This invention refers to a device to supervise impedance-earthed, i.e. non-directly-earthed power systems. By use of this device, herinafter referred to as a NX-ana¬ lyser, a continuous calculation of the attenuation (d) , dissymmetry (k) and mismatch (v) parameters of the system from the circle diagram uEN=f(v) is provided.

To the extent that the neutral point voltage criterion is used today for monitoring or control purposes, it is pure¬ ly the value of amplitude that is measured. Amplitude measurement is used, inter alia, for such purposes as indi¬ cation of abnormal conditions in the power system, such as for example single-phase earth faults. Use is also made of the resonance curve, or of the relationship between the amplitude of the neutral point voltage and the degree of mistuning in devices for automatic tuning of Petersen coils. On the other hand, the fact that a certain neutral point voltage of varying magnitude can occur even in the faultfree condition does limit the applicability of the amplitude criterion method for general monitoring purposes. Here the NX-analyser effects an improvement. The continuous calculation and processing of the values of the above- -mentioned system parameters creates a whole set of new criteria for various monitoring and control purposes in the above systems. The following, for example, can be considered:

1. Degree of mistuning (v) : Monitoring of the self- extinguishing condition in accordance with DIN 57288 and compliance with the current limiting requirement in accor¬ dance with various legal requirements are important means of monitoring non-directly-earthed high-voltage systems. Existing known means of providing such monitoring are connected to automatic tuning of Petersen coils. The majority of devices utilize as control criterion the resonance curve |U _EN | =f(v) and the fact that U _™ reaches its maximum value at the exact point of tuning (v=0) .

Another procedure makes use of the relationship where, as known, the angular change falls off with decreasing degree of mistuning (Swiss Patent No. 532854). However, the common feature of all known tuning procedures is that they require a stepless adjustable neutral point reactor. Monitoring/control is also limited to the control range of the reactor. Extraction of a quantitative criterion for the degree of mistuning, independently of the particular coil setting, here provides several benefits. Firstly, no controllable neutral point reactor is required, and secondly monitoring of the degree of mistuning can continue to operate also outside the setting range of the reactor. Use of the NX-analyser also facilitates separation of the monitoring and control functions. In many systems monitoring alone is quite sufficient, and any necessary ad¬ justment of the reactor coil on the few occasions that it is necessary can be done manually.

2. Attenuation (d) : The attenuation factor can also be expressed as the quotient of IR/I _C> where I _R is the resistive component of the earth fault current and I is the capacitive component. I _R is the result of various losses in the system, of which leakage losses across the surface of insulators generally constitute the major part. Leakage losses increase as the amount of dirt on the insulator surfaces increases. In areas with low levels of precipi¬ tation the gradual accumulation of dirt on the surface of insulators can give rise to severe operational problems. In such cases, continuous monitoring of the attenuation factor provides a means of improving the efficiency of preventive maintenance.

In combination with the degree of mistuning, ^' the attenuation factor can also be used for controlling compensation devices in accordance with Swedish Patent No. 8401365-5. By means of this, or similar devices, it is possible to compensate both the reactive and the active components in the earth fault current. Here the NX-analyser creates the conditions for automatic control.

3. Degree of dissymmetry (k)_: Continuous monitoring of the degree of dissymmetry, and in particular of its relative

changes, provides a highly sensitive criterion for detec¬ tion of various fault states in the power system. In particular the ability to detect high-impedance earth faults can be mentioned. The total degree of dissymmetry, k _{to a} - _ι - of the power system consists of the degrees of dissymmetry -L1 ' -L2 ^etc - °f ^tne individual line sections. These, in turn, are very characteristic, and arise as a result of the difference between the capacitive couplings of the phase conductors to earth as a result of their geometrical posi- tions. Switching in or out individual lines thus also changes the calculated total degree of dissymmetry as determined by the NX-analyser, which restricts the practical feasibility of making direct use of k , or of its rela¬ tive chang ^a es Δ—kt. _Λ ot.al. as an earth fault criterion. In order to get round this limitation, the NX-analyser generates a further criterion from Δ-_ _tota ^ and _ v. This is because it is possible to assume that the system structure only exceptionally will change at the same instant as a spontaneous earth fault occurs. In other words, the change in the degree of dissymmetry arising as the result of an earth fault generally occurs without a simultaneous alteration in the degree of mistuning. This factor is utilized in the NX-analyser to generate a criterion which makes it possible to detect even high resistance earth faults A more detailed description of the NX-analyzer requires reference to Figures 1-3, of which:

Figure 1 shows a typical circle diagram, (v) , in a given three-phase system.

Figure 2 shows the links between the three-phase system and earth and the external connections of the NX-analyser for measurement and control.

Figure 3 shows a flow diagram for the programcontrolled measurement, control and processing functions of the NX-analyser. The circular locus U _p ,-- ^* -f(v) , shown in Figure 1 , is determined from three points: the given point at which the curve is a tangent to the neutral point N of the three-phase system, and furthermore two essentially arbitrary measure¬ ment points. These two points are calculated by the N -ana-

lyser through application of a programcontrolled change in the zero sequence admittance Y . In principle, this change can be made in a number of different ways , including that as shown in Figure 2 through connection of a capacitive element C at the neutral point. Switching gives rise to the two measured points U _EN(1 - and U _EN ^ ₂ * ₎ ^{on he} circle diagram in Figure 1. The associated reactance values, ωL and (ωL + 1/ιdC), are assumed to be of known magnitude. Corres¬ ponding degrees of mistuning are obtained by projection of the measured points on a orthogonal scale on which also the point of resonance (v=0) is shown - see Figure 1. Scaling is linear and related to two known measured points. Derivation of the quotient ^makes determination of the circle diagram locus independent of load. in general, the following relationships apply for the relative neutral point voltage:

U _E N Ϊ _R ⁺ *2Y _S - aY _τ

UEN - = ^{* ( 1 )}

IRS YR + ΪS ⁺ ΪR ⁺ YO where v -= (2)

⁽ 3 ⁾

3s

Y _R + a ² Y _s -*- aY-

< =

which gives k_

HEN = (5 ⁾ v + d and, at the resonance point, where v = 0:

HEN ax = ^{( 6 )}

Corresponding derivation of d and k from the circle diagram Up _N =f(v) is as follows:

Equations (5) and (6) give the relationship: ENmax ( ^{2 +} d ² )0-5

= X (7)

"EN ^d with two solutions for v:

^v (a, _b ) - i (X2 - 1 )0.5 (8)

The two points v(a,b) for which x=2 ' are found from the scale and circle locus in Figure 1. With these two points, calculation of the two values that are required can finally be concluded from:

_d _ ^{γ " γ} b ⁽ 9 ⁾ and

_. = d UENmax ⁽¹⁰⁾

A more detailed description of the method of working of the NX-analyser is shown in Figure 3. Figures within brackets refer to sequence steps 001..039 in the flow chart.

The starting sequence (001-103) commences with an up¬ dating of limit value file A-E. Files F and G are used for storing values of neutral point reactans jL and (α)L + 1/ωC) respectively. After entry of the neutral point voltage, Up _N , and the reference voltage, U _R -., the initial value of the relative neutral point voltage, Up^, (005) is calculated, details of the amplitude and phase angle of which are stored in file J (006) . The reactance complement C (007) is then connected. The subsequently calculated value of Up^ is then stored in file K (008...010) . By means of the contents of files J and K, and the associated reactance values in files F and G, the NX-analyser calculates the circle diagram and the initial values for v, d and k which are then stored in files L, M and X, respectively (011 , 012). The starting sequence is then concluded by means of a jump to LOOP 1 (013) .

LOOP 1 starts, in turn, with calculation of a new starting value for i- , which is then loaded into file I (015...018). The initial value is continuously compared with the latest current value of u _pN in file J (019...022). If the limiting value of ZiU _pN is exceeded, the program jumps to LOOP 2 (023) . In order to provide regular calculation of system parameters, LOOP 1 in principle can be complemented by a turns counter or time control.

LOOP 2 starts with connection of the reactance comple- ment (025). It then continues by calculating u _EN (026...028), followed by v, d and k (029) . v and k are temporarily stored in files 0 and P (030) . If any values exceed the specified limiting values, an alarm will be generated (103...037). The relative change in the degree of dissymmetry, k, is monitored with respect to two limiting levels. Provided that the degree of mistuning is unchanged (033) , a comparison will be made with limiting ^s value k1max,' which,> in p_ ^*• rincip ITle, ^t can be set more tig °htly ' than k2max. LOOP 2 concludes with transfer of the temporarily stored values of v and k (038) and a jump back to LOOP 1 (039) .

The program structure described here can be implemented in any computer system capable of providing the necessary measurement, control and processing functions. A post- connected governing stage can be used to apply the calcu- lated value of degree of mistuning, v, as calculated by the NX-analyser, for automatic control of conventional Petersen coils. However, this controlling circuit requires feedback, in which file F is updated with information on the current coil setting. The two system parameters v and d can also be used for corresponding control of compensation devices in accordance with Swedish Patent No 84 01 365, or similar.