Method of determining a condition of an electrical power network and apparatus therefor

Abstract

The present invention relates to apparatus 30 for determining a condition of a network section 34 comprised in an electrical power network 32. The network section 34 is configured such that electrical power flows to or from each of plural locations in the network section. The apparatus 30 is configured to receive a first quantity in respect of a first location in the network section 34 and to receive a second quantity in respect of a second location in the network section, each of the first and second quantities corresponding to a signal amplitude and a signal phase angle at its respective location. The apparatus 30 comprises a processor 42 which is operative to determine a condition quantity corresponding to a loading condition of the network section 34 between the first and second locations in dependence on the first and second quantities.

Claims

1. A method of determining a condition of a network section comprised in an electrical power network, the network section being configured such that electrical power flows to or from each of plural locations in the network section, the method comprising: receiving a first quantity in respect of a first location in the network section and receiving a second quantity in respect of a second location in the network section, each of the first and second quantities corresponding to a signal amplitude and a signal phase angle at its respective location; and determining a condition quantity corresponding to a loading condition of the network section between the first and second locations in dependence on the first and second quantities, wherein there being plural electrical power flows to or from the network section at respective further locations between the first and second locations in the network section, wherein the condition quantity being determined in dependence on an electrical model of the network section between the first and second locations, the electrical model comprising a series impedance between the first and second locations and at least one shunt impedance between the series impedance and a reference potential, wherein determining the condition quantity comprises determining a loading quantity for the network section in dependence on first and second signal amplitudes and a difference between first and second signal phase angles, and wherein the loading quantity is calculated by way of: $.Math.S.Math.=\frac{{.Math.V_s.Math.}^2-.Math.V_s.Math..Math.V_r.Math.\left(\cos \left(\right)+i*\sin \left(\right)\right)}{Z_{\mathrm{eq}}}$ where |S| is the loading quantity, |V.sub.s| is the voltage amplitude at the first location, |V.sub.r| is the voltage amplitude at the second location, is the difference between the voltage phase angles at the first and second locations and Z.sub.eq is calculated by way of: $Z_{\mathrm{eq}}=\left(V_s-V_r\frac{I_s{V}_s+I_r{V}_r}{I_s{V}_r+I_r{V}_s}\right)/I_r$ where Z.sub.eq is the series impedance, V.sub.s is the voltage phasor at the first location, V.sub.r is the voltage phasor at the second location, l.sub.s is the current phasor at the first location and l.sub.r is the current phasor at the second location.

2. The method according to claim 1 further comprising: determining whether or not there is a voltage limit violation in the network section, which comprises determining whether or not a voltage amplitude at at least one of the first location and the second location exceeds a predetermined value; and controlling reactive power output of apparatus comprised in the electrical power network in dependence on the voltage limit violation determination.

3. The method according to claim 1 further comprising: determining whether or not there is a voltage limit violation in the network section, which comprises determining whether or not a loading quantity amplitude exceeds a predetermined loading quantity amplitude; and controlling real power output of apparatus comprised in the electrical power network in dependence on at least one of the loading quantity amplitude determination and a reactive power capacity being exceeded.

4. The method according to claim 3 further comprising forming a model of the network section and changing an operating circumstance of the model until a constraint violation occurs.

5. A method of determining a condition of a network section comprised in an electrical power network, the network section being configured such that electrical power flows to or from each of plural locations in the network section, the method comprising: receiving a first quantity in respect of a first location in the network section and receiving a second quantity in respect of a second location in the network section, each of the first and second quantities corresponding to a signal amplitude and a signal phase angle at its respective location; and determining a condition quantity corresponding to a loading condition of the network section between the first and second locations in dependence on the first and second quantities, wherein there being plural electrical power flows to or from the network section at respective further locations between the first and second locations in the network section, wherein the condition quantity being determined in dependence on an electrical model of the network section between the first and second locations, the electrical model comprising a series impedance between the first and second locations and at least one shunt impedance between the series impedance and a reference potential, and wherein determining the condition quantity comprises determining whether or not a thermal constraint is being violated and determining whether or not a thermal constraint is being violated comprises comparing a determined loading quantity with a predetermined loading quantity.

6. The method according to claim 5 in which determining the condition quantity does not depend on a further quantity received in respect of each of the further locations between the first and second locations.

7. The method according to claim 5 in which determining the condition quantity comprises determining at least one of: whether or not a voltage constraint between the first and second locations is being breached; if there has been a loading condition affecting change in the configuration of the network section between the first and second locations; and if there has been a loading condition affecting change in the configuration of the electrical power network.

8. The method according to claim 5 in which the condition quantity is determined in dependence on complex signals which reflect amplitude and phase information.

9. The method according to claim 5 in which the electrical power flows to and from the network section between the first and second locations are caused by electrical arrangements which are operative to at least one of source electrical energy to or sink electrical energy from the network section, each electrical arrangement comprising at least one of: a transmission or distribution line which is operative to convey electrical power to or from the network section; electrical apparatus which is operative to electrically load the network section; a generator; and energy storage apparatus.

10. The method according to claim 5 further comprising controlling the electrical power network in dependence on whether or not there is a thermal constraint violation.

11. A computer program comprising program instructions for causing a computer to perform the method according to claim 5.

12. A method of determining a condition of a network section comprised in an electrical power network, the network section being configured such that electrical power flows to or from each of plural locations in the network section, the method comprising: receiving a first quantity in respect of a first location in the network section and receiving a second quantity in respect of a second location in the network section, each of the first and second quantities corresponding to a signal amplitude and a signal phase angle at its respective location; determining a condition quantity corresponding to a loading condition of the network section between the first and second locations in dependence on the first and second quantities; and determining at least one of: a target voltage signal at the second location and a target transformer ratio for a transformer which is electrically coupled to the second location, the determination being made in dependence on voltage signals measured at the first and second locations in the network section, the first location being subject to a voltage signal limit, wherein there being plural electrical power flows to or from the network section at respective further locations between the first and second locations in the network section, and wherein the condition quantity being determined in dependence on an electrical model of the network section between the first and second locations, the electrical model comprising a series impedance between the first and second locations and at least one shunt impedance between the series impedance and a reference potential.

13. The method according to claim 12 in which the target voltage signal is determined, the target voltage signal being calculated by way of: $V_{\mathrm{r\_new}}=\frac{V_{\mathrm{ref}}\sqrt{V_{\mathrm{ref}}^2-4V_r\left(V_s-V_r\right)}}{2}$ where V.sub.r new is the target voltage signal, V.sub.ref is the target first location voltage signal, V.sub.r is a voltage phasor corresponding to a voltage signal amplitude and a voltage signal phase at the second location and V.sub.s is a voltage phasor corresponding to a voltage signal amplitude and a voltage signal phase at the first location.

14. The method according to claim 12 in which the target transformer ratio is determined, the target transformer ratio being calculated by way of: $\mathrm{ratio}=\frac{V_{\mathrm{ref}}\sqrt{V_{\mathrm{ref}}^2-4V_r\left(V_s-V_r\right)}}{2V_r}$ where ratio is the target transformer ratio, V.sub.ref is the target first location voltage signal, V.sub.r is a voltage phasor corresponding to a voltage signal amplitude and a voltage signal phase at the second location and V.sub.s is a voltage phasor corresponding to a voltage signal amplitude and a voltage signal phase at the first location.

15. Apparatus for determining a condition of a network section comprised in an electrical power network, the network section being configured such that electrical power flows to or from each of plural locations in the network section, the apparatus receiving a first quantity in respect of a first location in the network section and receiving a second quantity in respect of a second location in the network section, each of the first and second quantities corresponding to a signal amplitude and a signal phase angle at its respective location, and the apparatus comprising a processor which is operative to determine a condition quantity corresponding to a loading condition of the network section between the first and second locations in dependence on the first and second quantities, wherein there being plural electrical power flows to or from the network section at a respective further location between the first and second locations in the network section, wherein the condition quantity being determined in dependence on an electrical model of the network section between the first and second locations, the electrical model comprising a series impedance between the first and second locations and at least one shunt impedance between the series impedance and a reference potential, and wherein determining the condition quantity comprises determining whether or not a thermal constraint is being violated and determining whether or not a thermal constraint is being violated comprises comparing a determined loading quantity with a predetermined loading quantity.

16. An electrical power network comprising a network section and apparatus according to claim 15.

17. Apparatus for determining a condition of a network section comprised in an electrical power network, the network section being configured such that electrical power flows to or from each of plural locations in the network section, the apparatus receiving a first quantity in respect of a first location in the network section and receiving a second quantity in respect of a second location in the network section, each of the first and second quantities corresponding to a signal amplitude and a signal phase angle at its respective location, and the apparatus comprising a processor which is operative to determine a condition quantity corresponding to a loading condition of the network section between the first and second locations in dependence on the first and second quantities, wherein the condition quantity being determined in dependence on an electrical model of the network section between the first and second locations, the electrical model comprising a series impedance between the first and second locations and at least one shunt impedance between the series impedance and a reference potential, wherein determining the condition quantity comprises determining a loading quantity for the network section in dependence on first and second signal amplitudes and a difference between first and second signal phase angles, and wherein the loading quantity is calculated by way of: $.Math.S.Math.=\frac{{.Math.V_s.Math.}^2-.Math.V_s.Math..Math.V_r.Math.\left(\cos \left(\right)+i*\sin \left(\right)\right)}{Z_{\mathrm{eq}}}$ where |S| is the loading quantity, |V.sub.s| is the voltage amplitude at the first location, |V.sub.r| is the voltage amplitude at the second location, is the difference between the voltage phase angles at the first and second locations and Z.sub.eq is calculated by way of: $Z_{\mathrm{eq}}=\left(V_s-V_r\frac{I_s{V}_s+I_r{V}_r}{I_s{V}_r+I_r{V}_s}\right)/I_r$ where Z.sub.eq is the series impedance, V.sub.s is the voltage phasor at the first location, V.sub.r is the voltage phasor at the second location, l.sub.s is the current phasor at the first location and l.sub.r is the current phasor at the second location.

18. Apparatus for determining a condition of a network section comprised in an electrical power network, the network section being configured such that electrical power flows to or from each of plural locations in the network section, the apparatus receiving a first quantity in respect of a first location in the network section and receiving a second quantity in respect of a second location in the network section, each of the first and second quantities corresponding to a signal amplitude and a signal phase angle at its respective location, and the apparatus comprising a processor which is operative to determine a condition quantity corresponding to a loading condition of the network section between the first and second locations in dependence on the first and second quantities, wherein at least one of a target voltage signal at the second location and a target transformer ratio for a transformer which is electrically coupled to the second location is determined, the determination being made in dependence on voltage signals measured at the first and second locations in the network section, the first location being subject to a voltage signal limit, wherein there being plural electrical power flows to or from the network section at respective further locations between the first and second locations in the network section, and wherein the condition quantity being determined in dependence on an electrical model of the network section between the first and second locations, the electrical model comprising a series impedance between the first and second locations and at least one shunt impedance between the series impedance and a reference potential.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) Further features and advantages of the present invention will become apparent from the following specific description, which is given by way of example only and with reference to the accompanying drawings, in which:

(2) FIG. 1 represents a section of an electrical network subject to network management according to a known approach;

(3) FIG. 2 is a block diagram representation of apparatus according to the present invention;

(4) FIG. 3A is a representation of a network section and surrounding electrical power network according to the present invention;

(5) FIG. 3B shows an electrical model of the network section and surrounding electrical power network shown in FIG. 3A;

(6) FIG. 4 is a flow chart representation of a method according to a first embodiment of the present invention;

(7) FIG. 5 shows the relationship in graphical form between loading quantity and power flow in a line of the network section of FIG. 3A;

(8) FIG. 6 is a flow chart representation of a method according to a first embodiment in which reactive and real power generation are controlled;

(9) FIG. 7 is a representation of a network section and surrounding electrical power network according to a second embodiment of the present invention;

(10) FIG. 8 is a flow chart representation of a method according to the second embodiment of the present invention;

(11) FIG. 9 is a flow chart representation of a method according to the third embodiment of the present invention; and

(12) FIG. 10 is plot of equivalent reactance against equivalent resistance for the third embodiment.

DESCRIPTION OF EMBODIMENTS

(13) A section of an electrical network subject to network management according to a known approach is represented in FIG. 1. FIG. 1 is described above as background art.

(14) A block diagram representation of apparatus 30 according to the present invention is shown in FIG. 2. The apparatus 30 comprises an electrical power network 32 which for the purposes of the present description is a distribution network operative at power distribution levels, for example below 132 kV such as 11 kV or 33 kV. The electrical power network 32 comprises a network section 34. The network section 34 and the surrounding electrical power network 32 are described in further detail below with reference to FIG. 3A. A first Phasor Measurement Unit (PMU) 36 is operative to make voltage phasor and current phasor measurements at or near a first location at a boundary of the network section 34 and a second PMU 38 is operative to make voltage phasor and current phasor measurements at or near a second location at the boundary of the network section. Each of the PMUs is compliant with the IEEE C37 standard such as an Alstom P847 from Alstom Grid of St. Leonards Avenue, ST17 4LX, Stafford, United Kingdom. The PMUs are synchronised with one another either of themselves or by way of an external time reference, such as from a GPS time source. The apparatus further comprises computing apparatus 40, which in turn comprises a processor 42, data storage 44 and an output device 46. The computing apparatus 40 and its components will be of a form and function familiar to the skilled reader. The output device 46 of the computing apparatus 40 is operative under control of the processor 42 to display data to a user of the computing apparatus 40. The computing apparatus 40 is operative to receive measurements made by the first and second PMUs 36, 38. Measurements are received by the computing apparatus 40 by way of a communications channel 48 between the computing apparatus 40 and each PMU with the communications channels 48 being of a copper, optical fibre or wireless form.

(15) Operation of the apparatus 30 of FIG. 2 will be described below. In the meantime the network section 34 and surrounding electrical power network 32 will be described in more detail with reference to FIG. 3A. The network section 34 comprises a first bus 52, a second bus 54, a third bus 56 and a fourth bus 58. The surrounding electrical power network 32 comprises a renewable energy generator 64 and a local load 66 which are each connected to the fourth bus 58. The first PMU 36 is operative to measure the current phasor I.sub.s in the line between the third and fourth buses 56, 58 and the voltage phasor V.sub.s on the fourth bus 58 at or near where the renewable energy generator 64 and the local load 66 connect to the fourth bus 58. The points of connection of the renewable energy generator 64 and the local load 66 constitute a first location on the boundary of the network section 34. The surrounding electrical power network 32 further comprises a step-up transformer 60 which is connected at its high voltage side to the sub-transmission system 62 and is connected at its low voltage side to the first bus 52 to thereby establish a bulk power receiving point. The second PMU 38 is operative to measure the current phasor I.sub.r in the line between the first and second buses 52, 54 and the voltage phasor V.sub.r on the first bus at or near the bulk connection point at a second location which is on the boundary of the network section 34. Each of the first to fourth buses 52, 54, 56, 58 is connected to a distribution line which is operative to convey electrical power. The distribution lines between the first and fourth buses 52, 54, 56, 58 are operative to convey power within the network section 34. A further generator 70 is connected to the second bus 54.

(16) A network section such as the network section 34 of FIG. 3A can be treated as a transmission line model consisting of a series impedance Z.sub.eq between the first bus 52 and the fourth bus 58, a first shunt impedance

(17) $\frac{Y_{\mathrm{eq}}}{2}$
between the first bus and ground and a second shunt impedance

(18) $\frac{Y_{\mathrm{eq}}}{2}$
between the second bus and ground. An electrical model constituted by the series impedance and the two shunt impedances is represented in FIG. 3B. The complex series impedance Z.sub.eq is given by:

(19) $Z_{\mathrm{eq}}=\left(V_s-V_r\frac{I_s{V}_s+I_r{V}_r}{I_s{V}_r+I_r{V}_s}\right)/I_r$
and the complex shunt impedance Y.sub.eq is given by:

(20) $Y_{\mathrm{eq}}=\left(2\frac{I_s{V}_s+I_r{V}_r}{I_s{V}_r+I_r{V}_s}-2\right)/Z_{\mathrm{eq}}$
where V.sub.s is the voltage phasor (or complex voltage signal) at the first location (i.e. at the fourth bus), V.sub.r is the voltage phasor at the second location (i.e. at the first bus), I.sub.s is the current phasor (or complex current signal) at the first location and I.sub.r is the current phasor at the second location.

(21) Although the electrical model comprises two shunt impedances the present invention makes no use of them and relies on the series impedance, as will become apparent from the following description.

(22) A method according to a first embodiment of the present invention will now be described with reference to FIG. 4 which provides a flow chart representation 80 of steps involved in the method. The first embodiment involves determining on the basis of measurements made by the first and second PMUs 36, 38 whether or not a constraint comprised in the network section 34, such as a thermal constraint, is violated during operation of the electrical power network. A preliminary step of the first embodiment involves determining a limit imposed by a network section constraint. According to the first embodiment the limit imposed by the network section constraint is determined in the form of a predetermined loading quantity 82 or a critical predetermined loading quantity where the network section is subject to more than one constraint.

(23) The predetermined loading quantity is determined by way of modelling or simulation of the network section and the surrounding electrical power network. Worst-case network loading and generation conditions are determined and then modelled. A worst case scenario may, for example, be maximum generation with minimum load. The model is then used to determine the circumstances under which a constraint violation occurs. According to a first approach and when a constraint violation occurs, the voltage waveforms at the first and second locations on the boundary of the model of the network section are determined. Then the predetermined loading quantity is calculated by way of:
|S.sub.limit|.sub.limit=|V.sub.s|.sup.2|V.sub.sV.sub.r|(cos()+i*sin())
where |S.sub.limit|.sub.limit is the predetermined loading quantity, |V.sub.s| is the voltage amplitude at a first location of the two locations, |V.sub.r| is the voltage amplitude at a second of the two locations, and is the difference between the voltage phase angles at the first and second locations, i.e. .sub.s.sub.r. According to a second approach and when a constraint violation occurs, the voltage and current waveforms at the first and second locations on the boundary of the model of the network section are determined. Then the predetermined loading quantity is calculated by way of:

(24) $.Math.S_{\mathrm{limit}}.Math.{}_{\mathrm{limit}}=\frac{{.Math.V_s.Math.}^2-.Math.V_s.Math..Math.V_r.Math.\left(\cos \left(\right)+i*\sin \left(\right)\right)}{Z_{\mathrm{eq}}}$
where |S.sub.limit|.sub.limit is the predetermined loading quantity, |V.sub.s| is the voltage amplitude at a first location of the two locations, |V.sub.r| is the voltage amplitude at a second of the two locations, is the difference between the voltage phase angles at the first and second locations, i.e. .sub.s.sub.r, and Z.sub.eq is the complex series impedance between the two locations as calculated by the equation specified above. Of the two approaches the second, series impedance dependent approach yields a better modelled predetermined loading quantity.

(25) The constraint violation modelling process is repeated for each of plural different network loading and generation scenarios to provide a constraint violation for each scenario. The voltage phasors and optionally current phasors at the two locations on the boundary of the model of the network section are applied to one of the two predetermined loading quantity equations specified above to provide plural predetermined loading quantities. Then the most limiting of the plural predetermined loading quantities is identified as the critical predetermined loading quantity by comparing predetermined loading quantities. The network section may be subject to one or more constraints. Constraints include: a thermal constraint; a voltage rise constraint; a transformer reverse power flow constraint; a transient stability limit; a voltage stability limit; and an oscillation stability limit. The network section may be subject to more than one constraint of a particular type at different locations and/or plural constraints of different types. Where the network section is subject to plural constraints the constraint violation modelling process is repeated for each constraint. Each of all the constraints is translated into an equivalent loading quantity. For example, where a constraint is a voltage constraint it is translated into an equivalent loading quantity and where a constraint is a thermal constraint it is translated into an equivalent loading quantity. Then the most conservative of the plural predetermined loading quantities is identified as the critical predetermined loading quantity.

(26) The method of the first embodiment then progresses to monitoring the network section for a constraint violation. There are two alternative approaches according to the embodiment for monitoring for constraint violation: a first simpler approach which provides for less accurate monitoring; and a second more complex approach which provides for more accurate monitoring. According to the first approach a loading quantity is determined for the network section on the basis of voltage phasor measurements only 84, i.e. without relying on current phasor measurements. The first approach is appropriate, for example, where the PMUs provide only voltage phasor measurements or where only voltage phasor measurements or voltage phasor measurement information is received by the operator performing the monitoring process from, for example, the operator of the electrical power network. The loading quantity according to the first approach is determined by way of:
|S.sub.trim|.sub.trim=|V.sub.s|.sup.2|V.sub.sV.sub.r|(cos()+i*sin())
where |S.sub.trim|.sub.trim is the loading quantity, |V.sub.s| is the voltage amplitude at the first location, |V.sub.r| is the voltage amplitude at the second location, and is the difference between the voltage phase angles at the first and second locations, i.e. .sub.s.sub.r. The voltage amplitudes and phase angles are determined from the voltage phasor measurements. The next step comprises comparing the determined loading quantity with the predetermined loading quantity 86. If the determined loading quantity is less than or equal to the predetermined loading quantity there is no constraint violation and no indication is provided to the operator and no rectifying action is taken 88. On the other hand if the determined loading quantity is greater than the predetermined loading quantity there is a constraint violation and at least one of: an indication of constraint violation is provided to the operator 90; and rectifying action to control the electrical power network to bring the loading quantity within limit. Control of the electrical power network is described below in more detail with reference to FIG. 6. The steps of determining the loading quantity and comparing the determined loading quantity with the predetermined loading quantity are repeated at an appropriate interval, such as once every second.

(27) According to the second approach the next step is recalculation of the series impedance on the basis of fresh voltage and current phasor measurements 94. As will be appreciated from the equation for the series impedance which is specified below with reference to step 96 in FIG. 4, the series impedance is liable to change when there is a change in the network section loading or generation conditions. The series impedance is therefore recalculated on the basis of fresh voltage and current phasor measurements before each instance of determination in the following step of the loading quantity on the basis of voltage and current phasor measurements 94. The second approach is appropriate, for example, where the PMUs provide voltage and current phasor measurements or where voltage and current phasor measurements or voltage and current phasor measurement information is received by the operator performing the monitoring process. The loading quantity according to the second approach is determined by way of:

(28) 0$.Math.S.Math.=\frac{{.Math.V_s.Math.}^2-.Math.V_s.Math..Math.V_r.Math.\left(\cos \left(\right)+i*\sin \left(\right)\right)}{Z_{\mathrm{eq}}}$
where |S| is the loading quantity, |V.sub.s| is the voltage amplitude at the first location, |V.sub.r| is the voltage amplitude at the second location, is the difference between the voltage phase angles at the first and second locations, i.e. .sub.s.sub.r, and Z.sub.eq is the complex series impedance. The complex series impedance is determined on the basis of the equation for Z.sub.eq provided above. Thereafter the second approach proceeds as per the first approach. More specifically the next step comprises comparing the determined loading quantity with the predetermined loading quantity 86. If the determined loading quantity is less than or equal to the predetermined loading quantity there is no constraint violation and no indication is provided to the operator and no rectifying action is taken 88. On the other hand if the determined loading quantity is greater than the predetermined loading quantity there is a constraint violation and at least one of: an indication of constraint violation is provided to the operator 90; and rectifying action is taken to control the electrical power network to bring the loading quantity within limit. As with the first approach the steps of determining the loading quantity and comparing the determined loading quantity with the predetermined loading quantity are repeated at an appropriate interval, such as once every second.

(29) The determination of a predetermined loading quantity for the electrical power network shown in FIG. 3A will now be described further by way of an example scenario and with reference to the graph shown in FIG. 5. As stated above worst-case network loading and generation scenarios are determined and then modelled. According to the present example loading at the first to fourth buses 52, 54, 56, 58 is at a minimum and the generator 70 at the second bus is producing 20 MW. The power output of the generator 64 at the fourth bus 58 is increased progressively in 1 MW steps. When the power output of the generator 64 at the fourth bus 58 reaches 6 MW it is found by way of modelling that the MVA flow in the line between the first and second buses 52, 54 is 20.04 MVA which is slightly above the thermal rating of 20 MVA for this line. This constitutes a thermal violation for this particular scenario. The predetermined loading quantity corresponding to the power flow in the line between the first and second buses is then determined by way of application of one of the two loading quantity equations specified above. More specifically and depending on which of the two loading quantity equations is used either voltage waveform data for each of the first and second locations or voltage and current waveform data for each of the first and second locations is applied to the loading quantity equation with the applied waveform data corresponding to a range of values of power output from the generator at the fourth bus sufficient to span the line thermal rating of 20 MVA. The loading quantities obtained from the loading quantity equation are then plotted against the corresponding MVA flow values in the line having the thermal constraint. Such a plot according to the present example is shown in FIG. 5. Careful examination of FIG. 5 shows that a loading quantity of 12.31 MVA is obtained when the thermal constraint value of 20 MVA is breached. The loading quantity of 12.31 MVA is thus the predetermined loading quantity to be used during monitoring of the network section as described above. Where other thermal constraints are to be taken into consideration the above approach is followed for each of the other constraints and the lowest of the predetermined loading quantities obtained is selected as the critical predetermined loading quantity for use during monitoring of the network section as described above.

(30) A flow chart representation of a method according to an embodiment in which reactive and real power generation are controlled 110 is shown in FIG. 6. Controlling reactive power generation and real power generation independently of each other confers economic advantages. More specifically it may under certain circumstances be advantageous to change reactive power generation in preference to real power generation. Controlling reactive power generation to mitigate a bus voltage may, however, lead to an increase in thermal flow. It is therefore advantageous to know when controlling reactive power generation is no longer appropriate such that real power generation should be controlled instead. According to the method of FIG. 6 it is assumed that a voltage constraint is managed by a method other than the method involving the loading quantity |S| according to the invention which is employed for management of other constraints. Turning to consider the method of FIG. 6 as applied to an electrical power network as represented by way of example in FIG. 3A the first step 112 comprises determining whether or not there is a voltage limit violation or whether or not the loading quantity amplitude, |S|, exceeds the predetermined loading quantity amplitude. Determining whether or not there is a voltage limit violation comprises determining if at least one of the voltages at the first and fourth buses 52, 58 exceeds a predetermined value. If the predetermined value is not exceeded or if the loading quantity amplitude, |S|, does not exceed the predetermined loading quantity amplitude no control action is taken 114. If the predetermined value is exceeded the next step 115 is controlling reactive power generation to gradually decrease the imaginary part or angle of the loading quantity. A decrease in the angle of the loading quantity indicates that loading of the network section is more inductive whereby the voltage profile in the wider network is reduced. The following step 116 is determining whether or not the loading quantity amplitude, |S|, exceeds the predetermined loading quantity amplitude or whether or not the reactive power capacity has been reached. If the loading quantity amplitude, |S|, has not exceeded the predetermined loading quantity amplitude and the reactive power capacity has not been reached the method returns to the first step 112. If the loading quantity amplitude, |S|, has exceeded the predetermined loading quantity amplitude or the reactive power capacity has been reached, the next step 117 is reduction in real power generation, e.g. at the generator 64 at the fourth bus 58. Thereafter the method returns to the first step 112 whereby gradual control can be effected. If at the first step 112 the loading quantity amplitude, |S|, exceeds the predetermined loading quantity amplitude, the next step 118 is controlling reactive power generation to gradually move the angle of the loading quantity towards zero. Movement of the angle of the loading quantity towards zero indicates that the reactive power in the network section is reducing to thereby provide more room for real power flow. The following step 119 is determining whether or not there is a voltage limit violation or whether or not the reactive power capacity has been reached. If there is no voltage limit violation and the reactive power capacity has not been reached the method returns to the first step 112. If there is a voltage limit violation or the reactive power capacity has been reached, the next step 117 is reduction in real power generation. Thereafter the method returns to the first step 112 whereby gradual control can be effected.

(31) A method according to a second embodiment of the present invention will now be described with reference to FIG. 7 which is a representation of a network section and surrounding electrical power network and FIG. 8 which provides a flow chart representation 130 of steps involved in the method. The second embodiment involves determining on the basis of measurements made by first and second PMUs 36, 38 at respective first and second network section boundary locations either a target voltage signal at the transformer 60 or a target transformer ratio which is required to bring a voltage signal in the network section within regulatory limits. The network section and surrounding electrical power network 120 of FIG. 7 will be considered first. Components in common with the network section and surrounding electrical power network of FIG. 3A are designated in FIG. 7 by common reference numerals. The reader should refer to the description provided above with reference to FIG. 3A for a description of such common components. Components particular to FIG. 7 will now be described. FIG. 3A shows a four bus radial distribution network whereas FIG. 7 shows a five bus radial distribution network. The network of FIG. 7 therefore comprises a fifth bus 122 with the first PMU 36 making measurements at the fifth bus 122 instead of the fourth bus 58 and the renewable energy generator 64 being connected to the fifth bus 122 instead of the fourth bus 58. Furthermore the further generator 70 is connected to the third bus 56 instead of the second bus 54. The first and fifth buses 52, 122 therefore define a boundary of the network section at which measurements are made by the first and second PMUs 36, 38 at respective first and second locations. Turning now to the flow chart of FIG. 8 the method according to the second embodiment will now be described. The first step of the method comprises determining if the voltage signal at the first location, i.e. at the fifth bus 122 as measured by the first PMU 36, exceeds a regulatory limit 132. If the voltage signal at the first location exceeds the regulatory limit a target first location voltage signal, V.sub.ref, is then determined 134, the target first location voltage signal being within the regulatory limit. Then the target voltage signal, V.sub.r.sub._.sub.new, at the second location is determined 136, the target voltage signal being a new voltage signal at the second location which is required to change the voltage signal at the first location to the target first location voltage. The target voltage signal is calculated by way of:

(32) $V_{\mathrm{r\_new}}=\frac{V_{\mathrm{ref}}\sqrt{V_{\mathrm{ref}}^2-4V_r\left(V_s-V_r\right)}}{2}$
where V.sub.r.sub._.sub.new is the target voltage signal, V.sub.ref is the target first location voltage signal, V.sub.r is a voltage phasor corresponding to a voltage signal amplitude and a voltage signal phase at the second location and V.sub.s is a voltage phasor corresponding to a voltage signal amplitude and a voltage signal phase at the first location. Thereafter a target transformer ratio is determined 138 for the transformer 60 at the first bus 52. The target transformer ratio is calculated by way of:
ratio=V.sub.r.sub._.sub.new/V.sub.r.

(33) Alternatively the target transformer ratio is calculated directly by way of:

(34) $\mathrm{ratio}=\frac{V_{\mathrm{ref}}\sqrt{V_{\mathrm{ref}}^2-4V_r\left(V_s-V_r\right)}}{2V_r}$

(35) The transformer 60 at the first bus 52 is then reconfigured to have the thus determined target transformer ratio 140 by changing the transformer tap position to thereby reduce the voltage signal on the low, i.e. first bus 52 side, of the transformer which in turn brings the voltage signal at the first location, i.e. at the fifth bus 122, to within limit. Where the present tap position, t.sub.old, for the transformer is known a new position for the transformer can be determined in dependence on the present tap position and the target transformer ratio. More specifically the present tap position is calculated by way of: t.sub.new=t.sub.oldratio. The method of the second embodiment is employed in the reactive and real power generation control method shown in FIG. 6, although transformer control is not shown in FIG. 6. After steps 118 and 124 but before step 120 (i.e. real power generation control) of the method of FIG. 6 the reactive and real power generation control method comprises controlling the transformer in accordance with the second embodiment. After the transformer control step the reactive and real power generation control method returns to the first step 112.

(36) A method according to a third embodiment of the present invention will now be described with reference to FIG. 3A which is a representation of a network section and surrounding electrical power network and FIG. 9 which provides a flow chart representation 150 of steps involved in the method. The third embodiment involves detecting a change in a loading condition of a network section 34 and controlling the electrical power network where this is warranted by an extent of the detected change. The change in the network section is reflected in the complex series impedance, Z.sub.eq, of an electrical model of the network section. The first step of the method according to the third embodiment is determination of a threshold complex impedance by off-line simulations of various scenarios 152. The next step is determination of the change reflecting complex series impedance, Z.sub.eq, 154. The complex series impedance, Z.sub.eq, is calculated by way of:

(37) $Z_{\mathrm{eq}}=\left(V_s-V_r\frac{I_s{V}_s+I_r{V}_r}{I_s{V}_r+I_r{V}_s}\right)/I_r$
where V.sub.s is the voltage phasor at the first location (i.e. at the fourth bus), V.sub.r is the voltage phasor at the second location (i.e. at the first bus), I.sub.s is the current phasor at the first location and I.sub.r is the current phasor at the second location. Then the determined complex series impedance is compared with the threshold complex impedance 156. The threshold complex impedance 156 may be either an upper threshold value or a lower threshold value. If the determined complex series impedance is less than or equal to the upper threshold complex impedance the complex series impedance is determined again 154 and the comparison step 156 is repeated. If the determined complex series impedance is greater than the upper threshold complex impedance, this is indicative of a change that requires intervention and therefore control is exerted over the electrical power network 158. Control is exerted, for example, by more conservative utilisation of the network section 34 to reduce the likelihood of the upper threshold complex impedance being exceeded or to bring the complex series impedance within the upper threshold complex impedance. Where the threshold complex impedance 156 is a lower threshold value and a determined complex series impedance is less than the lower threshold complex impedance, this is also indicative of a change that requires intervention.

(38) Operation of the third embodiment is illustrated by way of FIG. 10. FIG. 10 is a plot of equivalent reactance, X.sub.eq, against equivalent resistance, R.sub.eq, where Z.sub.eq=R.sub.eq+X.sub.eq. Each circle plotted in FIG. 10 represents the equivalent reactance and equivalent resistance obtained by way of measurements made at the first and second locations under different circumstances involving the tripping or disconnection of a transmission line. The circular plots clustered together in the top right hand corner of the plot of FIG. 10 relate to disconnection events outside the network section 34. The remaining, scattered circular plots relate to disconnection events within the network section 34 between the first and second locations. It can therefore be appreciated from an inspection of FIG. 10 that the third embodiment provides an effective means of detecting a change in a loading condition of the network section which warrants intervention.