovoltaic active output fluctuation. And A is I, C is I, and I is an identity matrix. The size of B is determined by the reactive voltage sensitivity between the controlled node and the reactive power control equipment, BuA voltage sensitivity matrix representing the relation between photovoltaic grid-connected point voltage and photovoltaic reactive, BwAnd the voltage sensitivity matrix represents the relation between the photovoltaic grid-connected point voltage and the photovoltaic active power output and load.
It is assumed that the maximum delay time of transmission of the control system in each period is bounded and does not exceed the control period T, i.e. the maximum transmission delay
Figure GDA0002952256560000101
In this case, the control system can be designed with a communication delay of T, i.e. the control quantity u at the time k-1k-1Considering as the disturbance amount to the k-th time, the following discrete control system model can be established:
Figure GDA0002952256560000102
order to
Figure GDA0002952256560000103
The control model is further simplified to:
Figure GDA0002952256560000104
regarding establishment of multicellular models:
during modeling, the photovoltaic active power output P is measuredpvLoad active power PloadLoaded reactive QloadAs an uncertainty, i.e. the definition vector P ═ (P)pv,Pload,Qload) Constrained within a multicellular model. Considering the variation of load and photovoltaic output, setting a control vector of a control system as u ═ Δ Q, a reactive regulation vector of each photovoltaic, a state vector x ═ Δ V, and a voltage deviation vector Δ V of each photovoltaic grid-connected point, and then setting the reactive voltage control systemThe dynamic properties of the system may form a multicellular model of the system as follows:
Figure GDA0002952256560000105
in the formula: x is the number ofkIs the state quantity at the k moment; u. ofkIs the control quantity at the k moment; z is a radical ofkThe output quantity controlled at the moment k; w is akAnd (4) representing interference items of the voltage of the controlled node at the moment k, namely voltage fluctuation caused by fluctuation of load and photovoltaic active output. And A is I, C is I, and I is an identity matrix. Coefficient matrix Bu(p)、Bw(p) is determined by the uncertainty contained in the vector p, which is assumed to consist of N uncertainty, i.e. p ═ p, without loss of generality1,...,pN]Each uncertainty amount piBetween the minimum and maximum values for a bounded variable, i.e. N-3 in the method, the uncertainty quantity Ppv,Pload,QloadConstrained within the interval between its maximum and minimum values, i.e.:
Figure GDA0002952256560000111
uncertainty P in the inventionpv,Pload,QloadAre known according to the actual application. When the parameter matrix of the feedback controller is solved, the values of the 8 groups of uncertain quantities are determined according to the value intervals of the uncertain quantities.
Definition of piIs taken to be 2NEach vertex { v1,...,vLIn the convex polyhedron of which each vertex v isiCorresponding to the matrix [ Bu(pi),Bw(pi)]If, if
Figure GDA0002952256560000112
Is the pole of the lobe, then:
Figure GDA0002952256560000113
in the invention, if N is 3, the constructed convex polyhedron has 8 vertexes, and each vertex corresponds to a group of values of the uncertainty.
With respect to H∞Robust controller control parameter solution
Referring to the voltage controller structure shown in FIG. 3, z-1Representing a discrete integrator, if the control vector of the system is set to u ═ Δ Q and the state vector x ═ Δ V, then without loss of generality, equation (4) can be written as:
Figure GDA0002952256560000114
for the system (7) there is a state feedback controller which acts to minimise the gain of the disturbance to the output. In robust control system design, the gain of the output from the disturbance is usually converted into H∞Problem of norm bound, H∞The norm is valid for problems related to model uncertainty. Smaller norm indicates stronger suppression of disturbance. For a discrete system, the transfer function of the perturbation signal w to the output signal z is G (z), and the corresponding norm is expressed as:
Figure GDA0002952256560000115
wherein | · | purple sweet∞And | · | non-conducting phosphor2Respectively, infinite norm and 2 norm. For a given scalar γ > 0, if | | G (z) | luminance∞If < gamma, the system is said to have H∞The property γ.
For a discrete system, there is one H∞State feedback controller (u)k＝Kxk) If and only if a positive definite matrix X ∈ Rn*nAnd the matrix Y ∈ Rn*nSuch that the matrix inequality (i) in equation (9) holds, if there is a feasible solution Y*,X*Then u isk＝Y*(X*)-1xkIs one of a discrete system (7)Individual state feedback H∞A controller, wherein K ═ YX-1Is a feedback control matrix, K in fig. 3.
By solving the following optimization problem:
Figure GDA0002952256560000121
the optimal solution of the optimization problem can be used for obtaining the optimal H of the system∞The controller feeds back a control matrix K with a corresponding minimum disturbance rejection degree of
Figure GDA0002952256560000122
For all vertices in the multicellular model
Figure GDA0002952256560000123
The stability problem of different steady-state working points of the system can be solved only by satisfying the formula (i) in the formula (9).
The design process of multiple control parameters is simplified through the solving of the convex optimization problem, and engineering realization is facilitated.
Example 3
A power distribution network reactive voltage robust control system that accounts for photovoltaic and load uncertainty, comprising:
the discrete control system model building module is used for converting uncertain time lag brought by communication delay into determined time lag and building a discrete control system model of a controlled node of the power distribution network;
the multi-cell model building module is used for building a multi-cell model for describing the dynamic characteristics of the voltage control system of the power distribution network by taking the load and the photovoltaic accessed by the node as uncertain quantities based on the discrete control system model built in the S1, so that various values of the uncertain quantities are constrained in the multi-cell model and correspond to each vertex of the multi-cell;
H∞control parameter solving module of robust voltage controller using H∞Robust control principle for converting gain of node voltage disturbance to output into H∞The problem of norm boundary is solved by utilizing a linear matrix inequality optimization methodSolving the problem of minimizing gain to obtain a discrete system H which enables all vertexes in the multi-cell model to meet the linear matrix inequality∞Control parameters of the robust voltage controller;
H∞an application module of the robust voltage controller collects voltage vectors of controlled nodes of the power distribution network, and calculates to obtain node voltage deviation as H∞An input quantity of the robust voltage controller; discrete system H determined by using control parameters obtained in S3∞And the robust voltage controller obtains the reactive power regulating quantity corresponding to each photovoltaic access point in the controlled node, and performs reactive voltage control on the distributed photovoltaic accessed by the node according to the reactive power regulating quantity.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (4)

1.一种计及光伏和负荷不确定性的配电网无功电压鲁棒控制方法，其特征是，包括：1. a method for robust control of reactive power and voltage of distribution network considering photovoltaic and load uncertainty, is characterized in that, comprises: S1，将通信延迟带来的不确定时滞转化为确定时滞，建立配电网被控节点的离散控制系统模型；S1, convert the uncertain time delay caused by the communication delay into a definite time delay, and establish a discrete control system model of the controlled node of the distribution network; S2，基于S1建立的离散控制系统模型，将节点接入的负荷和光伏作为不确定量，建立描述配电网电压控制系统动态特性的多胞体模型，使得不确定量的各种取值被约束在多胞体模型内，并对应多胞体的各顶点；S2, based on the discrete control system model established by S1, the load and photovoltaic connected to the node are regarded as uncertain quantities, and a multi-cell model describing the dynamic characteristics of the voltage control system of the distribution network is established, so that the various values of the uncertain quantities are constrained. In the multicellular model, and corresponds to each vertex of the multicellular body; S3，利用H∞鲁棒控制原理，将节点电压扰动对输出的增益转化成H∞范数界的问题，利用线性矩阵不等式优化方法进行以增益最小化为目标的问题求解，得到使得多胞体模型中所有顶点满足线性矩阵不等式的离散系统H∞鲁棒电压控制器的控制参数；S3, using the H ∞ robust control principle, transform the gain of the node voltage disturbance to the output into the H ∞ norm bound problem, and use the linear matrix inequality optimization method to solve the problem with the goal of minimizing the gain, and obtain the multicellular model The control parameters of the H ∞ robust voltage controller for a discrete system in which all vertices satisfy the linear matrix inequalities; S4，采集配电网被控节点电压向量，计算得到节点电压偏差，作为H∞鲁棒电压控制器的输入量；利用S3得到的控制参数已确定的离散系统H∞鲁棒电压控制器，得到对应被控节点中各光伏接入点的无功调节量，根据无功调节量对节点接入的分布式光伏进行无功电压控制；S4, collect the voltage vector of the controlled node of the distribution network, calculate the node voltage deviation, and use it as the input of the H ∞ robust voltage controller; using the discrete system H ∞ robust voltage controller with the determined control parameters obtained from S3, obtain Corresponding to the reactive power adjustment amount of each photovoltaic access point in the controlled node, according to the reactive power adjustment amount, the reactive power and voltage control of the distributed photovoltaic connected to the node is performed; S1中，将不确定时滞转化成的确定时滞为鲁棒电压控制器的控制周期T为，将k-1时刻的控制量uk-1作为对第k时刻的扰动：将离散控制系统模型In S1, the definite time delay transformed into the uncertain time delay is the control period T of the robust voltage controller, and the control variable u k- 1 at time k-1 is used as the disturbance to the kth time: the discrete control system Model xk+1＝Axk+Buuk+Buuk-1+Bwwk x k+1 =Ax k +B u u k +B u u k-1 +B w w k zk＝Cxk (1)zk = Cxk (1) 转换为：translates to:
Figure FDA0002952256550000011
Figure FDA0002952256550000011
 zk＝Cxk (2)zk = Cxk (2) 其中，xk为k时刻控制系统的状态向量，包括各台光伏并网点的电压偏差向量ΔV；uk为k时刻控制系统的控制向量，包括各台光伏的无功调节向量ΔQ；zk为k时刻被控节点的控制输出量；wk表示第k时刻各台光伏并网点电压的干扰项，即负荷和光伏有功出力波动带来的电压波动；A＝I，C＝I，I为单位矩阵；Bu表示光伏并网点电压和光伏无功之间关系的电压灵敏度矩阵，Bw表示光伏并网点电压和光伏有功出力、负荷之间关系的电压灵敏度矩阵；Among them, x k is the state vector of the control system at time k, including the voltage deviation vector ΔV of each photovoltaic grid-connected point; uk is the control vector of the control system at time k , including the reactive power adjustment vector ΔQ of each photovoltaic system; z k is The control output of the controlled node at time k; w k represents the interference term of the voltage of each photovoltaic grid-connected point at time k, that is, the voltage fluctuation caused by the fluctuation of load and photovoltaic active power output; A=I, C=I, I is the unit matrix; B u represents the voltage sensitivity matrix of the relationship between photovoltaic grid-connected point voltage and photovoltaic reactive power, and B w represents the voltage sensitivity matrix of the relationship between photovoltaic grid-connected point voltage and photovoltaic active power output and load; 令[Bu Bw]＝Bw'，
Figure FDA0002952256550000021
则离散控制系统模型简化为：Let [B u B w ]=B w ',
Figure FDA0002952256550000021
Then the discrete control system model is simplified to:
Figure FDA0002952256550000022
Figure FDA0002952256550000022
 S2包括：S2 includes: 将光伏有功出力Ppv、负荷有功Pload、负荷无功Qload作为不确定量，定义向量p＝(Ppv,Pload,Qload)约束在多胞体模型内；Taking the photovoltaic active power output P pv , the load active power P load , and the load reactive power Q load as uncertain quantities, the definition vector p=(P pv , P load , Q load ) is constrained in the multicellular model; 考虑负荷和光伏出力的变化，设定控制向量为u＝ΔQ，状态向量x＝ΔV，则控制系统的动态特性形成的系统多胞体模型为：Considering the changes of load and photovoltaic output, set the control vector as u=ΔQ and the state vector x=ΔV, the system multicellular model formed by the dynamic characteristics of the control system is:
Figure FDA0002952256550000023
Figure FDA0002952256550000023
 式中，系数矩阵Bu(p)、Bw′(p)由不确定量Ppv、Pload和Qload决定，不确定量包含在向量p中，且Ppv,Pload,Qload约束在各自最大值和最小值之间的区间内：In the formula, the coefficient matrices B u (p), B w ′(p) are determined by the uncertain quantities P pv , P load and Q load , the uncertain quantities are included in the vector p, and P pv , P load , Q load are constrained In the interval between the respective maximum and minimum values:
Figure FDA0002952256550000024
Figure FDA0002952256550000024
 定义不确定量Ppv,Pload,Qload的取值在L＝2N个顶点{v1,...,vL}组成的凸多面体内，N为不确定量的组数，每个顶点vi对应一个向量p＝(Ppv,Pload,Qload)的取值pi，即一种矩阵[Bu(pi),Bw′(pi)]的取值，若
Figure FDA0002952256550000025
是凸胞体的顶点，则：Define the values of uncertain quantities P pv , P load , Q load in a convex polyhedron composed of L=2 N vertices {v 1 ,...,v L }, N is the number of groups of uncertain quantities, each The vertex v i corresponds to the value p i of a vector p=(P pv , P load , Q load ), that is, the value of a matrix [B u ( pi ), B w ′( pi )], if
Figure FDA0002952256550000025
is the vertex of the convex cell, then:
Figure FDA0002952256550000026
Figure FDA0002952256550000026
 2.根据权利要求1所述的方法，其特征是，离散系统H∞鲁棒电压控制器包括一个使得扰动对输出的增益最小化的状态反馈控制器uk＝Kxk；S3中，求解得到的离散系统H∞鲁棒电压控制器的控制参数为状态反馈控制器的控制参数矩阵K。2. The method according to claim 1, wherein the discrete system H ∞ robust voltage controller comprises a state feedback controller u k =K x k that minimizes the gain of the disturbance to the output; in S3, the solution obtains The control parameters of the discrete system H ∞ robust voltage controller are the control parameter matrix K of the state feedback controller. 3.根据权利要求1所述的方法，其特征是，S3包括：3. The method according to claim 1, wherein S3 comprises: S31，将扰动对输出的增益转化成H∞范数界的问题：定义扰动信号w到输出信号z的传递函数为G(z)，相应H∞的范数为：S31, the problem of converting the gain of the disturbance to the output into the H ∞ norm bound: define the transfer function from the disturbance signal w to the output signal z as G(z), and the corresponding H ∞ norm is:
Figure FDA0002952256550000031
Figure FDA0002952256550000031
 其中，||·||∞和||·||2分别表示无穷范数和2范数，对于给定的标量γ＞0，如果||G(z)||∞＜γ，则称系统具有H∞性能γ；Among them, ||·|| ∞ and ||·|| 2 represent the infinity norm and the 2-norm, respectively. For a given scalar γ>0, if ||G(z)|| ∞ <γ, then the system is called Has H ∞ performance γ; S32，建立以增益最小化为目标的线性矩阵不等式：S32, establish a linear matrix inequality aiming at minimizing the gain:
Figure FDA0002952256550000032
Figure FDA0002952256550000032
 其中，ρ代表最小扰动抑制度
Figure FDA0002952256550000033
的平方，上标T代表矩阵的转置；Among them, ρ represents the minimum disturbance rejection
Figure FDA0002952256550000033
The square of , the superscript T represents the transpose of the matrix; 假设对于离散控制系统，存在一个H∞状态反馈制器uk＝Kxk；当且仅当正定矩阵X∈Rn*n，Y∈Rn*n，若存在一个可行解Y*,X*，使得式(9)中的线性矩阵不等式成立，且多胞体模型的所有顶点满足式(9)中的(i)式，则uk＝Y*(X*)-1xk是离散控制系统的一个状态反馈H∞控制器，其中K＝Y*(X*)-1即为状态反馈控制器的控制参数矩阵K。Suppose that for discrete control system, there exists a H ∞ state feedback controller u k =Kx k ; if and only if the positive definite matrix X∈Rn *n , Y∈Rn *n , if there is a feasible solution Y * ,X * , so that the linear matrix inequality in equation (9) holds, and all vertices of the multicellular model satisfy equation (i) in equation (9), then u k =Y * (X * ) -1 x k is the discrete control system A state feedback H ∞ controller of , where K=Y * (X * ) -1 is the control parameter matrix K of the state feedback controller. 4.一种计及光伏和负荷不确定性的配电网无功电压鲁棒控制系统，其特征是，包括：4. A robust control system for reactive power and voltage of a distribution network that takes into account photovoltaic and load uncertainty, comprising: 离散控制系统模型构建模块，将通信延迟带来的不确定时滞转化为确定时滞，建立配电网被控节点的离散控制系统模型；The discrete control system model building module converts the uncertain time delay caused by communication delay into definite time delay, and establishes the discrete control system model of the controlled node of the distribution network; 多胞体模型构建模块，基于已建立的离散控制系统模型，将节点接入的负荷和光伏作为不确定量，建立描述配电网电压控制系统动态特性的多胞体模型，使得不确定量的各种取值被约束在多胞体模型内，并对应多胞体的各顶点；The multi-cell model building module, based on the established discrete control system model, takes the load and photovoltaic connected to the node as uncertain quantities, and establishes a multi-cell model describing the dynamic characteristics of the voltage control system of the distribution network, so that the various uncertain quantities can be determined. The value is constrained in the polytope model and corresponds to each vertex of the polytope; H∞鲁棒电压控制器的控制参数求解模块，利用H∞鲁棒控制原理，将节点电压扰动对输出的增益转化成H∞范数界的问题，利用线性矩阵不等式优化方法进行以增益最小化为目标的问题求解，得到使得多胞体模型中所有顶点满足线性矩阵不等式的离散系统H∞鲁棒电压控制器的控制参数；The control parameter solving module of the H ∞ robust voltage controller uses the H ∞ robust control principle to convert the gain of the node voltage disturbance to the output into the H ∞ norm bound problem, and uses the linear matrix inequality optimization method to minimize the gain. To solve the target problem, get the control parameters of the discrete system H ∞ robust voltage controller that make all vertices in the multicellular model satisfy the linear matrix inequality; H∞鲁棒电压控制器的应用模块，采集配电网被控节点电压向量，计算得到节点电压偏差，作为H∞鲁棒电压控制器的输入量；利用控制参数已确定的离散系统H∞鲁棒电压控制器，得到对应被控节点中各光伏接入点的无功调节量，根据无功调节量对节点接入的分布式光伏进行无功电压控制；The application module of the H ∞ robust voltage controller collects the voltage vector of the controlled nodes in the distribution network, calculates the node voltage deviation, and takes it as the input of the H ∞ robust voltage controller; using the discrete system H ∞ robust voltage controller whose control parameters have been determined The rod voltage controller obtains the reactive power adjustment amount of each photovoltaic access point in the controlled node, and performs reactive power and voltage control on the distributed photovoltaic connected to the node according to the reactive power adjustment amount; 所述离散控制系统模型构建模块将通信延迟带来的不确定时滞转化为确定时滞为：The discrete control system model building module converts the uncertain time delay caused by the communication delay into a definite time delay as: 将k-1时刻的控制量uk-1作为对第k时刻的扰动：将离散控制系统模型Take the control variable u k-1 at time k-1 as the disturbance to the k-th time: the discrete control system model xk+1＝Axk+Buuk+Buuk-1+Bwwk x k+1 =Ax k +B u u k +B u u k-1 +B w w k zk＝Cxk (1)zk = Cxk (1) 转换为：translates to:
Figure FDA0002952256550000041
Figure FDA0002952256550000041
 zk＝Cxk (2)zk = Cxk (2) 其中，xk为k时刻控制系统的状态向量，包括各台光伏并网点的电压偏差向量ΔV；uk为k时刻控制系统的控制向量，包括各台光伏的无功调节向量ΔQ；zk为k时刻被控节点的控制输出量；wk表示第k时刻各台光伏并网点电压的干扰项，即负荷和光伏有功出力波动带来的电压波动；A＝I，C＝I，I为单位矩阵；Bu表示光伏并网点电压和光伏无功之间关系的电压灵敏度矩阵，Bw表示光伏并网点电压和光伏有功出力、负荷之间关系的电压灵敏度矩阵；Among them, x k is the state vector of the control system at time k, including the voltage deviation vector ΔV of each photovoltaic grid-connected point; uk is the control vector of the control system at time k , including the reactive power adjustment vector ΔQ of each photovoltaic system; z k is The control output of the controlled node at time k; w k represents the interference term of the voltage of each photovoltaic grid-connected point at time k, that is, the voltage fluctuation caused by the fluctuation of load and photovoltaic active power output; A=I, C=I, I is the unit matrix; B u represents the voltage sensitivity matrix of the relationship between photovoltaic grid-connected point voltage and photovoltaic reactive power, and B w represents the voltage sensitivity matrix of the relationship between photovoltaic grid-connected point voltage and photovoltaic active power output and load; 令[Bu Bw]＝Bw'，
Figure FDA0002952256550000042
则离散控制系统模型简化为：Let [B u B w ]=B w ',
Figure FDA0002952256550000042
Then the discrete control system model is simplified to:
Figure FDA0002952256550000043
Figure FDA0002952256550000043
 所述多胞体模型构建模块，将光伏有功出力Ppv、负荷有功Pload、负荷无功Qload作为不确定量，定义向量p＝(Ppv,Pload,Qload)约束在多胞体模型内；The multi-cell model building module uses photovoltaic active power output P pv , load active power P load , load reactive power Q load as uncertain quantities, and defines a vector p=(P pv , P load , Q load ) within the multi-cell model. ; 考虑负荷和光伏出力的变化，设定控制向量为u＝ΔQ，状态向量x＝ΔV，则控制系统的动态特性形成的系统多胞体模型为：Considering the changes of load and photovoltaic output, set the control vector as u=ΔQ and the state vector x=ΔV, then the system multicellular model formed by the dynamic characteristics of the control system is:
Figure FDA0002952256550000051
Figure FDA0002952256550000051
 式中，系数矩阵Bu(p)、Bw′(p)由不确定量Ppv、Pload和Qload决定，不确定量包含在向量p中，且Ppv,Pload,Qload约束在各自最大值和最小值之间的区间内：In the formula, the coefficient matrices B u (p), B w ′(p) are determined by the uncertain quantities P pv , P load and Q load , the uncertain quantities are included in the vector p, and P pv , P load , Q load are constrained In the interval between the respective maximum and minimum values:
Figure FDA0002952256550000052
Figure FDA0002952256550000052
 定义不确定量Ppv,Pload,Qload的取值在L＝2N个顶点{v1,...,vL}组成的凸多面体内，N为不确定量的组数，每个顶点vi对应一个向量p＝(Ppv,Pload,Qload)的取值pi，即一种矩阵[Bu(pi),Bw′(pi)]的取值，若
Figure FDA0002952256550000053
是凸胞体的顶点，则：Define the values of uncertain quantities P pv , P load , Q load in a convex polyhedron composed of L=2 N vertices {v 1 ,...,v L }, N is the number of groups of uncertain quantities, each The vertex v i corresponds to the value p i of a vector p=(P pv , P load , Q load ), that is, the value of a matrix [B u ( pi ), B w ′( pi )], if
Figure FDA0002952256550000053
is the vertex of the convex cell, then:
Figure FDA0002952256550000054
Figure FDA0002952256550000054
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