CN104598728A

CN104598728A - Wind power generation-including power system state estimation method taking frequency change into consideration

Info

Publication number: CN104598728A
Application number: CN201510010384.XA
Authority: CN
Inventors: 卫志农; 李春; 孙国强; 孙永辉; 厉超; 陈�胜; 李逸驰
Original assignee: Hohai University HHU
Current assignee: Hohai University HHU
Priority date: 2015-01-08
Filing date: 2015-01-08
Publication date: 2015-05-06
Anticipated expiration: 2035-01-08
Also published as: CN104598728B

Abstract

The invention discloses a method for state estimation of power systems including wind power generation that takes into account frequency changes. With large-scale wind power connected to the power grid, the fluctuation of wind power output will have a significant impact on the frequency of the power grid. Therefore, the traditional state estimation model has been No longer applicable. Based on the quasi-steady-state model of the synchronous generator, the quasi-steady-state model of the load and the simplified RX model of the asynchronous fan, the present invention introduces the frequency deviation as a new state quantity into the state estimation process, and constructs a model for the generator and load nodes The new zero-injection power measurement finally establishes a state estimation model considering frequency deviation. The simulation results of the example show that the model can effectively take into account the frequency deviation of the system, and the accuracy of the state estimation results is significantly improved.

Description

A State Estimation Method for Power System Including Wind Power Generation Considering Frequency Variation

技术领域technical field

发明涉及一种计及频率变化的含风力发电的电力系统状态估计方法，属于电力系统运行和控制技术领域。The invention relates to a method for estimating the state of a power system including wind power generation in consideration of frequency changes, and belongs to the technical field of power system operation and control.

背景技术Background technique

作为能量管理系统(Energy Management System，EMS)的核心，电力系统状态估计通过对生数据的处理，获得状态量的最佳估计值。传统的加权最小二乘法(Weighted LeastSquares，WLS)状态估计算法估计质量和收敛性能很好，是状态估计的经典解法和理论基础，适应各种类型的量测系统。As the core of the Energy Management System (EMS), the state estimation of the power system obtains the best estimated value of the state quantity through the processing of raw data. The traditional Weighted Least Squares (WLS) state estimation algorithm has good estimation quality and convergence performance. It is a classic solution and theoretical basis for state estimation and is suitable for various types of measurement systems.

异步风机简化RX模型既充分考虑了异步发电机本身的特性，较详细地阐述了异步风力发电机的输出功率特性，又较传统RX模型的计算量小，精度满足计算要求。The simplified RX model of asynchronous wind turbine not only fully considers the characteristics of the asynchronous generator itself, but also elaborates the output power characteristics of the asynchronous wind turbine in more detail, and is less computationally intensive than the traditional RX model, and the accuracy meets the calculation requirements.

但现有技术中的状态估计模型仅仅考虑了风机的滑差，并未研究系统的频率变化。随着大规模风电接入电网，风电出力的波动性会对电网频率产生显著影响。However, the state estimation model in the prior art only considers the slip of the fan, and does not study the frequency change of the system. With the integration of large-scale wind power into the grid, the fluctuation of wind power output will have a significant impact on the frequency of the grid.

发明内容Contents of the invention

本发明提供一种计及频率变化的含风力发电的电力系统状态估计方法，将系统的频率偏差作为新的状态量建立新的状态估计模型，相关电力元件也采用考虑频率特性的模型，该方法能够有效计及系统的频率偏差，解决了现有技术中的问题，具有工程应用价值。The present invention provides a method for estimating the state of a power system including wind power generation that takes into account frequency changes. The frequency deviation of the system is used as a new state quantity to establish a new state estimation model, and the relevant power components also use a model that considers frequency characteristics. The method The frequency deviation of the system can be effectively taken into account, the problems in the prior art are solved, and the invention has engineering application value.

本发明为实现上述目的，采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical solutions:

一种计及频率变化的含风力发电的电力系统状态估计方法，依次包括以下步骤：A method for estimating the state of a power system including wind power generation in consideration of frequency changes, comprising the following steps in sequence:

(1)获得电力系统的网络参数和量测量；(1) Obtain network parameters and quantity measurements of the power system;

(2)利用步骤(1)获得的网络参数和量测量进行状态估计程序初始化；(2) utilize the network parameter and quantity measurement that step (1) obtains to carry out state estimation program initialization;

(3)建立计及频率变化的含风力发电的状态估计模型：(3) Establish a state estimation model including wind power generation that takes into account frequency changes:

min J(x)＝[z-h(x)]^TW[z-h(x)]min J(x)＝[zh(x)] ^T W[zh(x)]

其中，J是目标函数；T表示矩阵的转置；W为对角权重矩阵；x为状态量，维数n＝2N-1，N为节点数；z为量测量，维数m，m>n；h为m维非线性量测函数；Among them, J is the objective function; T represents the transposition of the matrix; W is the diagonal weight matrix; x is the state quantity, the dimension n=2N-1, N is the number of nodes; z is the quantity measurement, the dimension m, m> n; h is an m-dimensional nonlinear measurement function;

(4)考虑风机滑差s和系统频率偏差Δf建立新的雅克比矩阵：(4) Consider the fan slip s and the system frequency deviation Δf to establish a new Jacobian matrix:

$H h = = [\begin{matrix} \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; θ θ} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; Δf Δf} \\ \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; θ θ} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; Δf Δf} \\ \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; θ θ} & \frac{{&PartialD; &PartialD; P P}_{k k}}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; Δf Δ f} \\ \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; θ θ} & \frac{{&PartialD; &PartialD; Q Q}_{k k}}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; Δf Δf} \end{matrix}]$

其中，P和Q分别表示普通发电机对应的有功和无功；P_k和Q_k分别为异步风机的接入节点k对应的有功和无功；其中和的维数与系统中风电场节点的数目相同；Among them, P and Q respectively represent the active power and reactive power corresponding to the ordinary generator; P _k and Q _k are respectively the active power and reactive power corresponding to the access node k of the asynchronous fan; where and The dimension of is the same as the number of wind farm nodes in the system;

(5)由初始各状态量V⁽⁰⁾、θ⁽⁰⁾、s⁽⁰⁾、Δf⁽⁰⁾计算量测量的计算值h(x^(k))和雅克比矩阵H(x^(k))，其中，θ表示电压相角，V表示电压幅值，s是滑差，Δf是频率偏差量，0表示初始状态量；(5) Calculated value h(x ⁽ ^k) ⁾ and Jacobian matrix H ⁽ x ( ^k ⁾ ), where θ represents the voltage phase angle, V represents the voltage amplitude, s is the slip, Δf is the frequency deviation, and 0 represents the initial state quantity;

(6)求解状态修正量Δx^(k)，判断是否满足收敛条件，若max{ΔV^(k)|,|Δθ^(k)|,|Δs^(k)|,|Δf^(k)|}>λ，迭代次数k＝k+1，修正状态量V^(k+1)＝V^(k)+ΔV^(k)，θ^(k+1)＝θ^(k)+Δθ^(k)，s^(k+1)＝s^(k)+Δs^(k)，Δf^(k+1)＝Δf^(k)+ΔΔf^(k)，直到符合条件，输出结果，其中，k是迭代次数。(6) Solve the state correction amount Δx ^(k) to judge whether the convergence condition is satisfied, if max{ΔV ^(k) |,|Δθ ^(k) |,|Δs ^(k) |,|Δf ^(k) |}>λ , iteration times k=k+1, corrected state quantity V ^(k+1) = V ^(k) +ΔV ^(k) , θ ^(k+1) = θ ^(k) +Δθ ^(k) , s ^{(k+ 1)} =s ^(k) +Δs ^(k) , Δf ^(k+1) =Δf ^(k) +ΔΔf ^(k) , until the condition is met, output the result, where k is the number of iterations.

上述步骤(2)中，初始化的内容包括：设置迭代精度λ、最大迭代次数以及风力发电机滑差初值和频率偏差初值，形成节点导纳矩阵。In the above step (2), the initialization content includes: setting the iteration accuracy λ, the maximum number of iterations, and the initial value of the wind turbine slip and frequency deviation to form a node admittance matrix.

上述步骤(1)中，网络参数包括：母线编号、名称、补偿电容，输电线路的支路号、首端节点和末端节点编号、串联电阻、串联电抗、并联电导、并联电纳、变压器变比和阻抗，风电场的空气密度、风速，风机机型参数，系统初始频率。In the above step (1), the network parameters include: bus number, name, compensation capacitance, branch number of the transmission line, head node and end node numbers, series resistance, series reactance, parallel conductance, parallel susceptance, transformer transformation ratio and impedance, the air density and wind speed of the wind farm, the model parameters of the fan, and the initial frequency of the system.

上述步骤(1)中，量测量z包括：节点电压幅值、节点注入有功功率和无功功率，普通线路支路和变压器支路的有功功率和无功功率。In the above step (1), the quantity measurement z includes: node voltage amplitude, node injected active power and reactive power, active power and reactive power of ordinary line branch and transformer branch.

上述计及频率变化的含风力发电的电力系统状态估计是在同步发电机准稳态模型、负荷准稳态模型和异步风机简化RX模型的基础上，将频率偏差作为新的状态量引入到状态估计过程中，并且对发电机和负荷节点构造了新的零注入功率量测，最终建立了考虑频率偏差的状态估计模型。算例仿真结果表明该模型可有效计及系统的频率偏差，状态估计结果精度得到提高，具有工程应用前景。The above-mentioned state estimation of the power system including wind power generation considering the frequency change is based on the quasi-steady-state model of the synchronous generator, the quasi-steady-state model of the load and the simplified RX model of the asynchronous wind turbine, and introduces the frequency deviation as a new state quantity into the state In the estimation process, new zero-injected power measurements are constructed for generators and load nodes, and a state estimation model considering frequency deviation is finally established. The simulation results of the example show that the model can effectively take into account the frequency deviation of the system, and the accuracy of the state estimation results is improved, which has the prospect of engineering application.

附图说明Description of drawings

图1为本发明方法流程图。Fig. 1 is a flow chart of the method of the present invention.

图2为本发明提出的计及频率变化的含风力发电的电力系统状态估计所应用的算例系统，采用的是IEEE-14节点系统。Fig. 2 is a calculation example system applied to the state estimation of the power system including wind power generation in consideration of the frequency change proposed by the present invention, and the IEEE-14 node system is adopted.

图3为具体实施方式中异步电机的Γ形简化等效电路。Fig. 3 is a Γ-shaped simplified equivalent circuit of an asynchronous motor in a specific embodiment.

图4为两种状态估计模型电压平均估计误差。Figure 4 shows the average voltage estimation error of the two state estimation models.

具体实施方式Detailed ways

本发明以异步电机的准稳态模型为例分析风机的频率特性。为了简化计算，本发明采用RX模型。容量较大(大于40kW)的异步电机，由于其X₁<<X_m，且R₁和R_m可以忽略不计，可近似等效为图3所示的Γ形电路。The invention analyzes the frequency characteristics of the fan by taking the quasi-stable model of the asynchronous motor as an example. In order to simplify the calculation, the present invention adopts the RX model. An asynchronous motor with a large capacity (greater than 40kW), because its X ₁ <<X _m , and R ₁ and R _m can be ignored, can be approximately equivalent to the Γ-shaped circuit shown in Figure 3.

图3中R₁、R₂、R_m分别为定子电阻、转子电阻、励磁电阻，X₁、X₂和X_m分别表示定子电抗、转子电抗和励磁电抗，s是滑差，Δf是频率偏差量，P_G和Q_G分别表示有功功率值和无功功率值。In Figure 3, R ₁ , R ₂ , and R _m are stator resistance, rotor resistance, and excitation resistance, respectively; X ₁ , X ₂ , and X _m represent stator reactance, rotor reactance, and excitation reactance; s is slip; Δf is frequency deviation PG and Q _G represent active power value and _reactive power value respectively.

为了考虑电网侧频率偏差对同步发电机的影响，同步发电机采用下面的准稳态模型：In order to consider the impact of grid-side frequency deviation on the synchronous generator, the following quasi-steady-state model is adopted for the synchronous generator:

${P P}_{G G} = = {P P}_{G G__set set} - - \frac{{P P}_{R R}}{{R R}_{R R}} Δf Δf$

${Q Q}_{G G} = = {Q Q}_{G G__set set} + + {a a}_{Q Q} ((- - \frac{{P P}_{R R}}{{R R}_{R R}} Δf Δ f)) + + {b b}_{Q Q} {((- - \frac{{P P}_{R R}}{{R R}_{R R}} Δf Δ f))}^{22}$

式中：P_G和Q_G分别表示同步发电机输出的有功功率值和无功功率值，P_{G_set}和Q_{G_set}分别是同步发电机初始的有功功率值和无功功率值，P_R是额定有功功率值，R_R是对应同步发电机的调速率，a_Q和b_Q是同步发电机无功出力对应的调节系数，Δf表示频率偏差量，即系统稳态时频率与额定值的偏差。In the formula: PG _and Q _G respectively represent the active power value and reactive power value output by the synchronous generator, _{PG_set} and Q _{G_set} are the initial active power value and reactive power value of the synchronous generator respectively, _PR is the rated active power Power value, R _R is the regulation rate of the corresponding synchronous generator, a _Q and b _Q are the adjustment coefficients corresponding to the reactive output of the synchronous generator, Δf represents the frequency deviation, that is, the deviation between the frequency and the rated value in the steady state of the system.

负荷的准稳态数学模型采用考虑频率变化的静态模型，其多项式模型可表示如下：The quasi-steady-state mathematical model of the load adopts a static model considering the frequency change, and its polynomial model can be expressed as follows:

${P P}_{L L} = = {P P}_{L L__set set} ((11 + + {K K}_{p p} Δf Δ f)) (({p p}_{p p} + + {p p}_{c c} ((\frac{{V V}_{L L}}{{V V}_{LB LB}})) + + {p p}_{z z} {((\frac{{V V}_{L L}}{{V V}_{LB LB}}))}^{22}))$

${Q Q}_{L L} = = {P P}_{L L__set set} ((11 + + {K K}_{q q} Δf Δ f)) (({q q}_{p p} + + {q q}_{c c} ((\frac{{V V}_{L L}}{{V V}_{LB LB}})) + + {q q}_{z z} {((\frac{{V V}_{L L}}{{V V}_{LB LB}}))}^{22}))$

式中：P_L和Q_L分别表示该负荷的有功和无功值，P_{L_set}和Q_{L_set}分别表示该负荷的有功和无功的初始值，K_p和K_q分别表示负荷有功和无功对应的调节效应系数。p_p、p_c、p_z和q_p、q_c、q_z表示负荷模型静态电压特性系数，V_L和V_LB分别是该负荷的电压运行值和额定电压值，Δf是频率偏差量。In the formula: _PL and Q _L represent the active and reactive values of the load respectively, _{PL_set} and Q _{L_set} represent the initial values of active and reactive power of the load respectively, K _p and K _q represent the corresponding load active and reactive power adjustment effect coefficient. p _p , p _c , p _z and q _p , q _c , q _z represent the static voltage characteristic coefficients of the load model, V _L and V _LB are the voltage operating value and rated voltage value of the load respectively, and Δf is the frequency deviation.

电力系统状态估计的量测方程为：The measurement equation for power system state estimation is:

z＝h(x)+εz=h(x)+ε

式中：x为状态量(维数n＝2N-1，N为节点数)；z为量测量(维数m，m>n)；h为m维非线性量测函数；ε为m维量测误差。In the formula: x is the state quantity (dimension n=2N-1, N is the number of nodes); z is the quantity measurement (dimension m, m>n); h is the m-dimensional nonlinear measurement function; ε is the m-dimensional measurement error.

按最小二乘准则建立的目标函数如下：The objective function established according to the least squares criterion is as follows:

min J(x)＝[z-h(x)]^TW[z-h(x)]min J(x)＝[zh(x)] ^T W[zh(x)]

其中J是目标函数，T表示矩阵的转置，W为对角权重矩阵，W_ii＝1/σ_i ²，σ_i为标准差。Where J is the objective function, T represents the transpose of the matrix, W is the diagonal weight matrix, W _ii =1/σ _i ² , and σ _i is the standard deviation.

一般情况下，h(x)为非线性函数，故采用迭代的方法求解。令x₀是x的某一近似值，可以在x₀附近对h(x)进行泰勒展开，保留一次项，并忽略二次以上的非线性项，得到：In general, h(x) is a nonlinear function, so an iterative method is used to solve it. Let x ₀ be an approximate value of x, Taylor expansion can be performed on h(x) near x ₀ , the first-order items are retained, and the non-linear items above the second order are ignored, to obtain:

h(x)≈h(x₀)+H(x₀)Δxh(x)≈h(x ₀ )+H(x ₀ )Δx

式中Δx＝x-x₀，H(x)为h(x)的雅克比矩阵。将此式代入目标函数中，可得到：In the formula, Δx=xx ₀ , H(x) is the Jacobian matrix of h(x). Substituting this formula into the objective function, we can get:

J(x)＝[Δz-H(x₀)Δx]^TW[Δz-H(x₀)Δx]J(x)＝[Δz-H(x ₀ )Δx] ^T W[Δz-H(x ₀ )Δx]

式中Δz＝z-h(x₀)，将上式展开配方得到：In the formula, Δz=zh(x ₀ ), expand the above formula to get:

J(x)＝Δz^T[W-WH(x₀)Σ(x₀)H^T(x₀)W]ΔzJ(x)＝Δz ^T [W-WH(x ₀ )Σ(x ₀ )H ^T (x ₀ )W]Δz

+[Δx-Σ(x₀)H^T(x₀)WΔz]^TΣ^-1(x₀)[Δx-Σ(x₀)H^T +[Δx-Σ(x ₀ )H ^T (x ₀ )WΔz] ^T Σ ^-1 (x ₀ )[Δx-Σ(x ₀ )H ^T

×(x₀)WΔz]×(x ₀ )WΔz]

式中Σ(x₀)＝[H^T(x₀)WH(x₀)]^-1。In the formula, Σ(x ₀ )=[H ^T (x ₀ )WH(x ₀ )] ^-1 .

上式中右边第一项与Δx无关。因此，欲使J(x)极小，第二项应为0，从而有：The first term on the right side of the above formula has nothing to do with Δx. Therefore, to make J(x) extremely small, the second term should be 0, thus:

Δx^(l)＝[H^T(x^(l))WH(x^(l))]^-1H^T(x^(l))W[z-h(x^(l))]Δx ^(l) ＝[H ^T (x ^(l) )WH(x ^(l) )] ^-1 H ^T (x ^(l) )W[zh(x ^(l) )]

x^(l+1)＝x^(l)+Δx^(l) x ^(l+1) = x ^(l) +Δx ^(l)

其中l表示迭代次数，x按上式进行迭代修正，直到目标函数接近最小为止。Where l represents the number of iterations, and x is iteratively corrected according to the above formula until the objective function is close to the minimum.

因为风电的接入，本发明的状态估计模型在基本加权最小二乘法的基础上，不仅引入滑差s作为状态量引入修正方程，而且还考虑了频率偏移量Δf。所以状态估计的修正量扩展到Δx＝[Δθ ΔV Δs ΔΔf]^T，θ表示电压相角，V表示电压幅值，得到新的含有s和Δf的分块扩展雅可比矩阵为：Because of the access of wind power, the state estimation model of the present invention not only introduces the slip s as a state quantity into the correction equation on the basis of the basic weighted least square method, but also considers the frequency offset Δf. Therefore, the correction amount of the state estimation is extended to Δx=[Δθ ΔV Δs ΔΔf] ^T , θ represents the voltage phase angle, V represents the voltage amplitude, and the new block extended Jacobian matrix containing s and Δf is obtained as:

$H h = = [\begin{matrix} \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; θ θ} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; Δf Δ f} \\ \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; θ θ} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; Δf Δf} \\ \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; θ θ} & \frac{{&PartialD; &PartialD; P P}_{k k}}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; Δf Δf} \\ \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; θ θ} & \frac{{&PartialD; &PartialD; Q Q}_{k k}}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; Δf Δ f} \end{matrix}]$

式中：P和Q分别表示普通发电机对应的有功和无功。P_k和Q_k分别为异步风机的接入节点k对应的有功和无功。其中和的维数与系统中风电场节点的数目相同。In the formula: P and Q represent the active power and reactive power corresponding to the ordinary generator, respectively. P _k and Q _k are the active power and reactive power corresponding to the access node k of the asynchronous fan, respectively. in and The dimension of is the same as the number of wind farm nodes in the system.

系统中传统节点注入功率表示为：The injected power of traditional nodes in the system is expressed as:

${P P}_{i i} = = {V V}_{i i} {Σ Σ}_{j j = = 11}^{n no} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij}))$

${Q Q}_{i i} = = {V V}_{i i} {Σ Σ}_{j j = = 11}^{n no} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} + + {B B}_{ij ij} cos cos {θ θ}_{ij ij}))$

式中：P_i和Q_i分别表示节点i注入的有功和无功；V_i和V_j分别表示节点i和j的电压幅值；θ_ij是节点i到节点j的电压相角差；G_ij和B_ij则表示节点导纳阵中对应节点i和j之间的电导和电纳；n是系统节点总数。In the formula: P _i and Q _i represent the active power and reactive power injected by node i respectively; V _i and V _j represent the voltage amplitudes of nodes i and j respectively; θ _ij is the voltage phase angle difference from node i to node j; G _ij and B _ij represent the conductance and susceptance between the corresponding nodes i and j in the nodal admittance array; n is the total number of nodes in the system.

当计及发电机频率特性时，构建发电机节点零注入功率，此类发电机节点零注入功率可表达为：When the generator frequency characteristics are considered, the zero injection power of the generator node is constructed, and the zero injection power of this type of generator node can be expressed as:

${P P}_{Gi Gi} = = {P P}_{G G__set set} - - \frac{{R R}_{R R}}{{R R}_{R R}} Δf Δf + + {V V}_{i i} {Σ Σ}_{j j = = 11}^{n no} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) = = 00$

${Q Q}_{Gi Gi} = = {Q Q}_{G G__set set} + + {a a}_{Q Q} ((- - \frac{{P P}_{R R}}{{R R}_{R R}} Δf Δ f)) + + {b b}_{Q Q} {((- - \frac{{P P}_{R R}}{{R R}_{R R}} Δf Δ f))}^{22} + + {V V}_{i i} {Σ Σ}_{j j = = 11}^{n no} {V V}_{j j} (({G G}_{ij ij} {sin sin θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) = = 00$

式中：P_Gi和Q_Gi分别表示发电机i注入的有功和无功。In the formula: P _Gi and Q _Gi represent the active power and reactive power injected by generator i, respectively.

当计及负荷频率特性时，构建负荷节点的零注入功率，此时负荷节点的零注入功率可表达为：When the load frequency characteristics are considered, the zero injected power of the load node is constructed. At this time, the zero injected power of the load node can be expressed as:

$\begin{matrix} {P P}_{Li Li} = = {P P}_{L L__set set} ((11 + + {K K}_{p p} Δf Δf)) (({p p}_{p p} + + {p p}_{c c} ((\frac{{V V}_{L L}}{{V V}_{LB LB}})) + + {p p}_{z z} {((\frac{{V V}_{L L}}{{V V}_{LB LB}}))}^{22})) \\ + + {V V}_{i i} {Σ Σ}_{j j = = 11}^{n no} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) = = 00 \end{matrix}$

$\begin{matrix} {Q Q}_{Li Li} = = {Q Q}_{L L__set set} ((11 + + {K K}_{q q} Δf Δf)) (({q q}_{p p} + + {q q}_{c c} ((\frac{{V V}_{L L}}{{V V}_{LB LB}})) + + {q q}_{z z} {((\frac{{V V}_{L L}}{{V V}_{LB LB}}))}^{22})) \\ + + {V V}_{i i} {Σ Σ}_{j j = = 11}^{n no} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) = = 00 \end{matrix}$

式中：P_Li和Q_Li分别表示负荷i注入的有功和无功。In the formula: P _Li and Q _Li represent the active and reactive power injected by load i, respectively.

由前面各式可推导出雅可比矩阵H的各元素，其中部分分块矩阵元素如下：The elements of the Jacobian matrix H can be deduced from the previous formulas, and some of the elements of the block matrix are as follows:

$\frac{{&PartialD; &PartialD; P P}_{ki the ki}}{{&PartialD; &PartialD; V V}_{i i}} = = - - \frac{{22 s the s}_{i i} {R R}_{22 i i} {V V}_{i i}}{{s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δ f))}^{22} + + {R R}_{22 i i}^{22}}$

$\frac{{&PartialD; &PartialD; P P}_{ki the ki}}{{&PartialD; &PartialD; s the s}_{i i}} = = \frac{{R R}_{22 i i} {V V}_{i i}^{22} {s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δf))}^{22} - - {R R}_{22 i i}^{33} {V V}_{i i}^{22}}{{(({s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δf))}^{22} + + {R R}_{22 i i}^{22}))}^{22}}$

$\frac{{&PartialD; &PartialD; P P}_{ki the ki}}{&PartialD; &PartialD; Δf Δf} = = \frac{22 ((11 + + Δf Δ f)) {R R}_{22 i i} {V V}_{i i}^{22} {s the s}_{i i}^{33} {X x}_{1212 i i}^{22}}{{(({s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δf))}^{22} + + {R R}_{22 i i}^{22}))}^{22}}$

$\frac{&PartialD; &PartialD; {Q Q}_{ki the ki}}{{&PartialD; &PartialD; V V}_{i i}} = = - - \frac{22 {V V}_{i i}}{{X x}_{mi mi} ((11 + + Δf Δf))} - - \frac{{22 V V}_{i i} {s the s}_{i i}^{22} {X x}_{1212 i i} ((11 + + Δf Δf))}{{s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δf))}^{22} + + {R R}_{22 i i}^{22}}$

$\frac{{&PartialD; &PartialD; Q Q}_{ki the ki}}{&PartialD; &PartialD; {s the s}_{i i}} = = - - \frac{{22 s the s}_{i i} {V V}_{i i}^{22} {X x}_{1212 i i} ((11 + + Δf Δf)) {R R}_{22 i i}^{22}}{{(({s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δf))}^{22} + + {R R}_{22 i i}^{22}))}^{22}}$

$\frac{{&PartialD; &PartialD; Q Q}_{ki the ki}}{&PartialD; &PartialD; Δf Δf} = = \frac{{V V}_{i i}^{22}}{{X x}_{mi mi} {((11 + + Δf Δf))}^{22}} + + \frac{{V V}_{i i}^{22} {s the s}_{i i}^{22} {X x}_{1212 i i} (({s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δf))}^{22} - - {R R}_{22 i i}^{22}))}{{(({s the s}_{i i}^{22} {X x}_{1212 i i}^{22} {((11 + + Δf Δf))}^{22} + + {R R}_{22 i i}^{22}))}^{22}}$

$\frac{&PartialD; &PartialD; {P P}_{Gi Gi}}{&PartialD; &PartialD; Δf Δ f} = = - - \frac{{P P}_{R R}}{{R R}_{R R}}$

$\frac{{&PartialD; &PartialD; Q Q}_{Gi Gi}}{&PartialD; &PartialD; Δf Δf} = = - - {a a}_{Q Q} \frac{{P P}_{R R}}{{R R}_{R R}} + + {22 b b}_{Q Q} {((\frac{{P P}_{R R}}{{R R}_{R R}}))}^{22} Δf Δf$

$\frac{{&PartialD; &PartialD; P P}_{Li Li}}{&PartialD; &PartialD; {V V}_{i i}} = = {P P}_{L L__set set} ((11 + + {K K}_{p p} Δf Δf)) ((\frac{{p p}_{c c}}{{V V}_{LB LB}} + + \frac{{22 p p}_{z z} {V V}_{i i}}{{V V}_{LB LB}^{22}})) + + \frac{22}{{V V}_{i i}} (({G G}_{ii i} {V V}_{i i}^{22} + + {P P}_{i i}))$

$\frac{{&PartialD; &PartialD; Q Q}_{Li Li}}{&PartialD; &PartialD; {V V}_{i i}} = = {Q Q}_{L L__set set} ((11 + + {K K}_{q q} Δf Δf)) ((\frac{{q q}_{c c}}{{V V}_{LB LB}} + + \frac{{22 q q}_{z z} {V V}_{i i}}{{V V}_{LB LB}^{22}})) + + \frac{11}{{V V}_{i i}} ((- - {B B}_{ii i} {V V}_{i i}^{22} + + {Q Q}_{i i}))$

式中：P_ki和Q_ki分别表示风机节点i注入的有功和无功，s_i表示风机节点i对应的滑差。其中X₁₂＝X₁+X₂，下标i表示风机节点i对应的参数。In the formula: P _ki and Q _ki represent the active and reactive power injected by fan node i, respectively, and s _i represents the slip corresponding to fan node i. Where X ₁₂ =X ₁ +X ₂ , the subscript i represents the parameter corresponding to the fan node i.

根据上面的公式由初始各状态量V⁽⁰⁾、θ⁽⁰⁾、s⁽⁰⁾、Δf⁽⁰⁾计算量测量的计算值h(x^(k))和雅克比矩阵H(x^(k))，k是迭代次数，求解出状态修正量Δx^(k)，然后判断是否满足收敛条件，如果未达到收敛要求，修正状态量V^(k+1)＝V^(k)+ΔV^(k)，θ^(k+1)＝θ^(k)+Δθ^(k)，s^(k+1)＝s^(k)+Δs^(k)，Δf^(k+1)＝Δf^(k)+ΔΔf^(k)，重复上述操作，直到收敛精度达到要求。According to the above formula ^{, the} calculated value h(x ⁽ ^k ⁾ ) and the Jacobian matrix H ⁽ x ^(k ) ⁾ ), k is the number of iterations, solve the state correction quantity Δx ^(k) , and then judge whether the convergence condition is met, if the convergence requirement is not met, correct the state quantity V ^(k+1) = V ^(k) + ΔV ^(k) , θ ^(k+1) = θ ^(k) + Δθ ^(k) , s ^(k+1) = s ^(k) + Δs ^(k) , Δf ^(k+1) = Δf ^(k) + ΔΔf ^{(k )} , repeat the above operations until the convergence accuracy meets the requirements.

上述方法具体步骤如下：The specific steps of the above method are as follows:

(1)获得电力系统的网络参数和量测量。网络参数包括：母线编号、名称、补偿电容，输电线路的支路号、首端节点和末端节点编号、串联电阻、串联电抗、并联电导、并联电纳、变压器变比和阻抗，风电场的空气密度、风速，风机机型参数，系统初始频率；量测量z包括：节点电压幅值、节点注入有功功率和无功功率，普通线路支路和变压器支路的有功功率和无功功率；(1) Obtain network parameters and quantity measurements of the power system. Network parameters include: bus bar number, name, compensation capacitance, branch number of transmission line, head node and end node numbers, series resistance, series reactance, parallel conductance, parallel susceptance, transformer ratio and impedance, wind farm air Density, wind speed, fan model parameters, system initial frequency; measurement z includes: node voltage amplitude, node injected active power and reactive power, active power and reactive power of ordinary line branches and transformer branches;

(2)利用上面获得的参数进行状态估计程序初始化。初始化的内容包括：设置迭代精度λ、最大迭代次数，风力发电机滑差初值和频率偏差初值，形成节点导纳矩阵；(2) Use the parameters obtained above to initialize the state estimation program. The initialization content includes: setting the iteration accuracy λ, the maximum number of iterations, the initial value of the slip of the wind turbine and the initial value of the frequency deviation, and forming the node admittance matrix;

min J(x)＝[z-h(x)]^TW[z-h(x)]min J(x)＝[zh(x)] ^T W[zh(x)]

$H h = = [\begin{matrix} \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; θ θ} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; P P}{&PartialD; &PartialD; Δf Δ f} \\ \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; θ θ} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; Q Q}{&PartialD; &PartialD; Δf Δf} \\ \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; θ θ} & \frac{{&PartialD; &PartialD; P P}_{k k}}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; {P P}_{k k}}{&PartialD; &PartialD; Δf Δf} \\ \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; θ θ} & \frac{{&PartialD; &PartialD; Q Q}_{k k}}{&PartialD; &PartialD; V V} & \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; s the s} & \frac{&PartialD; &PartialD; {Q Q}_{k k}}{&PartialD; &PartialD; Δf Δf} \end{matrix}]$

(5)由初始各状态量V⁽⁰⁾、θ⁽⁰⁾、s⁽⁰⁾、Δf⁽⁰⁾计算量测量的计算值h(x^(k))和雅克比矩阵H(x^(k))；(5) Calculated value h(x ⁽ ^k) ⁾ ^and Jacobian matrix H(x ( ^k ⁾ );

(6)求解状态修正量Δx^(k)，判断是否满足收敛条件，若max{|ΔV^(k)|,|Δθ^(k)|,|Δs^(k)|,|Δf^(k)|}>λ，迭代次数k＝k+1，修正状态量V^(k+1)＝V^(k)+ΔV^(k)，θ^(k+1)＝θ^(k)+Δθ^(k)，s^(k+1)＝s^(k)+Δs^(k)，Δf^(k+1)＝Δf^(k)+ΔΔf^(k)，直到符合条件，输出结果。(6) Solve the state correction amount Δx ^(k) to judge whether the convergence condition is satisfied, if max{|ΔV ^(k) |,|Δθ ^(k) |,|Δs ^(k) |,|Δf ^(k) |}> λ, number of iterations k=k+1, corrected state quantity V ^(k+1) = V ^(k) +ΔV ^(k) , θ ^(k+1) = θ ^(k) + Δθ ^(k) , s ^{(k +1)} =s ^(k) +Δs ^(k) , Δf ^(k+1) =Δf ^(k) +ΔΔf ^(k) , until the condition is met, output the result.

本发明采用计及频率变化的含风力发电的电力系统状态估计，通过算例仿真，验证了本发明提出的模型效果显著，并且在电力系统估计结果的精度上，优于没有考虑频率偏差的模型。The present invention adopts the state estimation of the power system including wind power generation that takes into account the frequency change, and through the example simulation, it is verified that the model proposed by the present invention has a significant effect, and the accuracy of the power system estimation result is better than the model that does not consider the frequency deviation .

下面介绍本发明的实施例：Introduce the embodiment of the present invention below:

设风电场的平均空气密度为1.225kg/m³；风力发电机的扫掠面积为2642m²，初始滑差为-0.0044；风力发电机的切入风速、额定风速和切出风速分别为3m/s，16m/s和21m/s；风能利用系数C_p为0.1217。风力发电机的型号为V52-850，具体参数见表1：Suppose the average air density of the wind farm is 1.225kg/m ³ ; the swept area of the wind turbine is 2642m ² , and the initial slip is -0.0044; the cut-in wind speed, rated wind speed and cut-out wind speed of the wind turbine are 3m/s respectively , 16m/s and 21m/s; wind energy utilization coefficient C _p is 0.1217. The model of the wind turbine is V52-850, and the specific parameters are shown in Table 1:

表1V52-850机型参数Table 1 V52-850 model parameters

算例：Examples:

本发明采用图2所示的IEEE-14节点系统，为了对比两种模型的估计精度，当40台上述风力发电机构成的风电机组接入IEEE-14节点标准测试系统的3号节点，仿真结果如下表所示：The present invention adopts the IEEE-14 node system shown in Figure 2. In order to compare the estimation accuracy of the two models, when the wind turbines composed of 40 above-mentioned wind generators are connected to No. 3 node of the IEEE-14 node standard test system, the simulation results As shown in the table below:

表2估计结果及与真值的比较Table 2 Estimated results and comparison with the true value

由图4可知：未考虑频率偏差时，电压幅值和相角的平均估计误差分别为0.3570％和3.0257％；考虑频率偏差时，电压幅值和相角的平均估计误差分别为0.2662％和1.1151％。在估计结果上，未考虑频率的状态估计模型误差明显大于本文考虑频率的状态估计模型，充分说明了本文模型更能反映含风机系统的真实运行情况。It can be seen from Figure 4 that when the frequency deviation is not considered, the average estimation errors of the voltage amplitude and phase angle are 0.3570% and 3.0257% respectively; when the frequency deviation is considered, the average estimation errors of the voltage amplitude and phase angle are 0.2662% and 1.1151 respectively %. In the estimation results, the error of the state estimation model without considering the frequency is significantly larger than that of the state estimation model considering the frequency in this paper, which fully shows that the model in this paper can better reflect the real operation of the system with fans.

Claims

1. take into account the power system state estimation method containing wind-power electricity generation of frequency change, it is characterized in that: comprise the following steps successively:

(1) network parameter and the measurement amount of electric system is obtained;

(2) network parameter utilizing step (1) to obtain and measurement amount carry out state estimation procedure initialization;

(3) state estimation model containing wind-power electricity generation taking into account frequency change is set up:

min J(x)＝[z-h(x)] ^TW[z-h(x)]

Wherein, J is objective function; The transposition of T representing matrix; W is diagonal angle weight matrix; X is quantity of state, and dimension n=2N-1, N is nodes; Z is measurement amount, dimension m, m>n; H is that m ties up non-linear measurement function;

(4) consider that blower fan slippage s and system frequency deviation Δ f sets up new Jacobian matrix:

H = [\begin{matrix} \frac{&PartialD; P}{&PartialD; θ} & \frac{&PartialD; P}{&PartialD; V} & \frac{&PartialD; P}{&PartialD; s} & \frac{&PartialD; P}{&PartialD; Δf} \\ \frac{&PartialD; Q}{&PartialD; θ} & \frac{&PartialD; Q}{&PartialD; V} & \frac{&PartialD; Q}{&PartialD; s} & \frac{&PartialD; Q}{&PartialD; Δf} \\ \frac{{&PartialD; P}_{k}}{&PartialD; θ} & \frac{{&PartialD; P}_{k}}{&PartialD; V} & \frac{{&PartialD; P}_{k}}{&PartialD; s} & \frac{&PartialD; P_{k}}{&PartialD; Δf} \\ \frac{{&PartialD; Q}_{k}}{&PartialD; θ} & \frac{&PartialD; Q_{k}}{&PartialD; V} & \frac{{&PartialD; Q}_{k}}{&PartialD; s} & \frac{{&PartialD; Q}_{k}}{&PartialD; Δf} \end{matrix}]

Wherein, P and Q represents corresponding meritorious and idle of common generator respectively; P _kand Q _kbe respectively corresponding meritorious and idle of the access node k of asynchronous blower fan; Wherein with dimension identical with the number of system apoplexy electric field node;

(5) by initial each quantity of state V ⁽⁰⁾, θ ⁽⁰⁾, s ⁽⁰⁾, Δ f ⁽⁰⁾calculated value h (the x that calculated amount is measured ^(k)) and Jacobian matrix H (x ^(k)), wherein, θ represents voltage phase angle, and V represents voltage magnitude, and s is slippage, and Δ f is frequency departure amount, and 0 represents original state amount;

(6) solving state correction amount x ^(k), judge whether to meet the condition of convergence, if max{| Δ V ^(k)|, | Δ θ ^(k)|, | Δ s ^(k)|, | Δ f ^(k)| > λ, iterations k=k+1, revise quantity of state V ^(k+1)=V ^(k)+ Δ V ^(k), θ ^(k+1)=θ ^(k)+ Δ θ ^(k), s ^(k+1)=s ^(k)+ Δ s ^(k), Δ f ^(k+1)=Δ f ^(k)+ Δ Δ f ^(k), until eligible, Output rusults, wherein, k is iterations.

2. take into account the power system state estimation method containing wind-power electricity generation of frequency change as claimed in claim 1, it is characterized in that: in step (2), initialized content comprises: arrange iteration precision λ, maximum iteration time and aerogenerator slippage initial value and frequency departure initial value, forms bus admittance matrix.

3. take into account the power system state estimation method containing wind-power electricity generation of frequency change as claimed in claim 1 or 2, it is characterized in that: in step (1), network parameter comprises: bus numbering, title, building-out capacitor, the branch road of transmission line of electricity number, headend node and endpoint node numbering, resistance in series, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance, the atmospheric density of wind energy turbine set, wind speed, blower fan type parameter, system original frequency.

4. take into account the power system state estimation method containing wind-power electricity generation of frequency change as claimed in claim 1 or 2, it is characterized in that: in step (1), measurement amount z comprises: node voltage amplitude, node inject active power and reactive power, the active power of common line branch road and transformer branch and reactive power.