## Ryp min

p max where:

Upmin - minimal admitted operating voltage in kV (usually Upmin = 0,9 UN), Spmax - maximum apparent power in MVA, Ipmax - maximum admitted load.

A necessary condition of connecting DPGS to the HV network is researching whether the increase of load (especially in faulty conditions e.g. one of the lines is falling out) is not leading to an overlap. Because of the security reasons and the falsifying factors influencing the impedance evaluation, it is assumed that the protection will not unnecessarily pick-up if the impedance reach of operating zones will be shorter than 80% of the minimal expected load. This requirement will be practically impossible to meet especially when the MHO starting characteristics are used (Fig 15a). There are more possibilities when the protection realizes a distance protection function with polygonal characteristics (Fig. 15b). Using digital distance protections with polygonal characteristics is also very effective for HV lines equipped with high temperature low sag conductors or thermal line rating. In this case

^Z3 1p max the load can increase 2.5 times. Figure 16 shows the adaptation of an impedance area to the maximum expected power line load. Of course this implies serious problems with the recognition of faults with high resistances.

Fig. 15. Starting and operating characteristics a) MHO, b) polygonal

Fig. 16. Adaptation of operating characteristics to the load impedance area

5.2 Simulations

Figure 17 shows the network structure taken for the determination of the influence of selected factors on the impedance evaluation error. This is a part of the 110 kV network of the following parameters:

• short-circuit powers of equivalent systems: SkA = 1000 MVA, SkB = 500 MVA;

• wind farm consists of 30 wind turbines using double fed induction generators of the individual power PjN=2 MW with a fault ride-through function. Power of a wind farm is changing from 10% to 100% of the nominal power of the wind farm. WF is connected in the three-terminal line scheme,

• overhead power line AB:

• length: 30 km; resistance per km: rl=0.12 Q/km, reactance per km Xj=0.4 Q/km

• overhead power output line from WF:

• length: 2 km; resistance per km: rl=0.12 Q/km, reactance per km Xj=0.4 Q/km

• metallic three-phase fault on line AB between the M connection point and 100% of the line La-b length.

Initial and steady fault currents from the wind farm and system A have been evaluated for these parameters. It has been assumed that phases of these currents are equal. The initial fault current of individual wind turbines will be limited to 330% of the nominal current of the generator and wind turbines will generate steady fault current on the level of 110% of the nominal current of the generator. The following examples will now be considered.

Fig. 17. Network scheme for simulations Example 1

The network is operating in quasi-steady conditions. The farm is generating power of 60 MW and is connected at 10 % of the LA-B line length. The location of a fault changeable from 20 % to 100 % of the LA-B length with steps of 10 %. Table 1 presents selected results of simulations for faults of times not exceeding 50 ms. Results take into consideration the limitation of fault currents on the level of 330% of the nominal current of the generator. By analogy, Table 2 shows the results when the limitation is 110 % after a reaction of the control units.

 Fault location 1a 1c 1c/1a AR AX SR% SX% Rlaf Xlaf l X%Zlab [km] [%] [kA] [kA] [-] [Q] [Q] [%] [%] [Q] [Q] 6 20 3.93 0.801 0.204 0.073 0.245 10.191 10.191 0.720 2.400 9 30 3.591 0.732 0.204 0.147 0.489 13.590 13.590 1.080 3.600 12 40 3.305 0.674 0.204 0.220 0.734 15.295 15.295 1.440 4.800 15 50 3.061 0.624 0.204 0.294 0.979 16.308 16.308 1.800 6.000 18 60 2.851 0.581 0.204 0.367 1.223 16.982 16.982 2.160 7.200 21 70 2.667 0.545 0.204 0.441 1.471 17.516 17.516 2.520 8.400 24 80 2.505 0.511 0.204 0.514 1.714 17.849 17.849 2.880 9.600 27 90 2.362 0.481 0.204 0.586 1.955 18.101 18.101 3.240 10.800 30 100 2.234 0.455 0.204 0.660 2.200 18.330 18.330 3.600 12.000

Table 1. Initial fault currents and impedance errors for protection located in station A depending on the distance to the location of a fault (Case 1)

Table 1. Initial fault currents and impedance errors for protection located in station A depending on the distance to the location of a fault (Case 1)

where:

l - distance to a fault from station A, x%ZiAB - distance to a fault in the percentage of the LAB length,

IA - rms value of the initial fault current flowing from system A to the point of fault, IC - rms value of the initial current flowing from WF to the point of a fault, AR - absolute error of the resistance evaluation of the impedance AR = Re{(Ic/Ia ) Zlmf },

AX - absolute error of the reactance evaluation AX = Im{( Ic/Ia ) Zlmf },

RLAF - real value of the resistance of the fault loop, XLAF - real value of the reactance of the fault loop, SR% - relative error of the evaluation of the resistance SR% = AR/Rlaf , SX% - relative error of the evaluation of the resistance, SX% = AX/Xlaf .

algorithm, of the impedance algorithm,

 Fault location 1A(u) 1C (u) 1C( u)/ 1A( u) AR AX SR% l x%Zlab [km] [%] [kA] [kA] [-] [Q] [Q] [%] [%] 6 20 3.986 0.328 0.082 0.030 0.099 4.114 4.114 9 30 3.685 0.328 0.089 0.064 0.214 5.934 5.934 12 40 3.425 0.328 0.096 0.103 0.345 7.182 7.182 15 50 3.199 0.328 0.103 0.148 0.492 8.203 8.203 18 60 3 0.328 0.109 0.197 0.656 9.111 9.111 21 70 2.824 0.328 0.116 0.251 0.836 9.955 9.955 24 80 2.666 0.328 0.123 0.310 1.033 10.765 10.765 27 90 2.525 0.328 0.130 0.374 1.247 11.547 11.547 30 100 2.398 0.328 0.137 0.443 1.477 12.310 12.310

Table 2. Steady fault currents and impedance errors for protection located in station A depending on the distance to the location of a fault (Case 2)

Table 2. Steady fault currents and impedance errors for protection located in station A depending on the distance to the location of a fault (Case 2)

where:

IA(u) - rms value of steady fault current flowing from system A to the point of a fault,

IC (u) - rms value of steady fault current flowing from WF to the point of a fault,

The above-mentioned tests confirm that the presence of sources of constant generated power (WF) brings about the miscalculation of impedance components. The error is rising with the distancing from busbars in substation A to the point of a fault, but does not exceed 20 %. It can be observed at the beginning of a fault that the error level is higher than in the case of action of the wind farm control units. It is directly connected with the quotient of currents from system A and WF. In the first case it is constant and equals 0.204. In the second one it is lower but variable and it is rising with the distance from busbars of substation A to the point of a fault.

From the point of view of distance protection located in station C powered by WF, the error level of evaluated impedance parameters is much higher and exceeds 450 %. It is due to the high IA/IC ratio which is 4.9. Figure 18 shows a comparison of a relative error of estimated reactance component of the impedance fault loop for protection located in substation A (system A) and station C (WF).

Fig. 18. Relative error (%) of reactance estimation in distance protection in substation A and C in relation to the distance to a fault l [km]

Fig. 18. Relative error (%) of reactance estimation in distance protection in substation A and C in relation to the distance to a fault

Attempting to compare estimates of impedance components for distance protections in substations A, B and C in relation to the distance to a fault, the following analysis has been undertaken for the network structure as in Fig. 19. Again a three-terminal line of WF connection has been chosen as the most problematic one for power system protections. For this variant WF consists of 25 wind turbines equipped as before with DFIG generators each of 2 MW power. The selection of such a type of generator is dictated by its high fault currents when compared with generators with power converters in the power output path and the popularity of the first ones.

Figure 20 shows the influence of the location of a fault on the divergence of impedance components evaluation in substations A, B and C in comparison to the real expected values. The presented values are for the initial time of a three-phase fault on line A-B with the assumption that all wind turbines are operating simultaneously, generating the nominal power.

Fig. 19. Network scheme for the second stage of simulations

WF Pwf=50 MW

Fig. 19. Network scheme for the second stage of simulations a &

Distance protection ZA

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