CN111146778A - Multi-region power grid system design method based on adaptive event triggering dynamic output feedback control - Google Patents

Abstract

A multi-region power grid system design method based on self-adaptive event triggering dynamic output feedback control comprises the following steps: 1) establishing a multi-region power grid model adopting a load frequency control scheme; 2) designing a dynamic output feedback control law for each subsystem; 3) considering the condition of network-induced delay, designing a self-adaptive event triggering mechanism for each subsystem; 4) the method for ensuring that each power grid subsystem is asymptotically stable and has given H by utilizing the Lyapunov stability theory and the linear matrix inequality method_∞Controller algorithm for level γ. The invention uses the distributed dynamic output feedback control method, can guarantee the system performance and reduce the computation complexity under the condition of disturbance; a new self-adaptive event triggering mechanism is designed, and the threshold value is dynamically changed according to the local extreme point output by the system, so that the communication times are reduced to the greatest extent while the system performance is ensured.

Description

Multi-region power grid system design method based on adaptive event triggering dynamic output feedback control

Technical Field

The invention relates to the field of load frequency control of a multi-region power system, in particular to a control method based on a self-adaptive event trigger mechanism combined with distributed dynamic output feedback, which is applied to the multi-region power system and solves the problem of load frequency control with network induced time delay.

Background

Load frequency control has been used in multi-zone power systems for many years, and when the load changes, the power generation reference value is automatically adjusted to maintain the grid frequency and the inter-zone exchange power at a predetermined value. Although the traditional power system adopts a centralized control method, the decentralized load frequency control has the advantages of low computational complexity and good robustness to single-point faults. An open communication channel is often used in a modern power system to complete signal transmission between a prime mover and a local controller, and compared with a traditional special communication channel transmission mode, the method has the advantages of low cost and convenience in maintenance, and meanwhile breaks through the limitation of a physical area. However, network bandwidth limitation brings challenges to transmission reliability, such as network induced delay, packet loss, packet timing disorder, and the like. Therefore, in recent decades, the analysis and design of the open communication channel based distributed power system load frequency control has become a research focus. In addition, as many loads and power generation units compete for limited communication and computing resources in a multi-zone power system, there is also growing concern about how to design a reasonable communication and control scheme.

In recent years, event-triggered mechanisms have received much attention because they can reduce the number of controls while ensuring a given system performance. In an event-triggered control system, the sampled signal is sent according to an event-triggered strategy, i.e. is only transmitted when a given triggering criterion is met. Thus, the event-triggered control system does not require real-time sampling of information and real-time data transmission, which has the advantage of minimizing the use of unnecessary computational and communication resources. However, the conventional constant threshold event triggering mechanism achieves the expected control performance, but since the triggering parameters cannot be dynamically adjusted, a large amount of super-sampling data still needs to be transmitted on the communication network with limited bandwidth. On the other hand, dynamic output feedback is a strong control strategy, and has the characteristic of being more flexible compared with static output feedback. Designing a feedback control method based on adaptive event triggering dynamic output for a multi-region power system is still challenging under the premise of considering communication and computational efficiency.

Disclosure of Invention

In order to solve the problem of load frequency control with network induced time delay in a multi-region power grid system, the invention provides a multi-region power grid system design method based on self-adaptive event trigger dynamic output feedback control, and an analysis method based on an event trigger mechanism time delay system.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a multi-region power system design method based on adaptive event triggering dynamic output feedback control comprises the following steps:

1) establishing a distributed multi-zone power system model adopting a load frequency control scheme;

defining the variable quantity of the grid frequency as delta f_iThe amount of change in power of the tie line is Δ P_tie-iThe variation of the output mechanical torque of the prime mover is delta P_miPrime mover valve position variation Δ P_giLoad reference value is Δ P_rLoad variation amount is Δ P_diThe regulator has a time constant of

Time constant of prime mover

The rotational inertia of the generator is M_iDamping coefficient of generator is D_iThe velocity reduction coefficient is R_iThe tie-line synchronization coefficient between the region i and the region j is T_ijFrequency deviation coefficient of β_iLet x_i(t)＝[Δf_iΔP_tie-iΔP_miΔP_gi]^T，u_i(t)＝ΔP_r，

The dynamic model of the multi-zone power system is

Wherein the content of the first and second substances,

2) designing a dynamic output feedback controller;

based on the output signal y_i(t) design of dynamic output feedback controllers for each grid area as follows

Wherein x_ci(t)，

u_i(t) represents the state, input and output of the controller, respectively, A_Ki，B_Ki，C_Ki， D_KiIs the controller parameter to be designed;

3) designing a self-adaptive event triggering mechanism by considering network-induced time delay;

the network induced delay is defined as tau_l，τ_l∈[τ_m,τ_M) In which τ is_m，τ_MMinimum and maximum time delay, respectively, in the power system, the sensor uses adaptive event triggering, the actuator uses time triggering, the control signal uses a zero-order keeper, and the dynamic system model based on adaptive event triggering is described as:

wherein k is_lRepresenting the trigger moment of the ith time, the following self-adaptive event trigger conditions are designed:

wherein

t^jh represents the time corresponding to the jth local extremum point, and the dynamic output feedback control rate is rewritten into

If t is_kh+h+τ_M≥t_k+1h+τ_k+1In the interval t e [ t ∈ ]_kh+τ_k,t_k+1h+τ_k+1) Define τ (t) as t-t_kh， e_pi(t) ═ 0; if t is_kh+h+τ_M＜t_k+1h+τ_k+1Section of handle [ t_kh+τ_k,t_kh+h+τ_M)， [t_kh+lh+τ_M,t_kh+lh+h+τ_M) The following separations were performed:

Ω₀＝[t_kh+τ_k,t_k+τ_Mh+h)

Ω_j＝[t_kh+τ_M+jh,t_k+1+τ_Mh+jh+h)

Ω_d＝[t_kh+τ_M+d_Mh,t_k+1+τ_k+1)

definition of

Binding e_pi(k) And definition of τ (t), for t ∈ [ t ]_kh+τ_k,t_k+1h+τ_k+1)，E＝[I 0]The following equation holds

Considering the dynamic output feedback controller (7) and the system model (5), the closed loop system is represented as:

wherein the content of the first and second substances,

ψ_i(t) is the initial state of the ith subsystem and

4) designing a dynamic output feedback controller based on an adaptive event trigger mechanism;

the method for ensuring that each power grid subsystem is asymptotically stable and has given H by utilizing the Lyapunov stability theory and the linear matrix inequality method_∞Controller algorithm for level γ.

Further, the process of the step 4) is as follows:

4.1) selecting parameters h > 0 and sigma < 0_im＜1，γ＞0，τ_m≥0，τ_M≥τ_mσ satisfying the following three linear matrix inequalities_im0As an initial value, σ is set_im＝σ_im0；

Wherein the content of the first and second substances,

wherein, mu is h + tau_M-τ_m，

Φ_3i＝col{F_pi,Y_iF_pi},Φ_4i＝[C_piX_iC_pi],

4.2) selecting a suitable step value Δ σ_iIf equation (9) has a solution, let σ_im＝σ_im+Δσ_iReturn to 4.1), otherwise enter 4.3);

4.3) order σ_im＝σ_im-Δσ_iThe maximum threshold value sigma satisfying the inequality group (9) is obtained_imThen the dynamic output feedback controller parameters are expressed as:

the technical conception of the invention is as follows: firstly, a mathematical model of a multi-region power system is given, and a closed-loop time delay system combining network induced time delay, a self-adaptive event trigger mechanism and dynamic output feedback control is provided by using an analysis method of a time delay system. Then, the asymptotic stability and robustness of the system are analyzed by utilizing the Lyapunov theory, and a design method of the controller is derived. And finally, designing a feedback control algorithm based on self-adaptive event triggering dynamic output, acquiring controller parameters by using a linear matrix inequality toolbox, and acquiring an event triggering scheme with the minimum communication times.

The invention has the following beneficial effects: the distributed dynamic output feedback control method is more suitable for an actual power system, and the calculation complexity is reduced while the system performance is ensured; a new self-adaptive event trigger mechanism is designed, and the trigger threshold is dynamically changed according to the local extreme point output by the system, so that the communication times are reduced to the greatest extent while the system performance is ensured.

Drawings

FIG. 1 is a schematic diagram of a three-zone power system;

FIG. 2 is a diagram of a load frequency control model of the ith zone;

fig. 3 is a three-region system output simulation diagram.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

Referring to fig. 1 to 3, a method for designing a multi-region grid system based on adaptive event-triggered dynamic output feedback control includes the following steps:

1) establishing a distributed multi-zone power system model adopting a load frequency control scheme;

defining the variable quantity of the grid frequency as delta f_iThe amount of change in power of the tie line is Δ P_tie-iThe variation of the output mechanical torque of the prime mover is delta P_miPrime mover valve position variation Δ P_giLoad reference value is Δ P_rLoad variation amount is Δ P_diThe regulator time constant is T_GiTime constant of prime mover is T_tiThe rotational inertia of the generator is M_iDamping coefficient of generator is D_iThe velocity reduction coefficient is R_iThe tie-line synchronization coefficient between the region i and the region j is T_ijFrequency deviation coefficient of β_iLet x_i(t)＝[Δf_iΔP_tie-iΔP_miΔP_gi]^T，u_i(t)＝ΔP_r，

The dynamic model of the multi-zone power system is

Wherein the content of the first and second substances,

2) designing a dynamic output feedback controller;

based on the output signal y_i(t) designing a dynamic output feedback controller for each power domain as follows

Wherein x_ci(t)，

u_i(t) represents the state, input and output of the controller, respectively, A_Ki，B_Ki，C_Ki， D_KiIs the controller parameter to be designed;

3) designing a self-adaptive event triggering mechanism by considering network-induced time delay;

the network induced delay is defined as tau_l，τ_l∈[τ_m,τ_M) In which τ is_m，τ_MMinimum and maximum time delay, respectively, in the power system, the sensor uses adaptive event triggering, the actuator uses time triggering, the control signal uses a zero-order keeper, and the dynamic system model based on adaptive event triggering is described as:

wherein k is_lIs shown asAt the triggering time of one time, the following self-adaptive event triggering conditions are designed

Wherein

t^jh represents the time corresponding to the jth local extremum point, and the dynamic output feedback control rate is rewritten into

If t is_kh+h+τ_M≥t_k+1h+τ_k+1In the interval t e [ t ∈ ]_kh+τ_k,t_k+1h+τ_k+1) Define τ (t) as t-t_kh， e_pi(t) ═ 0; if t is_kh+h+τ_M＜t_k+1h+τ_k+1Section of handle [ t_kh+τ_k,t_kh+h+τ_M)， [t_kh+lh+τ_M,t_kh+lh+h+τ_M) The following separations were performed:

Ω₀＝[t_kh+τ_k,t_k+τ_Mh+h)

Ω_j＝[t_kh+τ_M+jh,t_k+1+τ_Mh+jh+h)

Ω_d＝[t_kh+τ_M+d_Mh,t_k+1+τ_k+1)

definition of

Synthesis e_pi(t) and τ (t) for t ∈ [ t ]_kh+τ_k,t_k+1h+τ_k+1)，E＝[I 0]The following equation holds:

considering the dynamic output feedback controller (7) and the system model (5), the closed loop system is represented as:

wherein the content of the first and second substances,

ψ_i(t) is the initial state of the ith subsystem and

4) designing a dynamic output feedback controller based on an adaptive event trigger mechanism;

the method for ensuring that each power grid subsystem is asymptotically stable and has given H by utilizing the Lyapunov stability theory and the linear matrix inequality method_∞Controller algorithm for level γ.

Further, the process of the step 4) is as follows:

4.1) selecting parameters h > 0 and sigma < 0_im＜1，γ＞0，τ_m≥0，τ_M≥τ_mσ satisfying the following three linear matrix inequalities_im0As an initial value, σ is set_im＝σ_im0；

Wherein the content of the first and second substances,

wherein, mu is h + tau_M-τ_m，

Φ_3i＝col{F_pi,Y_iF_pi},Φ_4i＝[C_piX_iC_pi],

4.2) selecting a step value Δ σ_iIf equation (9) has a solution, let σ_im＝σ_im+Δσ_iReturn to 4.1), otherwise enter 4.3);

4.3) order σ_im＝σ_im-Δσ_iThe maximum threshold value sigma satisfying the inequality group (9) is obtained_imThen the dynamic output feedback controller parameters are expressed as:

with reference to fig. 3, the three-area grid parameters are selected as follows:

region 1: t is_t1＝0.31s，T_g1＝0.05s，M₁＝0.2308p.u.·s，D₁＝0.016p.u./Hz， R₁＝3Hz/p.u.，

Region 2: t is_t2＝0.35s，T_g2＝0.06s，M₂＝0.2408p.u.·s，D₂＝0.018p.u./Hz， R₂＝2.87Hz/p.u.，

Region 3: t is_t3＝0.30s，T_g3＝0.08s，M₃＝0.2372p.u.·s，D₃＝0.013p.u./Hz， R₃＝2.92Hz/p.u.，

T₁₂＝0.52p.u./Hz，T₂₃＝0.47p.u./Hz，T₃₁＝0.55p.u./Hz

H is 0.01s, tau_m＝0.005，τ_M＝0.04，σ_imThe simulation experiment has certain initial frequency deviation, and the system output variation is enabled to be zero by triggering a dynamic output feedback control algorithm based on an adaptive event, wherein the frequency deviation is 0.8 and α is 0.1.

Claims (2)

1. A multi-region power grid system design method based on adaptive event triggering dynamic output feedback control is characterized by comprising the following steps;

1) establishing a multi-region power grid model adopting a load frequency control scheme;

defining the variable quantity of the grid frequency as delta f_iThe amount of change in power of the tie line is Δ P_tie-iThe variation of the output mechanical torque of the prime mover is delta P_miPrime mover valve position variation Δ P_giLoad reference value is Δ P_rLoad variation amount is Δ P_diThe regulator has a time constant of

Time constant of prime mover

The rotational inertia of the generator is M_iThe damping coefficient of the generator isD_iThe velocity reduction coefficient is R_iThe tie-line synchronization coefficient between the region i and the region j is T_ijFrequency deviation coefficient of β_iLet x_i(t)＝[Δf_iΔP_tie-iΔP_miΔP_gi]^T，u_i(t)＝ΔP_r，

The dynamic model of the multi-region grid is

Wherein the content of the first and second substances,

2) designing a dynamic output feedback controller;

based on the output signal y_i(t) design of dynamic output feedback controllers for each grid area as follows

Wherein x_ci(t)，

u_i(t) represents the state, input and output of the controller, respectively, A_Ki，B_Ki，C_Ki，D_KiIs the controller parameter to be designed;

3) designing a self-adaptive event triggering mechanism by considering network-induced time delay;

the network induced delay is defined as tau_l，τ_l∈[τ_m,τ_M) Whereinτ_m，τ_MMinimum and maximum time delay respectively, the sensor in the power system adopts self-adaptive event trigger, the actuator adopts time trigger, the control signal adopts zero-order retainer, and the dynamic system model based on the self-adaptive event trigger is described as

Wherein k is_lRepresenting the trigger moment of the ith time, the following self-adaptive event trigger conditions are designed:

σ_i(t^j)＝min{σ_im,λσ_i(t^j-1)}

wherein

0＜σ_im< 1, wherein t^jh represents the time corresponding to the jth local extremum point, and the dynamic output feedback control rate is rewritten into

If t is_kh+h+τ_M≥t_k+1h+τ_k+1In the interval t e [ t ∈ ]_kh+τ_k,t_k+1h+τ_k+1) Define τ (t) as t-t_kh，e_pi(t) ═ 0; if t is_kh+h+τ_M＜t_k+1h+τ_k+1Section of handle [ t_kh+τ_k,t_kh+h+τ_M)，[t_kh+lh+τ_M,t_kh+lh+h+τ_M) Is divided as follows

Ω₀＝[t_kh+τ_k,t_k+τ_Mh+h)

Ω_j＝[t_kh+τ_M+jh,t_k+1+τ_Mh+jh+h)

Ω_d＝[t_kh+τ_M+d_Mh,t_k+1+τ_k+1)

Definition of

Binding e_pi(t) and τ (t) for t ∈ [ t ]_kh+τ_k,t_k+1h+τ_k+1)，E＝[I 0]The following equation holds

Considering the dynamic output feedback controller (7) and the system model (5), the closed loop system is represented as:

wherein the content of the first and second substances,

ψ_i(t) is the initial state of the ith subsystem and

4) designing a dynamic output feedback controller based on an adaptive event trigger mechanism;

method for utilizing Lyapunov stability theory and linear matrix inequalityEach power grid subsystem is ensured to be asymptotically stable and has given H_∞Controller algorithm for level γ.

2. The method for designing a multi-region power grid system based on adaptive event-triggered dynamic output feedback control according to claim 1, wherein the process of the step 4) is as follows:

4.1) selecting proper parameters h > 0 and sigma < 0_im＜1，γ＞0，τ_m≥0，τ_M≥τ_mσ satisfying the following three linear matrix inequalities_im0As an initial value, σ is set_im＝σ_im0；

Wherein the content of the first and second substances,

wherein, mu is h + tau_M-τ_m，

Φ_2i＝col{0,W_2i},Φ_3i＝col{F_pi,Y_iF_pi},Φ_4i＝[C_piX_iC_pi],

4.2) selecting a step value Δ σ_iIf equation (9) has a solution, let σ_im＝σ_im+Δσ_iReturn to 4.1), otherwise enter 4.3);

4.3) order σ_im＝σ_im-Δσ_iThe maximum threshold value sigma satisfying the inequality group (9) is obtained_imThen the dynamic output feedback controller parameters are expressed as:

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