1. Introduction

2. Comprehensive Voltage Waveform Similarity Calculation

3. System Fault Characteristics and Protection Process

3.1. Hybrid DC Multi-Infeed AC/DC Interconnected System Topology Structure

The constructed hybrid AC/DC interconnected system with multiple DC inputs, as shown in Fig. 1, features the transmitting end's DC section consisting of two distinct ±500kV hybrid DC transmission lines: a bipolar double-end line commutated converter-modular multilevel converter (LCC-MMC) transmission system and a pseudo-bipolar double-end LCC-VSC transmission system. The receiving end's AC section comprises a 230kV dual-source system, with M and N denoting the positions of the protection units on both sides of the line. r_M represents the calculation reference point at end M, and r_N represents the calculation reference point at end N, defining the protection scope from the protection installation point to the reference point on that side. The overlap of the protection scopes at both ends indicates the range for determining internal faults, denoted by the green area in Fig. 1. This study focuses primarily on the central section, MN, where f₁ and f₅ represent faults occurring outside the protection scope, f₂ represents a fault occurring solely within the protection scope at end N but outside the reverse area, f₃ represents a fault occurring within the protection scope at both ends M and N, and f₄ represents a fault occurring solely within the protection scope at end M but outside the forward area.

In an LCC-VSC system, the rectifier side comprises two sets of twelve-pulse LCC converters connected in series. The rectifier side direct current is input into the constant current control circuit, which controls the α angle to regulate the rectifier-side converters. On the inverter side, low-cost and highly stable two-level VSC modules are employed. Through vector control, the modulated waves are input into the pulse width modulation (PWM) controller, which then produces the control signals.

In an LCC-MMC system, the rectifier side is similar to that of the LCC-VSC system, whereas the inverter side consists of two MMC modules connected in series. Input signals related to inverter-side power and current are sent to the inner and outer loop control circuits, and the output signals are directed to the bridge arms to control the inverter-side converters.

Figure 1. Topology diagram of the hybrid DC multi-feed system.

Figure 1. Topology diagram of the hybrid DC multi-feed system.

3.2. Reference Voltage Calculation and System Fault Characteristics

The similarity of the voltage waveforms between the measuring point and the reference point is calculated to determine if a fault has occurred, and the position of the reference point needs to be determined. The reference point is usually located outside the protection line to ensure sufficient sensitivity. Additionally, to reduce errors, the reference point should not be too far away; scholars both domestically and abroad typically position it within the range of 1.2 to 2.0 times the length of the protected line [23]. After extensive simulation experiments, it has been found that placing the reference point at 1.3 times the length of the line can meet the experimental requirements outlined in this paper, while allowing for flexible adjustments within the range based on specific protection needs and interference considerations.

Compared to traditional purely AC lines, in a multi-infeed interconnected grid, significant non-periodic components are introduced into the DC system after a fault occurs. This results in a more complex variation of electrical quantities in the AC lines. Obtaining accurate voltage phasors through traditional Fourier algorithms no longer guarantees accuracy. Instead, this paper proposes using instantaneous measurement methods to calculate the reference voltage, taking the M-side as an example.

In Fig. 2 (a), Z_SM and Z_SN represent the equivalent system impedances on both sides of the AC line, I_m and U_m represent the instantaneous measured currents and voltages, and I_r and U_r represent the instantaneous reference currents and voltages. Due to the rectifying sides of the hybrid multi-infeed DC system using constant current control, and the inverting side voltage being determined by the receiving-end AC bus, both can be considered equivalent to a voltage-controlled current source controlled by the receiving end. ΔI_dc.MMC and ΔI_dc.VSC represent the equivalent fault component currents for the LCC-MMC and LCC-VSC hybrid DC systems, respectively.

Based on the situation of the completed and ongoing multi-infeed AC/DC hybrid power grid projects, this paper sets a total line length of 160 km, using an equivalent π-type line model considering the electric shunt, as depicted in Fig. 2(b). After measuring the instantaneous current value I_m and the instantaneous voltage U_m, the reference voltage U_r can be obtained through the differential equation in Equation (12).

$$U_r=U_{\mathrm{m}}-[R\left(I_m-\frac{C}{2}\frac{d{U}_{\mathrm{m}}}{dt}\right)+L\frac{d\left(I_m-\frac{C}{2}\frac{d{U}_{\mathrm{m}}}{dt}\right)}{dt}]$$

(12)

Figure 2. Schematic diagram of system and line model (a) Simplify the system model; (b) Schematic diagram of system and line model.

Figure 2. Schematic diagram of system and line model (a) Simplify the system model; (b) Schematic diagram of system and line model.

Under normal operation, the voltage waveforms at the measurement point and reference point are similar. To analyze the fault characteristics of the system at different locations, we take the occurrence of a ground fault as an example and analyze the measured voltage U_m and the reference voltage U_r. Assuming the fault occurs at location k₁ as illustrated in Fig. 2(a), which represents an external fault in the opposite direction of M_rM, as shown in Fig. 3:

Figure 3. Schematic diagram of out-of-reverse fault system.

Figure 3. Schematic diagram of out-of-reverse fault system.

At this point in time, the actual current direction is opposite to the measured current direction during normal operation, hence Equation (12) can be rewritten as:

$${U^{\prime }}_{\mathrm{m}}=-\left[{R^{\prime }}_f\left({I^{\prime }}_m-\frac{{C^{\prime }}_f}{2}\frac{d{U^{\prime }}_{\mathrm{m}}}{dt}\right)+{L^{\prime }}_f\frac{d\left({I^{\prime }}_m-\frac{{C^{\prime }}_f}{2}\frac{d{U^{\prime }}_{\mathrm{m}}}{dt}\right)}{dt}\right]$$

(13)

$${U^{\prime }}_r=-\left[\begin{array}{l}{I^{\prime }}_m\left({R^{\prime }}_f-{R^{\prime }}_r\right)-\frac{d{U^{\prime }}_{\mathrm{m}}}{dt}\left(R_f\frac{{C^{\prime }}_f}{2}-R_r\frac{{C^{\prime }}_r}{2}\right)+\\ {L^{\prime }}_f\frac{d\left({I^{\prime }}_m-\frac{{C^{\prime }}_f}{2}\frac{d{U^{\prime }}_{\mathrm{m}}}{dt}\right)}{dt}-{L^{\prime }}_r\frac{d\left({I^{\prime }}_m-\frac{{C^{\prime }}_r}{2}\frac{d{U^{\prime }}_{\mathrm{m}}}{dt}\right)}{dt}\end{array}\right]$$

(14)

where Rʹ_f, Lʹ_f, and Cʹ_frepresent the resistance, inductance, and capacitance values from measurement point M to fault point k₁, respectively. Rʹ_r, Lʹ_r, and Cʹ_r represent the resistance, inductance, and capacitance values from measurement point M to reference point r_M, respectively. By comparing the two equations, it can be concluded that although there are differences in the amplitude of the measured voltage Uʹ_m and the reference voltage Uʹ_r, their variation trends are consistent. The computational relationship deduced from Equation (14) is identical to that of Equation (12), indicating that when an external fault occurs in the reverse direction area, the measured voltage and the reference voltage waveforms are similar.

Assuming that the fault occurs at position k₃ as shown in Fig. 2 (a), i.e., an external fault in the positive direction of M_rM, as illustrated in Fig. 4:

Figure 4. Schematic diagram of out-of-zone fault system.

Figure 4. Schematic diagram of out-of-zone fault system.

At this time, the actual current direction is the same as the measured current direction under normal operation, rewriting Equation (1) as follows:

$${U^{″}}_{\mathrm{m}}={R^{″}}_f\left({I^{″}}_m-\frac{{C^{″}}_f}{2}\frac{d{U^{″}}_{\mathrm{m}}}{dt}\right)+{L^{″}}_f\frac{d\left({I^{″}}_m-\frac{{C^{″}}_f}{2}\frac{d{U^{″}}_{\mathrm{m}}}{dt}\right)}{dt}$$

(15)

$${U^{″}}_r={I^{″}}_m\left({R^{″}}_f-{R^{″}}_r\right)-\frac{d{U^{″}}_{\mathrm{m}}}{dt}\left({R^{″}}_f\frac{{C^{″}}_f}{2}-{R^{″}}_r\frac{{C^{″}}_r}{2}\right)+{L^{″}}_f\frac{d\left({I^{″}}_m-\frac{{C^{″}}_f}{2}\frac{d{U^{″}}_{\mathrm{m}}}{dt}\right)}{dt}-{L^{″}}_r\frac{d\left({I^{″}}_m-\frac{{C^{″}}_r}{2}\frac{d{U^{″}}_{\mathrm{m}}}{dt}\right)}{dt}$$

(16)

where Rʺ_f, Lʺ_f, and Cʺ_frepresent the resistance, inductance, and capacitance values from measurement point M to fault point k₃, respectively. Rʺ_r, Lʺ_r, and Cʺ_r respectively represent the resistance, inductance, and capacitance values from measurement point M to reference point r_M. By comparing Equations (15) and (16), it can be observed that although there is a difference in the magnitude of the measured voltage Uʺ_m and the reference voltage Uʺ_r, their variation follows a consistent pattern. The computational relationship derived from Equation (16) is the same as Equation (12), indicating that when an external fault occurs, the measured voltage and the reference voltage waveforms are similar.

Suppose that the fault has occurred at k₂ in the area of M_rM, as shown in Fig. 2(a), depicting an internal fault in the M_rM area, as illustrated in Fig. 5:

Figure 5. Schematic diagram of fault system in the area.

Figure 5. Schematic diagram of fault system in the area.

At this time, the fault branch between Mr and M is increased, and the line structure is disrupted. Based on the characteristic that the distance from measuring point M to reference point r_M is greater than to the fault point during an internal fault, Equation (1) is modified as follows:

$${U^{‴}}_{\mathrm{m}}={R^{‴}}_f\left({I^{‴}}_m-\frac{{C^{‴}}_f}{2}\frac{d{U^{‴}}_{\mathrm{m}}}{dt}\right)+{L^{‴}}_f\frac{d\left({I^{‴}}_m-\frac{{C^{‴}}_f}{2}\frac{d{U^{‴}}_{\mathrm{m}}}{dt}\right)}{dt}$$

(17)

$$\begin{array}{c}{U^{‴}}_r=\left[{R^{‴}}_r\left({I^{‴}}_m-\frac{{C^{‴}}_r}{2}\frac{d{U^{‴}}_{\mathrm{m}}}{dt}\right)+L\frac{d\left({I^{‴}}_m-\frac{{C^{‴}}_r}{2}\frac{d{U^{‴}}_{\mathrm{m}}}{dt}\right)}{dt}\right]-{U^{‴}}_{\mathrm{m}}\\ =\frac{d{U^{‴}}_{\mathrm{m}}}{dt}\left({R^{‴}}_f\frac{{C^{‴}}_f}{2}-{R^{‴}}_r\frac{{C^{‴}}_r}{2}\right)-{I^{‴}}_m\left({R^{‴}}_f-{R^{‴}}_r\right)+\\ {L^{‴}}_f\frac{d\left(\frac{{C^{‴}}_f}{2}\frac{d{U^{‴}}_{\mathrm{m}}}{dt}-{I^{‴}}_m\right)}{dt}-{L^{‴}}_r\frac{d\left(\frac{{C^{‴}}_f}{2}\frac{d{U^{‴}}_{\mathrm{m}}}{dt}-{I^{‴}}_m\right)}{dt}\end{array}$$

(18)

where Rʺʹ_f, Lʺʹ_f, and Cʺʹ_frespectively represent the resistance value, inductance value, and capacitance value from measuring point M to fault point k₂. Rʺʹ_r, Lʺʹ_r, and Cʺʹ_r represent the resistance value, inductance value, and capacitance value from measuring point M to reference point r_M. By comparing Equations (17) and (18), it can be inferred that although there are differences in the amplitude of the measured voltage Uʺʹ_m and the reference voltage Uʺʹ_r, their variation trends remain consistent. Equation (18) deduces an operational relationship opposite to that of Equation (12), indicating that when an internal fault occurs, the measured voltage and the reference voltage waveforms are dissimilar.

In summary, it can be concluded that during an internal fault, the measured voltage and the reference voltage waveforms are dissimilar, whereas during normal operation and external fault occurrence, the voltage waveforms are similar. This provides a theoretical basis for the subsequent use of voltage comprehensive waveform similarity.

4. Experimental Verification

4.1. Introduction to the Experimental Platform

To verify the theoretical analysis and the feasibility of the protection scheme mentioned above, the PSCAD/EMTDC simulation platform is utilized to construct the hybrid DC multi-infeed system, as depicted in Fig. 1, for power system simulation. The electrical parameters are adjusted, and various fault occurrences are simulated under different conditions by controlling the fault area, line positions, and other interfering factors. Subsequently, the validation of the protection algorithm is carried out in MATLAB.

Figure 6. Schematic diagram of fault system in the area.

Figure 6. Schematic diagram of fault system in the area.

The sampling window for calculating the comprehensive voltage distance similarity in this paper is 1ms, and the sampling frequency for line protection is 10 kHz. Therefore, fault detection requires only 10 sampling points. In practical engineering applications, the synchronization error of the commonly used global positioning system (GPS) synchronization method is less than 2 μs. The protection algorithm investigated in this paper calculates the similarity value within the sampling interval and compares to find the maximum value, making it possible to accurately identify the fault position within a 1ms delay, without strict bi-directional timing and communication synchronization.

In conclusion, the simulated duration in this paper is set as 3s, and the fault occurs at 2.25s and lasts for 0.05s. Due to the rapid change in the current fault component, the protection can be activated in about 0.5ms, while the simulation data collection and the calculation of comprehensive voltage distance similarity can be completed within 2ms. Considering a certain margin, the proposed method can operate quickly and reliably within 3ms.

4.2. In-Zone Fault Simulation Result

In the positive direction of the AC line, a phase A-to-ground fault is set at a distance of 50 km. To stabilize the feed-in of the hybrid DC system, the fault is initiated at 2.25s and lasts for 0.05s. Taking the data at the M-end as an example, the simulation compares the waveform differences between the normal and fault states of both a pure AC system and a hybrid multi-feed-in system. The simulation window length is 0.025s, and the simulation results are shown in Fig. 4.

Figure 7. Comparison of measured voltage waveforms between pure AC system and hybrid multi-feed system (a) Comparison of measured voltage waveforms under normal operation; (b) Comparison of measured voltage waveforms under faults in the area.

Figure 7. Comparison of measured voltage waveforms between pure AC system and hybrid multi-feed system (a) Comparison of measured voltage waveforms under normal operation; (b) Comparison of measured voltage waveforms under faults in the area.

In Fig. 7, it is evident that after the introduction of multi-feed-in, both the voltage amplitude and phase undergo changes. Additionally, the system, besides experiencing voltage reduction after the fault, is also influenced by higher harmonics, leading to irregular oscillations in the fault waveform. By extracting data from the N-end and computing the reference voltage at both ends, Figure 8 compares the measured voltage and reference voltage waveforms.

Figure 8. Comparison of measured voltage waveforms between pure AC system and hybrid multi-feed system (a) Comparison of measured voltage waveforms under normal operation; (b) Comparison of measured voltage waveforms under faults in area.

Figure 8. Comparison of measured voltage waveforms between pure AC system and hybrid multi-feed system (a) Comparison of measured voltage waveforms under normal operation; (b) Comparison of measured voltage waveforms under faults in area.

In Figs 8(a) and 8(b), the measured voltage and reference voltage waveforms at terminals M and N both exhibit an upward trend before the fault occurs, with high waveform similarity. After the fault occurs, the measured voltage continues to rise, while the reference voltage decreases. The magnitudes of voltage fluctuations in both waveforms are quite similar, exhibiting an almost symmetrical relationship around 0kV, albeit with opposite directions. This aligns with the conclusion drawn in Section 1.2.

For irregular variations in fault waveforms in mixed multi-feed systems, directly applying a similarity algorithm focusing on detailed levels can lead to significant errors. However, after applying the waveform processing method in Section 2.1, waveform optimization can be achieved while retaining trend information, as illustrated in Fig. 9.

Figure 9. Comparison of voltage waveforms after treatment (a) Comparison of M-terminal voltage waveforms after optimization; (b) Comparison of N-terminal voltage waveforms after optimization.

Figure 9. Comparison of voltage waveforms after treatment (a) Comparison of M-terminal voltage waveforms after optimization; (b) Comparison of N-terminal voltage waveforms after optimization.

As shown in Fig. 9, the processed waveform is smoother and largely retains the trend information of the waveform changes, reducing errors in the subsequent calculation of the comprehensive distance similarity of voltage waveforms.

To study the changes in the comprehensive distance similarity of internal fault waveforms under various operating conditions, faults were set at 50km in the positive direction of lines M and N, with controlled transition resistance size. This involved simulating single-phase-to-ground faults (A-G), two-phase-to-ground faults (BC-G), three-phase-to-ground faults (ABC-G), and phase-to-phase short-circuit faults (BC). The fault initiation time was set at 2.25s, with a duration of 0.05s. Simulation data were tabulated in Table 1.

In Table 1, bolded data indicates values greater than the set value, and data marked in red, such as D_MA=4.4298 and D_NA=4.6376, represent the maximum values in this dataset. As Table 1 demonstrates, during the occurrence of faults, the comprehensive distance similarity of the faulted phase consistently exceeds the set value D_set, enabling correct action and non-operation for non-faulted phases. All of these are in line with the simulation results and theoretical analysis, meeting the protection requirements.

4.3. Out-of-Zone Fault Simulation Result

Referring to Fig. 1, a single-phase bolted fault (f₁) is established 40 km outside the M and N line in the opposite direction. Voltage and current data from both ends of M and N are extracted, the reference voltage is computed, and waveforms are processed. A comparison of the measured voltages at both ends and the reference voltage waveform is shown in Fig. 10.

In Fig. 10, the trends in the measured voltage and the reference voltage waveform are consistent, aligning with the conclusion derived from theoretical analysis concerning the similarity of the two voltage waveforms during an external fault. To further investigate the comprehensive distance similarity characteristics of the voltage waveform during external faults under various operating conditions, with reference to Fig. 1, f₁ and f₂ are faults set respectively 30 km and 10 km outside the opposite direction of the M, N line, and f₄ and f₅ are faults set respectively 10 km and 30 km outside the forward direction of the M, N line.

These faults simulate single-phase earth faults, two-phase earth faults, and three-phase earth faults. The fault initiation time is set at 2.25s, with a duration of 0.05s. The simulated data is summarized in Table 2.

Figure 10. Comparison of measured voltage and reference voltage waveform during out-of-zone fault (a) Comparison of M-terminal voltage waveforms; (b) Comparison of N-terminal voltage waveforms.

Figure 10. Comparison of measured voltage and reference voltage waveform during out-of-zone fault (a) Comparison of M-terminal voltage waveforms; (b) Comparison of N-terminal voltage waveforms.

Based on theoretical analysis, when an external fault occurs, the measured voltage and the reference voltage waveform are similar. In Table 2, bold data indicates values greater than the set value, while red data represents the maximum value within the dataset. For external faults occurring at f₁ and f₅, the data in Table 2 are all less than the set value (D_set), thus neither end of the protection devices act falsely. In the case of an f₂ external fault, as MAX(D_Mφ) remains consistently less than the set value D_set, both ends of the protection devices remain unaffected. Similarly, when an f₄ external fault occurs, as MAX(D_Nφ) consistently remains less than the set value D_set, both ends of the protection devices remain unaffected. In conclusion, the simulation results for external faults meet the protection requirements.

4.4. Protection Action Status

Currently, in practical engineering of AC transmission lines, the highest proportion of faults is single-phase-to-ground faults. Taking the occurrence of single-phase high-impedance ground faults as an example, simulated protection data is illustrated in Fig. 11.

Figure 11. Simulation results for internal and external faults identification.

Figure 11. Simulation results for internal and external faults identification.

From Fig. 11, it can be visually observed that the operating condition of D_Mφ > D_set and D_Nφ > D_set is satisfied only when an internal fault f₃ occurs. Selecting the setting value D_set = 1.2 provides a certain margin for the calculation results when the waveforms are similar. The proposed method can identify internal and external faults reliably and can meet the protection requirements.

5. Conclusions

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