CN111953009A - Fault diagnosis method for island multi-inverter parallel sensor - Google Patents

Fault diagnosis method for island multi-inverter parallel sensor Download PDF

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CN111953009A
CN111953009A CN201910422420.1A CN201910422420A CN111953009A CN 111953009 A CN111953009 A CN 111953009A CN 201910422420 A CN201910422420 A CN 201910422420A CN 111953009 A CN111953009 A CN 111953009A
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fuzzy
fault
inverter parallel
observer
control
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游国栋
房成信
王雪
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Tianjin University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
    • 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
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y04S10/52—Outage or fault management, e.g. fault detection or location

Abstract

The invention researches a micro-grid island multi-inverter parallel system under the influence of sensor faults and establishes a T-S fuzzy model of the nonlinear multi-inverter parallel system. Next, a fuzzy proportional integral observer is designed to effectively estimate the fault. Meanwhile, a special fuzzy observer is adopted, and faults are detected and isolated through a residual error reconstruction mechanism. Then, the stability is proved through the established fuzzy Taylor series expansion and Lyapunov proof to verify the sufficient condition of the system stability. And finally, simulating in a Simulink environment to verify the effectiveness of the fault diagnosis method. The fault diagnosis method based on the isolated island multi-inverter parallel sensor is reasonable in design, stable control under the condition of uncertain parameter faults and actuator faults can be well achieved, good tracking performance and fault tolerance are shown, a new thought is provided for the design of a multi-inverter parallel sensor fault diagnosis system in an isolated island mode, and the fault diagnosis method has good engineering application prospects.

Description

Fault diagnosis method for island multi-inverter parallel sensor
Technical Field
The invention belongs to the technical field of intelligent power grids, and particularly relates to a fault diagnosis method for an island multi-inverter parallel sensor.
Background
The distributed micro-grid generally adopts a multi-inverter parallel connection mode to carry out MPP tracking on current control of an inverter system, so that the micro-grid is connected with a large power grid. And simultaneously, the voltage of the inverter system is controlled to realize isolated island operation. An effective control strategy is adopted, and the stability of the voltage of an inverter system is ensured, which is one of the key problems for realizing the stable operation of the island distributed micro-grid. The island distributed microgrid has more complex operation conditions, can suffer from interference in many aspects in the operation process, has device parameter interference from the island distributed microgrid and perturbation from an external sensor and the like, and thus the nonlinearity degree of a microgrid model is increased. Robust controllers designed by linearization techniques and other methods, specifically designed to handle nonlinear dynamics, have been widely used in the research of distributed power generation control systems. Nonlinearity and parameter uncertainty are the most important problems to be solved when designing a controller capable of ensuring system stability and ideal closed-loop performance, and a fuzzy control method as a typical nonlinear dynamics control technology provides an effective control scheme to deal with complex, uncertain and ambiguous factors of a control system.
For a distributed micro-grid in an island mode, a traditional PID voltage control strategy is adopted, and the robustness of control performance cannot be ensured. Teodorescus R employs a proportional-resonant (PR) controller, which, while achieving quiet-error-free tracking of the system sinusoidal signals, affects the disturbance rejection capability of the control model. An adaptive sliding mode voltage control strategy is studied by virtue of heroic intelligence, the control algorithm realizes the global robust performance of the voltage of an inverter system under the island operation, and the disturbance takes the load current disturbance and the filter parameter perturbation of the inverter system into consideration.
Observer design is a very important issue in many practical nonlinear control systems. Liuhuan and R.Saktive a research fuzzy observers of a T-S fuzzy control system respectively, and a Lyapunov method proves progressive convergence of control performance, but one of the defects is that parameter uncertainty in the T-S fuzzy control system is not considered, and robustness of a closed-loop system is influenced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a novel robust T-S fuzzy fault-tolerant control method by establishing a mathematical model of a nonlinear microgrid multi-inverter parallel system under the influence of a fault on the topology of the microgrid multi-inverter parallel system in an island mode. The method for diagnosing the fault of the island multi-inverter parallel sensor based on the T-S fuzzy fault-tolerant control is reasonable in design and has good steady-state and dynamic performances.
The technical problem of the fault diagnosis method for the island multi-inverter parallel sensor is solved by adopting the following technical scheme, and the fault diagnosis method comprises the following steps:
step 1, researching and analyzing a micro-grid island multi-inverter parallel system through a nonlinear WES control strategy with uncertain parameters, and establishing a T-S fuzzy model of the nonlinear multi-inverter parallel system by utilizing the advantages of simple structure and strong approximation capability of a fuzzy theory.
And 2, designing a fuzzy proportional integral observer according to the mathematical model in the step 1, meanwhile, adopting a special fuzzy observer to compensate a stable closed-loop system affected by the fault, and detecting and isolating the fault through a residual error reconstruction mechanism.
And 3, verifying sufficient conditions for system stability and proving stability by fuzzy Taylor series expansion and Lyapunov proof of fuzzy system fault analysis by utilizing a general distribution compensation structure according to the mathematical model, the fixed control distribution law, the fuzzy proportional-integral observer and the special fuzzy observer in the step 1.
And 4, simulating in a Simulink environment, and verifying the effectiveness of the fault diagnosis method based on the island multi-inverter parallel sensor based on the T-S fuzzy fault-tolerant control.
The T-S fuzzy mathematical model of the multi-inverter parallel sensor system in the island mode is as follows:
Figure BSA0000183401050000031
in the formula
Figure BSA0000183401050000032
Figure BSA0000183401050000033
σqAre respectively as
Figure BSA0000183401050000034
And σqAbbreviation of (Δ Φ), AiRepresents the system matrix under the ith fuzzy rule, BiDenotes the control matrix under the ith fuzzy rule, CiShowing the observation matrix under the ith fuzzy rule.
In order to effectively estimate the parameter uncertainty of a distributed micro-grid multi-inverter parallel island mode and the fault caused by the sensor fault, a fuzzy proportional integral observer is designed, a special fuzzy observer is adopted to compensate a stable closed-loop system affected by the fault, and the fault is detected and isolated through a residual error reconstruction mechanism.
The fuzzy proportional integral observer is designed as follows:
Rule Ri：If
Figure BSA0000183401050000035
is Mi1 and....and
Figure BSA0000183401050000036
is Mik
can obtain the product
Figure BSA0000183401050000037
In the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000038
-a state vector estimated by an unknown fuzzy observer; ki-observing an error matrix; y (t) -the output vector,
Figure BSA0000183401050000039
-the final output of the unknown fuzzy observer;
Figure BSA00001834010500000310
-the final estimation error; 1, 2, 3, p where p is a fuzzy rule number.
The fuzzy special observer is designed as follows:
Rule Ri：If
Figure BSA00001834010500000311
is Mi1 and....and
Figure BSA00001834010500000312
is Miψ
can obtain the product
Figure BSA00001834010500000313
In the formula (I), the compound is shown in the specification,
Figure BSA00001834010500000314
-estimating the state vector of the mobile terminal,
Figure BSA00001834010500000315
-final output, NiGain, i ═ 1., p.
The residual error reconstruction mechanism adopts a deterministic method. The sensor fault function uses fuzzy special observers, each observer is output by a single sensor, and a fuzzy proportional integral observer is adopted to estimate the fault. The failure is first detected and then the failed sensor is determined. The state variable is then the reconstruction of the output from the normal sensor and the closed loop control system enters a degraded mode, ensuring stability and satisfactory state. Setting upsilonobs1,., and is the residual signal of the 1 st to g-th observers, whose residual value is compared with a threshold value. Wherein the residual is
Figure BSA0000183401050000041
Then:
Figure BSA0000183401050000042
formula III, Yres(t) -y (t) and
Figure BSA0000183401050000043
the residual error between.
Combination formula
Figure BSA0000183401050000044
We can get the T-S fuzzy control distribution law as:
Figure BSA0000183401050000045
and (3) deriving an estimated dynamic error of the fuzzy control system and a closed loop system:
Figure BSA0000183401050000046
enhancing the dynamic performance of a closed-loop system:
Figure BSA0000183401050000047
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000048
Figure BSA0000183401050000051
the invention has the advantages and positive effects that:
1. the invention establishes a T-S fuzzy global mathematical model of a distributed micro-grid nonlinear multi-inverter parallel system in an island mode. A new robust T-S fuzzy fault-tolerant control method is provided by establishing a mathematical model of a nonlinear microgrid multi-inverter parallel system under the influence of a fault on the topology of the microgrid multi-inverter parallel system in an island mode. Firstly, in order to solve the problems of complex, uncertain and undefined factors of a control system, a multi-inverter parallel system state equation is combined with a T-S fuzzy theory to process a distributed microgrid multi-inverter parallel nonlinear system, and a T-S fuzzy global mathematical model of the distributed microgrid multi-inverter parallel system in an island mode is established; secondly, designing a T-S fuzzy proportional integral observer for effectively estimating parameter uncertainty and faults caused by sensor faults in a distributed micro-grid multi-inverter parallel island mode, and simultaneously adopting a T-S fuzzy special observer to compensate a stable closed-loop system influenced by the faults; and then, a T-S fuzzy fault-tolerant controller is designed by utilizing a T-S fuzzy control distribution law so as to directly process faults of the actuator and ensure the stability of a closed-loop system under the condition that a plurality of inverters in an island mode run in parallel and have faults.
2. According to the control method, when two parallel T-S fuzzy fault-tolerant controlled inverters run in parallel under rated parameters, the starting speed is high, grid-connected voltage and current are basically not distorted in the stable running of the system, the waveform is smooth sine wave and is slightly distorted, and almost no harmonic exists in the grid-connected voltage and current waveform.
3. According to the control method, when two inverters in parallel T-S fuzzy fault-tolerant control stably run, a system parameter RsWhen a fault occurs suddenly, the change of the grid-connected voltage and the current of the system is extremely small, the system is transited to a corresponding stable state in an extremely short time, and the waveform is basically undistorted in the transition process, which shows that the grid-connected voltage and the current of the system are stable, the curve change is smooth, the distortion is small, and the influence of the fault is basically avoided under the influence of the fault with uncertain parameters of the inverter. The control method can track the given value with the precision very close to the ideal value and can well ensure the safety of the stable operation of the system.
4. According to the control method, when two inverters in parallel T-S fuzzy fault-tolerant control operate stably, voltage U is input at the direct current side of the invertersinWhen fault interference occurs, although output voltage and current fluctuate, the grid-connected voltage and current of the inverter change very little, the inverter is not affected by the fault of the input voltage basically, steady-state errors are very small, the inverter is transited to the tracking of a corresponding stable state in a very short time, distortion is not generated basically in the transition process, and the interference can be eliminated in one period. The inverter is shown to be influenced by parameter uncertainty, the output voltage and current starting speed is high by adopting the control strategy, and the waveform is basically undistorted. In general, the control method can better realize stable control under system faults, and shows good tracking performance, disturbance resistance performance and fault tolerance capability.
Drawings
FIG. 1 is a schematic diagram of distributed microgrid multi-inverter parallel operation;
FIG. 2 is the actual and estimated values of grid-connected voltage, current without fault;
FIG. 3 is a double failure (R)gFault sum UinFault) grid-connected current and voltage simulation waveforms of the inverter system;
FIG. 4 is RgGrid-connected voltage and current experimental waveforms during variation;
FIG. 5 is UinAnd when the grid-connected voltage and current experimental waveforms change, the voltage and current experimental waveforms change.
Detailed Description
The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:
a fault diagnosis method of an island multi-inverter parallel sensor based on T-S fuzzy fault-tolerant control is realized on a distributed micro-grid multi-inverter parallel operation schematic diagram shown in figure 1. The invention provides a fuzzy fault-tolerant control distribution method based on T-S by establishing a mathematical model of a multi-inverter parallel system under an island operation mode under the conditions of uncertain faults and faults. Firstly, in order to solve the problems of complex, uncertain and undefined factors of a control system, a multi-inverter parallel system state equation is combined with a T-S fuzzy theory to process a distributed microgrid multi-inverter parallel nonlinear system, and a T-S fuzzy global mathematical model of the distributed microgrid multi-inverter parallel system in an island mode is established; secondly, designing a T-S fuzzy proportional integral observer for effectively estimating parameter uncertainty and faults caused by sensor faults in a distributed micro-grid multi-inverter parallel island mode, and simultaneously adopting a T-S fuzzy special observer to compensate a stable closed-loop system influenced by the faults; and then, a T-S fuzzy fault-tolerant controller is designed by utilizing a T-S fuzzy control distribution law so as to directly process faults of the actuator and ensure the stability of a closed-loop system under the condition that a plurality of inverters in an island mode run in parallel and have faults.
The control method comprises the following steps:
step 1: considering that a plurality of interferences usually exist in the working state of an island multi-inverter parallel sensor system, a micro-grid island multi-inverter parallel system under the influence of sensor faults is researched and analyzed through a nonlinear WES control strategy with uncertain parameters, and a T-S fuzzy model of the nonlinear multi-inverter parallel system is established by utilizing the advantages of simple structure and strong approximation capability of a fuzzy theory and the characteristics of convenience in establishing a global T-S fuzzy model of the system and capability of processing the nonlinear system.
In the figure 1, when the distributed micro-grid multi-inverter parallel system runs in an island mode, each DC/AC inverter control model has the same structure, and the designed variables and LC filter parameters of the controller are all from the measured values of the corresponding inverters. According to kirchhoff's law, the mathematical model of an LC-type single inverter can be expressed as:
Figure BSA0000183401050000071
each DC/AC inverter control model has the same structure, with subscript "1" omitted, and defines state variables
Figure BSA0000183401050000072
Input vector u (t) uinThat is, the inverter output voltage reference value, y (t) is the output vector, the state equation of the multi-inverter parallel system is:
Figure BSA0000183401050000081
wherein A is a system matrix, B is a control matrix, C is an observation matrix, and
Figure BSA0000183401050000082
C＝[1 0 0]，
Figure BSA0000183401050000083
the T-S fuzzy control is a powerful tool for processing nonlinear system stability analysis and controller synthesis, and has unique superiority in solving the problems of complex, uncertain and undefined factors of a control system. And (3) processing the distributed micro-grid multi-inverter parallel nonlinear system by combining a T-S fuzzy theory to obtain a linear model of a formula (2) as follows:
Rule Ri：If x1 is Mi1 and....and xn is Min
Figure BSA0000183401050000084
in the formula, Ri-the ith fuzzy rule; mig-fuzzy set, g ═ 1, 2t，ψt3; i 1, 2, p, where p is a fuzzy rule number; a. theix(t)+Biu (t) -a subsystem of a linear system.
Set fuzzy weight as
Figure BSA0000183401050000085
And:
Figure BSA0000183401050000086
wherein (((x) (t)), (1(x1(t))，2(x2(t))，3(xp(t))，1(x1(t))，2(x2(t))，3(xp(t)) — measurable variables and not affected by faults;
Figure BSA0000183401050000087
Mig(g(x(t)))——Miging(x (t)) degree of membership. At the same time, satisfy
Figure BSA0000183401050000088
And
Figure BSA0000183401050000089
adding the fuzzy weight (4) into each submodel of the formula (3) to obtain a T-S fuzzy global model of the distributed micro-grid multi-inverter parallel system in the island mode:
Figure BSA0000183401050000091
considering uncertainty time-varying parameters and sensor fault dynamic characteristics, obtaining a dynamic model under an island mode as follows:
Figure BSA0000183401050000092
in the formula,. DELTA.Ai-uncertainty time-varying parameter fault matrix, Di-the matrix of known sensor failures is,
Figure BSA0000183401050000093
a sensor failure signal with a norm bounded, | d (t) | < α, α > 0,
Figure BSA0000183401050000094
and
Figure BSA0000183401050000095
respectively, current and voltage sensor faults.
Assume that 1: diIs a full rank matrix and satisfies [ Cix(t)+Did(t)]＝Ci(I + D) x (t), diagonal weighting matrix D (t) diag { k ═ k1(t)，k2(t)，k3(t) } is the residual performance matrix for sensor failure, and 0 < ki(t) < 1(i ═ 1, 2, 3), when ki(t) equals 1, 0, respectively, the ith sensor is in a failed and non-failed state.
The further simplification processing of formula (6) is as follows:
Figure BSA0000183401050000101
assume 2:
Figure BSA0000183401050000102
and the norm is bounded.
For Δ Φ, consider the T-S fuzzy rule:
Rule q：If Δφ11 is
Figure BSA0000183401050000103
and....andΔφnn is
Figure BSA0000183401050000104
Figure BSA0000183401050000105
thus, the correction of Δ Φ includes:
Figure BSA0000183401050000106
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000107
Figure BSA0000183401050000108
number of fuzzy rules, S2bAnd b is the number of uncertain elements in the delta phi.
In conclusion, the T-S fuzzy global model of the distributed micro-grid multi-inverter parallel system in the island mode is finally determined as follows:
Figure BSA0000183401050000109
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000111
Figure BSA0000183401050000112
σqare respectively as
Figure BSA0000183401050000117
And σqAbbreviation of (. DELTA.phi.).
Step two: according to the mathematical model in the step 1, in order to effectively estimate the parameter uncertainty of the distributed micro-grid multi-inverter parallel island mode and the fault caused by the sensor fault, a fuzzy proportional integral observer is designed. Meanwhile, a fuzzy special observer is adopted to compensate a stable closed-loop system affected by the fault, and the fault is detected and isolated through a residual error reconstruction mechanism.
Assume that 3: (A)i Ci) Is completely observable and controllable (A)i Bi Ci) Is the minimum phase. There is a gain matrix LiAnd NiAnd satisfies equation A0i＝Ai-LiCi，A1i＝Ai-NiCi。
Assume 4: presence of orthogonal matrix T0Satisfies the equation T by reversible transformation0Ci＝[C1i C2i]T，T0D＝[D1 0]TAnd D is1Is a non-singular matrix.
Further processing of equation (9) results in two equations for sensor failure:
Figure BSA0000183401050000113
where the first equation contains sensor faults and the second equation does not.
In order to effectively estimate the parameter uncertainty of a distributed micro-grid multi-inverter parallel island mode and the fault caused by the sensor fault, a fuzzy proportional integral observer is designed, a special fuzzy observer is adopted to compensate a stable closed-loop system affected by the fault, and the fault is detected and isolated through a residual error reconstruction mechanism.
The fuzzy proportional integral observer is designed as follows:
Rule Ri：If
Figure BSA0000183401050000114
is Mi1 and....and
Figure BSA0000183401050000115
is Mik
Figure BSA0000183401050000116
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000121
-a state vector estimated by an unknown fuzzy observer; ki-observing an error matrix; y (t) -the output vector,
Figure BSA0000183401050000122
-the final output of the unknown fuzzy observer;
Figure BSA0000183401050000123
-the final estimation error; 1, 2, 3, p where p is a fuzzy rule number.
The deblurring output is:
Figure BSA0000183401050000124
the fuzzy special observer is designed as follows:
Rule Ri：If
Figure BSA0000183401050000125
is Mi1 and....and
Figure BSA0000183401050000126
is Miψ
Figure BSA0000183401050000127
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000128
-estimating the state vector of the mobile terminal,
Figure BSA0000183401050000129
-final output, Ni-gain, i ═ 1., p.
The deblurring output is:
Figure BSA00001834010500001210
the residual error reconstruction mechanism adopts a deterministic method. The sensor fault function uses fuzzy special observers, each observer is output by a single sensor, and a fuzzy proportional integral observer is adopted to estimate the fault. The failure is first detected and then the failed sensor is determined. The state variable is then the reconstruction of the output from the normal sensor and the closed loop control system enters a degraded mode, ensuring stability and satisfactory state. Setting upsilonobs1,., and is the residual signal of the 1 st to g-th observers, whose residual value is compared with a threshold value. Wherein the residual is
Figure BSA00001834010500001211
Then:
Figure BSA0000183401050000131
formula III, Yres(t) -y (t) and
Figure BSA0000183401050000132
the residual error between.
And (3) combining the formula (7) to obtain a T-S fuzzy control distribution law as follows:
Rulej：If g1(t)is N1j and....and gk(t)is Nsj
Figure BSA0000183401050000133
in the formula (I), the compound is shown in the specification,j-the jth regular feedback gain vector, c-the number of rules, ω (t) as a reference input.
The control distribution law may then be expressed as:
Figure BSA0000183401050000134
the 1 st rule controlling the distribution law is defined as follows:
Rule l：If Δφ11 is
Figure BSA0000183401050000135
and....andΔφnn is
Figure BSA0000183401050000136
Figure BSA0000183401050000137
the control distribution law of the T-S fuzzy fault-tolerant controller can be deduced as follows:
Figure BSA0000183401050000138
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000139
and (3) deriving an estimated dynamic error of the fuzzy control system and a closed loop system:
Figure BSA0000183401050000141
in summary, the following are provided:
Figure BSA0000183401050000142
then the estimated dynamic error is output
Figure BSA0000183401050000143
Comprises the following steps:
Figure BSA0000183401050000144
the dynamic performance of the closed loop system can be further obtained as follows:
Figure BSA0000183401050000145
in the same way, the following can be obtained:
Figure BSA0000183401050000146
the dynamic performance of the closed loop system is enhanced by the formulas (23) and (24):
Figure BSA0000183401050000147
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000151
Figure BSA0000183401050000152
step three: according to the mathematical model, the fixed control distribution law, the fuzzy proportional integral observer and the special fuzzy observer in the step 1, a general distribution compensation structure is utilized, and the sufficient condition of system stability is verified through fuzzy Taylor series expansion and Lyapunov proof of fuzzy system fault analysis, so that the stability is proved.
Theorem 1 alpha T psiijqT-1]≤-||TΔψijqT-1||maxIf λ holds, then equation (25) gives that the fuzzy closed-loop control system, which is affected by parameter uncertainties and sensor failures, is stable. λ is a norm-bounded positive number.
And (3) proving that: normalizing both sides of equation (25) includes:
Figure BSA0000183401050000153
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000154
γmax(.) is the largest eigenvalue, which is the conjugate transpose.
Let eta T psiijqT-1]Satisfies alpha [ TyijqT-1]≤-||TyijqT-1||max- λ. Further, the method can further obtain the product,
Figure BSA0000183401050000155
in the formula, t > t0。
Assuming that t → ∞, when ω (t) ═ 0, | | | x (t) | → 0. Otherwise, when ω (t) ≠ 0, there is:
Figure BSA0000183401050000161
in the formula (I), the compound is shown in the specification,
Figure BSA0000183401050000162
if ω (t) is bounded, the right side of equation (28) is also bounded, and the system is bounded, the system is stable.
Theorem 2 gains of the controller and observer are set to
Figure BSA0000183401050000163
And
Figure BSA0000183401050000164
and four parameters Xi，Mφ11，YjAnd OiSatisfy the requirement of
Figure BSA0000183401050000165
The fuzzy closed loop control system of the system (25) is stable.
And (3) proving that: consider the quadratic Lyapunov helper function:
V(t)＝X(t)TPX(t) (30)
setting P as a positive definite matrix, there are:
Figure BSA0000183401050000166
matrix P, psiijq、
Figure BSA0000183401050000167
S and E can be set as:
Figure BSA0000183401050000168
Figure BSA0000183401050000169
Figure BSA00001834010500001610
a further inequality (31) can be written as:
Figure BSA0000183401050000171
suppose P1＝diag(Pφ11，Pφ22) And is multiplied by formula (32) to the left) Right ride
Figure BSA0000183401050000172
And use of Yi＝Mφ11 i，Oi＝Pφ22NiAnd
Figure BSA0000183401050000173
comprises the following steps:
Figure BSA0000183401050000174
when equation (33) is converted to equation, theorem 2 holds, and the system is stable.
Step four: and (3) carrying out simulation in a Simulink environment, and verifying the effectiveness of the fault diagnosis method based on the isolated island multi-inverter parallel sensor based on the T-S fuzzy fault-tolerant control.
In order to verify the rationality of a sensor fault control strategy of an island multi-inverter parallel system, a thesis establishes a simulation experiment platform by utilizing PSIM according to FIG. 1 to perform a simulation experiment. The system is subjected to linearization processing, and simulation parameters are set as follows: input direct voltage Uin350V, and outputting the network side alternating current power frequency voltage ugThe peak value is 220V, the system carrier frequency and the calculation frequency are respectively set to be 15kHz and 30kHz, and the filter parameter Lf、LgSet to 0.57mH and 1.49mH, R respectivelyf、RgAnd ZLRespectively set to 0.06 omega, 0.20 omega, 0.14 omega, CfThe temperature was set to 4.7. mu.F.
Simulation verification
When the two inverters run in parallel under rated parameters, PID type, conventional SMC and T-S fuzzy fault-tolerant control are respectively implemented, and a comparison graph of estimated values and actual values of grid-connected current and voltage is shown in figure 2. As can be seen from fig. 2, under the condition of no fault, the grid-connected current and voltage tracking effects of the 3 control modes are basically similar, no large distortion occurs in the tracking process, and the waveform is relatively smooth. However, the tracking speed of the method 3 is faster than that of the first two methods, and the control characteristics are more excellent than those of the first two methods, so that the expected control effect can be achieved.
Fig. 3 shows grid-connected current and voltage waveforms of two faults occurring when two inverters operate in parallel in an island mode. As shown in the figure, R is 0.02S for 3 control modes (PID type, conventional SMC and T-S fuzzy fault-tolerant control)gSuddenly increased to 1.00. omega. at 0.10s, UinIncreasing to 380V. In two faults, the current is changed slightly by about 4.50A under the PID control, and then the stable operation is recovered at 0.054s and 0.134s respectively. The current fluctuates a little by about 4.30A under the conventional SMC control, and then returns to the steady operation state at 0.052s, 0.132s, respectively. The current also changes slightly (3.50A) under the T-S fuzzy fault-tolerant control, and the stable operation state can be achieved in one period. Grid-connected voltage changes in two faults, voltage is oscillated by about 11V under PID control, and stable operation is recovered after 0.054s and 0.134 s. The voltage fluctuates by about 10.5V under the conventional SMC control, and returns to the steady operation state after 0.052s and 0.132 s. The voltage is also changed (to be 7V) under the T-S fuzzy fault-tolerant control, and the voltage returns to the stable operation state again in one period. It can be seen from the current and voltage variation waveforms that when the system fails, the former two control modes are slow in response, slow in the steady state recovery process, and large in distortion value of current and voltage. By adopting the T-S fuzzy fault-tolerant control strategy provided by the invention, the current and voltage change amplitudes are very small, the stable operation state is achieved within a very short time, and no distortion occurs in the transition process. Further, it can be seen that: the T-S fuzzy fault-tolerant control has good tracking response performance and fault-tolerant capability, and can well realize fault diagnosis and stable control of the sensor of the island multi-inverter parallel system.
The control strategy presented herein was further investigated in comparative experiments under simulated parameters. FIG. 4 shows the parameter R of the parallel system of two invertersgGrid-connected voltage and current waveforms when a fault occurs. As can be seen from the figure, the system has two faults at 0.2s and 0.6s, the first fault is to use the parameter RgSuddenly adjusted to 0.80 omega and the second failure was to suddenly restore it to the nominal value. Shown in the figure, twiceIn the fault, the PID control and the conventional SMC control grid-connected voltage have large amplitude (27V and 23V respectively), the current has large fluctuation (17A and 15A respectively), the current and the voltage are restored to a stable operation state after one period, and the waveform distortion occurs in the transition process. The third graph in fig. 4 shows that the voltage and the current also have small changes, but the changes are small (10V and 7A, respectively), and the voltage and the current also recover to a stable operation state after one period, the waveform distortion does not occur in the transition process, the frequency of the voltage and the current is 50Hz after the voltage and the current reach the stable state, the waveform is not distorted, and the voltage amplitude basically stabilizes at about 220V. When the parallel operation system of the two inverters adopts T-S fuzzy fault-tolerant control, under the condition of a fault with uncertain parameters, grid-connected voltage and current curves are smoothly changed, the distortion is small, and the parallel operation system is basically not influenced by the fault. The control strategy provided by the invention proves that the given value can be tracked with the precision very close to the ideal value, and the safety of stable operation of the system can be well ensured.
In the stable parallel operation of the two inverters, two virtual faults (the first input voltage U) are added at 0.2s and 0.6s respectivelyinThe voltage is changed from 350V to 380V, and the voltage is restored to 350V again for the second time), and the grid-connected voltage and current waveforms are as shown in fig. 5. As can be seen from the figure, in the first two control modes (PID-type control and conventional SMC control), the fluctuation of the grid-connected voltage is large (50V and 47V, respectively), the current also has large vibration (47V and 45A, respectively), and the waveform has distortion, which indicates that the steady-state error is large in the two control modes. The third graph in fig. 5 shows that, under T-S fuzzy fault-tolerant control, the inverter grid-connected voltage and current are not affected by the input voltage fault basically, the grid-connected voltage THD is about 1.32%, the steady-state error is small, and the tracking of the steady state is realized in a very short time, and no distortion occurs in the tracking process, thereby verifying that the control method provided herein has strong disturbance-resistant performance to the inverter input voltage.
The thesis utilizes a nonlinear WES control strategy with uncertain parameters to research and analyze an island operation microgrid multi-inverter parallel system under the influence of sensor faults, and provides a novel robust T-S fuzzy fault-tolerant control strategy. A nonlinear model of the multi-inverter parallel system is constructed through a T-S fuzzy theory. A state observer based on a T-S model is designed by using the concept of distributed compensation, and fault information existing in a multi-inverter parallel system is effectively estimated. For a multi-inverter parallel system influenced by sensor faults and other uncertain parameters, a T-S fuzzy control theory and a control distribution law are combined, a T-S fault-tolerant fuzzy controller based on a fixed control distribution scheme is designed, and sufficient conditions for keeping the system stable are deduced by combining Lyapunov and Taylor series.

Claims (5)

1. An island multi-inverter parallel sensor fault diagnosis method is characterized by comprising the following steps:
step 1, researching and analyzing a micro-grid island multi-inverter parallel system through a nonlinear WES control strategy with uncertain parameters, and establishing a T-S fuzzy model of the nonlinear multi-inverter parallel system by utilizing the advantages of simple structure and strong approximation capability of a fuzzy theory.
And 2, designing a fuzzy proportional integral observer according to the mathematical model in the step 1, meanwhile, adopting a special fuzzy observer to compensate a stable closed-loop system affected by the fault, and detecting and isolating the fault through a residual error reconstruction mechanism.
And 3, verifying sufficient conditions for system stability and proving stability by fuzzy Taylor series expansion and Lyapunov proof of fuzzy system fault analysis by utilizing a general distribution compensation structure according to the mathematical model, the fixed control distribution law, the fuzzy proportional-integral observer and the special fuzzy observer in the step 1.
And 4, simulating in a Simulink environment, and verifying the effectiveness of the fault diagnosis method based on the island multi-inverter parallel sensor based on the T-S fuzzy fault-tolerant control.
2. The island multi-inverter parallel sensor fault diagnosis method according to claim 1, wherein the T-S fuzzy mathematical model in an island mode is as follows:
Figure FSA0000183401040000011
in the formula of Chinese
Figure FSA0000183401040000012
σqAre respectively as
Figure FSA0000183401040000013
And σqAbbreviation of (Δ Φ), AiRepresents the system matrix under the ith fuzzy rule, BiDenotes the control matrix under the ith fuzzy rule, CiShowing the observation matrix under the ith fuzzy rule.
3. An island multi-inverter parallel sensor fault diagnosis method according to claim 1, characterized in that:
the fuzzy proportional integral observer is designed as follows:
Figure FSA0000183401040000021
in the formula (I), the compound is shown in the specification,
Figure FSA0000183401040000022
-a state vector estimated by an unknown fuzzy observer; ki-observing an error matrix; y (t) -the output vector,
Figure FSA0000183401040000023
-the final output of the unknown fuzzy observer;
Figure FSA0000183401040000024
-the final estimation error; 1, 2, 3, p where p is a fuzzy rule number.
The fuzzy special observer is designed as follows:
Figure FSA0000183401040000025
in the formula (I), the compound is shown in the specification,
Figure FSA0000183401040000026
-estimating the state vector of the mobile terminal,
Figure FSA0000183401040000027
-final output, NiGain, i ═ 1., p.
4. An island multi-inverter parallel sensor fault diagnosis method according to claim 1, characterized in that:
and (3) deriving an estimated dynamic error of the fuzzy control system and a closed loop system:
Figure FSA0000183401040000028
enhancing the dynamic performance of a closed-loop system:
Figure FSA0000183401040000029
5. an island multi-inverter parallel sensor fault diagnosis method according to claim 1, characterized in that:
further obtaining the dynamic performance of the closed loop system is as follows:
Figure FSA0000183401040000031
further enhanced closed loop system dynamic performance is obtained:
Figure FSA0000183401040000032
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