A Distributed Fixed-Time Control Method for AC Microgrids Considering Communication Delay and Actuator Saturation

Abstract

The present invention discloses a distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, comprising the following steps: 1) establishing an islanded AC microgrid model with communication delay and actuator saturation; 2) based on state transformation, transforming the islanded AC microgrid model with communication delay into an islanded AC microgrid model without communication delay; 3) designing an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing frequency restoration and active power distribution; 4) designing an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing average voltage restoration and reactive power distribution; 5) using the anti-saturation auxiliary controllers and distributed fixed-time controllers in steps 3) and 4) to realize the frequency and voltage regulation of the islanded AC microgrid model, as well as the distribution of active power and reactive power. The present invention adopts a fixed-time based control strategy, which can ensure that the upper bound convergence time of the system is not affected by the initial state.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed generation control in the scenario of an AC microgrid, and specifically to a distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation. Background Art

[0002] In recent years, renewable energy has made significant contributions to energy conservation and carbon reduction in modern power systems. While renewable energy improves the flexibility of the power system, it also greatly affects the stability of the system. As a micro power system, AC microgrids (MGs) can effectively integrate distributed generation (DG) resources and promote the consumption of renewable energy and distributed energy in the power system. When an AC microgrid based on a power electronic converter operates in parallel with the grid, its voltage and frequency are mainly supported by the large grid. In the case of islanded operation, its voltage and frequency are regulated by the power electronic converter. However, due to the randomness and intermittency of new energy output, the reliable operation of an islanded AC microgrid faces huge challenges. Therefore, in an islanded AC microgrid, it is necessary to effectively regulate the frequency and voltage to ensure the safe and reliable operation of the islanded AC microgrid.

[0003] In order to achieve the precise allocation of frequency, voltage recovery, and power in an AC microgrid under communication delay and actuator saturation, distributed control methods are mainly used at present. Distributed control strategies have the advantages of a simple communication network, high reliability, easy expansion, and fast data processing, but inevitably introduce communication delays to the control system, affect the convergence of system states, and even deteriorate the dynamic performance, resulting in system instability. In addition to communication delays, due to the limited bandwidth of physical actuators in real life, actuator saturation is also a common problem in control systems. Once the input saturation constraint is not considered in the controller design, the performance of the closed-loop control system will decline or even become unstable. Moreover, under the finite-time consensus control strategy, the upper bound convergence time of an islanded AC microgrid will increase with the increase of the initial conditions, affecting its dynamic performance. Summary of the Invention

[0004] The purpose of the present invention is to provide a distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, including the following steps:

[0005] 1) Establish an islanded AC microgrid model with communication delay and actuator saturation;

[0006] 2) Based on state transformation, transform the islanded AC microgrid model with communication delay into an islanded AC microgrid model without communication delay;

[0007] 3) Design an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing frequency recovery and active power distribution;

[0008] 4) Design an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing average voltage recovery and reactive power distribution;

[0009] 5) Use the anti-saturation auxiliary controller and the distributed fixed-time controller in steps 3) and 4) to realize the frequency and voltage regulation of the islanded AC microgrid model, as well as the distribution of active power and reactive power.

[0010] Furthermore, the islanded AC microgrid model includes multiple distributed generators;

[0011] The primary control of these distributed generators adopts a droop control strategy.

[0012] The frequency and voltage droop control equations of the distributed generators considering communication delay and actuator saturation are as follows:

[0013]

[0014]

[0015] Where, and are the first-order derivatives of ω i (t), and P i (t) respectively; and are the first-order derivatives of and respectively; u fi (t - τ i ), u vi (t - τ i ) are the secondary control inputs for frequency and voltage recovery with communication time delay respectively; τ i is the communication delay time; ω i (t) and represent the actual angular frequency and the rated angular frequency of the i-th distributed generator respectively, V i (t) and represent the actual output voltage amplitude and the rated voltage amplitude of the i-th distributed generator respectively, P i (t) and Q i (t) represent the active power and the reactive power output by the i-th distributed generator respectively, m i and κ i are the droop coefficients of P i (t) and Q i (t) respectively; Denote the actual output voltage amplitude V i the direct-axis part of (t);

[0016] The saturation function sat(·) is as follows:

[0017]

[0018] where u M and u m are the upper and lower bounds of the control input u respectively;

[0019] The rated angular frequency of the i-th distributed generator and the rated voltage amplitude V i n (t) are as follows:

[0020] s

[0021]

[0022] Among them, the auxiliary control input u pi (t - τ i ) of the active power of the i-th distributed generator and the auxiliary control input u qi (t - τ i ) of the reactive power of the i-th distributed generator are as follows:

[0023]

[0024]

[0025] where t is time.

[0026] Furthermore, the steps to construct the frequency and voltage droop control equations of the distributed generator include:

[0027] 1) Establish the original droop control equations of the frequency and voltage of the i-th distributed generator as follows:

[0028]

[0029] V i (t) = V i n (t) - κ i Q i (t) (9)

[0030] where ω i (t) and respectively represent the actual angular frequency and the rated angular frequency of the i-th distributed generator, V i (t) and respectively represent the actual output voltage amplitude and the rated voltage amplitude of the i-th distributed generator, P i (t) and Q i (t) respectively represent the active power and reactive power output by the i-th distributed generator, m i and κ i are respectively the droop coefficients of P i (t) and Q i (t);

[0031] 2) Perform Park transformation and Clark transformation on formula (9) to establish an improved voltage droop control equation, that is:

[0032]

[0033]

[0034] Among them, and respectively represent the direct-axis and quadrature-axis parts of the actual output voltage amplitude V i (t);

[0035] 3) According to formula (8) and formula (10), establish the frequency and voltage droop control equations of the distributed generator considering communication delay and actuator saturation.

[0036] Furthermore, the islanded AC microgrid model without communication delay is as follows:

[0037]

[0038]

[0039]

[0040]

[0041] Among them, is the frequency of the i-th distributed generator in the islanded AC microgrid model without communication delay; ω i (t) represents the actual angular frequency of the i-th distributed generator in the islanded AC microgrid model with communication delay; is the mean value of the direct-axis part of the output voltage of the islanded AC microgrid model without communication delay, is 's first derivative; P i z (t) is the active power of the i-th distributed generator in the islanded AC microgrid model without communication delay, is the reactive power of the i-th distributed generator in the islanded AC microgrid model without communication delay; m i and κ i are the droop coefficients of P i (t) and Q i (t) respectively; u fi (t), u vi (t) are the secondary control inputs for frequency and voltage restoration without communication time delay respectively; P i (t) and Q i (t) represent the active power and reactive power output by the i-th distributed generator respectively; u pi (t), u qi (t) represent the auxiliary control inputs for the active power and reactive power of the i-th distributed generator in the islanded AC microgrid model without communication time delay. is the mean value of the direct-axis part of the output voltage of the islanded AC microgrid model with communication delay.

[0042] Furthermore, the anti-saturation auxiliary controller and the distributed fixed-time controller for realizing frequency restoration are shown as follows respectively:

[0043]

[0044]

[0045] where, α ω , β ω are constants greater than 0; η1 is a constant between 0 and 1; sig(·) is the sigmoid function; Δu fi = sat(u fi (t)) - u fi (t) represents the difference between the actual frequency control input and the designed frequency control input of the i-th distributed generator; σ ω is a constant greater than 0; u fi (t) is the secondary control input for frequency without communication time delay; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid; the intermediate parameter b i is the gain coefficient; λ fi is the anti-saturation auxiliary control variable for realizing frequency restoration; z fi is the improved consensus error. α f , β f are constants greater than 0, η f is a constant between 0 and 1.

[0046] Furthermore, the anti-saturation auxiliary controller and the distributed fixed-time controller for realizing active power distribution are as follows:

[0047]

[0048]

[0049] where α p , β p are constants greater than 0; α p1 , β p1 are constants greater than 0; η p is a constant between 0 and 1; η2 is a constant between 0 and 1; sig(·) is the sigmoid function; Δu pi = sat(u pi (t)) - u pi (t) represents the difference between the actual active power control input and the designed active power control input of the i-th distributed generator; u pi (t) represents the auxiliary control input of the active power of the i-th distributed generator in the islanded AC microgrid model without communication time delay; σ p is a constant greater than 0; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid; λ pi is the anti-saturation auxiliary control variable for realizing active power distribution; σ p is a constant greater than 0; z pi is the improved consensus error.

[0050] Furthermore, the steps for designing the anti-saturation auxiliary controller and the distributed fixed-time controller for realizing frequency recovery and active power distribution include:

[0051] 1) Construct the fixed-time stability control objective for frequency recovery and active power distribution, that is:

[0052]

[0053] where ω ref is the reference angular frequency, m i is the droop coefficient of the active power P i (t) output by the i-th distributed generator; ω i (t) represents the actual angular frequency of the i-th distributed generator in the islanded AC microgrid model with communication delay; T is the upper bound of the convergence time; P j (t) is the active power output by the j-th distributed generator; m j is the droop coefficient of the active power Pj(t) output by the j-th distributed generator;

[0054] 2) Design the consistency error according to the control objective (20), i.e.:

[0055]

[0056] where e fi is the consistency error of the output angular frequency of the i-th distributed generator, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid. If the microgrid node i can receive information from node j, then a ij = 1; otherwise, a ij = 0; b i is the gain coefficient. If the microgrid node i can receive information from the leader node, then b i = 1; otherwise, b i = 0, N i is the neighborhood set of node i, and e pi is the consistency error of the output active power of the i-th distributed generator; is the frequency of the i-th distributed generator in the islanded AC microgrid model without communication delay; P i z (t) is the active power of the i-th distributed generator in the islanded AC microgrid model without communication delay; ω ref is the reference angular frequency; is the frequency of the j-th distributed generator in the islanded AC microgrid model without communication delay; is the active power of the j-th distributed generator in the islanded AC microgrid model without communication delay;

[0057] 3) Construct the differential equation of the consistency error according to formula (21), i.e.:

[0058]

[0059] where the intermediate parameter

[0060] 4) Design the anti-saturation auxiliary control variables λ fi and λ pi ;

[0061] 5) Establish the improved consistency error, i.e.:

[0062]

[0063] 6) Establish the differential equation of the improved consistency error according to formula (23), i.e.:

[0064]

[0065]

[0066] 7) Design a distributed fixed-time controller to make the improved consensus error \(z\) fi converge to 0.

[0067] Furthermore, the anti-saturation auxiliary controller and the distributed fixed-time controller for achieving average voltage restoration are as follows:

[0068]

[0069]

[0070] where the error \(z\) vi = \(e\) vi - \(\lambda\) vi ; \(\alpha\) v , \(\beta\) v , \(\sigma\) v , \(\alpha\) v1 , \(\beta\) v1 are constants greater than 0; \(\eta_1\), \(\eta\) v are constants between 0 and 1; \(\Delta u\) vi = \(sat(u\) vi (t)) - \(u\) vi (t) represents the difference between the actual voltage control input and the designed voltage control input of the \(i\)-th distributed generator, and \(\lambda\) vi is the anti-saturation auxiliary control variable for achieving average voltage restoration; the intermediate parameter \(a\) ij is the element in the \(i\)-th row and \(j\)-th column of the weighted adjacency matrix \(A=(a\) ij ) of the communication topology of the islanded AC microgrid. If the microgrid node \(i\) can receive information from node \(j\), then \(a\) ii = 1, otherwise \(a\) ij = 0; \(b\) i is the gain coefficient. If the microgrid node \(i\) can receive information from the leader node, then \(b\) i = 1, otherwise \(b\) i = 0; \(u\) vj (t) is the secondary control input for voltage restoration.

[0071] Furthermore, the anti-saturation auxiliary controller and the distributed fixed-time controller for achieving reactive power distribution are as follows:

[0072]

[0073]

[0074] where the error \(z\) qi = \(e\) qi-λ qi ; α q , β q , σ q , α q1 , β q1 are constants greater than 0; η2, η q are constants between 0 and 1, and Δu qi = sat(u qi (t)) - u qi (t) represents the difference between the actual uncontrolled input and the designed reactive power control input of the i-th distributed generator; u qi (t) is the secondary control input for realizing reactive power distribution; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid; λ qi is the anti-saturation auxiliary controller for realizing reactive power distribution.

[0075] Furthermore, the steps for designing the anti-saturation auxiliary controller and the distributed fixed-time controller for realizing average voltage recovery and reactive power distribution include:

[0076] 1) Construct the fixed-time stability control objective for average voltage recovery and reactive power distribution, that is:

[0077]

[0078] where V ref is the reference voltage, κ i is the droop coefficient of the reactive power Q i output by the i-th distributed generator. is the mean value of the direct-axis component of the output voltage of the islanded AC microgrid model with communication delay; κ j is the droop coefficient of the reactive power Q j output by the i-th distributed generator; T is the upper bound of the convergence time;

[0079] 2) Based on the output voltage of the i-th distributed generator and the average voltage of its neighbors, design a distributed fixed-time voltage observer, that is:

[0080]

[0081] where η av is a constant between 0 and 1, and α, β are constants greater than 0. is the direct-axis component of the output voltage of the islanded AC microgrid model with communication delay; is the direct-axis component of the output voltage of the j-th distributed generator of the islanded AC microgrid model with communication delay;

[0082] 3) To ensure that the average value of the output voltage of all distributed generators can converge to the reference value and achieve reactive power distribution, a consensus error is constructed, i.e.:

[0083]

[0084] where e vi is the consensus error of the average output voltage of the i-th distributed generator, and e qi is the consensus error of the reactive power output of the i-th distributed generator; is the mean value of the direct-axis component of the output voltage of the j-th distributed generator in the islanded AC microgrid model without communication delay;

[0085] 4) According to formula (32), a differential equation of the consensus error is constructed, i.e.:

[0086]

[0087] 5) Based on the consensus error, an anti-saturation auxiliary controller and a distributed fixed-time controller are designed to achieve average voltage recovery and reactive power distribution.

[0088] The technical effect of the present invention is beyond doubt. The present invention adopts a fixed-time-based control strategy, which can ensure that the upper bound convergence time of the system is not affected by the initial state. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 is the islanded AC microgrid system of the present invention;

[0090] Figure 2 is the control block diagram of the distributed generator of the present invention;

[0091] Figure 3 is the overall control architecture of voltage, frequency recovery and power distribution under parallel operation of multiple distributed generators of the present invention;

[0092] Figure 4 is the communication topology of the islanded AC microgrid of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0093] The present invention will be further described below in conjunction with embodiments, but it should not be understood that the above-mentioned subject scope of the present invention is limited to the following embodiments. Without departing from the above-mentioned technical idea of the present invention, various substitutions and changes should be included in the protection scope of the present invention according to the common general knowledge and conventional means in the art.

[0094] Embodiment 1:

[0095] See Figures 1 to 4, A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, comprising the following steps:

[0096] 1) Establish an island AC microgrid model with communication delay and actuator saturation;

[0097] 2) Based on state transformation, transform the island AC microgrid model with communication delay into an island AC microgrid model without communication delay;

[0098] 3) Design an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing frequency recovery and active power distribution;

[0099] 4) Design an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing average voltage recovery and reactive power distribution;

[0100] 5) Use the anti-saturation auxiliary controllers and distributed fixed-time controllers in steps 3) and 4) to realize the frequency and voltage regulation of the island AC microgrid model, as well as the distribution of active power and reactive power.

[0101] Embodiment 2:

[0102] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, the technical content is the same as that in Embodiment 1. Further, the island AC microgrid model includes multiple distributed generators;

[0103] The primary control of these distributed generators adopts a droop control strategy.

[0104] The frequency and voltage droop control equations of the distributed generators considering communication delay and actuator saturation are as follows:

[0105]

[0106]

[0107] Wherein, and are the first-order derivatives of ω i (t), and P i (t) respectively; and are the first-order derivatives of and respectively; u fi (t - τ i ), u vi (t - τ i ) are the secondary control inputs for frequency and voltage recovery with communication time delay respectively; τ i is the communication delay time; ωi (t) and represent the actual angular frequency and the rated angular frequency of the i-th distributed generator respectively, V i (t) and represent the actual output voltage amplitude and the rated voltage amplitude of the i-th distributed generator respectively, P i (t) and Q i (t) represent the active power and the reactive power output by the i-th distributed generator respectively, m i and κ i are respectively the i (t) and Q i (t) droop coefficients; represents the direct-axis part of the actual output voltage amplitude V i (t);

[0108] The saturation function sat(·) is as follows:

[0109]

[0110] wherein, u M , u m are the upper and lower bounds of the control input u;

[0111] The rated angular frequency and the rated voltage amplitude V i n (t) of the i-th distributed generator are as follows:

[0112]

[0113] V i n (t) = ∫(sat(u vi (t - τ i )) + sat(u qi (t - τ i )))dt (5)

[0114] wherein, the auxiliary control input u pi (t - τ i ) of the active power of the i-th distributed generator and the auxiliary control input u qi (t - τ i ) of the reactive power of the i-th distributed generator are as follows:

[0115]

[0116]

[0117] wherein, t is time.

[0118] Example 3:

[0119] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation. The technical content is the same as any one of Examples 1-2. Further, the steps of constructing the frequency and voltage droop control equations for distributed generators include:

[0120] 1) Establish the original droop control equations for the frequency and voltage of the i-th distributed generator as follows:

[0121]

[0122] V i (t) = V i n (t) - κ i Q i (t) (9)

[0123] where ω i (t) and respectively represent the actual angular frequency and the rated angular frequency of the i-th distributed generator, V i (t) and respectively represent the actual output voltage amplitude and the rated voltage amplitude of the i-th distributed generator, P i (t) and Q i (t) respectively represent the active power and the reactive power output by the i-th distributed generator, m i and κ i are respectively the droop coefficients of P i (t) and Q i (t);

[0124] 2) Perform Park transformation and Clark transformation on formula (9) to establish an improved voltage droop control equation, that is:

[0125]

[0126]

[0127] where, and respectively represent the direct-axis and quadrature-axis components of the actual output voltage amplitude V i (t);

[0128] 3) According to formula (8) and formula (10), establish the frequency and voltage droop control equations for distributed generators considering communication delay and actuator saturation.

[0129] Example 4:

[0130] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, the technical content is the same as any one of Embodiments 1-3. Further, the island AC microgrid model without communication delay is as follows:

[0131]

[0132]

[0133]

[0134]

[0135] Among them, is the frequency of the i-th distributed generator in the island AC microgrid model without communication delay; ω i (t) represents the actual angular frequency of the i-th distributed generator in the island AC microgrid model with communication delay; is the mean value of the direct-axis part of the output voltage in the island AC microgrid model without communication delay, is the first derivative of; P i z (t) is the active power of the i-th distributed generator in the island AC microgrid model without communication delay, is the reactive power of the i-th distributed generator in the island AC microgrid model without communication delay; m i and κ i are respectively the droop coefficients of P i (t) and Q i (t); u fi (t), u vi (t) are respectively the secondary control inputs for frequency and voltage restoration without communication time delay; P i (t) and Q i (t) respectively represent the active power and reactive power output by the i-th distributed generator; u pi (t), u qi (t) respectively represent the auxiliary control inputs of the active power and reactive power of the i-th distributed generator in the island AC microgrid model without communication time delay. is the mean value of the direct-axis part of the output voltage in the island AC microgrid model with communication delay.

[0136] Embodiment 5:

[0137] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, with the technical content being the same as any one of Embodiments 1-4. Further, the anti-saturation auxiliary controller and the distributed fixed-time controller for achieving frequency restoration are shown as follows:

[0138]

[0139]

[0140] Among them, α ω , β ω are constants greater than 0; η1 is a constant between 0 and 1; sig(·) is the sigmoid function; Δu fi = sat(u fi (t)) - u fi (t) represents the difference between the actual frequency control input of the i-th distributed generator and the designed frequency control input; σ ω is a constant greater than 0; u fi (t) is the secondary control input of the frequency without communication time delay; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid; the intermediate parameter b i is the gain coefficient; λ fi is the anti-saturation auxiliary control variable for achieving frequency restoration; z fi is the improved consensus error. α f , β f are constants greater than 0, and η f is a constant between 0 and 1.

[0141] Embodiment 6:

[0142] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, with the technical content being the same as any one of Embodiments 1-5. Further, the anti-saturation auxiliary controller and the distributed fixed-time controller for achieving active power distribution are as follows:

[0143]

[0144]

[0145] Among them, α p , β p are constants greater than 0; α p1 , β p1 are constants greater than 0; η p is a constant between 0 and 1; η2 is a constant between 0 and 1; σ pis a constant greater than 0; sig(·) is the sigmoid function; Δu pi = sat(u pi (t)) - u pi (t) represents the difference between the actual active power control input and the designed active power control input of the i-th distributed generator; u pi (t) represents the auxiliary control input of the active power of the i-th distributed generator in the islanded AC microgrid model without communication time delay; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid; λ pi is the anti-saturation auxiliary control variable for realizing active power distribution; z pi is the improved consensus error.

[0146] Embodiment 7:

[0147] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, the technical content is the same as any one of Embodiments 1-6. Further, the steps of designing an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing frequency recovery and active power distribution include:

[0148] 1) Construct the fixed-time stability control objective for frequency recovery and active power distribution, that is:

[0149]

[0150] Among them, ω ref is the reference angular frequency, m i is the droop coefficient of the active power P i (t) output by the i-th distributed generator; ω i (t) represents the actual angular frequency of the i-th distributed generator in the islanded AC microgrid model with communication delay; T is the upper bound of the convergence time; P j (t) is the active power output by the j-th distributed generator; m j is the droop coefficient of the active power P j (t) output by the j-th distributed generator;

[0151] 2) According to the control objective (20), design the consensus error, that is:

[0152]

[0153] Among them, e fi is the consensus error of the output angular frequency of the i-th distributed generator, a ij is the weighted adjacency matrix A = (a ijThe element in the i-th row and j-th column of ( ). If microgrid node i can receive information from node j, then a ij = 1, otherwise a ij = 0; b i is the gain coefficient. If microgrid node i can receive information from the leader node, then b i = 1, otherwise b i = 0, N i is the neighborhood set of node i, and e pi is the consistency error of the active power output of the i-th distributed generator; is the frequency of the i-th distributed generator in the islanded AC microgrid model without communication delay; P i z (t) is the active power of the i-th distributed generator in the islanded AC microgrid model without communication delay; ω ref is the reference angular frequency; is the frequency of the j-th distributed generator in the islanded AC microgrid model without communication delay; is the active power of the j-th distributed generator in the islanded AC microgrid model without communication delay;

[0154] 3) According to formula (21), construct the differential equation of the consistency error, that is:

[0155]

[0156] where the intermediate parameter

[0157] 4) Design the anti-saturation auxiliary control variables λ fi and λ pi ;

[0158] 5) Establish the improved consistency error, that is:

[0159]

[0160] 6) According to formula (23), establish the differential equation of the improved consistency error, that is:

[0161]

[0162]

[0163] 7) Design the distributed fixed-time controller to make the improved consistency error z fi converge to 0.

[0164] Example 8:

[0165] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, the technical content is the same as any one of Embodiments 1-7. Further, the anti-saturation auxiliary controller and the distributed fixed-time controller for realizing average voltage recovery are as follows:

[0166]

[0167]

[0168] Among them, the error z vi = e vi - λ vi ; α v , β v , σ v , α v1 , β v1 are constants greater than 0; η1, η v are constants between 0 and 1; Δu vi = sat(u vi (t)) - u vi (t) represents the difference between the actual voltage control input of the i-th distributed generator and the designed voltage control input, and λ vi is the anti-saturation auxiliary controller for realizing average voltage recovery; the intermediate parameter a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid. If the microgrid node i can receive information from node j, then a ij = 1, otherwise a ij = 0; b i is the gain coefficient. If the microgrid node i can receive information from the leader node, then b i = 1, otherwise b i = 0; u vi (t) is the secondary control input for voltage recovery.

[0169] Embodiment 9:

[0170] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, the technical content is the same as any one of Embodiments 1-8. Further, the anti-saturation auxiliary controller and the distributed fixed-time controller for realizing reactive power distribution are as follows:

[0171]

[0172]

[0173] Among them, the error z qi = e qi - λqi ; α q , β q , σ q , α q1 , β q1 are constants greater than 0; η2, η q are constants between 0 and 1; Δu qi = sat(u qi (t)) - u qi (t) represents the difference between the actual uncontrolled input and the designed reactive power control input of the i-th distributed generator; u qi (t) is the secondary control input for achieving reactive power distribution; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the islanded AC microgrid communication topology; λ qi is the anti-saturation auxiliary controller for achieving reactive power distribution.

[0174] Embodiment 10:

[0175] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, the technical content is the same as any one of Embodiments 1-9. Further, the steps of designing the anti-saturation auxiliary controller and the distributed fixed-time controller for achieving average voltage recovery and reactive power distribution include:

[0176] 1) Construct the fixed-time stability control objectives for average voltage recovery and reactive power distribution, that is:

[0177]

[0178] where, V ref is the reference voltage, κ i is the droop coefficient of the reactive power Q i output by the i-th distributed generator. is the mean value of the direct-axis part of the output voltage of the islanded AC microgrid model with communication delay; κ j is the droop coefficient of the reactive power Q j output by the i-th distributed generator; T is the upper bound of the convergence time;

[0179] 2) Based on the output voltage of the i-th distributed generator and the average voltage of its neighbors, design a distributed fixed-time voltage observer, that is:

[0180]

[0181] where, η av is a constant between 0 and 1, and α, β are constants greater than 0. is the direct-axis component of the output voltage of the islanded AC microgrid model with communication delay; is the direct-axis component of the output voltage of the j-th distributed generator in the islanded AC microgrid model with communication delay;

[0182] 3) To ensure that the average value of the output voltages of all distributed generators can converge to the reference value and achieve reactive power distribution, a consensus error is constructed, i.e.:

[0183]

[0184] where, e vi is the consensus error of the average output voltage of the i-th distributed generator, and e qi is the consensus error of the reactive power output of the i-th distributed generator; is the mean value of the direct-axis component of the output voltage of the j-th distributed generator in the islanded AC microgrid model without communication delay;

[0185] 4) According to formula (32), a differential equation of the consensus error is constructed, i.e.:

[0186]

[0187]

[0188] 5) Based on the consensus error, an anti-saturation auxiliary controller and a distributed fixed-time controller are designed to achieve average voltage restoration and reactive power distribution.

[0189] Example 11:

[0190] A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation includes the following steps:

[0191] 1) Establish an islanded AC microgrid model with communication delay and actuator saturation, the details are as follows:

[0192] Figure 1 This is the islanded AC microgrid system in the present invention. As shown in the figure, the islanded AC microgrid includes multiple distributed generators. Figure 2 This is the control block diagram of the distributed generator in the present invention. It can be seen from the figure that the primary control of the distributed generator in the present invention adopts a droop control strategy. For the i-th distributed generator, its droop control equations for frequency and voltage are established:

[0193]

[0194] V i (t) = V i n (t) - κ iQi ( t) (2)

[0195] where ω i (t) and represent the actual angular frequency and the rated angular frequency of the i-th distributed generator respectively, and V i (t) and represent the actual output voltage amplitude and the rated voltage amplitude of the i-th distributed generator respectively, P i (t) and Q i (t) represent the active power and the reactive power output by the i-th distributed generator respectively, m i and κ i are respectively the i (t) and Q i (t) droop coefficients.

[0196] Perform Park transformation and Clark transformation on formula (2) to establish an improved voltage droop control equation:

[0197]

[0198]

[0199] where and represent the direct-axis and quadrature-axis components of the actual output voltage amplitude V i (t) respectively, and satisfy

[0200] According to formula (1) and formula (3), establish frequency and voltage differential equations considering communication delay and actuator saturation:

[0201]

[0202]

[0203] where and are respectively the first derivatives of ω i (t), and P i (t), and are respectively and Q i (t)'s first derivatives, u fi (t - τ i ), u vi (t - τ i ) are respectively the secondary control inputs for frequency and voltage recovery with communication time delay, and τ iLet \(\tau\) be the communication delay time, and \(sat(\cdot)\) be the saturation function, whose expression is:

[0204]

[0205] where \(u\) M and \(u\) m are the upper and lower bounds of the control input \(u\);

[0206] Therefore, from equations (5) and (6), the rated angular frequency and the rated voltage amplitude of the \(i\)-th distributed generator can be obtained as:

[0207]

[0208] \(V\) i n \((t)=\int(sat(u\) vi (t - \tau i )) + sat(u\) qi (t - \tau i )))dt (9)

[0209] where \(u\) pi (t - \tau i ) and \(u\) qi (t - \tau i ) are the auxiliary control inputs for the active and reactive power distribution of the \(i\)-th distributed generator respectively, and their expressions are as follows:

[0210]

[0211]

[0212] 2) Based on state transformation, the islanded AC microgrid model with communication delay is transformed into a model without delay, and the details are as follows:

[0213] To ensure the stability of the islanded microgrid system with communication delay, state transformation is used to transform the system with delay into a simplified system without delay, and then the stability problem of the system considering the effect of delay is analyzed through the simplified system. Therefore, by performing state transformation on equations (5), (6), (10), and (11), the simplified system models for frequency, voltage recovery, and power distribution are obtained as:

[0214]

[0215]

[0216]

[0217]

[0218] wherein, is the frequency of the i-th distributed generator in the simplified system, is the mean value of the direct-axis part of the output voltage of the simplified system, is the first derivative of, is the active power of the i-th simplified system, is the reactive power of the i-th simplified system.

[0219] 3) Based on the simplified system, design and implement an anti-saturation auxiliary controller and a distributed fixed-time controller for frequency recovery and active power distribution. The details are as follows:

[0220] Figure 3 is the overall control architecture for voltage, frequency recovery, and power distribution under the parallel connection of multiple power electronic converters. As can be seen from the figure, the fixed-time stability control objective for frequency recovery and active power distribution is to design a fixed-time control algorithm such that the upper bound T of the convergence time is related to the control parameters but independent of the initial state, and the islanded AC microgrid satisfies the following conditions:

[0221]

[0222] wherein, ω ref is the reference angular frequency, m i is the droop coefficient of the active power P i (t) output by the i-th distributed generator.

[0223] According to the control objective (16), design the consensus error as:

[0224]

[0225] wherein, e fi is the consensus error of the output angular frequency of the i-th distributed generator, Figure 4 is the communication topology of the islanded AC microgrid of the present invention, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A=(a ij ) of the communication topology of the islanded AC microgrid. If the microgrid node i can receive information from node j, then a ij =1; otherwise, a ij =0. b i is the gain coefficient. If the microgrid node i can receive information from the leader node, then b i =1; otherwise, b i =0. N i is the neighborhood set of node i, and e pi is the consensus error of the active power output by the i-th distributed generator.

[0226] According to Equation (17), the differential equation of the consistency error is obtained as follows:

[0227]

[0228] where

[0229] To mitigate the impact of actuator saturation, an anti-saturation auxiliary control variable λ fi , λ pi is designed. The auxiliary control system can be designed as:

[0230]

[0231]

[0232] where α ω , β ω , α p , β p are constants greater than 0, η1 and η2 are numbers between 0 and 1, sig(·) is the sigmoid function, Δu fi = sat(u fi (t)) - u fi (t) represents the difference between the actual frequency control input and the designed frequency control input of the i-th distributed generator, and Δu pi = sat(u pi (t)) - u pi (t) represents the difference between the actual active power control input and the designed active power control input of the i-th distributed generator, and σ ω and σ p are constants greater than 0.

[0233] According to Equations (18), (19), and (20), an improved consistency error is established:

[0234]

[0235] According to Equation (21), the differential equation of the improved consistency error is established:

[0236]

[0237]

[0238] A distributed fixed-time controller is designed such that the improved consistency error z fi can converge to 0. Based on Equations (22) and (23), the distributed fixed-time controller u fi can be designed as:

[0239]

[0240] Among them, α f , β f are constants greater than 0, and η f is a number between 0 and 1.

[0241] Similarly, to achieve active power distribution, a distributed fixed-time controller u pi is designed as follows:

[0242]

[0243] Among them, α p1 , β p1 are constants greater than 0, and η p is a number between 0 and 1.

[0244] 4) Based on the simplified system, an anti-saturation auxiliary controller and a distributed fixed-time controller for average voltage restoration and reactive power distribution are designed, and the details are as follows:

[0245] As Figure 3 shown, the control objectives of voltage restoration and reactive power distribution are to design a fixed-time control algorithm such that the upper bound T of the convergence time is related to the control parameters but independent of the initial state, and the islanded AC microgrid satisfies the following conditions:

[0246]

[0247] Among them, V ref is the reference voltage, and κ i is the droop coefficient of the reactive power Q i output by the i-th distributed generator.

[0248] To ensure that the average output voltage of all distributed generators can converge to the rated value within a fixed time, based on the output voltage of the i-th distributed generator and the average voltage of its neighbors, a distributed fixed-time voltage observer is designed as:

[0249]

[0250] Among them, η av is a number between 0 and 1, and α, β are constants greater than 0.

[0251] To ensure that the average value of the output voltages of all distributed generators can converge to the reference value and achieve reactive power distribution, the consistency error is expressed as

[0252]

[0253] Among them, e viis the consistency error of the average voltage output of the i-th distributed generator, e qi is the consistency error of the reactive power output of the i-th distributed generator.

[0254] According to formula (28), the differential equation of the consistency error is obtained as:

[0255]

[0256]

[0257] To achieve the average voltage recovery under actuator saturation, an anti-saturation auxiliary controller λ vi and a distributed fixed-time controller u vi are designed as:

[0258]

[0259]

[0260] where z vi = e vi - λ vi , α v , β v , σ v , α v1 , β v1 are constants greater than 0, η v is a number between 0 and 1, and Δu vi = sat(u vi (t)) - u vi (t) represents the difference between the actual voltage control input and the designed voltage control input of the i-th distributed generator.

[0261] To achieve the reactive power distribution under actuator saturation, an anti-saturation auxiliary control variable λ qi and a distributed fixed-time controller u qi are designed as:

[0262]

[0263]

[0264] where z qi = e qi - λ qi , α q , β q , σ q , α q1 , β q1 are constants greater than 0, η q is a number between 0 and 1, and Δu qi = sat(uqi (t)) - u qi (t) represents the difference between the actual uncontrolled input and the designed reactive power control input of the i-th distributed generator.

Claims

1. A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation, characterized in that It includes the following steps: 1) Establish an island AC microgrid model with communication delay and actuator saturation; 2) Based on state transformation, transform the island AC microgrid model with communication delay into an island AC microgrid model without communication delay; 3) Design an anti-saturation auxiliary controller and a distributed fixed-time controller for frequency restoration and active power distribution; 4) Design an anti-saturation auxiliary controller and a distributed fixed-time controller for average voltage restoration and reactive power distribution; 5) Use the anti-saturation auxiliary controllers and distributed fixed-time controllers in steps 3) and 4) to achieve frequency and voltage regulation of the island AC microgrid model, as well as active power and reactive power distribution; The island AC microgrid model without communication delay is as follows: Among them, is the frequency of the i-th distributed generator in the island AC microgrid model without communication delay; ω i (t) represents the actual angular frequency of the i-th distributed generator in the island AC microgrid model with communication delay; is the mean value of the direct-axis part of the output voltage of the island AC microgrid model without communication delay, is the first derivative of; P i z (t) is the active power of the i-th distributed generator in the island AC microgrid model without communication delay, is the reactive power of the i-th distributed generator in the island AC microgrid model without communication delay; m i and κ i are respectively i (t) and Q i (t) droop coefficients; u fi (t), u vi (t) are respectively the secondary control inputs for frequency and voltage restoration without communication time delay; P i (t) and Q i (t) respectively represent the active power and reactive power output by the i-th distributed generator; u pi (t), u qi (t) respectively represent the auxiliary control inputs for the active power and reactive power of the i-th distributed generator in the island AC microgrid model without communication time delay; is the mean value of the direct-axis part of the output voltage of the island AC microgrid model with communication delay; The anti-saturation auxiliary controller and distributed fixed-time controller for frequency restoration are respectively as follows: where α ω , β ω are constants greater than 0; η1 is a constant between 0 and 1; sig(·) is the sigmoid function; Δu fi = sat(u fi (t)) - u fi (t) represents the difference between the actual frequency control input and the designed frequency control input of the i-th distributed generator; σ ω is a constant greater than 0; u fi (t) is the secondary control input of the frequency without communication time delay; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A=(a ij ) of the islanded AC microgrid communication topology; the intermediate parameter b i is the gain coefficient; λ fi is the anti-saturation auxiliary control variable for realizing frequency recovery; z fi is the improved consensus error; α f , β f are constants greater than 0, η f is a constant between 0 and 1; The anti-saturation auxiliary controller and distributed fixed-time controller for active power distribution are as follows: where, α p , β p are constants greater than 0; α p1 , β p1 are constants greater than 0; η p is a constant between 0 and 1; η2 is a constant between 0 and 1; sig(·) is the sigmoid function; Δu pi = sat(u pi (t)) - u pi (t) represents the difference between the actual active power control input and the designed active power control input of the i-th distributed generator; u pi (t) represents the auxiliary control input of the active power of the i-th distributed generator in the islanded AC microgrid model without communication time delay; σ p is a constant greater than 0; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid; λ pi is the anti-saturation auxiliary control variable for realizing active power distribution; σ p is a constant greater than 0; z pi is the improved consensus error; The anti-saturation auxiliary controller and distributed fixed-time controller for average voltage restoration are as follows: where the error z vi = e vi - λ vi ; α v , β v , σ v , α v1 , β v1 are constants greater than 0; η1, η v are constants between 0 and 1; Δu vi = sat(u vi (t)) - u vi (t) represents the difference between the actual voltage control input and the designed voltage control input of the i-th distributed generator; λ vi is an anti-saturation auxiliary control variable for realizing average voltage recovery; the intermediate parameter a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the communication topology of the islanded AC microgrid. If the microgrid node i can receive information from node j, then a ij = 1, otherwise a ij = 0; b i is the gain coefficient. If the microgrid node i can receive information from the leader node, then b i = 1, otherwise b i = 0; u vi (t) is the secondary control input for voltage recovery; The anti-saturation auxiliary controller and distributed fixed-time controller for reactive power distribution are as follows: where the error z qi = e qi - λ qi ; α q , β q , σ q , α q1 , β q1 are constants greater than 0; η2, η q are constants between 0 and 1, Δu qi = sat(u qi (t)) - u qi (t) represents the difference between the actual uncontrolled input and the designed reactive power control input of the i-th distributed generator; u qi (t) is the secondary control input for realizing reactive power distribution; a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A = (a ij ) of the islanded AC microgrid communication topology; λ qi is the anti-saturation auxiliary controller for realizing reactive power distribution.

2. A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation according to claim 1, characterized in that The island AC microgrid model includes multiple distributed generators; The primary control of these distributed generators adopts a droop control strategy; The frequency and voltage droop control equations of the distributed generators considering communication delay and actuator saturation are as follows: Wherein, and are respectively the first-order derivatives of ω i (t), and P i (t); and are respectively V i n (t) and the first-order derivatives of Q i (t); u fi (t - τ i ), u vi (t - τ i ) are respectively the secondary control inputs for frequency and voltage restoration with communication time delay; τ i is the communication delay time; ω i (t) and respectively represent the actual angular frequency and the rated angular frequency of the i-th distributed generator, and V i (t) and respectively represent the actual output voltage amplitude and the rated voltage amplitude of the i-th distributed generator; represents the direct-axis part of the actual output voltage amplitude V i (t); P i (t) and Q i (t) respectively represent the active power and the reactive power output by the i-th distributed generator, and m i and κ i are respectively the droop coefficients of P i (t) and Q i (t); The saturation function sat(·) is as follows: where \(u\) M and \(u\) m are the upper and lower bounds of the control input \(u\), respectively; Rated angular frequency of the i-th distributed generator and rated voltage amplitude V i n (t) are as follows: V i n v(t) = ∫(sat(u vi (t - τ i )) + sat(u qi (t - τ i )))dt (5) Among them, the auxiliary control input \(u\) of the active power of the \(i\)-th distributed generator pi (t - τ i ), and the auxiliary control input \(u\) of the reactive power of the \(i\)-th distributed generator qi (t - τ i ) are as follows: Where t is time.

3. A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation according to claim 1, characterized in that, The steps for constructing the frequency and voltage droop control equations of the distributed generators include: 1) Establish the original droop control equations for the frequency and voltage of the i-th distributed generator, as follows: V i V(t) = i n V(t) - κ i Q i Q(t) (21) Among them, ω i (t) and respectively represent the actual angular frequency and the rated angular frequency of the i-th distributed generator, V i (t) and respectively represent the actual output voltage amplitude and the rated voltage amplitude of the i-th distributed generator, P i (t) and Q i (t) respectively represent the active power and the reactive power output by the i-th distributed generator, m i and κ i are respectively i (t) and Q i (t)'s droop coefficients; 2) Perform Park transformation and Clark transformation on formula (21) to establish an improved voltage droop control equation, that is: Among them, and respectively represent the direct-axis and quadrature-axis components of the actual output voltage amplitude V i (t); 3) According to formula (20) and formula (22), establish the frequency and voltage droop control equations of the distributed generators considering communication delay and actuator saturation.

4. A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation according to claim 1, characterized in that, The steps for designing an anti-saturation auxiliary controller and a distributed fixed-time controller for frequency restoration and active power distribution include: 1) Construct the fixed-time stability control objective for frequency restoration and active power distribution, that is: Among them, ω ref is the reference angular frequency, m i is the droop coefficient of the active power P i (t) output by the i-th distributed generator; ω i (t) represents the actual angular frequency of the i-th distributed generator in the island AC microgrid model with communication delay; T is the upper bound of the convergence time; P j (t) is the active power output by the j-th distributed generator; m j is the droop coefficient of the active power P j (t) output by the j-th distributed generator; 2) According to the control objective (24), design the consensus error, that is: where, e fi is the consistency error of the output angular frequency of the i-th distributed generator, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix A=(a ij ) of the communication topology of the islanded AC microgrid. If the microgrid node i can receive information from node j, then a ij =1, otherwise a ij =0; b i is the gain coefficient. If the microgrid node i can receive information from the leader node, then b i =1, otherwise b i =0, N i is the neighborhood set of node i, e pi is the consistency error of the output active power of the i-th distributed generator; is the frequency of the i-th distributed generator of the islanded AC microgrid model without communication delay; P i z (t) is the active power of the i-th distributed generator of the islanded AC microgrid model without communication delay; ω ref is the reference angular frequency; is the frequency of the j-th distributed generator of the islanded AC microgrid model without communication delay; is the active power of the j-th distributed generator of the islanded AC microgrid model without communication delay; 3) According to formula (25), construct the differential equation of the consensus error, that is: Among them, the intermediate parameter 4) Design the anti-saturation auxiliary control variable λ fi and λ pi ; 5) Establish an improved consensus error, that is: 6) According to formula (27), establish the differential equation of the improved consensus error, that is: 7) Design a distributed fixed-time controller to make the improved consensus error z fi converge to 0.

5. A distributed fixed-time control method for an AC microgrid considering communication delay and actuator saturation according to claim 1, characterized in that, The steps for designing an anti-saturation auxiliary controller and a distributed fixed-time controller for average voltage restoration and reactive power distribution include: 1) Construct the fixed-time stability control objective for average voltage restoration and reactive power distribution, that is: Among them, V ref is the reference voltage, and κ i is the droop coefficient of the reactive power Q i output by the i-th distributed generator; is the mean value of the direct-axis component of the output voltage of the islanded AC microgrid model with communication delay; κ j is the droop coefficient of the reactive power Q j output by the i-th distributed generator; T is the upper bound of the convergence time; 2) Based on the output voltage of the i-th distributed generator and the average voltage of its neighbors, design a distributed fixed-time voltage observer, that is: where η av is a constant between 0 and 1, and α and β are constants greater than 0; is the direct-axis component of the output voltage of the islanded AC microgrid model with communication delay; is the direct-axis component of the output voltage of the j-th distributed generator in the islanded AC microgrid model with communication delay; 3) To ensure that the average value of the output voltages of all distributed generators can converge to the reference value and achieve reactive power distribution, construct the consensus error, that is: where, e vi is the consistency error of the average voltage output by the i-th distributed generator, and e qi is the consistency error of the reactive power output by the i-th distributed generator; is the mean value of the direct-axis component of the voltage output by the j-th distributed generator in the island AC microgrid model without communication delay; 4) According to formula (32), construct the differential equation of the consistency error, that is: 5) Based on the consistency error, design an anti-saturation auxiliary controller and a distributed fixed-time controller for realizing average voltage recovery and reactive power distribution.

Images