CN110619105A - Power transmission line temperature estimation method based on quantity measurement and heat balance equation - Google Patents
Power transmission line temperature estimation method based on quantity measurement and heat balance equation Download PDFInfo
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Abstract
The invention belongs to the field of power transmission line temperature estimation, and discloses a power transmission line temperature estimation method based on quantity measurement and a heat balance equation, which comprises the following steps of: inputting target transmission line parameters; acquiring electrical quantity measurement data at two ends of a target power transmission line and meteorological quantity measurement data of the position of the target power transmission line; calculating solar radiation heat absorption capacity, convection heat exchange capacity and radiation heat dissipation capacity by using the data; converting the line thermal balance differential equation into a line thermal balance differential equation and an electrical measurement equation, and simultaneously calculating to obtain a target transmission line temperature iteration value and update a target transmission line resistance parameter; and the state quantity completes iteration, the updated target transmission line resistance parameter is utilized, the iteration is repeated until the target transmission line temperature is converged, and the iterated target transmission line temperature value is output. The invention does not need to additionally install a temperature measuring device, has low cost, simple and rapid calculation on the premise of ensuring the calculation precision, easy programming realization, high calculation efficiency and good numerical stability.
Description
Technical Field
The invention belongs to the field of power transmission line temperature estimation, and particularly relates to a power transmission line temperature estimation method based on quantity measurement and a heat balance equation.
Background
With the rapid development of national economy, the power load is rapidly increased, and the power demand is continuously increased; meanwhile, the available coal reserves are gradually reduced, the thermal power generation pollution is aggravated, and the contradiction between power supply and demand needs to be solved urgently. In order to improve the transmission capacity of the transmission line, on one hand, a line corridor can be newly built, the transmission voltage level is improved, and the investment cost is undoubtedly increased; on the other hand, the dynamic capacity increasing technology is adopted, the load potential of the existing line is fully excavated, and the conveying capacity of the line is improved as much as possible on the premise of not increasing the equipment investment.
The temperature of the power transmission line is an important index for evaluating the transmission capacity of the line, contains rich decision information, and can be used as an important basis for evaluating the overload capacity of the line and realizing dynamic capacity increase. By monitoring the line temperature, the dynamic thermal setting value of the line is calculated, and the load scheduling and operation in the peak period are guided in real time, so that the method has great significance for the safe and stable operation of the power grid.
Transmission line temperature monitoring and estimation algorithms can be roughly divided into two categories. Firstly, develop high accuracy transmission line temperature on-line monitoring technique and device, easy operation is reliable, nevertheless can increase the equipment investment undoubtedly, receives meteorological condition influence along the line moreover, and the line temperature of difference probably has great difference, consequently need install many temperature-detecting device on a circuit, and the cost is very high. And secondly, calculating to obtain the line temperature by measuring the line current and meteorological measurement data such as air temperature, wind speed, wind direction and illumination intensity by using a heat balance equation. The method does not need to install a temperature measuring device, greatly saves equipment investment, and obviously improves economic performance, but the existing method estimates the line resistance parameter through an electrical measurement equation at first and then reversely deduces the line temperature by utilizing the monotonic relation between the line resistance and the temperature, so the method does not use a thermal balance equation as constraint, and the electrical measurement error influence is obvious.
In summary, the prior art has the following problems:
(1) the development of high-precision transmission line temperature on-line monitoring technology and device increases equipment investment, is influenced by meteorological conditions along the line, has great difference in line temperature at different points, and needs to install a plurality of temperature detection devices on one line, thereby increasing cost.
(2) The line temperature is obtained through calculation of measured line current and meteorological measurement data by using a thermal balance equation, but the line resistance parameter is estimated by using the electrical measurement equation, and the line temperature is reversely deduced by using the monotonic relation between the line resistance and the temperature.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides a method for estimating the temperature of a power transmission line based on a quantity measurement and a heat balance equation, so as to solve the above-mentioned technical problems.
The invention provides a power transmission line temperature estimation method based on quantity measurement and a heat balance equation, which comprises the following steps:
inputting parameters of a target power transmission line; the target power transmission line is a power transmission line needing temperature estimation;
collecting electrical quantity measurement data at two ends of a target power transmission line and collecting meteorological quantity measurement data of the position of the target power transmission line;
calculating the solar radiation heat absorption capacity, the convection heat exchange capacity and the radiation heat dissipation capacity on the unit-length power transmission line of the target power transmission line by using the electric quantity measurement data and the meteorological quantity measurement data;
step four: converting a circuit thermal balance differential equation into a circuit thermal balance differential equation by adopting an implicit trapezoidal integration method; combining a line thermal balance differential equation and an electrical measurement equation, correcting and iterating the state quantity by a weighted least square method, solving by a Newton method, and calculating to obtain a target transmission line temperature iteration value;
step five: updating the resistance parameter of the target power transmission line by using the calculated temperature iteration value of the target power transmission line; and the state quantity completes k iterations, and the iterations are repeated by using the updated target transmission line resistance parameter until the target transmission line temperature is converged, and the converged target transmission line temperature value is output.
Further, the parameters of the target power transmission line in the step one include: resistance R, reactance X, conductance G, susceptance B, line length l, and line rated voltage level UbHeat capacity mC of power transmission line materialp。
Further, the step two of measuring the electrical quantities at the two ends of the target transmission line includes: the method comprises the following steps of adopting electrical quantity measurement data collected by a data collection and monitoring control system and electrical quantity measurement data collected by a synchronous phasor measurement unit measurement device of a wide area monitoring system;
the meteorological measurement data of the position of the target power transmission line comprises: real time ambient temperature TaIllumination intensity QsReal-time wind speed VwAnd a real-time wind direction angle mu.
Further, the electrical quantity measurement data collected by the data collection and monitoring control system comprises:
(1) line i side voltage amplitude ViActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、PijAnd QijNotation ZSCADA,i；
(2) Line j side voltage amplitude VjActive power flow P in j-i direction of linejiAnd the j-i direction reactive power flow Q of the linejiSaid V isj、PjiAnd QjiNotation ZSCADA,j；
The electrical quantity measurement data collected by the synchronous phasor measurement unit measurement device of the wide area monitoring system comprises:
(1) line i side voltage amplitude ViI-side voltage phase angle theta of lineiI-j direction current active component I of lineij,realI-j direction current reactive component I of lineij,imagActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、θi、Iij,real、Iij,imag、PijAnd QijNotation ZPMU,i；
(2) Line j side voltage amplitude VjLine j side voltage phase angle thetajActive component I of j-I directional current of lineji,realReactive component I of current in j-I direction of lineji,imagActive power flow Pji in the j-i direction of the line and reactive power flow Q in the j-i direction of the linejiSaid V isj、θj、Iji,real、Iji,imagPji and stream QjiNotation ZPMU,j；
Wherein, the i side of the line represents one end of the target transmission line, and the j side of the line represents the other end of the target transmission line; the line i-j direction represents the direction from the i side to the j side of the target transmission line, and the line j-i direction represents the direction from the j side to the i side of the target transmission line.
Further, in the third step, the calculation formula of the solar radiation heat absorption capacity, the convection heat exchange capacity and the radiation heat dissipation capacity is as follows:
qs＝αQsesin(θ)A′
qc＝Ac·[T(t)-Ta]
qr＝Ar{[T(t)+273]4-(Ta+273)4}
wherein q issIs the solar radiation heat absorption; q. q.scIs the convection heat exchange quantity; q. q.srIs the radiant heat dissipation; alpha is conductor heat absorption coefficient; qseIs the intensity of solar radiation (W/m)2) (ii) a θ is the effective angle of incidence of the sun (°); a' is the projected area of the wire (m)2/m)；AcThe heat convection coefficient (W/m DEG C) of the lead is shown; t isaAmbient temperature (deg.C); a. therThe radiation heat transfer coefficient (W/m DEG C) of the lead is shown; t (t) is the target transmission line temperature (deg.c).
Further, converting the circuit thermal balance differential equation into a circuit thermal balance differential equation by adopting an implicit trapezoidal integration method; the method comprises the following steps of combining a line thermal balance difference equation and an electrical measurement equation, correcting and iterating state quantities by a weighted least square method, solving by a Newton method, and calculating to obtain a target transmission line temperature iteration value, wherein the method specifically comprises the following steps:
(1) adopts an implicit trapezoidal integration method to balance the line heat with a differential equation
Discretizing a line thermal balance differential equation by a differential step length delta t to obtain the line thermal balance differential equation:
wherein, TtIs the temperature of the transmission line at the moment t; t ist-ΔtThe temperature of the power transmission line at the time t-delta t; Δ t is the time interval; m is the mass of the transmission line with unit length; cpIs the specific heat capacity of the transmission line material; i ist-ΔtAt t- Δ tThe current value flowing through the power transmission line is measured; r (T)t-Δt) For transmission line temperature of Tt-ΔtThen, the alternating current resistance value of the transmission line of unit length; q. q.ss(t-delta t) is the solar radiation heat absorption capacity of the transmission line with unit length at the time of t-delta t; q. q.sc(Tt-Δt) For transmission line temperature of Tt-ΔtThe convection heat exchange quantity of the transmission line with unit length is measured; q. q.sr(Tt-Δt) For transmission line temperature of Tt-ΔtThe radiation heat dissipation capacity of the transmission line with unit length is measured; i istIs composed oftThe current value flowing through the power transmission line at the moment; r (T)t) For transmission line temperature of TtThen, the alternating current resistance value of the transmission line of unit length; q. q.ss(t) is the solar radiation heat absorption capacity of the transmission line of unit length at the moment t; q. q.sc(Tt) The temperature of the transmission line is TtThe convection heat exchange quantity of the transmission line with unit length is measured; q. q.sr(Tt) The temperature of the transmission line is TtThe radiation heat dissipation capacity of the transmission line with unit length is measured;
(3) measuring data Z of target transmission line electric quantitySCADA,i、ZSCADA,j、ZPMU,i、ZPMU,jAnd a summary of the measurement of the artifact, namely: z is ═ zSCADA,i zPMU,i zSCADA,j zPMU,j 0]T(ii) a The pseudo quantity is measured as a right-end term of a target transmission line heat balance differential equation, namely 0;
summarizing the state quantities, namely: x ═ Vi Vj θi θj Tl]T(ii) a The state quantity comprises a voltage amplitude value and a phase angle of two ends of the target power transmission line and the temperature of the target power transmission line;
the differential equation of the line thermal balance and the electrical measurement equation are combined, namely:
h＝[hSCADA,i hPMU,i hSCADA,j hPMU,j hHBE]T
the measurement equation corresponding to the voltage amplitude and the phase angle at the two ends of the target power transmission line is as follows:
the target transmission line power and the target transmission line current measurement are obtained by using the state quantity and the target transmission line parameter expression, and the measurement equation is as follows:
Iij,real＝Vigcosθi-Vjgcosθj-Vibsinθi+Vjbsinθj+Vi(gccosθi-bcsinθi)
Iij,imag＝Vibcosθi-Vjbcosθj+Vigsinθi-Vjgsinθj+Vi(bccosθi+gcsinθi)
Pij＝Vi 2(g+gc)-ViVjgcosθij-ViVjbsinθij
Qij＝-Vi 2(b+bc)-ViVjgsinθij+ViVjbcosθij
(3) after a circuit thermal balance difference equation and an electrical measurement equation are combined, firstly, a state quantity is corrected and iterated by adopting a weighted least square method, namely:
J(x)＝[z-h(x)]TR-1[z-h(x)]
wherein: r-1To measure the diagonal weight matrix, the weight matrix is chosen as the inverse of the variance of each measurement, i.e., R ═ diag (1/σ)i 2)；
Then, the iterative formula for obtaining the state quantity by using the Newton method is as follows:
wherein: k is the number of iterations; h is the augmented Jacobian matrix, anTo calculate the residual column vector, and Δ z-h (x)(k))；
Finally, the obtained line temperature iteration value formula is as follows:
x(k+1)＝x(k)+Δx(k)。
further, the augmented jacobian matrix H is:
wherein, the sub-matrix H11、H12、H21And H22Have identical empirical values of the elements of, the submatrix H13And H23The calculation formula of each element is as follows:
submatrix H31、H32And H33The calculation formula of the related elements:
further, in the fifth step, the resistance parameter of the target power transmission line is updated by using the calculated temperature of the target power transmission line; the state quantity completes k iterations and uses the updated target transmission line resistance parameter to repeat the iterations until the target transmission line temperature is converged, and then the target transmission line temperature value is output, specifically:
(1) updating the resistance parameter of the target power transmission line by using the calculated temperature iteration value of the target power transmission line, wherein the specific formula is as follows:
R(Tt)＝Rref·[1+α·(T-Td)]
wherein, alpha is the temperature coefficient of resistance; t isdIs a reference temperature; rrefFor rating the resistance of the line, i.e. at line temperature TdLine resistance of time is Rref；
(2) After the kth iteration is completed and the resistance parameter of the target power transmission line is updated by the calculated line temperature, the kth +1 th iteration is continued; infinite norm | Δ x of the difference between the two iteration state quantities(k)||∞<And e, after the e is a preset smaller threshold value, proving that the time step iteration converges, and outputting the target transmission line temperature.
And when the data acquisition and monitoring control system at the next moment t + delta t and the electric quantity measurement data and meteorological quantity measurement data acquired by the synchronous phasor measurement unit measurement devices of the wide area monitoring system are continuously acquired, calculating the line temperature at the next moment according to the steps from the first step to the fifth step.
The invention has the beneficial effects that:
(1) the invention can utilize the existing electric quantity measurement and meteorological quantity measurement to calculate and obtain the line temperature by a mathematical method, further judge the line conveying capacity and realize the purpose of dynamic capacity increase, does not need to add a new line temperature measuring device and has low cost.
(2) The method differentiates the line thermal balance equation, combines the differentiated line thermal balance equation with the electrical measurement equation, adopts Newton method iteration to solve, and has the advantages of simple and accurate algorithm, high calculation efficiency and easy programming realization.
(3) The refresh frequency of the electrical quantity measurement and the meteorological quantity measurement is high, the data acquisition rate of the synchronous phasor measurement unit measurement devices of the data acquisition and monitoring control system and the wide-area monitoring system is in the second level, and the acquisition rate of the meteorological quantity measurement is in the minute level, so that the algorithm can calculate and output the temperature in the minute level, namely, the real-time temperature measurement function is realized.
Drawings
In order to more clearly illustrate the embodiments or technical solutions in the prior art of the present invention, the drawings used in the description of the embodiments or prior art will be briefly described below, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for estimating the temperature of a power transmission line based on a quantity measurement and a heat balance equation provided by the invention.
Fig. 2 is a flowchart of a method for estimating a temperature of a power transmission line based on a quantity measurement and a heat balance equation according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a lumped parameter model and measurement of power transmission lines according to an embodiment of the present invention.
Fig. 4 is an exemplary wiring diagram of an IEEE39 node according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of typical weather data of a northern area in 5 months in 2017 on the minute scale according to an embodiment of the present invention.
Fig. 6 is a schematic diagram of load data at the minute level of a typical day in a northern area of 5 months in 2017 according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of measurement data of a SCADA and PMU device provided by an embodiment of the present invention on a typical day.
Fig. 8 is a schematic diagram of a plurality of estimated line temperature values calculated by a 39-node algorithm according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of a calculation value table of 19 measurement equations corresponding to the measurement of the quantity in the embodiment of the present invention.
Fig. 10 is a schematic diagram of a residual column vector table obtained by calculation in the embodiment of the present invention.
Fig. 11 is a schematic diagram of a diagonal matrix table with a weight matrix R of 19 × 19 according to an embodiment of the present invention.
FIG. 12 is a diagram illustrating a 19 × 5 dimensional matrix table as an H matrix in an embodiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to solve the technical problem in the prior art, the invention provides a power transmission line temperature estimation method based on quantity measurement and a heat balance equation. Firstly, the electrical quantity measurement of an SCADA device and a PMU device and the meteorological quantity measurement of a meteorological measurement device are determined, the state quantity is node voltage and line temperature, and the measurement is expressed as a nonlinear function of the state quantity by acquiring electrical measurement data and meteorological measurement data in real time and utilizing a line thermal balance equation and a node power equation. Because the line heat balance equation is a differential equation and the electrical quantity measurement equation is an algebraic equation, and the complexity of solution of a differential-algebraic equation set is considered, the method adopts an implicit trapezoidal integral method, converts the line heat balance differential equation into a differential algebraic equation, then solves the differential algebraic equation and the electrical quantity measurement equation simultaneously, and calculates the line temperature. According to the power transmission line temperature estimation method based on the quantity measurement and the heat balance equation, a temperature measurement device does not need to be additionally arranged, the cost is low, the temperature of the line is measured and calculated only by utilizing various electric quantity measurements and meteorological quantity of the line, and the method has the advantages of simplicity and rapidness in calculation, easiness in programming realization, high calculation efficiency and good numerical stability on the premise of ensuring the calculation accuracy.
FIGS. 1 and 12 illustrate one embodiment of the present invention;
the method for estimating the temperature of the power transmission line based on the quantity measurement and the heat balance equation comprises the following steps:
s101, inputting parameters of a target power transmission line; the target power transmission line is a power transmission line needing temperature estimation;
s102, collecting electrical quantity measurement data at two ends of a target power transmission line and collecting meteorological quantity measurement data of the position of the target power transmission line;
s103, calculating solar radiation heat absorption capacity, convection heat exchange capacity and radiation heat dissipation capacity on the unit-length power transmission line of the target power transmission line by using the electric quantity measurement data and the meteorological quantity measurement data;
s104, converting the circuit thermal balance differential equation into a circuit thermal balance differential equation by adopting an implicit trapezoidal integration method; combining a line thermal balance differential equation and an electrical measurement equation, correcting and iterating the state quantity by a weighted least square method, solving by a Newton method, and calculating to obtain a target transmission line temperature iteration value;
s105, updating the resistance parameter of the target power transmission line by using the calculated temperature iteration value of the target power transmission line; and the state quantity completes k iterations, and the iterations are repeated by using the updated target transmission line resistance parameter until the target transmission line temperature is converged, and the converged target transmission line temperature value is output.
In an embodiment of the present invention, a method for estimating a temperature of a power transmission line based on a quantity measurement and a heat balance equation specifically comprises:
(1) inputting the resistance R, reactance X, conductance G and susceptance B of the power transmission line i-j needing temperature estimation, and the lineLength l, line voltage class UbHeat capacity mC of power transmission line materialpAnd the like.
And taking the line 1-2 of the IEEE39 node calculation example as an example, and carrying out real-time estimation on the temperature of the power transmission line.
The line parameters are as follows:
line resistance R0.0035, reactance X0.0411, conductance G0, susceptance B0.3494, length l 31.53km, voltage level Ub345kV, material heat capacity mCp＝852.72J/(m·℃)。
(2) The method comprises the following steps of collecting measurement data of electrical quantities at two ends of a power transmission line i-j needing temperature estimation, wherein the measurement data mainly comprises the following two types:
(2-1) electrical quantity measurement data collected by a data collection and monitoring control System (SCADA), comprising:
i side voltage amplitude V of lineiActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、PijAnd QijIs recorded as zSCADA,i；
Voltage amplitude V at j side of linejActive power flow P in j-i direction of linejiAnd the j-i direction reactive power flow Q of the linejiSaid V isj、PjiAnd QjiIs recorded as zSCADA,j。
Wherein, the i side of the line represents one end of the target transmission line, and the j side of the line represents the other end of the target transmission line; the line i-j direction represents the direction from the i side to the j side of the target transmission line, and the line j-i direction represents the direction from the j side to the i side of the target transmission line.
The measurement of the simulated SCADA device to obtain the electrical quantity measurement data collected by the data collection and monitoring control System (SCADA) on a typical day is shown in fig. 7, and it should be noted that the data is from the result of the power flow calculation performed on the 39-node calculation example.
The measurement data (after per unit) of the SCADA device at a certain time is given as follows:
V1＝1.0515，P12＝-1.2325，Q12＝-0.1928，V2＝1.0151，P21＝1.3270，Q21＝-0.5064。
(2-2) the electrical quantity measurement data collected by a synchronous Phasor Measurement Unit (PMU) device of a Wide Area Monitoring System (WAMS) comprises:
i side voltage amplitude V of lineiI-side voltage phase angle theta of lineiI-j direction current active component I of lineij,realI-j direction current reactive component I of lineij,imagActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、θi、Iij,real、Iij,imag、PijAnd QijIs recorded as zPMU,i；
Voltage amplitude V at j side of linejLine j side voltage phase angle thetajActive component I of j-I directional current of lineji,realReactive component I of current in j-I direction of lineji,imagActive power flow Pji in the j-i direction of the line and reactive power flow Q in the j-i direction of the linejiSaid V isj、θj、Iji,real、Iji,imagPji and stream QjiIs recorded as zPMU,j。
The simulated SCADA device measurement is used for obtaining electrical quantity measurement data collected by a synchronous Phasor Measurement Unit (PMU) device of the Wide Area Monitoring System (WAMS) on a typical day as shown in fig. 7, and it should be noted that the data is obtained from a result of load flow calculation performed on a 39-node algorithm.
The following simulated PMU devices measure electrical quantity measurement data collected by a synchronous Phasor Measurement Unit (PMU) measurement device of the Wide Area Monitoring System (WAMS) at a time as follows:
V1＝1.0448，θ1＝0.2552，I12,real＝-1.2042，I12,imag＝-0.1352，P12＝-1.2524，Q12＝-0.1805，
V2＝1.0424，θ2＝0.3031，I21,real＝1.0039，I21,imag＝0.8360，P21＝1.2577，Q21＝-0.5196
(3) collecting power transmission requiring temperature estimationReal-time meteorological measurements of a location of a link i-j, comprising: real time ambient temperature TaIllumination intensity QsReal-time wind speed VwAnd a real-time wind direction angle mu.
The simulated SCADA device measures the meteorological data of a typical day in a certain area in north of 5 months in 2017 as shown in fig. 5, and the data of the meteorological data measured at a certain moment in fig. 5 is given as follows:
real time ambient temperature Ta14.7 ℃ and light intensity Qs0 (night in this case), real-time wind speed Vw2.6m/s, and 202 deg. of real-time wind direction angle mu
(4) Calculating the solar radiation heat absorption capacity q of the transmission line with unit length according to the existing heat calculation formula by using the electrical quantity measurement and the meteorological quantity measurementsConvection heat transfer quantity qcAnd radiation heat dissipation qr。
The specific calculation formula is as follows:
qs＝αQsesin(θ)A′
qc＝Ac·[T(t)-Ta]
qr＝Ar{[T(t)+273]4-(Ta+273)4}
in the formula, qsIs the solar radiation heat absorption capacity, W/m; q. q.scW/m is convection heat exchange quantity; q. q.srW/m is the radiation heat dissipation capacity; alpha is conductor heat absorption coefficient; qseIs the intensity of solar radiation, W/m2(ii) a Theta is the effective incident angle of the sun, °; a' is the projected area of the wire, m2/m；AcThe heat convection coefficient of the lead is W/m DEG C; t isaAmbient temperature, deg.C; t is the temperature of the transmission line, DEG C; a. therIs the radiation heat transfer coefficient of the wire, W/m.
Since the line temperature t (t) in the above formula is the amount to be estimated and is not yet obtained, the line temperature calculated at the previous time may be used as the initial value of the line temperature at the current time, and certainly, the ambient temperature at the current time may also be selected as the initial value of the line temperature, and the line temperature at the current time is obtained through subsequent calculation and then is continuously updated, and the final result is not affected.
Selecting the initial value T (T) of the line temperature as the environmental temperature T at the momentaI.e. T (T) ═ Ta14.7 ℃. Calculated by substituting into a formula to obtain the solar radiation heat absorption capacity qs0, convection heat transfer qc4.8586, radiation heat dissipation qr＝0.5086。
(5) Discretizing a line thermal equilibrium differential equation into a differential equation:
differential equation of line heat balance isDiscretizing the equation by a difference step length delta t to obtain a line thermal balance difference equation as follows:
the solar radiation heat absorption capacity q is obtained by measuring and calculating real-time meteorological quantitysConvection heat transfer quantity qcAnd radiation heat dissipation qrThe above equation can then be introduced into the temperature estimation model as a pseudo measurement.
(6) In summary, the electrical quantity measurement, the state quantity to be estimated, and the measurement equation required by the present invention are summarized as follows:
(6-1) the total of 19 measurements needed to make the temperature estimates of the transmission lines i-j include:
1) the data acquisition and supervisory control and data acquisition (SCADA) system collects 6 electrical quantity measurement data, including:
i side voltage amplitude V of lineiActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、PijAnd QijIs recorded as zSCADA,i；
Voltage amplitude V at j side of linejActive power flow P in j-i direction of linejiAnd the j-i direction reactive power flow Q of the linejiSaid V isj、PjiAnd QjiIs recorded as zSCADA,j。
2) The electric quantity measured data that synchronous Phasor Measurement Unit (PMU) unit measurement of Wide Area Monitoring System (WAMS) gathered includes 12:
i side voltage amplitude V of lineiI-side voltage phase angle theta of lineiI-j direction current active component I of lineij,realI-j direction current reactive component I of lineij,imagActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、θi、Iij,real、Iij,imag、PijAnd QijIs recorded as zPMU,i；
Voltage amplitude V at j side of linejLine j side voltage phase angle thetajActive component I of j-I directional current of lineji,realReactive component I of current in j-I direction of lineji,imagActive power flow Pji in the j-i direction of the line and reactive power flow Q in the j-i direction of the linejiSaid V isj、θj、Iji,real、Iji,imagPji and stream QjiIs recorded as zPMU,j。
3) The pseudo-quantity is measured 1 (as 0), i.e.:
z＝[zSCADA,i zPMU,i zSCADA,j zPMU,j 0]T
in this example, the data items of z at this time are:
(6-2) the number of state quantities to be estimated is 5, including voltage amplitude and phase angle of two ends of the target power transmission line, and line temperature, namely:
x＝[Vi Vj θi θj Tl]T
in this example, the state quantity is x ═ V1 V2 θ1 θ2 T1-2]T。
(6-3) measurement equations corresponding to the above-mentioned quantity measurements, 19 in total
h＝[hSCADA,i hPMU,i hSCADA,j hPMU,j hHBE]T，
The measurement equation corresponding to the node voltage amplitude and phase angle measurement is as follows:
the target transmission line power and the target transmission line current measurement need to be obtained by using state quantity and line parameter representation, and the measurement equation is as follows:
Iij,real＝Vigcosθi-Vjgcosθj-Vibsinθi+Vjbsinθj+Vi(gccosθi-bcsinθi)
Iij,imag＝Vibcosθi-Vjbcosθj+Vigsinθi-Vjgsinθj+Vi(bccosθi+gcsinθi)
Pij＝Vi 2(g+gc)-ViVjgcosθij-ViVjbsinθij
Qij＝-Vi 2(b+bc)-ViVjgsinθij+ViVjbcosθij
the calculated values of the measurement equation of the line 19 obtained by the calculation are shown in fig. 9.
(7) Similar to state estimation, an objective function is established to minimize the weighted residual sum of squares, and state quantity correction and iteration are performed by adopting a WLS (weighted least squares) method as follows:
J(x)＝[z-h(x)]TR-1[z-h(x)]
in the formula: r-1To measure the diagonal weight matrix, the calculation method is shown in step (8).
The iterative formula for obtaining the state quantity by using the Newton method is shown as the following formula:
in the formula: k is the number of iterations; h is the augmented Jacobian matrix, anThe calculation method is shown in step (9); Δ z is the calculated residual column vector, and Δ z ═ z-h (x)(k))。
The calculated residual column vectors are shown in the table of fig. 10.
The line parameters are updated with the calculated line temperature, and the calculation method is shown in step (10).
The state quantity after the calculation and the update is as follows:
x＝[Vi Vj θi θj Tl]T＝[1.0450 1.0424 0.2550 0.3030 17.1755]T。
(8) because of the difference between the measurement accuracy of the SCADA and that of the PMU, weights of different sizes need to be given to the measurements from these two different sources, which is beneficial to speed up the convergence of the iterative process and improve the estimation accuracy, and in this method, the weight matrix is generally selected as the inverse of the variance of each measurement, i.e., R ═ diag (1/σ), which is the inverse of the variance of each measurementi 2) Wherein the standard deviation of the various types of measurements of SCADA and PMU, as shown in table 1:
TABLE 1 Standard deviation of various types of measurements of SCADA and PMU
A diagonal matrix with a weight matrix R of 19 × 19 is calculated as shown in the table of fig. 11.
(9) The elements of the augmented Jacobian matrix H are derived below, the H matrix first being written as follows:
wherein, the sub-matrix H11、H12、H21And H22Element of (2) and conventional state estimation modelAccordingly, they will not be described in detail herein. Matrix H13And H23The formula for calculating the medium element is as follows:
submatrix H31、H32And H33The calculation formula of the related elements:
in this example, since the number of the quantity measurements is 19 and the number of the state quantities is 5, the H matrix is a 19 × 5 dimensional matrix, as shown in fig. 12.
(10) Updating the line parameters using the calculated line temperature, the formula being as follows:
R(Tt)＝Rref·[1+α·(T-Td)]
wherein T isdIs a reference temperature, RrefFor rating the resistance of the line, i.e. at line temperature TdLine resistance of time is Rref。
Resistance parameters of the corrected lines 1-2:
R(Tt)＝Rref·[1+α·(T-Td)]＝0.0035*[1-0.0039*(17.18-20)]＝0.0034
(11) and after the kth iteration is finished and the resistance parameters of the line are corrected by using the calculated line temperature, continuing to perform the (k + 1) th iteration. Infinite norm | Δ x of the difference between the two iteration state quantities(k)||∞<And e, proving that the time step iteration converges and outputting the line temperature value.
In this example, the threshold ε is chosen to be 0.0001, Δ x | after the first iteration(k)||∞＝0.0122，||Δx(k)||∞＝1.97×10-5Therefore, the circuit can be converged after two-step iteration, and the temperature of the circuit 1-2 at the output moment is 17.18 ℃.
(12) And then continuously acquiring the electrical quantity measurement and the meteorological quantity measurement of the SCADA and PMU device at the next moment t + delta t, and calculating the line temperature at the moment according to the steps (1) to (11).
According to the steps, the real-time temperature of each line on the typical day is calculated, the result is shown in fig. 8, the line temperature obtained by adopting the algorithm for estimation is very close to the actual line temperature, the estimation error is less than 0.3%, and the effectiveness of the method is verified.
As shown in table 2, the voltage and temperature estimation errors for each line are less than 0.5%. 1440 time sections are totally needed in one day, so the program needs to be executed 1440 times, the total time consumption is 1.7s, the average iteration time of each step is 2 times, the calculation efficiency of the program is high, and the requirements of online application and real-time analysis are met.
Estimation error and computational efficiency of the algorithm presented in Table 2
The method for estimating the temperature of the power transmission line based on the quantity measurement and the heat balance equation provided by the invention takes actual measurement data of an electrical and gas image measurement device as the quantity measurement, takes the line temperature as the quantity to be estimated, and simultaneously calculates the line temperature by the electrical measurement equation and the line heat balance equation, so that the method not only has urgent research value, but also has good economic benefit and industrial application potential, which is the basis of the power completed by the method.
Although the present invention has been described in detail by referring to the drawings in connection with the preferred embodiments, the present invention is not limited thereto. Various equivalent modifications or substitutions can be made on the embodiments of the present invention by those skilled in the art without departing from the spirit and scope of the present invention, and these modifications or substitutions are within the scope of the present invention/any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (8)
1. A power transmission line temperature estimation method based on quantity measurement and a heat balance equation is characterized by comprising the following steps of:
inputting parameters of a target power transmission line; the target power transmission line is a power transmission line needing temperature estimation;
collecting electrical quantity measurement data at two ends of a target power transmission line and collecting meteorological quantity measurement data of the position of the target power transmission line;
calculating the solar radiation heat absorption capacity, the convection heat exchange capacity and the radiation heat dissipation capacity on the unit-length power transmission line of the target power transmission line by using the electric quantity measurement data and the meteorological quantity measurement data;
step four: converting a circuit thermal balance differential equation into a circuit thermal balance differential equation by adopting an implicit trapezoidal integration method; combining a line thermal balance differential equation and an electrical measurement equation, correcting and iterating the state quantity by a weighted least square method, solving by a Newton method, and calculating to obtain a target transmission line temperature iteration value;
step five: updating the resistance parameter of the target power transmission line by using the calculated temperature iteration value of the target power transmission line; and the state quantity completes k iterations, and the iterations are repeated by using the updated target transmission line resistance parameter until the target transmission line temperature is converged, and the converged target transmission line temperature value is output.
2. The method for estimating transmission line temperature based on quantity measurement and heat balance equation according to claim 1, wherein the parameters of the target transmission line in the first step include: resistance R, reactance X, conductance G, susceptance B, line length l, and line rated voltage level UbHeat capacity mC of power transmission line materialp。
3. The method for estimating transmission line temperature based on quantity measurement and heat balance equation according to claim 1, wherein the step two includes the following steps: the method comprises the following steps of adopting electrical quantity measurement data collected by a data collection and monitoring control system and electrical quantity measurement data collected by a synchronous phasor measurement unit measurement device of a wide area monitoring system;
the meteorological measurement data of the position of the target power transmission line comprises: real time ambient temperature TaIllumination intensity QsReal-time wind speed VwAnd a real-time wind direction angle mu.
4. The method for estimating the temperature of the power transmission line based on the quantity measurement and the heat balance equation according to claim 3, wherein the data acquisition and monitoring of the electrical quantity measurement data acquired by the control system comprises:
(1) line i side voltage amplitude ViActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、PijAnd QijNotation ZSCADA,i；
(2) Line j side voltage amplitude VjActive power flow P in j-i direction of linejiAnd the j-i direction reactive power flow Q of the linejiSaid V isj、PjiAnd QjiNotation ZSCADA,j；
The electrical quantity measurement data collected by the synchronous phasor measurement unit measurement device of the wide area monitoring system comprises:
(1) line i side voltage amplitude ViI-side voltage phase angle theta of lineiI-j direction current active component I of lineij,realI-j direction current reactive component I of lineij,imagActive power flow P in i-j direction of lineijAnd the i-j direction reactive power flow Q of the lineijSaid V isi、θi、Iij,real、Iij,imag、PijAnd QijNotation ZPMU,i；
(2) Line j side voltage amplitude VjLine j side voltage phase angle thetajActive component I of j-I directional current of lineji,realReactive component I of current in j-I direction of lineji,imagActive power flow Pji in the j-i direction of the line and reactive power flow Q in the j-i direction of the linejiSaid V isj、θj、Iji,real、Iji,imagPji and stream QjiNotation ZPMU,j；
Wherein, the i side of the line represents one end of the target transmission line, and the j side of the line represents the other end of the target transmission line; the line i-j direction represents the direction from the i side to the j side of the target transmission line, and the line j-i direction represents the direction from the j side to the i side of the target transmission line.
5. The method for estimating the temperature of the power transmission line based on the quantity measurement and the heat balance equation according to claim 1, wherein the calculation formulas of the solar radiation heat absorption quantity, the convection heat exchange quantity and the radiation heat dissipation quantity in the third step are as follows:
qs＝αQsesin(θ)A’
qc＝Ac·[T(t)-Ta]
qr＝Ar{[T(t)+273]4-(Ta+273)4}
wherein q issIs the solar radiation heat absorption; q. q.scIs the convection heat exchange quantity; q. q.srIs the radiant heat dissipation; alpha is conductor heat absorption coefficient; qseIs the intensity of solar radiation; theta is the effective incident angle of the sun; a' is the projection area of the lead; a. thecIs the convective heat transfer coefficient of the lead; t isaIs ambient temperature; a. therThe heat transfer coefficient of the radiation of the lead; and T is the temperature of the power transmission line.
6. The method for estimating the temperature of the power transmission line based on the quantity measurement and the heat balance equation according to claim 1, wherein in the fourth step, an implicit trapezoidal integration method is adopted to convert the differential equation of the line heat balance into the differential equation of the line heat balance; the method comprises the following steps of combining a line thermal balance difference equation and an electrical measurement equation, correcting and iterating state quantities by a weighted least square method, solving by a Newton method, and calculating to obtain a target transmission line temperature iteration value, wherein the method specifically comprises the following steps:
(1) adopts an implicit trapezoidal integration method to balance the line heat with a differential equation
Discretizing a line thermal balance differential equation by a differential step length delta t to obtain the line thermal balance differential equation:
wherein, TtIs the temperature of the transmission line at the moment t; t ist-ΔtThe temperature of the power transmission line at the time t-delta t; Δ t is the time interval; m is the mass of the transmission line with unit length; cpIs the specific heat capacity of the transmission line material; i ist-ΔtIs t-deltathe current value flowing through the power transmission line at the time t; r (T)t-Δt) For transmission line temperature of Tt-ΔtThen, the alternating current resistance value of the transmission line of unit length; q. q.ss(t-delta t) is the solar radiation heat absorption capacity of the transmission line with unit length at the time of t-delta t; q. q.sc(Tt-Δt) For transmission line temperature of Tt-ΔtThe convection heat exchange quantity of the transmission line with unit length is measured; q. q.sr(Tt-Δt) For transmission line temperature of Tt-ΔtThe radiation heat dissipation capacity of the transmission line with unit length is measured; i istIs composed oftThe current value flowing through the power transmission line at the moment; r (T)t) For transmission line temperature of TtThen, the alternating current resistance value of the transmission line of unit length; q. q.ss(t) is the solar radiation heat absorption capacity of the transmission line of unit length at the moment t; q. q.sc(Tt) The temperature of the transmission line is TtThe convection heat exchange quantity of the transmission line with unit length is measured; q. q.sr(Tt) The temperature of the transmission line is TtThe radiation heat dissipation capacity of the transmission line with unit length is measured;
(2) measuring data Z of target transmission line electric quantitySCADA,i、ZSCADA,j、ZPMU,i、ZPMU,jAnd a summary of the measurement of the artifact, namely: z is ═ zSCADA,i zPMU,i zSCADA,j zPMU,j 0]T(ii) a The pseudo quantity is measured as a right-end term of a target transmission line heat balance differential equation, namely 0;
summarizing the state quantities, namely: x ═ Vi Vj θi θj Tl]T(ii) a The state quantity comprises a voltage amplitude value and a phase angle of two ends of the target power transmission line and the temperature of the target power transmission line;
the differential equation of the line thermal balance and the electrical measurement equation are combined, namely:
h＝[hSCADA,i hPMU,i hSCADA,j hPMU,j hHBE]T
the measurement equation corresponding to the voltage amplitude and the phase angle at the two ends of the target power transmission line is as follows:
the target transmission line power and the target transmission line current measurement are obtained by using the state quantity and the target transmission line parameter expression, and the measurement equation is as follows:
Iij,real＝Vigcosθi-Vjgcosθj-Vibsinθi+Vjbsinθj+Vi(gccosθi-bcsinθi)
Iij,imag＝Vibcosθi-Vjbcosθj+Vigsinθi-Vjgsinθj+Vi(bccosθi+gcsinθi)
Pij＝Vi 2(g+gc)-ViVjgcosθij-ViVjbsinθij
Qij＝-Vi 2(b+bc)-ViVjgsinθij+ViVjbcosθij
(3) after a circuit thermal balance difference equation and an electrical measurement equation are combined, firstly, a state quantity is corrected and iterated by adopting a weighted least square method, namely:
J(x)＝[z-h(x)]TR-1[z-h(x)]
wherein: r-1To measure the diagonal weight matrix, the weight matrix is chosen as the inverse of the variance of each measurement, i.e., R ═ diag (1/σ)i 2)；
Then, the iterative formula for obtaining the state quantity by using the Newton method is as follows:
wherein: k is the number of iterations; h is the augmented Jacobian matrix, anTo calculate the residual column vector, and Δ z-h (x)(k))；
Finally, the obtained line temperature iteration value formula is as follows:
x(k+1)＝x(k)+Δx(k)。
7. the method of claim 6, wherein the augmented Jacobian matrix H is:
wherein, the sub-matrix H11、H12、H21And H22Have identical empirical values of the elements of, the submatrix H13And H23The calculation formula of each element is as follows:
submatrix H31、H32And H33The calculation formula of the related elements:
8. the power transmission line temperature estimation method based on quantity measurement and heat balance equation according to claim 1, characterized in that, in the fifth step, the calculated iteration value of the target power transmission line temperature is used for updating the resistance parameter of the target power transmission line; the state quantity completes k iterations, and the iteration is repeated by using the updated target transmission line resistance parameter until the target transmission line temperature is converged, and the converged target transmission line temperature value is output, specifically:
(1) updating the resistance parameter of the target power transmission line by using the calculated temperature iteration value of the target power transmission line, wherein the specific formula is as follows:
R(Tt)＝Rref·[1+α·(T-Td)]
wherein, alpha is the temperature coefficient of resistance; t isdIs a reference temperature; rrefFor rating the resistance of the line, i.e. at line temperature TdLine resistance of time is Rref；
(2) After the kth iteration is completed and the resistance parameter of the target power transmission line is updated by the calculated line temperature, the kth +1 th iteration is continued; infinite norm | Δ x of the difference between the two iteration state quantities(k)||∞<E, wherein e is a predetermined smaller threshold value, which is provedAnd step (5) iterative convergence, and outputting the target transmission line temperature.
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