CN116581764A - Dynamic stability control method for controllable load optimal interaction process - Google Patents
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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
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
- H02J3/14—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by switching loads on to, or off from, network, e.g. progressively balanced loading
- H02J3/144—Demand-response operation of the power transmission or distribution network
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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
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- 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
- H02J2310/00—The network for supplying or distributing electric power characterised by its spatial reach or by the load
- H02J2310/50—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads
- H02J2310/56—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads characterised by the condition upon which the selective controlling is based
- H02J2310/58—The condition being electrical
- H02J2310/60—Limiting power consumption in the network or in one section of the network, e.g. load shedding or peak shaving
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- 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
- Y04S20/00—Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
- Y04S20/20—End-user application control systems
- Y04S20/222—Demand response systems, e.g. load shedding, peak shaving
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Abstract
The invention relates to a dynamic stability control method used in the optimal interaction process of controllable load, which comprises the following steps: establishing a dynamic stability control model in the optimal interaction process of the controllable load; establishing load regulation constraints of input voltage safety; formulating the output voltage of the stability control unit under different load regulation and control requirements in the load optimization interaction process; and designing a self-adaptive dynamic surface regulation strategy of a load stability control unit taking a load regulation target as a desired curve, so that the load change of the power system is quickly and stably controlled. The invention has the advantages that: the control strategy can be adaptively adjusted according to the change of the load state, so that the control system can be better adapted to different load working states, quickly respond to the change of the load state, control in real time and further guarantee the instantaneity and stability of the control system.
Description
Technical Field
The invention relates to the field of power load control, in particular to a dynamic stability control method used in an optimal interaction process of controllable loads.
Background
With the increase of power demand, the load of the power system is also larger and larger, so that the stability and the reliability of the power system face a great challenge, and how to maximize the utilization of the controllable load on the premise of ensuring the optimal interaction of power supply and demand becomes a new hot spot of current power research. The dynamic stability control method is to monitor and control the power system in real time and adjust the parameters of the power system in time according to the requirements so as to ensure the stability of the power system. The stability control of the power system can be realized through the control of the controllable load, so that the controllable load is utilized to the maximum extent, and the economy and the reliability of the power system are improved. However, load control of the power system is not only affected by factors such as climate, economy and power market, but also is difficult to control due to inaccuracy of load prediction and non-ideal response effect, so that realizing efficient dynamic stable load control is always a problem to be solved in the field of power systems.
The purpose of the load control is to achieve the effect of balancing the supply and demand relation of the power system by controlling the parameters of the load, such as current, voltage, frequency and the like. In an electric power system, a Buck circuit is commonly used to change a load voltage to control the magnitude of a load, and the Buck circuit is called a stability control unit. The stabilizing unit is a step-down DC/DC converter which can convert high voltage input into low voltage output. The brightness of the electric lamp in the load can be reduced by controlling the voltage, the charging efficiency and stability of the electrochemical energy storage in the transferable load can be improved, or the motor rotating speed in the production process can be changed to realize the dispatching of the electric load.
However, in the process of controlling an electric load by using the stability control unit, a problem of limited state is always encountered, that is, a limited range of variation of load voltage exists on the load side due to the operation condition limitation of an electric appliance or a sensor, and the limited range is rarely considered in the design of a traditional load control method. It is very difficult to ensure both a fast response and stability of the load control and that the load voltage is in a limited range all the time during the control process. Therefore, considering how to improve the control performance of the power load by using a high-efficiency control strategy, the capability of stabilizing the output load side voltage against the input voltage of the non-minimum phase system is improved, and the core problem of the research of the load control strategy has been already developed.
Disclosure of Invention
The invention aims to provide a dynamic stability control method for a controllable load optimal interaction process, which is used for designing a Lyapunov function, and processing a load regulation constraint problem considering input voltage safety and a time delay problem in a regulation system by using a fuzzy logic system and a finite coverage theory method.
In order to achieve the above purpose, the present invention is realized by the following technical scheme:
a dynamic stability control method for a controllable load optimal interaction process comprises the following steps:
step S1, establishing a dynamic stability control model in the optimal interaction process of controllable load;
s2, establishing load regulation and control constraint of input voltage safety;
step S3, formulating the output voltage of the stability control unit under different load regulation and control requirements in the load optimization interaction process;
and S4, designing a self-adaptive dynamic surface regulation strategy of a load stabilizing unit taking a load regulation target as a desired curve, so that the load change of the power system is quickly and stably controlled.
In step S1, the state space equation of the dynamic stability control model in the controllable load optimal interaction process, formula (1) is as follows:
in the formula (1), u B Representing load side voltage, unit V; i.e L Representing inductor current, unit a; u (U) DC The direct current busbar voltage of the direct current micro-grid is represented by a unit V; l is the load side inductance, unit mH; c (C) B The unit mF is a load side filter capacitor; r is the internal resistance of the battery, the unit omega is not lost, the influence of external disturbance on the formula (1) is considered, all coefficients in the formula (1) are assumed to be unknown, the formula (1) is rewritten into a state space expression shown in the formula (2) in a mathematical transformation mode, and the state space expression is used as a mathematical model of a controlled object, and the mathematical model is as follows:
in the formula (2), x 1 Representing load side voltage u B Units (V); x is x 2 Representing the inductor current i L Unit (a); parameters (parameters)τ 1 Representing unknown time delay constants generated in the measuring and transmitting processes of the sensor; delta i (x 1 ,x 1 (t-τ 1 ) I=1, 2, representing an unknown smoothness and with a time delay with respect to the load side voltage u B Is a nonlinear function of (2); d, d i I=1, 2, representing an external disturbance input signal; u represents the duty ratio of the MOS tube, namely the control input signal of the stability control unit; y epsilon R represents the output of the stability control unit;
the control objective of dynamic stabilization is to keep the output y of the stabilization unit stably tracking a given desired signal y r ；
For the mathematical model of the controlled object represented by formula (2), the following assumptions are made:
suppose 1: g i Not equal to 0, i=1, 2, representing an unknown constant, and there is a positive number g min And g max So that it satisfies the relationship: 0 < g min ≤|g i |≤g max ；
Suppose 2: desired tracking y r Is a smooth and bounded function;belongs to a tight set and satisfiesAnd->Where i represents the ith derivative of the desired tracking, A 0 、A 1 、A 2 、/>All are positive numbers;
suppose 3: τ 1 Represents an unknown positive number and satisfies the relationship: τ is 0 or less 1 ≤τ M Wherein τ M Denoted τ 1 Is the maximum value of (2);
suppose 4: unknown external disturbance input signal d i I=1, 2, satisfies the relationship:
in order to solve the load regulation constraint of the input voltage safety in the step S2, a primer 1 to a primer 4 are introduced as theoretical basis for the design and stability analysis of a control algorithm, and the specific contents are as follows:
lemma 1: for any positive constantDefinitions->i=1..n, where z i Represents the ith state variable, and +.>Is an open set;
there is a variable η= [ ω, z i ] T E o, function h R + ×o→R l+i Is piecewise continuous with respect to time t, and is at R + The ×o is stable with respect to η local Li Puxi z; first derivative of variable η with respect to time tEquation (3) is shown below:
assuming that there is a continuously differentiable positive function U: R l →R + And V is j :H→R + In their respective fields, formula (4) is as follows:
in the formula (4), ρ 1 And ρ 2 For K ∞ Class function, V j (z j ) Representing the state variable z j Is represented by a continuous slightly positive function with respect to the variable ω, letWherein V (η) represents the Lyapunov function with respect to the variable η, z i (0) Belonging to set H, if the inequality is expressed as:
and satisfies eta e o, constant c > 0, v > 0, then z i (t) remain in the open set H, < >>In (a) and (b);
and (4) lemma 2: for any arbitraryEquation (5) holds:
in the formula (5) of the present invention,representing design parameters, S 0 Represents an arbitrary variable;
online approximation of unknown smooth functions in mathematical models of controlled objects using fuzzy logic systemsWherein (1)>Representing a given tight set;
first, the Fuzzy Logic System (FLS) is a set of modesThe "if-then" rule of the paste will input vector U i ∈R m Mapping to scalar output Y i E R, equation (6) is as follows:
in the formula (6) of the present invention,and->(l=1,) N, k=1, & gt, m, i=1, & gt, N) are fuzzy sets described by fuzzy membership functions, respectively +.>And->Nv1 is ζ i ＝[ξ i,1 ,ξ i,2 ,…ξ i,m ] T ∈U i Is the number of fuzzy rules; zeta type toy i And Y i ∈V i Respectively input and output of a Fuzzy Logic System (FLS), considering an 'if-then' fuzzy rule in a formula (6), the Fuzzy Logic System (FLS) has the characteristics of single instance fuzzification, a product inference engine and a central average defuzzifier, and a formula (7) is as follows:
in the formula (7) of the present invention,
is an ideal weight vector, +.>Is a fuzzy basis function vector; />
And (3) lemma 3: for any given set of incumbentsIn a real continuous function f i :R n R, any real number is presentSo that equation (7) satisfies the form described by equation (8), as follows:
let epsilon i (ξ i ) To approximate the error, delta i (ξ i ) Described as shown in equation (9):
in equation (9), the approximation error An upper bound value representing an estimation error of the fuzzy logic system; />Is theta i Defining equation (10) as follows:
when the nonlinear function has an unknown time delay constant tau i When, for example, delta i (ζ i ,ζ i (t-τ i ) Direct estimation by a fuzzy logic system is not possible; however, due to the tight setIs to be added to the unknown function by means of a fuzzy logic system combined with finite coverage arguments>Performing approximation;
and 4, lemma: let us assume the input vector xi i ＝(ξ i ,ξ i (t-τ i ) In line with time t, where τ i ∈[0,τ M ]Is an unknown time delay constant and then, for any given errorThere is a finite interval [0, τ ] independent of time t M ]Equation (11) is shown below:
0＜t 1 ＜…＜t m ＜τ M (11)
from one of the time points, equation (12) is satisfied as follows:
equation (13) is available as follows:
assume that: τ 1 Represents an unknown positive number and satisfies the relationship: τ is 0 or less 1 ≤τ M Wherein τ M Denoted τ 1 Is the maximum value of (2); in combination with the lemma 3, there are a plurality of time points τ 1/1 ,...,τ n/n ∈{t 1 ,...,t m An unknown smooth function with time delay, equation (14) is shown below:
in the formula (14) of the present invention,representing the estimation error of the finite coverage lemma, therefore, in combination with the expression of the fuzzy logic system approximation unknown function, equation (14) is approximated as shown in equation (15):
in formula (15), δ i Upper bound value representing fuzzy logic system estimation errorEstimation error with limited coverage lemma +.>And inputs a vector, equation (16) is as follows:
ξ i ＝(x 1 ,...,x i ,...,x 1 (t-t 1 ),...,x k (t-τ k/k ),...,x i (t-t m )) (16)。
in step S4, the adaptive dynamic surface regulation strategy includes the following steps:
step S41, defining a first dynamic surface error S 1 Equation (17) is shown below:
S 1 ＝x 1 -y r (17)
y in formula (17) r Is the desired tracking, consider equation (2),represent S 1 With respect to the derivative of time, equation (18) is as follows:
design obstacle Lyapunov candidate function V 1 Equation (19) is shown below:
in the formula (19), log (χ) represents the natural logarithm of χ, V 1 In a compact collectionIs continuous in thatDesign parameters->
The first derivative of equation (19) with respect to time is equation (20), as follows:
according to the assumption: unknown external disturbance input signal d i I=1, 2, satisfies the relationship:equation (21) is obtained using the young's inequality as follows:
therefore, in connection with the formula (21), the formula (20) is rewritten as the formula (22), as follows:
in order to process the nonlinear function with unknown time delay in equation (22), using a Fuzzy Logic System (FLS) as an estimator, equation (22) is rewritten as equation (23), as follows:
in equation (23), the vector is inputAnd has the formula (24) as follows:
further, according to the assumption: g i Not equal to 0, i=1, 2, representing an unknown constant, and there is a positive number g min And g max So that it satisfies the relationship: 0 < g min ≤|g i |≤g max The method comprises the steps of carrying out a first treatment on the surface of the Equation (25) is derived using the young's inequality as follows:
in the formula (25), v 1 Representing design parameters, the values of which are positive numbers, thus V 1 Is rewritten as equation (26) as follows:
in equation (26), the constantx 2d Representing a virtual control law, wherein the virtual control law is as shown in formula (27):
in the formula (27), k 1 Representing a design parameter, the value of which is a positive number,is theta * Will give its weight update law in step S42; a first order low pass filter as shown in equation (28) will be introduced to calculate the derivative of the virtual control quantity as follows:
in formula (28), iota 2 Representing the time constant, the value being positive, thus obtaining a new filter output z 2 ；
Step S42, defining a second dynamic surface error formula (29), as follows:
S 2 ＝x 2 -z 2 (29)
S 2 the derivative formula (30) of (b) is as follows:
design obstacle Lyapunov candidate function V 2 Equation (31) is shown below:
in the formula (31), V 2 In a compact collectionThe upper part is continuous and the tightening set +.>Design parametersEstimation error->Wherein (1)>Is theta * Is a function of the estimated value of (2); gamma ray θ Is a design parameter, the value is a positive number; using a Fuzzy Logic System (FLS) as an estimator, equation (32) holds as follows;
in equation (32), the vector is inputUsing the Young's inequality to obtain V n The derivative formula (33) of (2) is as follows:
in the formula (33), the constantDesigning the control signal according to equation (33) results in equation (34) as follows:
self-adaptive lawDesign formula (35), as follows:
compared with the prior art, the invention has the beneficial effects that:
1. the control strategy can be adaptively adjusted according to the change of the load state, so that the control system can be better adapted to different load working states, quickly respond to the change of the load state, control in real time and further guarantee the instantaneity and stability of the control system;
2. the output voltage of the stabilizing and controlling unit under different load regulation and control requirements in the load optimization interaction process is formulated, and the load regulation and control dynamic stability control in the controllable load optimal interaction process can be realized by controlling the output voltage of the stabilizing and controlling unit;
3. calculating the derivative of a virtual control law by introducing a first-order low-pass filter, avoiding the generation of differential explosion phenomenon, taking a load regulation target as a desired curve, and realizing a given tracking performance index by constructing a proper barrier Lyapunov function on the basis of considering the safety of input voltage;
4. the fuzzy logic system is combined with the finite coverage primer, so that not only can the unknown smooth nonlinear function be estimated, but also the unknown time delay generated in the sensor measurement transmission process can be compensated, thereby reducing tracking error and improving control performance;
5. the stability analysis shows that the designed self-adaptive controller can ensure that all update laws and design parameters in a control system are semi-globally consistent and finally bounded by using a control law u (t) designed by the self-adaptive state constraint dynamic surface control method, and tracking errors of the system can be converged to an adjustable tight set by means of an initialization skill and meet the condition of load regulation and control state constraint in the system.
Drawings
Fig. 1 is a schematic diagram of a topology of a stability control unit.
FIG. 2 is a schematic diagram of experimental equipment and environment.
Fig. 3 is a schematic diagram of the experimental system.
Fig. 4 is a tracking performance schematic.
Fig. 5 is a schematic diagram of tracking error.
Detailed Description
The present invention will be described in detail below with reference to the drawings of the specification, but it should be noted that the practice of the present invention is not limited to the following embodiments.
The following examples are given by way of illustration of detailed embodiments and specific procedures based on the technical scheme of the present invention, but the scope of the present invention is not limited to the following examples. The methods used in the examples described below are conventional methods unless otherwise specified.
[ example 1 ]
In the optimal interaction process of the controllable load of the power system, the rapid dynamic stable control of the controllable load is realized, and the working principle is that the voltage change at the load side is rapidly stabilized when the electric load such as an electric lamp and electrochemical energy storage is regulated and controlled, and the dynamic stable control of the load is finally realized; the output voltage of the stability control unit under the load regulation and control requirement is formulated, further, the load regulation and control is realized by changing the form of the load input voltage, the rapid stability control during the change of the output voltage of the stability control unit is researched, and is shown in fig. 1-5, fig. 1 is a schematic diagram of the topology structure of the stability control unit, fig. 2-3 are schematic diagrams of a semi-physical simulation platform, the stability control unit shown in fig. 1 is built on the simulation platform, the self-adaptive dynamic surface regulation and control strategy is embedded into an experiment table, the validity of the proposed regulation and control strategy is verified, and the result is shown in fig. 4-5.
A dynamic stability control method for a controllable load optimal interaction process comprises the following steps:
step S1, establishing a dynamic stability control model in the optimal interaction process of the controllable load, wherein the content is as follows:
the state space equation of the dynamic stability control model in the controllable load optimal interaction process is shown in the following formula (1):
in the formula (1), u B The load side voltage is indicated as such,a unit V; i.e L Representing inductor current, unit a; u (U) DC The direct current busbar voltage of the direct current micro-grid is represented by a unit V; l is the load side inductance, unit mH; c (C) B The unit mF is a load side filter capacitor; r is the internal resistance of the battery, and is the unit omega; see FIG. 1, wherein V 1 ，V 2 The method comprises the steps of representing a diode, taking the influence of external disturbance on a formula (1) into consideration, and assuming that all coefficients in the formula (1) are unknown, and adopting a mathematical transformation mode to rewrite the formula (1) into a state space expression shown in a formula (2) as a mathematical model of a controlled object, wherein the diode is used for unidirectional conduction:
in the formula (2), x 1 Representing load side voltage u B Units (V); x is x 2 Representing the inductor current i L Unit (a); parameters (parameters)τ 1 Representing unknown time delay constants generated in the measuring and transmitting processes of the sensor; delta i (x 1 ,x 1 (t-τ 1 ) I=1, 2, representing an unknown smoothness and with a time delay with respect to the load side voltage u B Is a nonlinear function of (2); d, d i I=1, 2, representing an external disturbance input signal; u represents the duty ratio of the MOS tube, namely the control input signal of the stability control unit; y epsilon R represents the output of the stability control unit;
the control objective of dynamic stabilization is to keep the output y of the stabilization unit stably tracking a given desired signal y r ；
For the mathematical model of the controlled object represented by formula (2), the following assumptions are made:
suppose 1: g i Not equal to 0, i=1, 2, representing an unknown constant, and there is a positive number g min And g max So that it satisfies the relationship: 0 < g min ≤|g i |≤g max ；
Suppose 2: desired tracking y r Is a smooth and bounded letterA number;belongs to a tight set and satisfiesAnd->Where i represents the ith derivative of the desired tracking, A 0 、A 1 、A 2 、/>All are positive numbers;
suppose 3: τ 1 Represents an unknown positive number and satisfies the relationship: τ is 0 or less 1 ≤τ M Wherein τ M Denoted τ 1 Is the maximum value of (2);
suppose 4: unknown external disturbance input signal d i I=1, 2, satisfies the relationship:
s2, establishing load regulation and control constraint of input voltage safety, and introducing an axiom 1 to an axiom 4 as a theoretical basis for design and stability analysis of a control algorithm, wherein the specific contents are as follows:
lemma 1: for any positive constantDefinitions->i=1..n, where z i Represents the ith state variable, and +.>Is an open set;
there is a variable η= [ ω, z i ] T E o, function h R + ×o→R l+i Is about time t minutesContinuous in segments and at R + The ×o is stable with respect to η local Li Puxi z; first derivative of variable η with respect to time tEquation (3) is shown below:
assuming that there is a continuously differentiable positive function U: R l →R + And V is j :H→R + In their respective fields, formula (4) is as follows:
in the formula (4), ρ 1 And ρ 2 For K ∞ Class function, V j (z j ) Representing the state variable z j Is represented by a continuous slightly positive function with respect to the variable ω, letWherein V (η) represents the Lyapunov function with respect to the variable η, z i (0) Belonging to set H, if the inequality is expressed as:
and satisfies eta e o, constant c > 0, v > 0, then z i (t) remain in the open set H, < >>In (a) and (b);
and (4) lemma 2: for any arbitraryEquation (5) holds:
in the formula (5) of the present invention,representing design parameters, S 0 Represents an arbitrary variable;
online approximation of unknown smooth functions in mathematical models of controlled objects using fuzzy logic systemsWherein (1)>Representing a given tight set;
first, the Fuzzy Logic System (FLS) is a fuzzy set of "if-then" rules that will input the vector U i ∈R m Mapping to scalar output Y i E R, equation (6) is as follows:
in the formula (6) of the present invention,and->(l=1,) N, k=1, & gt, m, i=1, & gt, N) are fuzzy sets described by fuzzy membership functions, respectively +.>And->Nv1 is ζ i ＝[ξ i,1 ,ξ i,2 ,…ξ i,m ] T ∈U i Is the number of fuzzy rules; zeta type toy i And Y i ∈V i Respectively are provided withConsidering "if-then" fuzzy rules in formula (6) for input and output of a Fuzzy Logic System (FLS), the Fuzzy Logic System (FLS) has the characteristics of single instance fuzzification, product inference engine, and central average defuzzifier, and formula (7) is as follows:
in the formula (7) of the present invention,
is an ideal weight vector, +.>Is a fuzzy basis function vector; />
And (3) lemma 3: for any given set of incumbentsIn a real continuous function f i :R n R, any real number is presentSo that equation (7) satisfies the form described by equation (8), as follows:
let epsilon i (ξ i ) To approximate the error, delta i (ξ i ) Described as shown in equation (9):
in equation (9), the approximation error An upper bound value representing an estimation error of the fuzzy logic system; />Is thatDefining equation (10) as follows:
when the nonlinear function has an unknown time delay constant tau i When, for example, delta i (ζ i ,ζ i (t-τ i ) Direct estimation by a fuzzy logic system is not possible; however, due to the tight setIs to be added to the unknown function by means of a fuzzy logic system combined with finite coverage arguments>Performing approximation;
and 4, lemma: let us assume the input vector xi i ＝(ξ i ,ξ i (t-τ i ) In line with time t, where τ i ∈[0,τ M ]Is an unknown time delay constant and then, for any given errorThere is a finite interval [0, τ ] independent of time t M ]Equation (11) is shown below:
0＜t 1 ＜…＜t m ＜τ M (11)
from one of the time points, equation (12) is satisfied as follows:
equation (13) is available as follows:
combining lemma 3 and hypothesis 3, there are multiple time points τ 1/1 ,...,τ n/n ∈{t 1 ,...,t m An unknown smooth function with time delay, equation (14) is shown below:
in the formula (14) of the present invention,representing the estimation error of the finite coverage lemma, therefore, in combination with the expression of the fuzzy logic system approximation unknown function, equation (14) is approximated as shown in equation (15):
in formula (15), δ i Upper bound value representing fuzzy logic system estimation errorEstimation error with limited coverage lemma +.>And inputs a vector, equation (16) is as follows: />
ξ i ＝(x 1 ,...,x i ,...,x 1 (t-t 1 ),...,x k (t-τ k/k ),...,x i (t-t m )) (16)。
Step S3, formulating the output voltage of the stability control unit under different load regulation and control requirements in the load optimization interaction process;
s4, designing a load stabilizing control unit self-adaptive dynamic surface regulation strategy taking a load regulation target as a desired curve, so that the load change of the power system is quickly and stably controlled; an adaptive dynamic surface regulation strategy comprising the steps of:
step S41, defining a first dynamic surface error S 1 Equation (17) is shown below:
S 1 ＝x 1 -y r (17)
in the formula (17), y r Is the desired tracking, consider equation (2),represent S 1 With respect to the derivative of time, equation (18) is as follows:
design obstacle Lyapunov candidate function V 1 Equation (19) is shown below:
in the formula (19), log (χ) represents the natural logarithm of χ, V 1 In a compact collectionIs continuous in thatDesign parameters->
The first derivative of equation (19) with respect to time is equation (20), as follows:
from hypothesis 4, equation (21) is derived using the young's inequality, as follows:
therefore, in connection with the formula (21), the formula (20) is rewritten as the formula (22), as follows:
in order to process the nonlinear function with unknown time delay in equation (22), a Fuzzy Logic System (FLS) is used as an estimator, and in conjunction with the lemma 4, equation (22) is rewritten as equation (23), as follows:
in equation (23), the vector is inputAnd has the formula (24) as follows: />
Further, according to hypothesis 1, equation (25) is obtained using the young's inequality as follows:
in the formula (25), v 1 Representing design parameters, the values of which are positive numbers, thus V 1 Is rewritten as equation (26) as follows:
in equation (26), the constantx 2d Representing a virtual control law, wherein the virtual control law is as shown in formula (27):
in the formula (27), k 1 Representing a design parameter, the value of which is a positive number,is theta * Will give its weight update law in step S42; a first order low pass filter as shown in equation (28) will be introduced to calculate the derivative of the virtual control quantity as follows:
in formula (28), iota 2 Representing the time constant, the value being positive, thus obtaining a new filter output z 2 ；
Step S42, defining a second dynamic surface error formula (29), as follows:
S 2 ＝x 2 -z 2 (29)
S 2 the derivative formula (30) of (b) is as follows:
design obstacle Lyapunov candidate function V 2 Equation (31) is shown below:
in the formula (31), V 2 In a compact collectionThe upper part is continuous and the tightening set +.>Design parametersEstimation error->Wherein (1)>Is theta * Is a function of the estimated value of (2); gamma ray θ Is a design parameter, the value is a positive number; using a Fuzzy Logic System (FLS) as an estimator, in combination with the lemma 4, there is a formula (32) established as follows;
in equation (32), the vector is inputUsing the Young's inequality to obtain V n The derivative formula (33) of (2) is as follows:
in the formula (33), the constantDesigning the control signal according to equation (33) results in equation (34) as follows:
self-adaptive lawDesign formula (35), as follows:
the validity of the dynamic stability control method is verified by building a semi-physical simulation platform, and the method is shown in fig. 2 and 3; in the establishment of the power electronic real-time simulation experiment platform, a second-order state space model of the stability control unit in the formula (1) is considered to be used as a controlled object, a programmed controlled object model and a controller algorithm are built by Simulink in Matlab, codes are generated through a real-time simulator and a rapid control prototype respectively and downloaded into experiment equipment, a closed loop is formed with physical hardware, and real-time simulation and online verification experiments are carried out.
In the simulation experiment, parameters of the stability control unit are set as follows: u (U) DC ＝1000V，L＝10mH，C B =1mf and r=0.1Ω; the state is limited to the range |x 1 |＜510,|x 2 In < 20, the initial value of the selected state is x 1 (0)＝500,x 2 (0)＝0,Setting the initialized design parameters of the self-adaptive dynamic surface regulation strategy: k (k) 1 ＝13,k 2 ＝1.3,k b1 ＝1,k b2 ＝25,v 1 ＝0.1,v 2 ＝0.9,γ θ ＝0.3,δ θ =20; the time constant of the first order low pass filter is τ=0.01; select reference signal y r ＝500。
Referring to fig. 3, the abscissa represents the simulation time in units: second, wherein the second is; the ordinate represents the voltage value in units of: volts; the solid line represents the desired signal, with a value of 500V; the dashed line represents the output voltage of the system; referring to fig. 4, the abscissa represents the simulation time in units: second, wherein the second is; the ordinate represents the voltage value, units: volts; the dashed line represents the tracking error of the system.
Referring to fig. 3 and 4, experimental results show that the control strategy provided by the invention can realize effective tracking performance, and the tracking error is finally stabilized near 0.01V.
According to the invention, through designing a proper barrier Lyapunov function, the load regulation and control constraint of the input voltage safety is ensured, a given performance index is realized, and a limited coverage primer is combined with a fuzzy logic system, so that not only can an unknown smooth nonlinear function be estimated on line, but also the unknown time delay generated in the measuring and transmitting process of a sensor can be compensated, the stability and the anti-interference capability of the output voltage of a Buck circuit stability control unit can be improved, and the rapid and stable regulation and control of the power load can be finally realized.
Stability analysis is carried out on the designed self-adaptive dynamic surface regulation strategy, and the content is as follows:
theorem: for the stability control unit described by the formula (2), 1 to 4 are assumed to be true, and the stability control unit is assembledi=1, 2, the virtual control law x in the design formula (27) 2d Control signal u (t) in equation (34) and the weight adaptation law in equation (35); selecting design parameter k i 、v i 、γ θ 、δ θ And defining a positive constant +.>And->Wherein, the liquid crystal display device comprises a liquid crystal display device,and->The method comprises the following proving steps:
proving step 1, defining a filtering error y 1 Equation (36) is shown below:
in the formula (36), x 2d Given in equation (27), in combination with equation (27) and equation (36), according to the equationThe resulting equation (37) holds as follows:
b in formula (37) 2 Is a continuous function;
proving that step 2, defining a Lyapunov function V, and the formula (38) is as follows:
in equation (38), the time derivative of the Liapunov function VEquation (39) is as follows:
from equation (29) and equation (36), equation (40) is derived as follows:
x 2 ＝S 2 +y 1 +x 2d (40)
substituting equation (27) and equation (40) into equation (26) to obtain equation (41), respectively, is as follows:
substituting equation (34) into equation (33) yields equation (42) as follows:
equation (43) is derived from the adaptive law (35) as follows:
substituting the formulas (41) to (43) into the formula (39) to obtain the formula (44) as follows:
from hypothesis 2, a set formula (45) is derived, as follows:
at R 3 Is compact in B 1 > 0, resulting in a set of formulas (46) as follows:
at R 4 In (c) is compact, and p is a positive constant, note γ 1 ×γ 2 At R 7 Is also compact, thus |B 2 I is in compact set gamma 1 ×γ 2 With a maximum value M 2 Using the Young's inequality and taking into account equation (44), a formula is obtainedFormula (47) as follows:
where j is an arbitrary constant, the value of which is a positive number, and according to the lemma 2, the inequality (51) holds as follows:
substituting equations (49) - (51) into (48) yields equation (52) as follows:
order theConstant->Constant->Equation (52) is rewritten as equation (53) as follows:
combined with the primer 1, there areEquation (54) is obtained as follows:
let any normal numberWhen V (0) =p +.>Always true, meaning that for all t.gtoreq.0, V (t). Ltoreq.p, therefore V (t). Ltoreq.p is a constant set, by solving equation (54), equation (55) is obtained as follows:
by solving the equation (55), the equation (56) is obtained as follows:
all signals of closed loop systems, e.g. S i ,And y 1 Are semi-globally consistent and ultimately bounded; by selecting a suitable design parameter gamma θ ,k 1 ,k 2 ,ι 2 ,lim t→∞ V (t) can be arbitrarily small, thereby indicating that the tracking error converges to a bounded tight set; as can be seen from the formula (56), V (0). Ltoreq.p, & lt/EN & gt>This means that equation (57) holds as follows:
in equation (57), a bounded setAnd filter error y 1 The relation between them satisfies->According to hypothesis 2, due to x 1 ＝S 1 +y r ,|y r |≤A 0 And->For establishment, see->And x 2 ＝S 2 +z 2 ＝S 2 +y 1 +x 2d The method comprises the steps of carrying out a first treatment on the surface of the Due to x 1 ,ν 1 ,y r And->Is bounded and takes into account the virtual control signal x designed in equation (27) 2d Inequality ofEstablishment; the full state constraint in the closed loop system is guaranteed. The syndrome is known.
The control system is used for accurately controlling the controllable load under the load regulation constraint condition of the input voltage safety, and can adaptively adjust the control strategy according to the change of the load state, so that the control system can be better adapted to different load working states, quickly respond to the change of the load state, control in real time and further ensure the instantaneity and the stability of the control system; the output voltage of the stabilizing and controlling unit under different load regulation and control requirements in the load optimization interaction process is formulated, and the load regulation and control dynamic stability control in the controllable load optimal interaction process can be realized by controlling the output voltage of the stabilizing and controlling unit; calculating the derivative of a virtual control law by introducing a first-order low-pass filter, avoiding the generation of differential explosion phenomenon, taking a load regulation target as a desired curve, and realizing a given tracking performance index by constructing a proper barrier Lyapunov function on the basis of considering the safety of input voltage; the fuzzy logic system is combined with the finite coverage primer, so that not only can the unknown smooth nonlinear function be estimated, but also the unknown time delay generated in the sensor measurement transmission process can be compensated, thereby reducing tracking error and improving control performance; the stability analysis shows that the designed self-adaptive controller can ensure that all update laws and design parameters in a control system are semi-globally consistent and finally bounded by using a control law u (t) designed by the self-adaptive state constraint dynamic surface control method, and tracking errors of the system can be converged to an adjustable tight set by means of an initialization skill and meet the condition of load regulation and control state constraint in the system.
Claims (4)
1. The dynamic stability control method for the controllable load optimal interaction process is characterized by comprising the following steps of:
step S1, establishing a dynamic stability control model in the optimal interaction process of controllable load;
s2, establishing load regulation and control constraint of input voltage safety;
step S3, formulating the output voltage of the stability control unit under different load regulation and control requirements in the load optimization interaction process;
and S4, designing a self-adaptive dynamic surface regulation strategy of a load stabilizing unit taking a load regulation target as a desired curve, so that the load change of the power system is quickly and stably controlled.
2. The method for dynamic stability control in a controllable-load optimal interaction process according to claim 1, wherein in step S1, a state space equation of a dynamic stability control model in the controllable-load optimal interaction process is shown in the following formula (1):
in the formula (1), u B Representing load side voltage, unit V; i.e L Representing inductor current, unit a; u (U) DC The direct current busbar voltage of the direct current micro-grid is represented by a unit V; l is the load side inductance, unit mH; c (C) B The unit mF is a load side filter capacitor; r is the internal resistance of the battery, the unit omega is not lost, the influence of external disturbance on the formula (1) is considered, all coefficients in the formula (1) are assumed to be unknown, the formula (1) is rewritten into a state space expression shown in the formula (2) in a mathematical transformation mode, and the state space expression is used as a mathematical model of a controlled object, and the mathematical model is as follows:
in the formula (2), x 1 Representing load side voltage u B Units (V); x is x 2 Representing the inductor current i L Unit (a); parameters (parameters)τ 1 Representing unknown time delay constants generated in the measuring and transmitting processes of the sensor; delta i (x 1 ,x 1 (t-τ 1 ) I=1, 2, representing an unknown smoothness and with a time delay with respect to the load side voltage u B Is a nonlinear function of (2); d, d i I=1, 2, representing an external disturbance input signal; u represents the duty ratio of the MOS tube, namely the control input signal of the stability control unit; y epsilon R represents the output of the stability control unit;
the control objective of dynamic stabilization is to keep the output y of the stabilization unit stably tracking a given desired signal y r ；
For the mathematical model of the controlled object represented by formula (2), the following assumptions are made:
suppose 1: g i ≠0，i=1, 2, represents an unknown constant, and there is a positive number g min And g max So that it satisfies the relationship: 0 < g min ≤|g i |≤g max ；
Suppose 2: desired tracking y r Is a smooth and bounded function;belongs to a tight set and satisfiesAnd->Where i represents the ith derivative of the desired tracking, A 0 、A 1 、A 2 、/>All are positive numbers;
suppose 3: τ 1 Represents an unknown positive number and satisfies the relationship: τ is 0 or less 1 ≤τ M Wherein τ M Denoted τ 1 Is the maximum value of (2);
suppose 4: unknown external disturbance input signal d i I=1, 2, satisfies the relationship:
3. the dynamic stability control method for the controllable load optimal interaction process according to claim 1, wherein, in order to solve the load regulation constraint of the input voltage safety in the step S2, a primer 1 to a primer 4 are introduced as theoretical basis for design and stability analysis of a control algorithm, and the specific contents are as follows:
lemma 1: for any positive constantDefinitions-> Wherein z is i Represents the ith state variable and o: -is:>is an open set;
there is a variable η= [ ω, z i ] T E o, function h R + ×o→R l+i Is piecewise continuous with respect to time t, and is at R + The ×o is stable with respect to η local Li Puxi z; first derivative of variable η with respect to time tEquation (3) is shown below:
assuming that there is a continuously differentiable positive function U: R l →R + And V is j :H→R + In their respective fields, formula (4) is as follows:
in the formula (4), ρ 1 And ρ 2 For K ∞ Class function, V j (z j ) Representing the state variable z j Is represented by a continuous slightly positive function with respect to the variable ω, letWherein V (η) represents the Lyapunov function with respect to the variable η, z i (0) Belonging to set H, e.g.The inequality is expressed as: />And satisfies eta e o, constant c > 0, v > 0, then z i (t) remain in the open set H, < >>In (a) and (b);
and (4) lemma 2: for any arbitraryEquation (5) holds:
in the formula (5) of the present invention,representing design parameters, S 0 Represents an arbitrary variable;
on-line approximation of unknown smooth function delta in mathematical model of controlled object using fuzzy logic system i :Wherein (1)>Representing a given tight set;
first, the Fuzzy Logic System (FLS) is a fuzzy set of "if-then" rules that will input the vector U i ∈R m Mapping to scalar output Y i E R, equation (6) is as follows:
in the formula (6) of the present invention,and->Is a fuzzy set described by fuzzy membership functions, respectively +.>And->Is xi i ＝[ξ i,1 ,ξ i,2 ,…ξ i,m ] T ∈U i Is the number of fuzzy rules; zeta type toy i And Y i ∈V i Respectively input and output of a Fuzzy Logic System (FLS), considering an 'if-then' fuzzy rule in a formula (6), the Fuzzy Logic System (FLS) has the characteristics of single instance fuzzification, a product inference engine and a central average defuzzifier, and a formula (7) is as follows:
in the formula (7) of the present invention,
is an ideal weight vector, +.>Is a fuzzy basis function vector; />
And (3) lemma 3: for any given set of incumbentsIn a real continuous function f i :R n R, any real number is presentSo that equation (7) satisfies the form described by equation (8), as follows:
let epsilon i (ξ i ) To approximate the error, delta i (ξ i ) Described as shown in equation (9):
in equation (9), the approximation error An upper bound value representing an estimation error of the fuzzy logic system; />Is->Defining equation (10) as follows:
when the nonlinear function has an unknown time delay constant tau i When, for example, delta i (ζ i ,ζ i (t-τ i ) Not directly estimated using fuzzy logic systemsThe method comprises the steps of carrying out a first treatment on the surface of the However, due to the tight setIs to be added to the unknown function by means of a fuzzy logic system combined with finite coverage arguments>Performing approximation;
and 4, lemma: let us assume the input vector xi i ＝(ξ i ,ξ i (t-τ i ) In line with time t, where τ i ∈[0,τ M ]Is an unknown time delay constant and then, for any given errorThere is a finite interval [0, τ ] independent of time t M ]Equation (11) is shown below:
0＜t 1 ＜…＜t m ＜τ M (11)
from one of the time points, equation (12) is satisfied as follows:
equation (13) is available as follows:
assume that: τ 1 Represents an unknown positive number and satisfies the relationship: τ is 0 or less 1 ≤τ M Wherein τ M Denoted τ 1 Is the maximum value of (2); in combination with the lemma 3, there are a plurality of time points τ 1/1 ,...,τ n/n ∈{t 1 ,…,t m An unknown smooth function with time delay, equation (14) is shown below:
in the formula (14) of the present invention,representing the estimation error of the finite coverage lemma, therefore, in combination with the expression of the fuzzy logic system approximation unknown function, equation (14) is approximated as shown in equation (15):
in formula (15), δ i Upper bound value representing fuzzy logic system estimation errorEstimation error with limited coverage lemma +.>And inputs a vector, equation (16) is as follows:
ξ i ＝(x 1 ,…,x i ,…,x 1 (t-t 1 ),...,x k (t-τ k/k ),...,x i (t-t m )) (16)。
4. the method for dynamic stability control in a controllable-load optimal interaction process according to claim 1, wherein in step S4, the adaptive dynamic surface control strategy comprises the following steps:
step S41, defining a first dynamic surface error S 1 Equation (17) is shown below:
S 1 ＝x 1 -y r (17)
y in formula (17) r Is the desired tracking, consider equation (2),represent S 1 With respect to the derivative of time, equation (18) is as follows:
design obstacle Lyapunov candidate function V 1 Equation (19) is shown below:
in the formula (19), log (χ) represents the natural logarithm of χ, V 1 In a compact collectionIs continuous in thatDesign parameters->
The first derivative of equation (19) with respect to time is equation (20), as follows:
according to the assumption: unknown external disturbance input signal d i I=1, 2, satisfies the relationship:equation (21) is obtained using the young's inequality as follows:
therefore, in connection with the formula (21), the formula (20) is rewritten as the formula (22), as follows:
in order to process the nonlinear function with unknown time delay in equation (22), using a Fuzzy Logic System (FLS) as an estimator, equation (22) is rewritten as equation (23), as follows:
in equation (23), the vector is inputAnd has the formula (24) as follows:
further, according to the assumption: g i Not equal to 0, i=1, 2, representing an unknown constant, and there is a positive number g min And g max So that it satisfies the relationship: 0 < g min ≤|g i |≤g max The method comprises the steps of carrying out a first treatment on the surface of the Equation (25) is derived using the young's inequality as follows:
in the formula (25), v 1 Representing design parameters, the values of which are positive numbers, thus V 1 Is rewritten as equation (26) as follows:
in equation (26), the constantx 2d Representing a virtual control law, wherein the virtual control law is as shown in formula (27):
in the formula (27), k 1 Representing a design parameter, the value of which is a positive number,is theta * Will give its weight update law in step S42; a first order low pass filter as shown in equation (28) will be introduced to calculate the derivative of the virtual control quantity as follows:
in formula (28), iota 2 Representing the time constant, the value being positive, thus obtaining a new filter output z 2 ；
Step S42, defining a second dynamic surface error formula (29), as follows:
S 2 ＝x 2 -z 2 (29)
S 2 the derivative formula (30) of (b) is as follows:
design obstacle Lyapunov candidate function V 2 Equation (31) is shown below:
in the formula (31), V 2 In a compact collectionThe upper part is continuous and the tightening set +.>Design parametersEstimation error->Wherein (1)>Is->Is a function of the estimated value of (2); gamma ray θ Is a design parameter, the value is a positive number; using a Fuzzy Logic System (FLS) as an estimator, equation (32) holds as follows;
in equation (32), the vector is inputUsing the Young's inequality to obtain V n The derivative formula (33) of (2) is as follows:
in the formula (33), the constantDesigning the control signal according to equation (33) results in equation (34) as follows:
self-adaptive lawDesign formula (35), as follows:
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