METHOD FOR FAST AND ACCURATELY SENSING POWER GRID INFORMATION BASED ON NONLINEAR ROBUST ESTIMATION

Abstract

A method for sensing power grid information based on nonlinear robust estimation, including: acquiring an actual power grid phase voltage signal; obtaining a nonlinear state-space distorted power grid model based on the actual power grid phase voltage signal and a phase voltage signal virtual orthogonal signal; establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model, converting an H∞ smoothing estimation problem into a generalized H2 smoothing estimation problem according to the H∞ smoothing estimation performance indicator, and constructing an H∞ smoothing estimator; and obtaining an initial sensed amplitude value and an initial sensed phase value of a power grid voltage signal by using the H∞ smoothing estimator, and performing zero-crossing point detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of a distorted voltage.

Description

The present disclosure claims priority to Chinese Patent Application No. 202111237471.0, filed on Oct. 25, 2021 in China National Intellectual Property Administration and entitled “METHOD FOR FAST AND ACCURATELY SENSING POWER GRID INFORMATION BASED ON NONLINEAR ROBUST ESTIMATION”, which is hereby incorporated by reference in its entirety.

TECHNICAL FIELD

The present disclosure relates to the field of power grid voltage amplitude/frequency/phase information sensing technologies, and in particular, to a method for fast and accurately sensing power grid information based on nonlinear robust estimation.

BACKGROUND

Descriptions of this part only mention a background technology related to the present disclosure, and do not necessarily constitute the related art.

Developing new energy is a key way to solve energy crisis and environmental pollution. However, as new energy is connected to a power grid on a large scale, problems about reliable grid connection for power generation have become increasingly prominent and strictly restricted healthy development of the industry. Particularly, a new energy station is often located at the end of a power grid architecture, and equivalent impedance between a grid connection point and a remote main grid is high. As a result, the problems of drop, distortion, frequency instability, and the like are easy to occur in the power grid voltage, and inadequate sensing control, which may make the new energy station off-grid and even threaten safe and stable running of a local power grid without inadequate sensing control.

Grid-connected equipment is a core of energy conversion in a new-energy power generation system, and its performance directly determines stable running and power quality of the system. Fast and accurately sensing power grid information (amplitude/frequency/phase) is an important foundation for safe running and energy control of the grid-connected equipment.

Many scholars have conducted in-depth research on power grid information sensing technologies, for example, a hardware-circuit-based zero-crossing method, a fundamental-wave Fourier transformation method, a Kalman filtering method, and a dq-transformation-based synchronous reference frame (SRF) phase locking method. However, in the new-energy power generation system, a waveform (amplitude/frequency/phase) of the power grid voltage is distorted seriously, so it is hard to meet a requirement of the grid-connected equipment of the new-energy power generation system for quick and accurate sensing of power grid information by using the foregoing existing methods. In an open-loop linear filtering sensing method, a deviation is great. The larger a window length of a filter is, the slower a dynamic response is. In a moving average filtering sensing method, the window length needs to make a compromise between a response speed and a filtering effect. For a feedback-principle-based phase-locked loop method, it is hard to reconcile a conflict between sensing accuracy and high speed.

SUMMARY

In order to overcome shortcomings of an existing method, for example, poor robustness, incapability of real-time calculation, low estimation accuracy, and low tracking speed, the present disclosure proposes a method for fast and accurately sensing power grid information based on nonlinear robust estimation. Mechanism analysis and discretizing are performed on a power grid voltage signal to establish a type of Lipschitz nonlinear system model, and a Lipschitz nonlinear smoother is further constructed based on a space mapping technology and an output reconstruction method to improve robustness and accuracy of sensing fundamental information (amplitude/frequency/phase) of a distorted power grid.

The method for fast and accurately sensing power grid information based on nonlinear robust estimation includes:

• • acquiring a phase voltage signal of an actual power grid;
  • obtaining a nonlinear state-space distorted power grid model based on the phase voltage signal of the actual power grid and a virtual orthogonal signal of the phase voltage signal;
  • establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model, converting an H∞ smoothing estimation problem into a generalized H₂ smoothing estimation problem, and constructing an H∞ smoothing estimator; and
  • obtaining an initial sensed amplitude value and an initial sensed phase value of a power grid voltage signal by using the H∞ smoothing estimator, and performing zero-crossing point detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain actual sensed amplitude, frequency and phase values of a distorted voltage.

Compared with the prior art, the present disclosure has the following beneficial effects.

The method of the present disclosure is mainly used for fast and accurately sensing a fundamental frequency, an amplitude, and a phase of a power grid voltage. Compared with a conventional phase-locked loop, the method has the advantages that a transient tracking transition process is eliminated, and high speed and accuracy are ensured. According to the method, an amplitude/frequency/phase of a signal is sensed according to the distorted power grid model by using the space mapping technology and the output reconstruction method, without dependence on a conventional linearization method, and integrity of the signal is ensured by using a nonlinear method. The present disclosure provides a method for robustly and fast calculating a parameter. Simulation shows that the method and parameter selection proposed in the present disclosure have good effects in extraction of a fundamental component and a harmonic component of a power grid.

Advantages of additional aspects of the present disclosure will be partially presented in the following descriptions or get understood by implementing the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings of the specification, which constitute a part of the present disclosure, are used for providing a further understanding of the present disclosure. Schematic embodiments of the present disclosure and descriptions thereof are used for explaining the disclosure and do not form improper limitations on the present disclosure.

FIG. 1 is a structural diagram of a method for fast and accurately sensing power grid information based on nonlinear robust estimation according to Embodiment 1 of the present disclosure;

FIG. 2 shows a fundamental signal according to Embodiment 1 of the present disclosure;

FIG. 3 (a) to FIG. 3 (d) show an original signal, a filtered signal, and errors between the original signal as well as the filtered signal and the fundamental signal;

FIG. 4 (a) to FIG. 4 (d) show the original signal, five-step smoothing, and errors between the original signal as well as five-step smoothing and the fundamental signal;

FIG. 5 shows frequency sensing (zero-crossing point detection) according to Embodiment 1 of the present disclosure; and

FIG. 6 (a) to FIG. 6 (d) show a sensing signal and error (zero-crossing point frequency detection+real-time amplitude sensing) and a sensing signal and error (zero-crossing point frequency detection+zero-crossing point amplitude sensing) according to Embodiment 1 of the present disclosure.

DETAILED DESCRIPTION

It is to be noted that the following detailed descriptions are all exemplary and intended to further describe the present disclosure. All technical and scientific terms used herein have the same meanings as commonly understood by those of ordinary skill in the technical art to which the present disclosure belongs, unless otherwise specified.

Embodiment

This embodiment provides a method for fast and accurately sensing power grid information based on nonlinear robust estimation.

As shown in FIG. 1, the method for fast and accurately sensing power grid information based on nonlinear robust estimation includes:

S101: acquiring a phase voltage signal of an actual power grid;

S102: Obtaining a nonlinear state-space distorted power grid model based on the phase voltage signal of the actual power grid and a virtual orthogonal signal of the phase voltage signal;

S103: establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model, converting an H∞ smoothing estimation problem into a generalized H₂ smoothing estimation problem according to the H∞ smoothing estimation performance indicator, and constructing an H∞ smoothing estimator; and

S104: obtaining an initial sensed amplitude value and an initial sensed phase value of a power grid voltage signal by using the H∞ smoothing estimator, and performing zero-crossing detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of a distorted voltage.

Further, the method further includes:

S105: controlling a grid-connected inverter based on the sensed amplitude, frequency and phase values of the distorted voltage.

Further, the converting H∞ smoothing estimation problem into the generalized H₂ smoothing estimation problem specifically includes: converting the H∞ smoothing estimation problem into the generalized H₂ smoothing estimation problem in a space mapping manner according to the H∞ smoothing estimation performance indicator.

Further, the constructing an H∞ smoothing estimator specifically includes: performing processing by using an output reconstruction method according to the generalized H₂ smoothing estimation problem to construct the H∞ smoothing estimator.

Further, the obtaining a nonlinear state-space distorted power grid model based on the phase voltage signal of the actual power grid and a virtual orthogonal signal of the phase voltage signal in S102 specifically includes:

The phase voltage signal v of the actual power grid and the virtual orthogonal signal u of the phase voltage signal are represented as sums of a series of harmonics, defined as:

$\begin{array}{cc}\{\begin{array}{c}v={\sum }_{h=0}{v}_h={\sum }_{h=0}{V}_h\cos {\theta }_h={\sum }_{h=0}{V}_h\cos \left(h\omega t+{\phi }_h\right)\\ u={\sum }_{h=0}{u}_h={\sum }_{h=0}{V}_h\sin {\theta }_h={\sum }_{h=0}{V}_h\sin \left(h\omega t+{\phi }_h\right)\end{array},& \left(1\right)\end{array}$

where

h represents a harmonic component order, V_h represents an amplitude of an h^th harmonic component, θ_h represents a phase angle of the hu harmonic component, φ_h represents an initial phase angle of the h^th harmonic component, ω represents an angular frequency of the actual power grid, t represents running time, v_h represents an h^th harmonic component of the phase voltage signal v of the power grid, and u_h represents an h^th harmonic component of the virtual orthogonal signal u.

The huh harmonic components are represented as:

$\begin{array}{cc}\left[\begin{array}{c}{\stackrel{.}{v}}_h\\ {\stackrel{.}{u}}_h\end{array}\right]=\left[\begin{array}{cc}0& -h\omega \\ h\omega & 0\end{array}\right]\left[\begin{array}{c}{v}_h\\ u_h\end{array}\right],& \left(2\right)\end{array}$

where

v_h represents a derivative of v_h, and u_h represents a derivative of u_h; ω is an intermediate variable, and it is complex to estimate ω, so that Ω is set as a frequency parameter to be estimated, and the following equations are defined:

$\begin{array}{cc}\Omega =\frac{{\omega }^2}{\varpi },& \left(3-1\right)\end{array}$ $\begin{array}{cc}{\psi }_h=\frac{\varpi }{\omega }{u}_h,& \left(3-2\right)\end{array}$

where

ψ_h represents a corrected virtual orthogonal signal, and u_h represents an actual virtual orthogonal signal.

then,

$\begin{array}{cc}\left[\begin{array}{c}{\dot{v}}_h\\ {\dot{\psi }}_h\end{array}\right]=\left[\begin{array}{cc}0& -h\Omega \\ h\varpi & 0\end{array}\right]\left[\begin{array}{c}{v}_h\\ {\psi }_h\end{array}\right],& \left(4\right)\end{array}$

where

ω represents a set initial power grid frequency, and a sign with “′” above represents a derivative of a variable.

A fundamental signal of a phase voltage is extracted, an orthogonal signal is constructed, and if a sampling period T is short enough, the formula (4) is discretized as:

$\begin{array}{cc}\frac{x_0\left(k+1\right)-x_0\left(k\right)}{T}=\left[\begin{array}{cc}0& 0\\ \stackrel{\_}{\omega }& 0\end{array}\right]x_0\left(k\right)+\left[\begin{array}{cc}0& -1\\ 0& 0\end{array}\right]x_0\left(k\right)\Omega +w_0\left(k\right),& \left(5\right)\end{array}$

where

$x_0\left(k\right)=\left[\begin{array}{c}{x}_{01}\left(k\right)\\ x_{02}\left(k\right)\end{array}\right]=\left[\begin{array}{c}v\left(k\right)\\ \psi \left(k\right)\end{array}\right],$

and w₀(k) represents a hypothetical process noise.

If

$\begin{array}{cc}\Omega \left(k+1\right)=\Omega \left(k\right)+w_1\left(k\right),& \left(6\right)\end{array}$

where

w₁(k) represents a hypothetical process noise, based on the formula (5) and the formula (6), a state equation is redescribed as:

$\begin{array}{cc}\left[\begin{array}{c}{x}_1\left(k+1\right)\\ x_2\left(k+1\right)\\ x_3\left(k+1\right)\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ T\overline{\omega }& 1& 0\\ 0& 0& 1\end{array}\right]+\left[\begin{array}{c}-T\\ 0\\ 0\end{array}\right]x_2\left(k\right)x_3\left(k\right)+w\left(k\right),& \left(7\right)\end{array}$

where

$x\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\end{array}\right]=\left[\begin{array}{c}v\left(k\right)\\ \psi \left(k\right)\\ \Omega \left(k\right)\end{array}\right],$

and w(k) represents a hypothetical process noise.

Further, a first observation equation is constructed:

$\begin{array}{cc}y{x}_1\left(k\right)=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]x\left(k\right)+v_1\left(k\right),& \left(8\right)\end{array}$

where

yx₁(k) represents an observed value, and v₁(k) represents an observed noise.

If an ideal voltage signal is:

α(k)=A cos(2πwkT)

β(k)=A sin(2πwkT)

then a second observation equation is:

$\begin{array}{cc}y{x}_2\left(k\right)=\frac{a\tan \left(\frac{\beta \left(k\right)}{\alpha \left(k\right)}\right)}{2\pi kT}=\left[\begin{array}{ccc}0& 0& 1\end{array}\right]x\left(k\right)+v_2\left(k\right),& \left(9\right)\end{array}$

where

yx₂ (k) represents an observed value, and v₂ (k) represents an observed noise.

Based on the above discussion, a phase voltage model is represented as follows:

$\begin{array}{cc}\{\begin{array}{c}x\left(k+1\right)=Ax\left(k\right)+B\varnothing \left(x\left(k\right)\right)+w\left(k\right)\\ y\left(k\right)=Cx\left(k\right)+v\left(k\right)\\ z\left(k\right)=Lx\left(k\right)\\ x\left(0\right)=x_0\end{array},& \left(10\right)\end{array}$

where

$A=\left[\begin{array}{ccc}1& 0& 0\\ T\overline{\omega }& 1& 0\\ 0& 0& 1\end{array}\right],B=\left[\begin{array}{c}-T\\ 0\\ 0\end{array}\right],C=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\end{array}\right],$ $y\left(k\right)=\left[\begin{array}{c}y{x}_1\left(k\right)\\ y{x}_2\left(k\right)\end{array}\right],v\left(k\right)=\left[\begin{array}{c}{v}_1\left(k\right)\\ v_2\left(k\right)\end{array}\right],$

x₀ represents an initial state of x(k), L represents a unit matrix, and z(k) is a signal to be sensed.

Ø(x(k))=x₂ (k) x₃ (k) is a nonlinear term satisfying the following Lipschitz condition:

$\begin{array}{cc}\varnothing \left(x\left(k\right)\right)-\varnothing \left(\hat{x}\left(k\right)\right)\le {\gamma }_1F\left(x\left(k\right)-\hat{x}\left(k\right)\right),& \left(11\right)\end{array}$

y₁ and F respectively represent a Lipschitz constant and a constant matrix, and {circumflex over (x)}(k) represents a state estimate of x(k).

Further, the nonlinear state-space distorted power grid model is a Lipschitz nonlinear system model.

Further, the establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model in S103 specifically includes:

if the H∞ estimation performance indicator is a given scalar γ>0, a smoothing step number/≥0, and an observation sequence {y(i)}_i=0^k, seeking for an estimator ž (k_l|k) (k_l=k−l) satisfying the performance indicator for a signal z (k):

$\begin{array}{cc}\begin{array}{c}\sup \\ \left(x_0,w,v\right)\end{array}\ne 0\frac{{\sum }_{k=0}^N{\stackrel{︶}{z}\left(k_l|k\right)-z\left(k\right)}^2}{{x_0-{\stackrel{︶}{x}}_0}_{P_0^{-1}}^2+{\sum }_{k=0}^N{w\left(k\right)}^2+{\sum }_{k=0}^N{v\left(k\right)}^2}<{\gamma }^2& \left(12\right)\end{array}$

where

{hacek over (x)}₀ and P₀ respectively represent a given state estimate initial value and a positive definite matrix.

Further, the converting an H∞ smoothing estimation problem into a generalized H₂ smoothing estimation problem according to the H∞ smoothing estimation performance indicator and constructing an H∞ smoothing estimator in S103 specifically includes:

S1031: setting an H∞ indicator upper limit constant γ>0, a moment i=k_l=0, a state estimate initial value {hacek over (x)}₀=0, and a Riccati equation initial value P₀=I, N being a specific time point:

$\begin{array}{c}{C}_2={\left[\begin{array}{ccc}{C}^T& F^T& L^T\end{array}\right]}^T\\ Q_2\left(i\right)=\mathrm{diag}\left\{I,-{\gamma }_1^{-2}I,-{\gamma }^{2}I\right\}\\ {\tilde{y}}_2\left(i,2\right)=y_2\left(i\right)-C_2\hat{x}\left(i,2\right)\\ y_2\left(i\right)={\left[\begin{array}{ccc}{y}^T\left(i\right)& {\stackrel{︶}{z}}_{\varnothing }^T\left(i|i\right)& {\stackrel{︶}{z}}^T\left(i|i+l\right)\end{array}\right]}^T\end{array},\mathrm{and}$

• • calculating
  • a second-piece output error variance R₂ (i,2):

$\begin{array}{cc}{R}_2\left(i,2\right)=C_2{P}_2\left(i\right)C_2^T+Q_2\left(i\right),& \left(13\right)\end{array}$

• • a second-piece gain parameter K₂ (i):

$\begin{array}{cc}{K}_2\left(i\right)=A{P}_2\left(i\right)C_2^T{R}_2^{-1}\left(i,2\right),& \left(14\right)\end{array}$

• • a second-piece Riccati equation P₂ (i+1):

$\begin{array}{cc}{P}_2\left(i+1\right)={\mathrm{AP}}_2\left(i\right)A^T+{\mathrm{BB}}^T+I-K_2\left(i\right)R_2\left(i,2\right)K_2^T\left(i\right)& \left(15-1\right)\end{array}$ $\begin{array}{cc}{P}_2\left(0\right)=P_0,& \left(15-2\right)\end{array}$

and

• • a second-piece state estimation equation {circumflex over (x)}(i+1,2):

$\begin{array}{cc}\hat{x}\left(i+1,2\right)=A\hat{x}\left(i,2\right)+\varnothing \left(\stackrel{⌣}{x}\left(i❘i\right)\right)+K_2\left(i\right){\tilde{y}}_2\left(i,2\right)& \left(16-1\right)\end{array}$ $\begin{array}{cc}\hat{x}\left(0,2\right)={\stackrel{⌣}{x}}_0;& \left(16-2\right)\end{array}$

S1032: setting a first-piece initial state value £ (i, 1)={circumflex over (x)}(i, 2) and a first-piece Riccati equation initial value P₁(i)=P₂ (i), and calculating

• • a zeroth-piece output error variance R₀(i):

$\begin{array}{cc}{R}_0\left(i\right)={\mathrm{CP}}_1\left(i\right)C^T+I,& \left(17\right)\end{array}$

• • a zeroth-piece state gain parameter K₀(i):

$\begin{array}{cc}{K}_0\left(i\right)={\mathrm{FP}}_1\left(i\right)C^T{R}_0^{-1}\left(i\right),& \left(18\right)\end{array}$

and

• • an estimation error variance R_ø(i|i) of a virtual output Ž_ø:

$\begin{array}{cc}{R}_{\varnothing }\left(i❘i\right)={\mathrm{FP}}_1\left(i\right)F^T-{\gamma }_1^{-2}I-K_0\left(i\right)R_0\left(i\right)K_0^T\left(i\right);& \left(19\right)\end{array}$

• • S1033: if R₀(i)>0 and R_ø(i|i)<0 are satisfied, calculating
  • an estimation equation Ž_ø(i|i) of the virtual output Ž_ø:

$\begin{array}{cc}{\stackrel{⌣}{z}}_{\varnothing }\left(i❘i\right)=F\hat{x}\left(i,1\right)+K_0\left(i\right){\tilde{y}}_0\left(i\right),& \left(20\right)\end{array}$

• • a zeroth-piece output estimation error {tilde over (y)}₀(i) is:

${\tilde{y}}_0\left(i\right)=y\left(i\right)-C\hat{x}\left(i,1\right)$

where

• • further performing S1034; or
  • if R₀(i)>0 and R_ø(i|i)<0 are not satisfied, resetting the value of y, and performing S1031;
  • S1034: setting an initial value of a smoothing gain parameter to be R_x,kl^kl=P₁(k_l),

$\begin{array}{c}{C}_1={\left[\begin{array}{cc}{C}^T& F^T\end{array}\right]}^T\\ Q_1\left(k_l\right)=\mathrm{diag}\left\{I,-{\gamma }_1^{-2}I\right\}\end{array},$

• • calculating
  • a first-piece output error variance R₁(k_l, 1):

$\begin{array}{cc}{R}_1\left(k_l,1\right)=C_1{P}_1\left(k_l\right)C_1^T+Q_1\left(k_l\right),& \left(21\right)\end{array}$

and

• • a filtering estimation error variance R_z (k_l|k_l) of a signal to be estimated:

$\begin{array}{cc}{R}_z\left(k_l❘k_l\right)={\mathrm{LP}}_1\left(k_l\right)L^T-{\gamma }^{2}I-K_z\left(k_l\right)R_1\left(k_l,1\right)K_z^T\left(k_l\right),& \left(22\right)\end{array}$

where

$K_z\left(k_l\right)={\mathrm{LP}}_1\left(k_l\right)C_1^T{R}_1^{-1}\left(k_l,1\right)$

if R₂ (k_l|k_l)<0, calculating an H∞ filtering estimate ž(k_l|k_l):

$\begin{array}{cc}\stackrel{⌣}{z}\left(k_l❘k_l\right)=L\hat{x}\left(k_l,1\right)+{\mathrm{LR}}_{x,k_l}^{k_l}{C}_1^T{R}_1^{-1}\left(k_l,1\right){\tilde{y}}_1\left(k_l,1\right),& \left(23\right)\end{array}$

where

• • a first-piece output estimation error {tilde over (y)}₁(k_l, 1) and an output signal y₁(k_l) are as follows:

${\tilde{y}}_1\left(k_l,1\right)=y_1\left(k_l\right)-C_1\hat{x}\left(k_l,1\right)y_1\left(k_l\right)={\left[\begin{array}{cc}{y}^T\left(k_l\right)& {\stackrel{⌣}{z}}_{\varnothing }^T\left(k_l❘k_l\right)\end{array}\right]}^T$

• • further performing S1035; or
  • if R_z (k_l|k_l)<0 is not satisfied, resetting the value of y, and performing S1031; S1035: setting i=i+1, calculating R₁(i, 1) according to (21), calculating
  • a first-piece state gain parameter K₁(i):

$\begin{array}{cc}{K}_1\left(i\right)={\mathrm{AP}}_1\left(i\right)C_1^T{R}_1^{-1}\left(i,1\right),& \left(24\right)\end{array}$

• • a first-piece Riccati equation P₁(i+1):

$\begin{array}{cc}{P}_1\left(i+1\right)={\mathrm{AP}}_1\left(i\right)A^T+{\mathrm{BB}}^T+I-K_1\left(i\right)R_1\left(i,1\right)K_1^T\left(i\right)P_1\left(k_l\right)=P_2\left(k_l\right),\mathrm{and}& \left(25\right)\end{array}$

• • a first-piece state estimation equation x(i+1,1):

$\begin{array}{cc}\hat{x}\left(i+1,1\right)=A\hat{x}\left(i,1\right)+\varnothing \left(\stackrel{⌣}{x}\left(i|i\right)\right)+K_1\left(i\right){\tilde{y}}_1\left(i,1\right),& \left(26\right)\end{array}$ $\hat{x}\left(k_l,1\right)=\hat{x}\left(k_l,2\right)$

• • calculating R₀(i), K₀(i), and R_ø(i|i) according to formulas (17) to (19), and
  • if R₀(i)>0 and R_ø(i|i)<0, calculating Žo (i|i) according to (20), and performing S1036; or if R₀(i)>0 and R_ø(i|i)<0 are not satisfied, resetting the value of y, and performing S1031;

S1036: calculating the smoothing gain parameter R_x,kl^l:

$\begin{array}{cc}\{\begin{array}{c}{R}_{x,k_l}^i={R_{x,k_l}^{i-1}\left(A-K_1\left(i-1\right)C_1\right)}^T\\ R_{x,k_l}^{k_l}=P_1\left(k_l\right)\end{array},& \left(27\right)\end{array}$

and

• • a smoothing estimation error variance R_z(k_l|i):

$\begin{array}{cc}{R}_z\left(k_l|i\right)=L{P}_1\left(k_l\right)L^T-{\gamma }^{2}I-K_z\left(k_l\right)R_1\left(k_l,1\right)K_z^T\left(k_l\right)-\sum _{j=k_l+1}^i{R}_{k_l}^j{R}_1\left(j,1\right){\left(R_{k_l}^j\right)}^T,& \left(28\right)\end{array}$

• • where

$R_{k_l}^j={\mathrm{LR}}_{x,k_l}^j{C}_1^T{R}_1^{-1}\left(j,1\right),$

• • if R_z(k_l|i)<0, calculating an H∞ smoothing estimate ž (k_l|i):

$\begin{array}{cc}\stackrel{⌣}{z}\left(k_l❘i\right)=\hat{z}\left(k_l|i-1\right)+L{R}_{x,k_l}^i{C}_1^T{R}_1^{-1}\left(i,1\right){\tilde{y}}_1\left(i,1\right);& \left(29\right)\end{array}$

or

• • if R_z(k_l|i)<0 is not satisfied, resetting the value of y, and performing $1031;
  • S1037: repeating S1035 to S1036 until i=k; and
  • S1038: setting k=k+1, and repeating S1031 to S1037 until k=N.

Further, the H∞ smoothing estimator is a Riccati-equation-based recursive H∞ smoothing estimator.

Further, the obtaining an initial sensed amplitude value and an initial sensed phase value of a power grid voltage signal by using the H∞ smoothing estimator and performing zero-crossing detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of a distorted voltage in S104 specifically includes:

• • determining, according to whether adjacent signals are opposite in sign, whether zero is crossed; and using a first zero-crossing point as a frequency determining standard, and using an amplitude of a zero-crossing point as an amplitude in a first half of a period.

It is to be understood that since the signal is a discrete signal, and may not cross zero everywhere, whether zero is crossed is determined according to whether adjacent signals are opposite in sign. Since the signal may jitter at a zero-crossing point under the impact of a noise, a harmonic and the like, but H∞ filtering processing has weaken or eliminate the jitter, the first zero-crossing point is used as the frequency determining standard.

Like the frequency, the amplitude is affected by the noise and the harmonic, and fluctuates all the time, which greatly affects a sinusoidal waveform. Therefore, the amplitude of the zero-crossing point is used as the amplitude in the first half of the period to correct the waveform.

Further, the controlling a grid-connected inverter based on the sensed amplitude, frequency and phase values of the distorted voltage in S105 refers to ensuring in current loop control of the inverter that a phase difference between an output current and a grid-side fundamental voltage is 0, so as to implement grid connection under a unit power factor.

A basic principle of the present disclosure is that an H∞ problem is converted into an H₂ problem, that is, converted into a generalized Kalman filtering problem, by using a space mapping technology based on an established Lipschitz nonlinear model, and further, an H∞ filter and a smoothing estimator are designed by using an output reconstruction method to perform zero-crossing point detection on a signal to be estimated to sense a phase and an amplitude of a fundamental component.

The method is suitable for a power grid signal whose frequency changes slowly, is an efficient power grid voltage amplitude/frequency/phase sensing technology capable of fast sensing a frequency and an amplitude, and helps determine a failure such as frequency change and voltage drop.

In a robust nonlinear amplitude/frequency/phase sensor process proposed in the present disclosure, both an H∞ filtering problem and a smoothing problem are considered. In an experiment or a simulation process, H∞ filtering estimation or smoothing estimation is selected according to requirements for accuracy and high speed. In addition, an estimator algorithm is specifically described in SUMMARY.

Simulation results:

• • modeling simulation is performed, by using MATLAB, on a method for robust nonlinear sensing of an amplitude/frequency/phase of a distorted power grid. A sampling frequency is set to 10 kHz, and a distorted signal is as follows:

$v\left(i\right)=\{\begin{array}{cc}\begin{array}{c}{H}_0\cos \left(100\pi \mathrm{iT}\right)+H_1\cos \left(300\pi \mathrm{iT}\right)+\\ H_1\cos \left(500\pi \mathrm{iT}\right)+H_1\cos \left(700\pi \mathrm{iT}\right)+\\ H_1\cos \left(900\pi \mathrm{iT}\right)\end{array}& i\le 350\\ \begin{array}{c}0.3H_0\cos \left(100\pi \mathrm{iT}\right)+0.3H_1\cos \left(300\pi \mathrm{iT}\right)+\\ 0.3H_1\cos \left(500\pi \mathrm{iT}\right)+0.3H_1\cos \left(700\pi \mathrm{iT}\right)+\\ 0.3H_1\cos \left(900\pi \mathrm{iT}\right)\end{array}& i>350\end{array}$

H₀=311V. H₁=0.05×H₀, and T=10⁻⁴s. A fundamental wave (as shown in FIG. 2) of the distorted signal is estimated by using the space mapping technology based on a nonlinear model (10).

FIG. 3(a) to FIG. 3(d) show simulation results obtained by a filter designed by using the space mapping technology and a projection formula. It can be seen from the simulation results that a filtering technology has a denoising function, an effect in sensing v (i) is good, but the fundamental signal cannot be completely extracted.

FIG. 4(a) to FIG. 4(d) show simulation results obtained by a five-step smoother (l=5) designed by using the space mapping technology, the output reconstruction method, and a projection formula. It can be seen from the simulation results that a smoothing technology has a denoising function, an effect in sensing v(i) is good, but the fundamental signal cannot be completely extracted.

FIG. 5 shows an estimated frequency value obtained by performing zero-crossing point detection on a signal to be subjected to smoothing estimation. It can be seen that a frequency value can be well sensed by the algorithm, and the frequency jitters when the amplitude of the voltage attenuates greatly.

FIG. 6(a) to FIG. 6(d) respectively simulate a fundamental sensing signal and error in case of using zero-crossing point frequency detection and real-time amplitude sensing and a fundamental sensing signal and error in case of using zero-crossing point frequency detection and zero-crossing point amplitude sensing. It is apparent from a sensed waveform and an error waveform that the fundamental signal can be tracked more accurately by using zero-crossing point frequency detection and zero-crossing point amplitude sensing.

In the present disclosure, according to the distorted power grid model, the fundamental signal of the signal is extracted and the orthogonal signal is constructed, and mechanism analysis and discretizing are performed to establish a type of Lipschitz nonlinear space-state model. H∞ filtering and smoothing estimation performance indicators are proposed, and a Riccati-equation-based recursive filtering and smoothing estimator is constructed by using a space projection technology and the output reconstruction method to preliminarily sense the amplitude and the phase of the voltage signal. Zero-crossing point detection is performed on the preliminarily sensed voltage signal to obtain the sensed amplitude/frequency/phase value of the fundamental signal in the distorted voltage. According to the method, a nonlinear robust estimator is designed by using the space mapping technology based on the distorted power grid model, without dependence on a conventional linearization method, and integrity of the signal is ensured.

The above is only the preferred embodiments of the present disclosure and not intended to limit the present disclosure. Those skilled in the art may make various modifications and variations to the present disclosure. Any modification, equivalent replacement, improvement, and the like made within the spirit and principle of the present disclosure shall fall within the protection scope of the present disclosure.

Claims

1. A method for fast and accurately sensing power grid information based on nonlinear robust estimation, comprising: acquiring a phase voltage signal of an actual power grid;obtaining a nonlinear state-space distorted power grid model based on the phase voltage signal of the actual power grid and a virtual orthogonal signal of the phase voltage signal;establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model, converting an H∞ smoothing estimation problem into a generalized H2 smoothing estimation problem according to the H∞ smoothing estimation performance indicator, and constructing an H∞ smoothing estimator; andobtaining an initial sensed amplitude value and an initial sensed phase value of a power grid voltage signal by using the H∞ smoothing estimator, and performing zero-crossing point detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of a distorted voltage, whereinthe converting an H∞ smoothing estimation problem into a generalized H2 smoothing estimation problem according to the H∞ smoothing estimation performance indicator and constructing an H∞ smoothing estimator specifically comprises:(1) setting an H∞ indicator upper limit constant γ>0, a moment i=kl=0, a state estimate initial value {hacek over (x)}0=0, and a Riccati equation initial value P0=1, N being a specific time point:

2. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, further comprising: controlling a grid-connected inverter based on the sensed amplitude, frequency and phase values of the distorted voltage.

3. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, wherein the converting an H∞ smoothing estimation problem into a generalized H2 smoothing estimation problem specifically comprises: converting the H∞ smoothing estimation problem into the generalized H2 smoothing estimation problem in a space mapping manner according to the H∞ smoothing estimation performance indicator.

4. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, wherein the constructing an H∞ smoothing estimator specifically comprises: performing processing by using an output reconstruction method according to the generalized H2 smoothing estimation problem to construct the H∞ smoothing estimator.

5. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, wherein the obtaining a nonlinear state-space distorted power grid model based on the phase voltage signal of the actual power grid and a virtual orthogonal signal of the phase voltage signal specifically comprises: the phase voltage signal v of the actual power grid and the virtual orthogonal signal u of the phase voltage signal are represented as sums of a series of harmonics, defined as:

6. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, wherein the nonlinear state-space distorted power grid model is a Lipschitz nonlinear system model.

7. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, wherein the establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model specifically comprises: if the H∞ estimation performance indicator is a given scalar γ>0, a smoothing step number l≥0, and an observation sequence {y(i)}i=0k, seeking for an estimator ž(kl|k)(kl=k−l) satisfying the performance indicator for a signal z(k):

8. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, wherein the H∞ smoothing estimator is a Riccati-equation-based recursive H∞ smoothing estimator.

9. The method for fast and accurately sensing power grid information based on nonlinear robust estimation according to claim 1, wherein the obtaining an initial sensed amplitude value and an initial sensed phase value of a power grid voltage signal by using the H∞ smoothing estimator and performing zero-crossing point detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of a distorted voltage specifically comprises: determining, according to whether adjacent signals are opposite in sign, whether zero is crossed; and using a first zero-crossing point as a frequency determining standard, and using an amplitude of a zero-crossing point as an amplitude in a first half of the period.