CN112564154A - Method for estimating state of undetectable signal of nonlinear constant-power load of direct-current micro-grid - Google Patents

Method for estimating state of undetectable signal of nonlinear constant-power load of direct-current micro-grid Download PDF

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CN112564154A
CN112564154A CN202011325834.1A CN202011325834A CN112564154A CN 112564154 A CN112564154 A CN 112564154A CN 202011325834 A CN202011325834 A CN 202011325834A CN 112564154 A CN112564154 A CN 112564154A
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power load
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解相朋
夏雪洁
葛辉
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Nanjing University of Posts and Telecommunications
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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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • 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
    • H02J1/00—Circuit arrangements for dc mains or dc distribution 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
    • 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
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention discloses an undetectable signal state estimation method for a nonlinear constant power load of a direct current micro-grid, which comprises the following steps: establishing a nonlinear constant power load dynamic model of a direct current micro-grid system; step two, constructing an equivalent T-S fuzzy model according to the dynamic model; step three, discretizing and model reduction are carried out on the obtained nonlinear constant power load T-S fuzzy model of the direct current micro-grid system; designing a switching type fuzzy state observer of the nonlinear constant power load of the direct-current micro-grid and solving a gain matrix of the switching type fuzzy state observer in an off-line manner; and fifthly, the observer gain is assigned to a switching type fuzzy state observer of the nonlinear constant-power load of the direct-current micro-grid, and the function of estimating the state of the undetectable signal of the nonlinear constant-power load of the system is achieved on line. The method can enlarge the observable domain range of the immeasurable signal state estimation of the DC micro-grid nonlinear constant power load by applying the state observer design method based on the T-S fuzzy model.

Description

Method for estimating state of undetectable signal of nonlinear constant-power load of direct-current micro-grid
Technical Field
The invention belongs to the technical field of power system automation, and particularly relates to an undetectable signal state estimation method for a direct current micro-grid nonlinear constant power load.
Background
With the continuous improvement of the quantity and quality of global energy demand, the problems of energy shortage and environmental pollution become more serious, and the problem of low intelligent degree of a centralized power generation system is highlighted, so that the development of renewable energy sources is promoted. In order to effectively solve the problem that renewable energy is connected into a power grid, researchers integrate the renewable energy with an energy storage device, a load, an energy conversion device and a monitoring and protecting device, so that a micro-grid system technology is generated. Since traditional grids relied on alternating current systems, early research on micro grids focused primarily on Alternating Current (AC) micro grid systems. Compared with an alternating-current micro-grid, the direct-current micro-grid has the advantages of higher efficiency, low reactive power, high harmonic performance and the like. The DC micro-grid consists of various power sources and DC/AC loads, and is connected together through a power electronic converter and a filter. Generally, an interface converter is applied in a dc microgrid to connect a sustainable power source to a charging device such as a public power bus. Furthermore, the power electronic converters are connected in parallel to form a distributed structure of the system.
In the related research of the dc micro grid, a lot of attention has been paid to the real-time control and state estimation problem of the dc micro grid equipped with a constant power load (cpl). From the function perspective of the constant power load device, the constant power load device is important for the stable operation of the direct current micro-grid, such as the charging and discharging of the marine island micro-grid, the charging of an electric automobile, the peak clipping and valley filling of the micro-grid and other application scenes. In the prior art, technicians use current distribution to stabilize the entire dc microgrid, and the negative impedance characteristic of a constant power load may make the entire microgrid system unstable or even crash. What is worse, the constant power load usually has a nonlinear link and the key signal parameters cannot be directly measured, so that the direct current micro-grid has the troublesome problems of inaccurate measurement, difficult control and the like. To date, scholars at home and abroad have proposed several nonlinear state estimation methods to perform online state estimation on an unmeasured signal of a nonlinear link, and the state estimation result is used for stable monitoring of a direct current micro-grid system so as to reduce adverse effects caused by negative impedance characteristics of a constant power load. Therefore, the state estimation technology has been widely researched and paid attention in recent years as one of the key technologies for ensuring the safe and reliable operation of the dc micro-grid system. Particularly, the state observer design method based on the Takagi-Sugeno (T-S) fuzzy model is widely applied to the measurement and control of a complex nonlinear system and is favored by technical personnel in the field; the reason for this is that the parallel distributed compensation idea (PDC) and the powerful Linear Matrix Inequality (LMI) based techniques make it easier for field engineers to understand and the design process simple and fast. However, when the state observer design method based on the T-S fuzzy model is actually applied to a direct-current micro-grid system, the problem that the observable domain of a signal is too small generally exists, so that a feasible solution of the fuzzy observer meeting the soft measurement performance index cannot be obtained when the method is applied to the state estimation of the non-measurable signal of a non-linear constant-power load, and the essential reason is caused by the fact that the existing state observer design method based on the T-S fuzzy model is too conservative. On the other hand, the higher order of the constant power load model also leads to the higher order of the designed fuzzy state observer, thereby increasing the additional computational burden and hardware cost.
Disclosure of Invention
In order to solve the problems, the invention provides an undetectable signal state estimation method for a nonlinear constant power load of a direct current micro-grid, which is used for solving the problem that a signal observable domain is too small when a novel switching type fuzzy state observer is designed and applied to a direct current micro-grid system by performing model order reduction on the nonlinear constant power load of the direct current micro-grid. The designed switching type fuzzy state observer covers fuzzy membership information at the past moment, partition switching is carried out according to the interval of a fuzzy membership function value, more information of each partition subinterval is considered in an activated switching mode, the conservatism of the method for estimating the non-measurable signal state of the direct-current micro-grid nonlinear constant-power load is further reduced, and the calculation burden of the fuzzy state observer is relieved. In addition, the gain matrix of the switching type fuzzy state observer for the nonlinear constant-power load of the direct-current microgrid can be obtained by offline solving by using a developed LMI program, and then the gain matrix is used for online implementation of the state estimation of the undetectable signal of the nonlinear constant-power load of the direct-current microgrid.
In order to achieve the purpose, the invention is realized by the following technical scheme:
the invention relates to an undetectable signal state estimation method for a nonlinear constant power load of a direct current micro-grid, which comprises the following steps:
step one, establishing a dynamic model of a nonlinear constant power load of a direct current micro-grid system;
secondly, constructing an equivalent T-S fuzzy model according to the dynamic model;
step three, discretizing and model order reduction are carried out on the obtained nonlinear constant power load T-S fuzzy model of the direct current micro-grid system;
designing a novel switching type fuzzy state observer of the nonlinear constant power load of the direct-current micro-grid, and solving a gain matrix of the switching type fuzzy state observer in an off-line manner;
and fifthly, assigning the obtained observer gain to the designed switching type fuzzy state observer of the direct current micro-grid nonlinear constant power load, and realizing the function of estimating the state of the undetectable signal of the nonlinear constant power load of the direct current micro-grid system on line.
The invention is further improved in that: in the first step, the first step is carried out,
according to the principle of a direct current link, a dynamic model of a Constant Power Load (CPL) and a filter is established as follows:
Figure BDA0002794259220000031
wherein r isLRepresenting the resistance in the RLC filter, L representing the inductance in the RLC filter, C representing the capacitance in the RLC filter, vcRepresenting the capacitor voltage, i, in the RLC filterLRepresenting the inductor current, V, in an RLC filtereRepresenting the dc link voltage, P represents the constant power of the Constant Power Load (CPL), and furthermore P satisfies the following constraint:
Figure BDA0002794259220000032
wherein, VdcRepresenting the voltage of a DC voltage source, vc0Represents the voltage at which the system is at equilibrium, PmaxThe maximum power of the Constant Power Load (CPL),
meanwhile, the DC voltage source is connected with the filter and an Energy Storage System (ESS) which passes through the current source iesModeling, listing the dynamic equation, as follows:
Figure BDA0002794259220000041
wherein r issRepresenting the resistance, L, in an RLC filtersRepresenting inductance, C, in RLC filterssRepresenting the capacitance, v, in an RLC filterC，sRepresenting the capacitor voltage, i, in the RLC filterL，SRepresenting the inductor current, V, in an RLC filterdcRepresenting the voltage of a DC voltage source, iesRepresenting the current through the current source;
by changing the states of the nonlinear systems (1) and (2), a new nonlinear dynamical system with an origin balance point is obtained, and the transformation is helpful for the stability analysis of the nonlinear system based on the Lyapunov stability theory, for which, by considering the change of coordinates, the dynamics (1) and (2) are converted into the following state expressions (3) and (4), respectively:
Figure BDA0002794259220000042
Figure BDA0002794259220000043
by coordinate change, and with iesAs a control input, the entire dc MG, whose spatial expression is as follows:
Figure BDA0002794259220000051
a, D, B thereines、BsA matrix of real coefficients is represented which,
Figure BDA0002794259220000058
which represents the current through the current source,
Figure BDA0002794259220000052
which represents the voltage of the voltage source,
Figure BDA0002794259220000053
is the corresponding probability of the fuzzy membership function.
The invention is further improved in that: in the second step, the first step is carried out,
the equivalent T-S fuzzy model of the nonlinear system is systematically calculated by utilizing a fan-shaped nonlinear method, each nonlinear item of the original system is in two linear sectors, and then all groups of the two sectors are aggregated to obtain a membership function of the T-S fuzzy model:
Figure BDA0002794259220000054
substituting (6) into equation (5) to obtain an equivalent T-S fuzzy model of the system:
Figure BDA0002794259220000055
Figure BDA0002794259220000056
Figure BDA0002794259220000057
Figure BDA0002794259220000061
wherein: a. the1，A2，Bes，BSAs a spatial expression, is a real coefficient matrix, rSRepresenting the resistance, L, in an RLC filtersRepresenting inductance, C, in RLC filterssRepresenting the capacitance, U, in the RLC filtermax、UminRespectively representing the maximum and minimum voltage values achievable in the system, M1，M2In the form of a fuzzy membership function,
Figure BDA0002794259220000062
which represents the current through the current source,
Figure BDA0002794259220000063
representing the voltage of the voltage source.
The invention is further improved in that: in the third step, the first step is executed,
discretizing and model reducing a nonlinear constant power load T-S fuzzy model of the four-dimensional direct current micro-grid system by a step response invariant method and a Dissipativity-Preserving type model reducing method to obtain a discrete two-dimensional T-S fuzzy model:
Figure BDA0002794259220000064
wherein: the unmeasured system state vector is noted as x (t) E R2The control input vector is denoted as u (t) e R1The system output vector is denoted as y (t) e R1The available preconditions are denoted as v (t), and the ith normalized fuzzy weighting function of the current time is denoted as hi(v (t)), further, Ai∈R2×2，Bi∈R2×1，Ci∈R1×2Are three pairs of known matrix value parameters.
The invention is further improved in that: in the fourth step, in the first step,
due to the state vector x (t) e R of the model (9)2Is unknown and requires the design of a fuzzy state observer to estimate the state vector x (t) e R2Firstly, m +1 switching modes of the fuzzy state observer are constructed, specifically, m monotone increasing positive real number sets { alpha ] which are more than 0 and less than 1 are selected1，…,αmWill close the interval[0,1]Dividing the space into m +1 non-overlapping subintervals, namely: [0, α ]1)，[α1,α2)，…,[αm,1]Sequentially marking sequence numbers of the m +1 subintervals, wherein j belongs to { 1., m +1 }; at each sampling time, the ith normalized fuzzy weighting function is selected and recorded as hi(v (t)) and determining the subinterval in which the subinterval is positioned and identifying a subinterval sequence number j;
on the basis, a new switching type fuzzy state observer is designed, and has possible switching modes in m + 1:
Figure BDA0002794259220000071
where j ∈ {1,.., m +1}, the gain matrix
Figure BDA0002794259220000072
And
Figure BDA0002794259220000073
belonging to the following forms:
Figure BDA0002794259220000074
Figure BDA0002794259220000075
wherein,
Figure BDA0002794259220000076
and
Figure BDA0002794259220000077
the observer gain matrix of the switching type fuzzy state observer, which is designed for the present invention off-line, and at the same time,
Figure BDA0002794259220000078
and
Figure BDA0002794259220000079
the specific value of (c) can be obtained by solving the following linear matrix inequalities (11) to (13) offline:
Figure BDA00027942592200000710
Figure BDA00027942592200000711
Figure BDA00027942592200000712
wherein:
Figure BDA0002794259220000081
Figure BDA0002794259220000082
Figure BDA0002794259220000091
more often:
Figure BDA0002794259220000092
Figure BDA0002794259220000093
Figure BDA0002794259220000094
Figure BDA0002794259220000095
Figure BDA0002794259220000096
Figure BDA0002794259220000097
Figure BDA0002794259220000098
Figure BDA0002794259220000101
Figure BDA0002794259220000102
Figure BDA0002794259220000103
the invention is further improved in that: in the fifth step, in the first step,
at each sampling instant, first, the ith normalized fuzzy weighting function is recorded as hi(v (t)) and identifying the subinterval number j, and then, corresponding to the jth switching mode
Figure BDA0002794259220000104
And
Figure BDA0002794259220000105
and weighting all normalized fuzzy weighting functions of the fuzzy models at the current time and the previous time to obtain the gain of the observer
Figure BDA0002794259220000106
And
Figure BDA0002794259220000107
and substituting the formula (10) to carry out online state estimation on the undetectable signal of the nonlinear constant power load of the direct current micro-grid system.
The invention has the beneficial effects that: according to the method, model reduction is carried out on the nonlinear constant power load of the direct current micro-grid, a novel switching type fuzzy state observer is designed, the conservatism of the state observer design method based on the T-S fuzzy model and the calculation burden of the fuzzy state observer can be obviously reduced at the same time, and the observable domain range of the immeasurable signal state estimation of the nonlinear constant power load of the direct current micro-grid by applying the state observer design method based on the T-S fuzzy model can be expanded.
Drawings
Fig. 1 is a flowchart illustrating an implementation of a method for estimating an undetectable signal state of a dc microgrid nonlinear constant-power load according to an embodiment of the present invention.
Fig. 2 is an overall framework diagram of the dc microgrid in the embodiment of the present invention.
Fig. 3 is a single Constant Power Load (CPL) dc link configuration in an embodiment of the present invention.
Fig. 4 is a single Constant Power Load (CPL) energy storage system configuration in an embodiment of the present invention.
FIG. 5 is a comparison graph of the actual value and the estimated value of the inductor current in the embodiment of the present invention.
Detailed Description
In the following description, for purposes of explanation, numerous implementation details are set forth in order to provide a thorough understanding of the embodiments of the invention. It should be understood, however, that these implementation details are not to be interpreted as limiting the invention. That is, in some embodiments of the invention, such implementation details are not necessary. In addition, some conventional structures and components are shown in simplified schematic form in the drawings.
The technical problem to be solved by the invention is to provide an unmeasured signal state estimation method for the nonlinear constant power load of the direct current micro-grid aiming at the defects of the background technology, solve the problem of the undersize signal observable domain when the traditional method is applied to a direct current micro-grid system by performing model order reduction on the nonlinear constant power load of the direct current micro-grid and designing a novel switching type fuzzy state observer, and reduce the calculation burden of the fuzzy state observer.
Specifically, as shown in fig. 1 to 5, the present invention is a method for estimating an undetectable signal state of a nonlinear constant power load of a dc microgrid, comprising the steps of:
step one, establishing a dynamic model of a nonlinear constant power load of a direct current micro-grid system;
according to the principle of a direct current link, a dynamic model of a Constant Power Load (CPL) and a filter is established as follows:
Figure BDA0002794259220000111
wherein r isLRepresenting the resistance in the RLC filter, L representing the inductance in the RLC filter, C representing the capacitance in the RLC filter, vcRepresenting the capacitor voltage, i, in the RLC filterLRepresenting the inductor current, V, in an RLC filtereRepresenting the dc link voltage, P represents the constant power of the Constant Power Load (CPL), and furthermore P satisfies the following constraint:
Figure BDA0002794259220000121
wherein, VdcRepresenting the voltage of a DC voltage source, vC0Represents the voltage at which the system is at equilibrium, PmaxMaximum power of a Constant Power Load (CPL).
Meanwhile, the DC voltage source is connected with the filter and an Energy Storage System (ESS) which passes through the current source iesModeling, listing the dynamic equation, as follows:
Figure BDA0002794259220000122
wherein r issRepresenting the resistance, L, in an RLC filtersRepresenting inductance, C, in RLC filterssRepresenting the capacitance, v, in an RLC filterc，sRepresenting the capacitor voltage, i, in the RLC filterL，SRepresenting the inductor current, V, in an RLC filterdcRepresenting the voltage of a DC voltage source, iesRepresenting the current through the current source.
By changing the states of the nonlinear systems (1) and (2), a new nonlinear dynamical system with an origin balance point is obtained, and the transformation is helpful for the stability analysis of the nonlinear system based on the Lyapunov stability theory, for which, by considering the change of coordinates, the dynamics (1) and (2) are converted into the following state expressions (3) and (4), respectively:
Figure BDA0002794259220000123
Figure BDA0002794259220000131
by coordinate change, and with iesAs a control input, the entire dc MG, whose spatial expression is as follows:
Figure BDA0002794259220000132
a, D, B thereines、BsA matrix of real coefficients is represented which,
Figure BDA0002794259220000133
which represents the current through the current source,
Figure BDA0002794259220000134
which represents the voltage of the voltage source,
Figure BDA0002794259220000135
is the corresponding probability of the fuzzy membership function.
Secondly, constructing an equivalent T-S fuzzy model according to the dynamic model;
the equivalent T-S fuzzy model of the nonlinear system is systematically calculated by utilizing a fan-shaped nonlinear method, each nonlinear item of the original system is in two linear sectors, and then all groups of the two sectors are aggregated to obtain a membership function of the T-S fuzzy model:
Figure BDA0002794259220000136
substituting (6) into equation (5) to obtain an equivalent T-S fuzzy model of the system:
Figure BDA0002794259220000137
Figure BDA0002794259220000138
Figure BDA0002794259220000141
Figure BDA0002794259220000142
wherein: a. the1，A2，Bes，BSAs a spatial expression, is a real coefficient matrix, rSRepresenting the resistance, L, in an RLC filtersRepresenting inductance, C, in RLC filterssRepresenting the capacitance, U, in the RLC filtermax、UminRespectively representing the maximum and minimum voltage values achievable in the system, M1，M2In the form of a fuzzy membership function,
Figure BDA0002794259220000143
which represents the current through the current source,
Figure BDA0002794259220000144
representing the voltage of the voltage source.
Step three, discretizing and model order reduction are carried out on the obtained nonlinear constant power load T-S fuzzy model of the direct current micro-grid system;
discretizing and model reducing a nonlinear constant power load T-S fuzzy model of the four-dimensional direct current micro-grid system by a step response invariant method and a discretization-forecasting model order reducing method to obtain a discretized two-dimensional T-S fuzzy model, which can effectively reduce the calculation burden of a fuzzy state observer:
Figure BDA0002794259220000145
wherein: the unmeasured system state vector is noted as x (t) E R2The control input vector is denoted as u (t) e R1The system output vector is denoted as y (t) e R1The available preconditions are denoted as v (t), and the ith normalized fuzzy weighting function of the current time is denoted as hi(v (t)), further, Ai∈R2×2，Bi∈R2×1，Ci∈R1×2Three pairs of known matrix value parameters, of which there are in the present embodiment
Figure BDA0002794259220000151
C1＝[δ 1.0]，C2＝[1.0 1.0]. It is particularly noted that δ is a variable parameter, for an unswitched fuzzy state observer, which has a range of feasible solutions of [ -0.4, 467]。
Designing a novel switching type fuzzy state observer of the nonlinear constant power load of the direct-current micro-grid, and solving a gain matrix of the switching type fuzzy state observer in an off-line manner;
due to the state vector x (t) e R of the model (9)2Is unknown and requires the design of a fuzzy state observer to estimateState vector x (t) e R2In the present embodiment, m is 3 and α are selected1＝0.2，α2＝0.5，α3Then, 4 switching modes of the fuzzy state observer are constructed, specifically: will close the interval [0, 1]Dividing the space into m +1 non-overlapping subintervals, namely: [0,0.2),[0.2,0.5),[0.5,0.8),[0.8,1]Sequentially marking sequence numbers of the 4 subintervals, wherein j belongs to { 1., m +1 }; at each sampling time, the ith-1 normalized fuzzy weighting function is selected and recorded as hi(v (t)) and determining the subinterval in which the subinterval is positioned and identifying a subinterval sequence number j;
on the basis, a new switching type fuzzy state observer is designed, and has possible switching modes in m + 1:
Figure BDA0002794259220000152
where j ∈ {1,.., m +1}, the gain matrix
Figure BDA0002794259220000153
And
Figure BDA0002794259220000154
belonging to the following forms:
Figure BDA0002794259220000155
Figure BDA0002794259220000161
wherein,
Figure BDA0002794259220000162
and
Figure BDA0002794259220000163
the observer gain matrix of a switched-mode fuzzy state observer, which is designed for the purposes of the present invention in an off-line manner, and to this endAt the same time, the user can select the desired position,
Figure BDA0002794259220000164
and
Figure BDA0002794259220000165
the specific value of (c) can be obtained by solving the following linear matrix inequalities (11) to (13) offline:
Figure BDA0002794259220000166
Figure BDA0002794259220000167
Figure BDA0002794259220000168
wherein:
Figure BDA0002794259220000169
Figure BDA0002794259220000171
Figure BDA0002794259220000172
more often:
Figure BDA0002794259220000173
Figure BDA0002794259220000174
Figure BDA0002794259220000175
Figure BDA0002794259220000176
Figure BDA0002794259220000181
Figure BDA0002794259220000182
Figure BDA0002794259220000183
Figure BDA0002794259220000184
Figure BDA0002794259220000185
Figure BDA0002794259220000186
for the present embodiment, δ is a variable parameter, and the range of feasible solutions for the switching type fuzzy state observer proposed by the present invention is [ -0.4,2725], and the feasible domain is increased to 483.5% of the conventional technology. Further, when δ is selected to 2725, the conventional method cannot provide a feasible state estimation scheme, and the switching fuzzy state observer provided by the invention has a feasible solution:
switching pattern j is 1:
Figure BDA0002794259220000187
Figure BDA0002794259220000188
Figure BDA0002794259220000191
switching pattern j is 2:
Figure BDA0002794259220000192
Figure BDA0002794259220000193
Figure BDA0002794259220000194
switching pattern j is 3:
Figure BDA0002794259220000195
Figure BDA0002794259220000196
Figure BDA0002794259220000197
switching pattern j is 4:
Figure BDA0002794259220000198
Figure BDA0002794259220000199
Figure BDA00027942592200001910
and fifthly, assigning the obtained observer gain to the designed switching type fuzzy state observer of the direct current micro-grid nonlinear constant power load, and realizing the function of estimating the state of the undetectable signal of the nonlinear constant power load of the direct current micro-grid system on line.
At each sampling instant, first, the ith normalized fuzzy weighting function is recorded as hi(v (t)) and identifying the subinterval number j, and then, corresponding to the jth switching mode
Figure BDA00027942592200001911
And
Figure BDA00027942592200001912
and weighting all normalized fuzzy weighting functions of the fuzzy models at the current time and the previous time to obtain the gain of the observer
Figure BDA00027942592200001913
And
Figure BDA00027942592200001914
and substituting the formula (10) to carry out online state estimation on the undetectable signal of the nonlinear constant power load of the direct current micro-grid system.
In the present embodiment, fig. 5 shows the estimation error
Figure BDA0002794259220000201
And a value-taking map of the working mode j of the corresponding sampling point, wherein iL(t) is the actual value of the inductive current of the nonlinear constant power load,
Figure BDA0002794259220000202
for non-linear constant power load estimated on-line by means of a switching fuzzy state observer of the inventionThe value of the inductance current. As can be seen from fig. 5, the system state estimation error approaches to the vicinity of the zero point within 0.1 second, and a total of 3 operation modes are triggered to operate, that is, the switching mode j can be executed according to hiThe value (v (t)) changes at different sampling points, so that more information can be collected and used at each sampling point for estimation, and finally the task of estimating the online state of the immeasurable signal of the DC microgrid nonlinear constant-power load is completed.
According to the real-time partition-based switching law given by the invention, the designed switching type fuzzy state observer has possible working modes in m + 1; under each working mode, the real-time information of the current nonlinear constant-power load of the direct-current micro-grid can be more sufficiently used, so that the conservatism of the designed state observer design method is remarkably reduced, and the problem that the observable domain of signals is too small commonly existing when the state observer design method based on the T-S fuzzy model is practically applied to the direct-current micro-grid system can be effectively solved.
The above description is only an embodiment of the present invention, and is not intended to limit the present invention. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (6)

1. A method for estimating the state of an undetectable signal of a nonlinear constant-power load of a direct-current micro-grid is characterized by comprising the following steps: the method comprises the following steps:
step one, establishing a dynamic model of a nonlinear constant power load of a direct current micro-grid system;
secondly, constructing an equivalent T-S fuzzy model according to the dynamic model;
step three, discretizing and model order reduction are carried out on the obtained nonlinear constant power load T-S fuzzy model of the direct current micro-grid system;
designing a novel switching type fuzzy state observer of the nonlinear constant power load of the direct-current micro-grid, and solving a gain matrix of the switching type fuzzy state observer in an off-line manner;
and fifthly, assigning the obtained observer gain to the designed switching type fuzzy state observer of the direct current micro-grid nonlinear constant power load, and realizing the function of estimating the state of the undetectable signal of the nonlinear constant power load of the direct current micro-grid system on line.
2. The method for estimating the undetectable signal state of the nonlinear constant power load of the direct current microgrid according to claim 1, characterized in that: in the first step, the first step is carried out,
according to the principle of a direct current link, a dynamic model of a Constant Power Load (CPL) and a filter is established as follows:
Figure FDA0002794259210000011
wherein r isLRepresenting the resistance in the RLC filter, L representing the inductance in the RLC filter, C representing the capacitance in the RLC filter, vcRepresenting the capacitor voltage, i, in the RLC filterLRepresenting the inductor current, V, in an RLC filtereRepresenting the dc link voltage, P represents the constant power of the Constant Power Load (CPL), and furthermore P satisfies the following constraint:
Figure FDA0002794259210000012
wherein, VdcRepresenting the voltage of a DC voltage source, vC0Represents the voltage at which the system is at equilibrium, PmaxThe maximum power of the Constant Power Load (CPL),
meanwhile, the DC voltage source is connected with the filter and an Energy Storage System (ESS) which passes through the current source iesModeling, listing itThe dynamic equation is as follows:
Figure FDA0002794259210000021
wherein r issRepresenting the resistance, L, in an RLC filtersRepresenting inductance, C, in RLC filterssRepresenting the capacitance, v, in an RLC filterc，sRepresenting the capacitor voltage, i, in the RLC filterL，SRepresenting the inductor current, V, in an RLC filterdcRepresenting the voltage of a DC voltage source, iesRepresenting the current through the current source;
by changing the states of the nonlinear systems (1) and (2), a new nonlinear dynamical system with an origin balance point is obtained, and the transformation is helpful for the stability analysis of the nonlinear system based on the Lyapunov stability theory, for which, by considering the change of coordinates, the dynamics (1) and (2) are converted into the following state expressions (3) and (4), respectively:
Figure FDA0002794259210000022
Figure FDA0002794259210000023
by coordinate change, and with iesAs a control input, the entire dc MG, whose spatial expression is as follows:
Figure FDA0002794259210000031
a, D, B thereines、BsA matrix of real coefficients is represented which,
Figure FDA0002794259210000032
which represents the current through the current source,
Figure FDA0002794259210000033
which represents the voltage of the voltage source,
Figure FDA0002794259210000034
is the corresponding probability of the fuzzy membership function.
3. The method for estimating the undetectable signal state of the nonlinear constant power load of the direct current microgrid according to claim 1, characterized in that: in the second step, the first step is carried out,
the equivalent T-S fuzzy model of the nonlinear system is systematically calculated by utilizing a fan-shaped nonlinear method, each nonlinear item of the original system is in two linear sectors, and then all groups of the two sectors are aggregated to obtain a membership function of the T-S fuzzy model:
Figure FDA0002794259210000035
substituting (6) into equation (5) to obtain an equivalent T-S fuzzy model of the system:
Figure FDA0002794259210000036
Figure FDA0002794259210000037
Figure FDA0002794259210000041
Figure FDA0002794259210000042
wherein: a. the1，A2，Bes，BsAs a spatial expression, is a real coefficient matrix, rsRepresenting the resistance, L, in an RLC filtersRepresenting inductance, C, in RLC filterssRepresenting the capacitance, U, in the RLC filtermax、UminRespectively representing the maximum and minimum voltage values achievable in the system, M1，M2In the form of a fuzzy membership function,
Figure FDA0002794259210000043
which represents the current through the current source,
Figure FDA0002794259210000044
representing the voltage of the voltage source.
4. The method for estimating the undetectable signal state of the nonlinear constant power load of the direct current microgrid according to claim 1, characterized in that: in the third step, the first step is executed,
discretizing and model reducing a nonlinear constant power load T-S fuzzy model of the four-dimensional direct current micro-grid system by a step response invariant method and a Dissipativity-Preserving type model reducing method to obtain a discrete two-dimensional T-S fuzzy model:
Figure FDA0002794259210000045
wherein: the unmeasured system state vector is noted as x (t) E R2The control input vector is denoted as u (t) e R1The system output vector is denoted as y (t) e R1The available preconditions are denoted as v (t), and the ith normalized fuzzy weighting function of the current time is denoted as hi(v (t)), further, Ai∈R2×2，Bi∈R2×1，Ci∈R1×2Are three pairs of known matrix value parameters.
5. The method for estimating the undetectable signal state of the nonlinear constant power load of the direct current microgrid according to claim 1, characterized in that: in the fourth step, in the first step,
due to the state vector x (t) e R of the model (9)2Is unknown and requires the design of a fuzzy state observer to estimate the state vector x (t) e R2Firstly, m +1 switching modes of the fuzzy state observer are constructed, specifically: selecting m monotone increasing positive real number sets (alpha) larger than 0 and smaller than 11，...，αmWill close the interval [0, 1 ]]Dividing the space into m +1 non-overlapping subintervals, namely: [0, α ]1)，[α1，α2)，...，[αm，1]Sequentially marking sequence numbers of the m +1 subintervals, wherein j belongs to { 1., m +1 }; at each sampling time, the ith normalized fuzzy weighting function is selected and recorded as hi(v (t)) and determining the subinterval in which the subinterval is positioned and identifying a subinterval sequence number j;
on the basis, a new switching type fuzzy state observer is designed, and has possible switching modes in m + 1:
Figure FDA0002794259210000051
where j ∈ {1,.., m +1}, the gain matrix
Figure FDA0002794259210000052
And
Figure FDA0002794259210000053
belonging to the following forms:
Figure FDA0002794259210000054
Figure FDA0002794259210000055
wherein,
Figure FDA0002794259210000056
and
Figure FDA0002794259210000057
the observer gain matrix of the switching type fuzzy state observer, which is designed for the present invention off-line, and at the same time,
Figure FDA0002794259210000058
and
Figure FDA0002794259210000059
the specific value of (c) can be obtained by solving the following linear matrix inequalities (11) to (13) offline:
Figure FDA0002794259210000061
Figure FDA0002794259210000062
Figure FDA0002794259210000063
wherein:
Figure FDA0002794259210000064
Figure FDA0002794259210000071
Figure FDA0002794259210000072
more often:
Figure FDA0002794259210000073
Figure FDA0002794259210000074
Figure FDA0002794259210000075
Figure FDA0002794259210000076
Figure FDA0002794259210000081
Figure FDA0002794259210000082
Figure FDA0002794259210000083
Figure FDA0002794259210000084
Figure FDA0002794259210000085
Figure FDA0002794259210000086
6. the method for estimating the undetectable signal state of the nonlinear constant power load of the direct current microgrid according to claim 1, characterized in that: in the fifth step, in the first step,
at each sampling instant, first, the ith normalized fuzzy weighting function is recorded as hi(v (t)) and identifying the subinterval number j, and then, corresponding to the jth switching mode
Figure FDA0002794259210000087
And
Figure FDA0002794259210000088
and weighting all normalized fuzzy weighting functions of the fuzzy models at the current time and the previous time to obtain the gain of the observer
Figure FDA0002794259210000089
And
Figure FDA00027942592100000810
and substituting the formula (10) to carry out online state estimation on the undetectable signal of the nonlinear constant power load of the direct current micro-grid system.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114188934A (en) * 2022-01-14 2022-03-15 国网河北省电力有限公司经济技术研究院 Method and device for constructing disturbance stability analysis model of double-ring control direct current system

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114188934A (en) * 2022-01-14 2022-03-15 国网河北省电力有限公司经济技术研究院 Method and device for constructing disturbance stability analysis model of double-ring control direct current system
CN114188934B (en) * 2022-01-14 2023-10-13 国网河北省电力有限公司经济技术研究院 Double-loop control direct current system disturbance stability analysis model construction method and device

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