CN104765962A - Temperature variation considering type state estimation method of power system - Google Patents

Abstract

The invention provides a temperature variation considering type state estimation method of a power system. The traditional state estimation calculation remains the same line resistance all the time, the transmission line resistance changes as the outside temperature changes, so that a novel state estimation model and a calculation method are needed to solve the problem. The method is that temperature is introduced into the state estimation process as a new state value, in order to build a temperature variation considering type state estimation model. According to the method, the resistance value is continuously modified during calculation, so that the electro-thermal coupling ideal can be shown; the temperature of a branch is effectively considered, and moreover, the state estimation result precision is improved.

Description

A kind of power system state estimation method taking into account temperature variation

Technical field

Invention relates to a kind of power system state estimation method taking into account temperature variation, belongs to Operation of Electric Systems and control technology field.

Background technology

As the core of energy management system (Energy Management System, EMS), Power system state estimation, by the process to raw data, obtains the best estimate of quantity of state.Traditional weighted least-squares method (Weighted LeastSquares, WLS) state estimation algorithm estimated quality and constringency performance very well, are classical solution and the theoretical foundation of state estimation, adapt to various types of measurement system.

Suppose that transmission line of electricity resistance parameter is constant all the time in traditional state estimation computation process, calculate with fixing grid nodes admittance matrix.But the research that electro thermal coupling is relevant shows, the temperature of transmission line of electricity and resistance change along with the difference of the external environments such as environment temperature, light radiation, wind direction and wind velocity and line energizing flow.So take into account electro thermal coupling, branch resistance can change along with the change of temperature, and when conventional sense is estimated to calculate, negligible resistance change, can cause the error between result of calculation and actual conditions.If the error of calculation is excessive, then must take into account its impact, otherwise the result of calculation that will lead to errors.

The power system state estimation method taking into account temperature variation that the present invention proposes, in computation process, constantly revise resistance value, embody the thought of electro thermal coupling, not only effectively take into account the temperature of branch road, and improve the precision of state estimation result, there is engineer applied and be worth.

Summary of the invention

Goal of the invention: the invention provides a kind of power system state estimation method taking into account temperature variation, improve the precision of state estimation result.

Technical scheme: the present invention proposes a kind of power system state estimation method taking into account temperature variation, first obtains network parameter and the measurement amount of electric system, further comprising the steps of:

Branch road temperature and Resistance model for prediction is set up according to metallic resistance temperature relation and thermal resistance model;

Set up the state estimation model taking into account temperature variation:

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, comprises voltage phase angle θ, voltage magnitude V and branch road temperature t; Z is measurement amount, dimension m; H is that m ties up non-linear measurement function;

State estimation model according to taking into account temperature variation calculates Jacobian matrix H:

$H=\left[\begin{array}{ccc}\frac{\∂P}{\∂\mathrm{\θ}}& \frac{\∂P}{\∂V}& \frac{\∂P}{\∂t}\\ \frac{\∂Q}{\∂\mathrm{\θ}}& \frac{\∂Q}{\∂V}& \frac{\∂Q}{\∂t}\\ \frac{\∂L}{\∂\mathrm{\θ}}& \frac{\∂L}{\∂V}& \frac{\∂L}{\∂t}\end{array}\right]$

In formula, P and Q represents the meritorious and idle of corresponding node respectively, and L represents the power function on system branch, and V represents voltage magnitude, and t represents branch road temperature;

Described state estimation model and Jacobian matrix is utilized to calculate the variation delta x of system state amount ^(k);

Judge Δ x ^(k)whether meet the condition of convergence, if max{ Δ θ ^(k)|, | Δ V ^(k)|, | Δ t ^(k)| namely > λ when not restraining, iterations k from adding one, and revises quantity of state θ ^(k+1)=θ ^(k)+ Δ θ ^(k), V ^(k+1)=V ^(k)+ Δ V ^(k), t ^(k+1)=t ^(k)+ Δ t ^(k), iteration is until meet condition of convergence Output rusults again, on the contrary convergence then direct Output rusults.

Preferably, the described content setting up branch road temperature and Resistance model for prediction according to metallic resistance temperature relation and thermal resistance model comprises: the reference value arranging iteration precision λ, maximum iteration time k, system branch initial temperature and correlation parameter, forms the bus admittance matrix under Current Temperatures.

Preferably, the network parameter of described acquisition electric system and measurement amount, wherein 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 reference temperature of the Current Temperatures of system branch and a regulation.

Preferably, the network parameter of described acquisition electric system and measurement amount, wherein measurement amount z comprises: node voltage amplitude, node inject active power and reactive power, the active power under common line branch road and transformer branch Current Temperatures and reactive power.

Beneficial effect: a kind of power system state estimation method taking into account temperature variation of the present invention, based on electro thermal coupling thought, temperature is incorporated in state estimation procedure as new quantity of state, and measure for branch road temperature constructs zero new injecting power, finally establish the state estimation model taking into account temperature variation.The method constantly revises resistance value in computation process, embodies the thought of electro thermal coupling, not only effectively takes into account the temperature of branch road, and improve the precision of state estimation result, have future in engineering applications.

Accompanying drawing explanation

Fig. 1: the inventive method process flow diagram;

Fig. 2: the thermal resistance model that electric system branched portion of the present invention simplifies.

Embodiment

The resistance of metallic conductor and temperature have following relation:

$R=R_{\mathrm{Ref}}\·\frac{t+t_F}{t_{\mathrm{Ref}}+t_F}$

Wherein, R is the resistance of conductor, and t is the temperature of conductor, R _refthe resistance of conductor under reference temperature, t _refreference temperature, t _fit is fixing temperature (general copper cash is 234.5 DEG C, and hard-drawn aluminium wire is 228.1 DEG C, and aluminium Transformer Winding is 225.0 DEG C).

Famous thermal resistance model as shown in Figure 2, depicts the thermal coupling phenomenon of equipment.In thermal resistance model, the ascending amount of device temperature and the loss of equipment are approximated to linear relationship, and coefficient is R _θ, be formulated as follows:

$\frac{t_{\mathrm{Rise}}}{P_{\mathrm{Loss}}}=\frac{t_{\mathrm{RatedRise}}}{P_{\mathrm{RatedLoss}}}=R_{\mathrm{\θ}}$

Wherein, t _risethe temperature that equipment exceeds external environment, P _lossthe all loss of device interior, t _ratedRisespecified raised temperature, P _ratedLossit is corresponding specified loss.

The temperature t of common line upper conductor is ambient temperature t _ambthe temperature t risen with conductor _risesum, is expressed as:

$t=t_{\mathrm{Amb}}+\left(\frac{P_{\mathrm{Loss}}}{P_{\mathrm{RatedLoss}}}\right)t_{\mathrm{RatedRise}}$

Wherein, the P of certain branch road ij _{loss, ij}calculate by following formula:

$P_{\mathrm{Loss},\mathrm{ij}}=g_{\mathrm{ij}}({V_i}^2+V_j^2)-2g_{\mathrm{ij}}{V}_i{v}_j\cos ({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)$

In formula: g _ijrepresent the conductance between node i and node j, V _iand V _jrepresent the voltage magnitude of node i and j respectively, θ _iand θ _jrepresent the voltage phase angle of node i and j respectively.

For transformer branch, its temperature model can be expressed as:

$t_{\mathrm{Rise}}=t_{\mathrm{RatedRise}}{\left(\frac{I}{I_{\mathrm{Rated}}}\right)}^{2n}$

Wherein, I and I _ratedelectric current respectively on indication transformer branch road and rated current, n depends on Cooling Methods of Transformers: hermetically sealed type transformer gets 0.7, and natural cold type transformer gets 0.8, and air blast cooling transformer gets 1.0.

After having set up the model of branch road temperature and resistance, consider the Power system state estimation model taking into account temperature variation.The measurement equation of Power system state estimation is:

z＝h(x)+ε

In formula: x is quantity of state, comprise voltage phase angle θ, voltage magnitude V and branch road temperature t; Z is measurement amount (dimension m); H is that m ties up non-linear measurement function; ε is that m ties up error in measurement.

The objective function set up by criterion of least squares is as follows:

min J(x)＝[z-h(x)] ^TW[z-h(x)]

Wherein, J is objective function, the transposition of T representing matrix, and W is diagonal angle weight matrix, σ _ifor standard deviation.

Generally, h (x) is nonlinear function, therefore adopts the method for iteration to solve.Make x ₀the a certain approximate value of x, can at x ₀near Taylor expansion is carried out to h (x), retain once item, and ignore the nonlinear terms of more than secondary, obtain:

h(x)≈h(x ₀)+H(x ₀)Δx

Δ x=x-x in formula ₀, the Jacobian matrix that H (x) is h (x).This formula is substituted in objective function, can obtain:

J(x)＝[Δz-H(x ₀)Δx] ^TW[Δz-H(x ₀)Δx]

Δ z=z-h (x in formula ₀), above formula is launched formula and obtains:

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

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

×(x ₀)WΔz]

Σ (x in formula ₀)=[H ^t(x ₀) WH (x ₀)] ^-1.

In above formula, the right Section 1 and Δ x have nothing to do.Therefore, make J (x) minimum, Section 2 should be 0, thus has:

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

x ^(l+1)＝x ^(l)+Δx ^(l)

Wherein l represents iterations, and x carries out iterated revision by above formula, until objective function is close to minimum.

Because taken into account the temperature variation on branch road, state estimation model of the present invention, on the basis of basic weighted least-squares method, also will consider temperature variable t.So the correction of state estimation expands to Δ x=[Δ θ Δ V Δ t] ^t, obtaining the new piecemeal Expanded Jacobian matrix containing t is:

$H=\left[\begin{array}{ccc}\frac{\∂P}{\∂\mathrm{\θ}}& \frac{\∂P}{\∂V}& \frac{\∂P}{\∂t}\\ \frac{\∂Q}{\∂\mathrm{\θ}}& \frac{\∂Q}{\∂V}& \frac{\∂Q}{\∂t}\\ \frac{\∂L}{\∂\mathrm{\θ}}& \frac{\∂L}{\∂V}& \frac{\∂L}{\∂t}\end{array}\right]$

Wherein, H represents Jacobian matrix; P and Q represents the meritorious and idle of corresponding node respectively; L represents the related function of branch road temperature; θ represents voltage phase angle, and V represents voltage magnitude, and t represents branch road temperature;

After considering branch road temperature, system interior joint injecting power can be expressed as:

$P_i=V_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{V}_j(G_{\mathrm{ij}}\left(t\right)\cos {\mathrm{\θ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\left(t\right)\sin {\mathrm{\θ}}_{\mathrm{ij}})$

$Q_i=V_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{V}_j(G_{\mathrm{ij}}\left(t\right)\sin {\mathrm{\θ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\left(t\right)\cos {\mathrm{\θ}}_{\mathrm{ij}})$

In formula: P _iand Q _irepresent that node i is injected respectively meritorious and idle; V _iand V _jrepresent the voltage magnitude of node i and j respectively; θ _ijit is the phase difference of voltage that node i arrives node j; G _ij(t) and B _ijconductance when () then represents that temperature is t t in node admittance battle array between corresponding node i and j and susceptance; N is system node sum.

When taking into account temperature variation, needing to build new zero injecting power taking into account temperature to branch power, can be expressed as:

$L_{\mathrm{ij}}=t_{\mathrm{ij}}-(t_{\mathrm{Amb}}+R_{\mathrm{\θ},\mathrm{ij}}\·(g_{\mathrm{ij}}\left(t\right)\·({V_i}^2+V_j^2)-2g_{\mathrm{ij}}\left(t\right)\·V_i{V}_j\cos {\mathrm{\θ}}_{\mathrm{ij}}))=0$

In formula: L _ijrepresent the flowing power on branch road ij, t _ijrepresent the temperature on branch road ij, t _ambrepresent extraneous environment temperature, R _{θ, ij}represent the thermal resistivity that branch road ij is corresponding, g _ijconductance during (t) expression t temperature between node i and node j, V _iand V _jrepresent the voltage magnitude of node i and j respectively, θ _ijrepresent the phase difference of voltage between node i and j.

When asking the element of corresponding Jacobian matrix, due to the relation between branch resistance and temperature, element in corresponding Jacobian matrix not being obtained by immediate derivation, needs chain rule, wherein only to gain merit P with the injection of node i _ifor example, shown in specific as follows:

$\frac{\∂P_i}{\∂t_{\mathrm{pq}}}=\frac{\∂P_i}{\∂g_{\mathrm{pq}}}\·\frac{\∂g_{\mathrm{pq}}}{\∂R_{\mathrm{pq}}}\·\frac{\∂R_{\mathrm{pq}}}{\∂t_{\mathrm{pq}}}+\frac{\∂P_i}{\∂b_{\mathrm{pq}}}\·\frac{\∂b_{\mathrm{pq}}}{\∂R_{\mathrm{pq}}}\·\frac{\∂R_{\mathrm{pq}}}{\∂t_{\mathrm{pq}}}$

$g_{\mathrm{pq}}=\frac{R_{\mathrm{pq}}}{R_{\mathrm{pq}}^2+X_{\mathrm{pq}}^2}$

$b_{\mathrm{pq}}=\frac{X_{\mathrm{pq}}}{R_{\mathrm{pq}}^2+X_{\mathrm{pq}}^2}$

$\frac{\∂R_{\mathrm{pq}}}{\∂t_{\mathrm{pq}}}=\frac{R_{\mathrm{Ref},\mathrm{pq}}}{t_{\mathrm{Ref},\mathrm{pq}}+t_{F,\mathrm{pq}}}$

Wherein, t _pqthe temperature on branch road pq, g _pqthe conductance between node p and node q, b _pqthe susceptance between node p and node q, R _pqthe resistance between node p and node q, X _pqthe reactance between node p and node q, R _{ref, pq}the reference resistance between node p and node q, t _{ref, pq}the reference temperature on branch road pq, t _{f, pq}it is stationary temperature on branch road pq.By chain rule, between above-mentioned each variable, there is direct relation, obtain required amount by immediate derivation, be finally multiplied and obtain the element of Jacobian matrix, in like manner can be used for the differentiate of reactive power to temperature.

According to formula above by initial each quantity of state V ⁽⁰⁾, θ ⁽⁰⁾, t ⁽⁰⁾calculated value h (the x that calculated amount is measured ^(k)) and Jacobian matrix H (x ^(k)), k is iterations, obtains status maintenance positive quantity Δ x ^(k), then judge whether to meet the condition of convergence, if do not reach convergent requirement, revise quantity of state V ^(k+1)=V ^(k)+ Δ V ^(k), θ ^(k+1)=θ ^(k)+ Δ θ ^(k), t ^(k+1)=t ^(k)+ Δ t ^(k), calculate the admittance matrix at new temperature, repeat aforesaid operations, until convergence precision reaches requirement.

Said method concrete steps are as follows:

Branch road temperature and Resistance model for prediction is set up according to metallic resistance temperature relation and thermal resistance model;

Set up the state estimation model taking into account temperature variation:

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, comprises voltage phase angle θ, voltage magnitude V and branch road temperature t; Z is measurement amount, dimension m; H is that m ties up non-linear measurement function;

State estimation model according to taking into account temperature variation calculates Jacobian matrix H:

$H=\left[\begin{array}{ccc}\frac{\∂P}{\∂\mathrm{\θ}}& \frac{\∂P}{\∂V}& \frac{\∂P}{\∂t}\\ \frac{\∂Q}{\∂\mathrm{\θ}}& \frac{\∂Q}{\∂V}& \frac{\∂Q}{\∂t}\\ \frac{\∂L}{\∂\mathrm{\θ}}& \frac{\∂L}{\∂V}& \frac{\∂L}{\∂t}\end{array}\right]$

In formula, P and Q represents the meritorious and idle of corresponding node respectively, and L represents the power function on system branch, and V represents voltage magnitude, and t represents branch road temperature;

Described state estimation model and Jacobian matrix is utilized to calculate the variation delta x of system state amount ^(k);

Judge Δ x ^(k)whether meet the condition of convergence, if max{ Δ θ ^(k)|, | Δ V ^(k)|, | Δ t ^(k)| namely > λ when not restraining, iterations k from adding one, and revises quantity of state θ ^(k+1)=θ ^(k)+ Δ θ ^(k), V ^(k+1)=V ^(k)+ Δ V ^(k), t ^(k+1)=t ^(k)+ Δ t ^(k), iteration is until meet condition of convergence Output rusults again, on the contrary convergence then direct Output rusults.

Preferably, the described content setting up branch road temperature and Resistance model for prediction according to metallic resistance temperature relation and thermal resistance model comprises: the reference value arranging iteration precision λ, maximum iteration time k, system branch initial temperature and correlation parameter, forms the bus admittance matrix under Current Temperatures.

Preferably, the network parameter of described acquisition electric system and measurement amount, wherein 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 reference temperature of the Current Temperatures of system branch and a regulation.

Preferably, the network parameter of described acquisition electric system and measurement amount, wherein measurement amount z comprises: node voltage amplitude, node inject active power and reactive power, the active power under common line branch road and transformer branch Current Temperatures and reactive power.

A kind of power system state estimation method taking into account temperature variation provided by the invention, is incorporated in state estimation procedure using temperature as new quantity of state, establishes the state estimation model taking into account temperature variation.The power system state estimation method taking into account temperature variation proposed based on new model constantly revises resistance value in computation process, embody the thought of electro thermal coupling, not only effectively take into account the temperature of branch road, and improve the precision of state estimation result, solve the problems of the prior art, there is engineer applied and be worth.

Claims (4)

1. take into account a power system state estimation method for temperature variation, first obtain network parameter and the measurement amount of electric system, it is characterized in that: further comprising the steps of:

Branch road temperature and Resistance model for prediction is set up according to metallic resistance temperature relation and thermal resistance model;

Set up the state estimation model taking into account temperature variation:

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, comprises voltage phase angle θ, voltage magnitude V and branch road temperature t; Z is measurement amount, dimension m; H is that m ties up non-linear measurement function;

State estimation model according to taking into account temperature variation calculates Jacobian matrix H:

$H=\left[\begin{array}{ccc}\frac{\∂P}{\∂\mathrm{\θ}}& \frac{\∂P}{\∂V}& \frac{\∂P}{\∂t}\\ \frac{\∂Q}{\∂\mathrm{\θ}}& \frac{\∂Q}{\∂V}& \frac{\∂Q}{\∂t}\\ \frac{\∂L}{\∂\mathrm{\θ}}& \frac{\∂L}{\∂V}& \frac{\∂L}{\∂t}\end{array}\right]$

In formula, P and Q represents the meritorious and idle of corresponding node respectively, and L represents the power function on system branch, and V represents voltage magnitude, and t represents branch road temperature;

Described state estimation model and Jacobian matrix is utilized to calculate the variation delta x of system state amount ^(k);

Judge Δ x ^(k)whether meet the condition of convergence, if max{| Δ θ ^(k)|, | Δ V ^(k)|, | Δ t ^(k)| namely > λ when not restraining, iterations k from adding one, and revises quantity of state θ ^(k+1)=θ ^(k)+ Δ θ ^(k), V ^(k+1)=V ^(k)+ Δ V ^(k), t ^(k+1)=t ^(k)+ Δ t ^(k), iteration is until meet condition of convergence Output rusults again, on the contrary convergence then direct Output rusults.

2. take into account the power system state estimation method of temperature variation as claimed in claim 1, it is characterized in that: the described content setting up branch road temperature and Resistance model for prediction according to metallic resistance temperature relation and thermal resistance model comprises: the reference value arranging iteration precision λ, maximum iteration time k, system branch initial temperature and correlation parameter, forms the bus admittance matrix under Current Temperatures.

3. take into account the power system state estimation method of temperature variation as claimed in claim 1 or 2, it is characterized in that: the network parameter of described acquisition electric system and measurement amount, wherein 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 reference temperature of the Current Temperatures of system branch and a regulation.

4. take into account the power system state estimation method of temperature variation as claimed in claim 1 or 2, it is characterized in that: the network parameter of described acquisition electric system and measurement amount, wherein measurement amount z comprises: node voltage amplitude, node inject active power and reactive power, the active power under common line branch road and transformer branch Current Temperatures and reactive power.