CN104765962B - A kind of power system state estimation method of meter and temperature change - Google Patents
A kind of power system state estimation method of meter and temperature change Download PDFInfo
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Abstract
The present invention proposes a kind of meter and the power system state estimation method of temperature change.Remain that line resistance is constant in traditional state estimation calculating process, but because transmission line of electricity resistance is can change with the change of ambient temperature, it is therefore desirable to which new state estimation model and computational methods solve problem.The present invention is incorporated into temperature as new quantity of state in state estimation procedure as background, establishes meter and the state estimation model of temperature change.Meter proposed by the present invention and the power system state estimation method of temperature change constantly correct resistance value in calculating process, embody the thought of electro thermal coupling, not only the effectively temperature of meter and branch road, and improve the precision of state estimation result.
Description
Technical Field
The invention relates to a power system state estimation method considering temperature change, and belongs to the technical field of power system operation and control.
Background
As a core of an Energy Management System (EMS), power System state estimation obtains an optimal estimation value of a state quantity by processing raw data. The traditional Weighted Least Square (WLS) state estimation algorithm has good estimation quality and convergence performance, is a classical solution and a theoretical basis of state estimation, and is suitable for various types of measurement systems.
In the traditional state estimation calculation process, the resistance parameters of the power transmission line are assumed to be invariable all the time, and the calculation is carried out by using a fixed power grid node admittance matrix. However, the electric-thermal coupling related researches show that the temperature and the resistance of the power transmission line change along with the difference of the ambient temperature, the illumination radiation, the wind direction, the wind speed and other external environments and the line current carrying. Therefore, considering the electrothermal coupling, the branch resistance changes with the temperature change, and the resistance change is ignored in the conventional state estimation calculation, which results in an error between the calculation result and the actual situation. If the calculation error is too large, its effect must be accounted for, otherwise an erroneous calculation result will result.
The method for estimating the state of the power system considering the temperature change continuously corrects the resistance value in the calculation process, embodies the idea of electrothermal coupling, not only effectively considers the temperature of the branch, but also improves the precision of the state estimation result, and has engineering application value.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a power system state estimation method considering temperature change, which improves the accuracy of a state estimation result.
The technical scheme is as follows: the invention provides a power system state estimation method considering temperature change, which comprises the following steps of firstly obtaining network parameters and measurement of the power system, and further comprises the following steps:
establishing a branch temperature and resistance model according to the metal resistance temperature relation and the thermal resistance model;
establishing a state estimation model taking temperature changes into account:
min J(x)＝[z-h(x)] T W[z-h(x)]
wherein J is an objective function; t represents the transpose of the matrix; w is a diagonal weight matrix; x is a state quantity comprising a voltage phase angle theta, a voltage amplitude V and a branch temperature t; z is a measurement, dimension m; h is an m-dimensional nonlinear measurement function;
calculating a Jacobian matrix H according to the state estimation model taking temperature changes into account:
in the formula, P and Q respectively represent active power and reactive power of corresponding nodes, L represents a power function on a system branch, V represents a voltage amplitude value, and t represents branch temperature;
calculating the variation delta x of the system state quantity by using the state estimation model and the Jacobian matrix (k) ；
Determination of Δ x (k) If the convergence condition is satisfied, if max { Delta theta } (k) |,|ΔV (k) |,|Δt (k) When | } > λ is not converged, the iteration times k are self-increased by one, and the state quantity θ is corrected (k+1) ＝θ (k) +Δθ (k) ，V (k+1) ＝V (k) +ΔV (k) ，t (k+1) ＝t (k) +Δt (k) And iterating again until the convergence condition is met and outputting the result, otherwise, directly outputting the result if the convergence condition is met.
Preferably, the content of establishing the branch temperature and the resistance model according to the metal resistance temperature relationship and the thermal resistance model includes: and setting iteration precision lambda, the maximum iteration times k, the initial temperature of the system branch and the reference value of the related parameter to form a node admittance matrix at the current temperature.
Preferably, the obtaining network parameters and measurements of the power system includes: the bus number, name, compensation capacitance, branch number, head end node and tail end node number, series resistance, series reactance, parallel conductance, parallel susceptance, transformer transformation ratio and impedance of the transmission line, the current temperature of the system branch and a specified reference temperature.
Preferably, the obtaining network parameters and measurements of the amount of power system, wherein the measuring z comprises: the node voltage amplitude and the node injection active power and reactive power, and the active power and reactive power of the common line branch and the transformer branch at the current temperature.
Has the advantages that: the invention relates to a power system state estimation method considering temperature change, which introduces temperature serving as new state quantity into a state estimation process based on an electrothermal coupling idea, constructs new zero injection power measurement for branch temperature, and finally establishes a state estimation model considering temperature change. The method continuously corrects the resistance value in the calculation process, embodies the idea of electrothermal coupling, not only effectively takes the temperature of the branch into account, but also improves the precision of the state estimation result, and has engineering application prospect.
Drawings
FIG. 1: a method flow diagram of the invention;
FIG. 2: the invention discloses a simplified thermal resistance model of a branch part of an electric power system.
Detailed Description
The resistance of a metal conductor is related to temperature as follows:
where R is the resistance of the conductor, t is the temperature of the conductor, R Ref Is the resistance of the conductor at a reference temperature, t Ref Is the reference temperature, t F Is a fixed temperature (typically 234.5 ℃ for copper wire, 228.1 ℃ for hard aluminum wire, and 225.0 ℃ for aluminum transformer winding).
A well-known thermal resistance model is shown in fig. 2, which depicts the thermal coupling phenomenon of a device. In the thermal resistance model, the rising amount of the temperature of the equipment is approximately in linear relation with the loss of the equipment, and the coefficient is R θ Is formulated as follows:
wherein, t Rise Is the temperature of the apparatus above the external environment, P Loss Is the total loss inside the device, t RatedRise Is the nominal elevated temperature, P RatedLoss Is the corresponding nominal loss.
The temperature t of the conductor on a normal line is the ambient temperature t Amb Temperature t rising from conductor Rise Sum of (2) representsComprises the following steps:
wherein P of a branch ij Loss,ij Can be calculated by the following formula:
in the formula: g ij Representing the conductance between node i and node j, V i And V j Representing the voltage amplitudes, θ, of nodes i and j, respectively i And theta j Representing the voltage phase angles of nodes i and j, respectively.
For a transformer branch, its temperature model can be expressed as:
wherein, I and I Rated Respectively representing the current and the rated current on the branch of the transformer, n depends on the cooling mode of the transformer: the sealed transformer is 0.7, the natural cooling transformer is 0.8, and the forced air cooling transformer is 1.0.
After the models of the branch temperature and the resistance are established, the power system state estimation model considering the temperature change is considered. The measurement equation of the state estimation of the power system is as follows:
z＝h(x)+ε
in the formula: x is a state quantity comprising a voltage phase angle theta, a voltage amplitude V and a branch temperature t; z is a measurement (dimension m); h is an m-dimensional nonlinear measurement function; ε is the m-dimensional measurement error.
The objective function established according to the least squares criterion is as follows:
min J(x)＝[z-h(x)] T W[z-h(x)]
where J is the objective function, T represents the transpose of the matrix, W is the diagonal weight matrix,σ i is the standard deviation.
In general, h (x) is a nonlinear function, so an iterative method is adopted for solving. Let x 0 Is some approximation of x, which may be at x 0 And (3) carrying out Taylor expansion on h (x) nearby, reserving a first-order term, and neglecting a nonlinear term with more than two orders to obtain:
h(x)≈h(x 0 )+H(x 0 )Δx
wherein Δ x = x-x 0 H (x) is the Jacobian matrix of H (x). Substituting this equation into the objective function yields:
J(x)＝[Δz-H(x 0 )Δx] T W[Δz-H(x 0 )Δx]
wherein Δ z = z-h (x) 0 ) And (3) developing the formula to obtain:
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] T Σ -1 (x 0 )[Δx-Σ(x 0 )H T
×(x 0 )WΔz]
where ∑ (x) 0 )＝[H T (x 0 )WH(x 0 )] -1 。
The first term on the right in the above equation is independent of Δ x. Thus, to make J (x) very small, the second term should be 0, so that there is:
Δx (l) ＝[H T (x (l) )WH(x (l) )] -1 H T (x (l) )W[z-h(x (l) )]
x (l+1) ＝x (l) +Δx (l)
wherein l represents the iteration number, and x is iteratively corrected according to the formula until the objective function is close to the minimum.
Because the temperature variation on the branch is taken into account, the state estimation model of the invention also takes the temperature variable t into account on the basis of the basic weighted least squares method.The correction amount of the state estimation is extended to Δ x = [ Δ θ Δ V Δ t] T Obtaining a new block extended jacobian matrix containing t as follows:
wherein H represents a Jacobian matrix; p and Q respectively represent active power and reactive power of corresponding nodes; l represents a correlation function of branch temperature; theta represents a voltage phase angle, V represents a voltage amplitude, and t represents a branch temperature;
taking into account the branch temperature, the node injection power in the system can be expressed as:
in the formula: p i And Q i Respectively representing active power and reactive power injected by the node i; v i And V j Respectively representing the voltage amplitudes of nodes i and j; theta ij Is the voltage phase angle difference from node i to node j; g ij (t) and B ij (t) represents the conductance and susceptance between corresponding nodes i and j in the node admittance array at the temperature t; n is the total number of system nodes.
When accounting for temperature changes, a new zero injection power accounting for temperature needs to be built for branch power, which can be expressed as:
in the formula: l is a radical of an alcohol ij Representing the flow power, t, on branch ij ij Denotes the temperature, t, on branch ij Amb Denotes the ambient temperature of the environment, R θ,ij Represents the thermal resistivity, g, corresponding to the branch ij ij (t) Denotes the conductance between node i and node j at temperature t, V i And V j Representing the voltage amplitudes, θ, of nodes i and j, respectively ij Representing the voltage phase angle difference between nodes i and j.
When the corresponding elementsof the Jacobian matrix is solved, the element in the corresponding Jacobian matrix cannot be obtained by direct derivation due to the relationship between branch resistance and temperature, and the method is completed by a chain rule, wherein the element is only injected with active power P of a node i i For example, the following are specific:
wherein, t pq Is the temperature in the branch pq, g pq Is the conductance between node p and node q, b pq Is the susceptance between node p and node q, R pq Is the resistance between node p and node q, X pq Is the reactance between node p and node q, R Ref，pq Is the reference resistance between node p and node q, t Ref，pq Is the reference temperature, t, on branch pq F，pq Is the constant temperature on branch pq. Through a chain rule, direct relations exist among all the variables, the solved quantity can be obtained through direct derivation, and finally, the elements of the Jacobian matrix are obtained through multiplication, and the method can be used for derivation of reactive power to temperature in the same way.
From the initial state quantities V according to the above formula (0) 、θ (0) 、t (0) Calculated value h (x) of the calculated quantity measurement (k) ) And Jacobian matrix H (x) (k) ) K is the number of iterations, and the state correction amount Deltax is obtained (k) Then judging whether the convergence condition is satisfied, if the convergence requirement is not satisfied, correcting the state quantity V (k+1) ＝V (k) +ΔV (k) ，θ (k+1) ＝θ (k) +Δθ (k) ，t (k+1) ＝t (k) +Δt (k) And calculating the admittance matrix at the new temperature, and repeating the operation until the convergence accuracy meets the requirement.
The method comprises the following specific steps:
establishing a branch temperature and resistance model according to the metal resistance temperature relation and the thermal resistance model;
establishing a state estimation model taking temperature changes into account:
min J(x)＝[z-h(x)] T W[z-h(x)]
wherein J is an objective function; t represents the transpose of the matrix; w is a diagonal weight matrix; x is a state quantity comprising a voltage phase angle theta, a voltage amplitude V and a branch temperature t; z is a measurement, dimension m; h is an m-dimensional nonlinear measurement function;
calculating a Jacobian matrix H according to the state estimation model taking temperature changes into account:
in the formula, P and Q respectively represent active power and reactive power of corresponding nodes, L represents a power function on a system branch, V represents a voltage amplitude, and t represents branch temperature;
calculating the variation delta x of the system state quantity by using the state estimation model and the Jacobian matrix (k) ；
Determination of Δ x (k) If the convergence condition is satisfied, if max { Delta theta } (k) |,|ΔV (k) |,|Δt (k) When | } > λ is not converged, the iteration times k are self-increased by one, and the state quantity θ is corrected (k+1) ＝θ (k) +Δθ (k) ，V (k+1) ＝V (k) +ΔV (k) ，t (k+1) ＝t (k) +Δt (k) And iterating again until the convergence condition is met and outputting the result, otherwise, directly outputting the result if the convergence condition is met.
Preferably, the content of establishing the branch temperature and the resistance model according to the metal resistance temperature relationship and the thermal resistance model includes: and setting iteration precision lambda, the maximum iteration times k, the initial temperature of the system branch and the reference value of the related parameter to form a node admittance matrix at the current temperature.
Preferably, the obtaining network parameters and measurements of the power system includes: the bus number, name, compensation capacitance, branch number, head end node and tail end node number, series resistance, series reactance, parallel conductance, parallel susceptance, transformer transformation ratio and impedance of the transmission line, the current temperature of the system branch and a specified reference temperature.
Preferably, the obtaining network parameters and measurements of the amount of power system, wherein the measuring z comprises: the node voltage amplitude and the node injection active power and reactive power, and the active power and reactive power of the common line branch and the transformer branch at the current temperature.
According to the power system state estimation method considering the temperature change, the temperature is taken as a new state quantity to be introduced into the state estimation process, and a state estimation model considering the temperature change is established. The power system state estimation method considering the temperature change, which is provided based on the new model, continuously corrects the resistance value in the calculation process, embodies the idea of electrothermal coupling, not only effectively considers the temperature of the branch, but also improves the precision of the state estimation result, solves the problems in the prior art, and has engineering application value.
Claims (4)
1. A power system state estimation method considering temperature change firstly obtains network parameters and measurement of the power system, and is characterized in that: further comprising the steps of:
1) Establishing a branch temperature and resistance model according to the metal resistance temperature relation and the thermal resistance model:
the temperature t of the conductor on a normal line is the ambient temperature t Amb Temperature t rising from conductor Rise The sum, expressed as:
wherein, P Loss Is all losses inside the device, t RatedRise Is the nominal elevated temperature, P RatedLoss Is P of a branch ij corresponding to a rated loss Loss,ij Can be calculated by the following formula:
in the formula: g is a radical of formula ij Denotes the conductance between node i and node j, V i And V j Representing the voltage amplitudes, θ, of nodes i and j, respectively i And theta j Respectively representing the voltage phase angles of the nodes i and j;
for a transformer branch, its temperature model can be expressed as:
wherein, I and I Rated Respectively representing the current and the rated current on the branch of the transformer, n depends on the cooling mode of the transformer: the sealed transformer is 0.7, the natural cooling transformer is 0.8, and the forced air cooling transformer is 1.0;
2) Establishing a state estimation model taking temperature changes into account:
min J(x)＝[z-h(x)] T W[z-h(x)]
wherein J is an objective function; t represents the transpose of the matrix; w is a diagonal weight matrix; x is a state quantity comprising a voltage phase angle theta, a voltage amplitude V and a branch temperature t; z is a measurement, dimension m; h is an m-dimensional nonlinear measurement function;
3) Calculating a Jacobian matrix H according to the state estimation model taking temperature changes into account:
in the formula, P and Q respectively represent active power and reactive power of corresponding nodes, L represents a power function on a system branch, V represents a voltage amplitude, and t represents branch temperature; meanwhile, solving the Jacobian matrix by utilizing a chain rule;
4) Calculating the variation delta x of the system state quantity by using the state estimation model and the Jacobian matrix (k) ；
5) Determination of Δ x (k) If the convergence condition is satisfied, if max { Delta theta } (k) |,|ΔV (k) |,|Δt (k) |}&And when the number is not converged, the iteration number k is added by one and the state quantity theta is corrected (k+1) ＝θ (k) +Δθ (k) ，V (k+1) ＝V (k) +ΔV (k) ，t (k+1) ＝t (k) +Δt (k) And (3) iterating again until the convergence condition is met and outputting the result, otherwise, directly outputting the result if the convergence condition is met.
2. A power system state estimation method taking into account temperature variations according to claim 1, characterized by: the content of establishing the branch temperature and the resistance model according to the metal resistance temperature relation and the thermal resistance model comprises the following steps: and setting iteration precision lambda, the maximum iteration times k, the initial temperature of the system branch and the reference value of the related parameter to form a node admittance matrix at the current temperature.
3. A power system state estimation method taking into account temperature variations according to claim 1 or 2, characterized by: the method comprises the steps of obtaining network parameters and measurement values of the power system, wherein the network parameters comprise: the bus number, name, compensation capacitance, branch number, head end node and tail end node number, series resistance, series reactance, parallel conductance, parallel susceptance, transformer transformation ratio and impedance of the transmission line, the current temperature of the system branch and a specified reference temperature.
4. A power system state estimation method taking into account temperature variations according to claim 1 or 2, characterized by: the obtaining network parameters and measurements of quantities of the power system, wherein measuring z comprises: the node voltage amplitude and the node injection active power and reactive power, and the active power and reactive power of the common line branch and the transformer branch at the current temperature.
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| CN108984966B (en) * | 2018-08-20 | 2020-10-09 | 山东大学 | Wind energy grid-connected limit calculation method considering electric-thermal coupling effect of power transmission line |
| CN109412163B (en) * | 2018-11-30 | 2021-07-30 | 国网山东省电力公司经济技术研究院 | Accurate load flow calculation method for distributed wind power connected to power distribution network |
| CN110021928B (en) * | 2018-11-30 | 2023-05-23 | 南京南瑞继保电气有限公司 | State estimation decoupling method considering temperature influence |
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