Technical field

The present invention relates to a method for determining the load state for the components of a power system in an electric power system, and a system for carrying out the method. The method and the system are especially related to the resistive temperature dependence of electric power system components.

The device comprises measurement and control equipment intended to be used in an electric power system.

Background of the invention and prior art

Electric power systems are planned and designed for normal as well as disturbed operation, and the dimensioning crite- ria laid down relating to system quantities and power transmissions are used for that purpose. The load state, expressed as temperature, through power, current, voltage, linear expansion or sagging, for components in various parts of the electric power system, is one such quantity. This load state, related to a limit or reference value, is a measure of the degree of utilization of the component and sometimes also a measure of the margin of stability of the system.

To achieve cost effectiveness, it becomes increasingly more important to utilize the different components of the power system up to their thermal limits, which in turn are dependent on factors such as material changes, line sag, or the risk of breakdown in insulating material. Since the operation of the power systems is limited by thermal transmission limits, it is also increasingly becoming a requirement from clients to enclose thermal overload protective devices in the electric power systems.

To be able to utilize the power system components in the proper way, some form of temperature estimation is thus required, which is currently performed by measurement or calculation. For power system components of a moderate extent, for example transformers, generators and shunt elements, temperature sensors may be mounted into the apparatus itself, which is a method that is not equally suited for elongated components, such as power cables and overhead transmission lines.

Especially for lines, but also for transformers, methods have been developed for determining the temperature in the various parts of the component, based on the second main theorem of the thermodynamics [Gabriel Benmoyal and co- authors, Western Protective Relay Conference, Spokane, 2003] . Unfortunately, these calculations contain many quantities that are associated with the heat dissipation and are difficult to determine, such as cooling by wind and precipitation, radiation from the sun, etc., and therefore have a clearly limited value for practical use since it is relatively simple to set up the equations and define the parameters and quantities included, but it is very difficult to determine the parameters that are characteristic of the power system component under consideration.

Another method is to utilize the variation with the temperature of the electric resistance in different materials, which is used in various types of temperature sensors for point-by-point or local temperature measurement.

Objects and most important characteristics of the invention

The object of the invention is to suggest a method and a system for determining the load state of power system com- ponents, based on an accurate determination of the conductor resistance of the component, preferably based on measured current and voltage, in order to determine, from the temperature dependence of the resistance, the conductor temperature for the conductor material of the component in question.

The above object and other objects are achieved according to the invention by a method according to claim 1, by a system according to claim 7, and by a computer program according to claim 13.

By basing the temperature measurement on an accurate resistance measurement, all uncertainties based on uncertain and variable data influencing the heat dissipation, such as meteorological data, are avoided.

For determining the thermal load state on a line, current and voltage are measured at both end points of the line, preferably synchronized measurement of the complex phase quantities but also the positive-sequence components may be mea- sured, and the current contribution from the equivalent shunt elements, and any shunt elements connected to the line, are calculated. Thereafter, the resistance of the line is calculated, and with knowledge of the temperature dependence of the conductor material and the resistance of the conductor at a certain reference temperature, the conductor temperature may be determined.

Brief description of the accompanying drawings

The invention will be described in greater detail below with reference to the accompanying figures.

Figure 1 shows a line in an electric power system with circuit breakers at both ends, equivalent shunt branches and in- strument .transformers.

Figure 2 shows an embodiment of a calculating unit for determining the load state of a line.

Figure 3 shows an embodiment of the invention in a flow chart, based on the components in Figure 2.

Description of preferred embodiments of the invention

Figure 1 shows a line Ll in an electric power system with associated circuit breakers Sl, S2 at both ends of the line, equivalent shunt branches ZsI, Zs2, instrument transformers EIa,b and E2a,b for measuring the currents II, 12 as well as the voltages Ul, U2. The measuring unit Ml is placed at the transmitter end of the line Ll and the measuring unti M2 at the receiver end of the line Ll. The calculating unit Bl is connected to the transmitter end of the line Ll and includes the measuring unit Ml. A communication Cl between the measuring units Ml, M2 is achieved via, for example, an optical fibre or a microwave link. The synchronization of the measurements at both end points of the line may be made via GPS- controlled time synchronization C2.

Figure 2 shows an embodiment of the described calculating unit Bl that determines the load state of a line. Instrument transformers E3, E4 are arranged for measuring voltage and current, respectively, of the line Ll in question. The instrument transformers E3, E4 are connected to the measuring unit Ml and provide, together with the parameter set ParSetl, the measurement quantities Ul and Il, which together with the measurement quantities U2 and 12, from the remote end of the line, via the communication link Cl, and the parameter set ParSet2, form the basis for calculating the resistance R of the line in the calculating element BlI. In the calculating element B12, the temperature θ of the line is calculated, based on the calculated resistance R and ParSet3. In the cal- culating element B13, an estimation of how the temperature will develop with respect to time Φ(t+) is made under the assumptions specified in ParSet4. In the calculating element B14, the calculated value of the conductor temperature Φ and the time function Φ(t+) of the estimated temperature are finally compared with a number of limit values that may be time- or temperature-related, specified in ParSet5, and binary alarm signals Al-An are set at the outputs. The measuring unit Ml and all the calculating elements B11-B14 may

advantageously be arranged in the same physical calculating unit Bl.

Figure 3 shows an embodiment of the invention in the form of a flow chart based on the components in Figure 2. The calculation is started and initiated by reading the parameters in the parameter sets ParSetl - ParSet5. Thereafter, the measured values Ul and Il are detected in the measuring unit Ml. In the next step BlI, the measured values U2, 12 from the other end of the line Ll are read, whereupon the line resistance R is calculated and outputted. After this, the conductor temperature θ. is calculated and outputted in the calculating unit B12, whereupon an estimate of the development of the temperature with respect to time f)-(t+) is determined and outputted in the calculating unit B13. Finally, the calculated temperature θ and its estimated time function Φ(t+) are compared with a number of limit values to provide an alarm on time and temperature criteria.

In a preferred embodiment of the invention, an estimated value of the conductor temperature is updated regularly, for example every second. The calculation is suitably carried out in two stages, where in the first stage (1) the resistance, R, is determined as follows:

R

where

Ux = the complex voltage at the transmitter end of the line; EJ ₂ = the complex voltage at the receiver end of the line; I ₁ = the complex current out on the line at the transmitter end;

I _shunt i = the complex current component from a shunt contribution at the transmitter end.

Thereafter, the resistivity p[$) of the conductor material, at the temperature deviation, ¹ Q, is determined from the equation:

where

& = the deviation of the conductor material from the reference temperature; β{$) = the resistivity of the conductor material at the temperature in question; l(Φ) = the length of the conductor at the temperature in question;

A(#] = the equivalent area of the conductor at the temperature in question.

For reasonable values of the temperature deviation, equation (2) may be written as follows:

where

Po = the resistivity of the conductor material at the reference temperature;

I ₀ = the length of the conductor at the reference temperature; A _Q = the equivalent area of the conductor at the reference temperature.

Equation ( 3 ) may now be written as follows:

Correction for the linear and area expansions, respectively, of the conductor with increased temperature may now be included in the temperature coefficient CC of the conductor, which gives:

A still better approximation may be obtained by taking into consideration the temperature dependence of the temperature coefficient, which may be of interest if the conductor temperature deviates considerably from the reference temperature. A simple method for determining the relationship between conductor temperature and conductor resistance may be to measure the line resistance at a few different values of the ambient temperature when the current is near zero.

In still another advantageous embodiment of the invention, also the current at the receiver end, I ₂ , is utilized in the calculation algorithm, in which case a calculation may be made at each conductor end, whereupon, for example, a mean value may be formed.

In yet another embodiment of the invention, compensation is made for the capacitance change between power transmission lines and ground as a result of increased sagging at an increased conductor temperature.

In yet a- further embodiment of the- invention,- corona losses- are compensated for.

In a still further advantageous development of the invention, a computer program comprises program instructions that control a computer or a computer process to control or simulate a method for determining the load state of power system components in an electric power system in accordance with the invention.

In an additional advantageous development of the invention, a computer program that controls a computer or a computer process to control or simulate a method for determining the load state of power system components in an electric power system in accordance with the invention is recorded or stored on one or more computer-readable media.

The system comprises members, shown in the figures as flow diagrams and block diagrams. The block diagrams may be con- ceived both as a signal flow diagram and a block diagram describing a piece of equipment for the system. A function performed in a flow diagram or by a block shown in the block diagram may in applicable parts be implemented by analog and/or digital technique but is advantageously performed as programs in a microprocessor, in a computer program or as a computer program code element performed in a computer or in a computer process. It is to be understood that when the flows and blocks shown in the figure are referred to in a physical embodiment as a device, an apparatus, etc., they are to be conceived as means for achieving a desired function, especially when the function is implemented as software in a microprocessor. Consequently, as the case may be in this case, the expression "signal" may also be interpreted as a value generated by a computer program and also appear in this form only. The blocks are described only as a functional description since these functions may be implemented by a person skilled in the art in a manner known per se.

The above invention has been described with reference to different preferred embodiments. The invention is not, of course, limited to these embodiments but other variants of embodiments are also embraced by the scope of protection of the patent.