Fault Section Identification for Hybrid Transmission Lines Considering the Weak-Feed Characteristics of Floating Photovoltaic Power Plant Inverters

Abstract

The overhead line (OHL)–cable hybrid transmission line, which connects floating photovoltaic (PV) power plants, needs to be considered regarding whether to block reclosing operations or not. However, due to the weak-feed characteristics of PV inverters, existing methods are difficult to apply in this scenario. This paper proposes a criterion for fault section identification in the transmission lines of floating PV power plants based on traveling wave power and the zero-sequence impedance angle. Firstly, the fault current characteristics of photovoltaic inverters under dual-vector control are analyzed, and the applicability of the sequence component impedance directional criterion in this scenario is discussed. Then, the transmission, refraction, and reflection processes of traveling waves in OHL–cable hybrid lines are analyzed, and a traveling wave energy criterion is designed to determine the fault section. Finally, based on the scope of application of the zero-sequence impedance angle and traveling wave energy criterion, a fault section identification method for the hybrid lines of floating PV power plants is established. A deployment method for the proposed method, based on feeder terminal units (FTUs) at the connection points between the OHL and cable is proposed. This method identifies fault sections through traveling waves and zero-sequence impedance angles, which are unaffected by PV week feed characteristics, can be applied to all the AC fault types, and do not rely on multi-terminal synchronous sampling. The proposed method is verified on a 1MW PV system built in the PSCAD.

1. Introduction

With the increase in the scale of new energy development, utilizing water surfaces to deploy floating photovoltaic (PV) power generation systems has become a popular mode of new energy generation [1]. The power delivery line of floating PV power generation systems must be a cable and overhead line (OHL) hybrid. The weak-feed characteristics of PV inverters make it difficult to identify the fault section to determine whether to block reclosing operations or not [2].

After a short-circuit fault occurs in an OHL, the line can restore its insulation characteristics once the temporary fault has been isolated [3,4]. Therefore, the power supply can be restored by reclosing the circuit breaker, improving the reliability of the system power supply. In contrast, after a short-circuit fault occurs in a cable, most of the fault is permanent, making it difficult to restore insulation [5,6,7]. In this case, reclosing will cause another short-circuit fault, impacting the power system and potentially leading to serious consequences. Therefore, cable faults are generally considered for block reclosing [8,9].

To determine whether to block reclosing for OHL–cable hybrid lines, the decision should be based on the respective proportions of the cable and OHL in the total length of the line [10]. However, since the probability of faults occurring in OHLs and cables differs, this method only reduces the probability of reclosing malfunctions, resulting in low reliability. Therefore, it is essential to identify the section where the fault occurs in OHL–cable hybrid lines to decide whether to block the reclosing operation.

The current literature has proposed various methods to identify fault sections in OHL–cable hybrid lines. Study [11] introduced a method using a new type of relay to measure the current on both sides of the line to determine the faulty section. Study [12] analyzed the voltage traveling wave transmission principle on the fault line and compared it with measured values at both ends to identify the faulty section. Study [13] designed a fault section discriminating functions based on the voltage and current measured synchronously at both ends of the hybrid line. The fault section can be identified by the positive and negative values of the real and imaginary parts of the function. Study [14] calculated the fault point current and then constructed an ideal zero-sequence reactor based on the fault point current to discriminate the fault section, relying on synchronized current sampling at both ends of the hybrid line. The essence of these methods is the fault range. Therefore, these methods are challenging to identify faults near OHL and cable connections and rely on synchronized sampling at both ends of the hybrid line.

Moreover, the short-circuit weak-feeding characteristics of PV power generation differ significantly from those of traditional synchronous machines [15]. Some of the aforementioned methods are challenging to adapt to hybrid lines connected to PV power plants.

By adding a current measurement unit at the connection point of the hybrid line, the line is divided into two differential segments. Based on current differential protection, study [16] proposes a method to identify the fault section of the hybrid line. However, this method requires synchronous sampling at all ends. Study [17] also adds a current measurement unit at the connection point of the hybrid line. Based on the current phase change caused by the fault, the fault section can be identified. However, this method can only be applied to single-phase grounding faults. Study [18] installed a filter at the connection point of the hybrid line, creating an artificial high-frequency boundary. The fault section can then be identified by fault high-frequency characteristics. However, the added filter may alter the fault characteristics and have some disadvantages for protection.

In summary, existing methods generally rely on multi-end synchronous sampling or manually constructed features to achieve fault section identification. These methods are challenging to adapt to the short-circuit current feature changes caused by PV weak-feed characteristics. In this paper, the fault current characteristics on the PV plant side are analyzed, and the adaptability of traditional directional components is studied. Additionally, the fault-traveling wave characteristics of the OHL–cable hybrid line and the hybrid line traveling wave reflection law are analyzed. Finally, a fault section identification method is proposed, which is constructed using the traveling wave power characteristics and the zero-sequence direction of the impedance angle. By installing an FTU at the connection point between the OHL and cable, a voltage and current measurement unit can be added, along with communication capabilities. Consequently, the proposed method can be easily applied in water-surface-floating PV power plants. This method applies to all fault types, and its feasibility is verified by the PSCAD simulation.

2. Applicability Analysis of the Traditional Directional Components

2.1. Fault Characteristic Analysis of PV Power Plants

Considering the ecological impact on underwater ecosystems, large-scale floating PV power stations have been designed with a floating layout. To enhance the system’s reliability and maintainability, a centralized inverter and transformer are typically employed to transmit the generated power. This overall structure is illustrated in Figure 1. Consequently, the transmission lines for floating PV power stations are OHL–cable hybrid lines.

Since the fault current characteristics on the system’s side are primarily determined by the grid of synchronous generators, this section focuses on studying the fault current characteristics on the PV power station side and the operational performance of traditional directional elements. The fault current characteristics on the PV side are closely related to the control methods employed in the grid-connected inverters. Currently, the dual-vector control method is commonly used in engineering to achieve grid connection for PV systems. To achieve low-voltage ride-through, it is typically necessary to regulate and control the positive-sequence and negative-sequence current components within the current inner loop. The control block diagrams for positive-sequence and negative-sequence currents are illustrated in Figure 2.

In the figure, i_d1, i_q1, i_d2, and i_q2 represent the current values in the forward and reverse synchronous rotating dq coordinate systems during the fault, respectively. i*_d1, i*_q1, i*_d2, and i*_q2 represent the current reference values in the forward and reverse synchronous rotating dq coordinate systems during the fault, respectively. u_d1, u_q1, u_d2, and u_q2 represent the voltage values of the grid voltage in the forward and reverse synchronous rotating dq coordinate systems, respectively; u*_d1, u*_q1, u*_d2, and u*_q2 represent the voltage vectors in the forward and reverse synchronous rotating dq coordinate systems under the dual-vector control strategy, respectively; u*_α1, u*_β1, u*_α2, and u*_β2 represent the reference voltage vectors in the stationary coordinate system under the dual-vector control strategy, respectively; and S_a, S_b, and S_c are the switching control signals of the PV grid-connected inverter.

In the case of an asymmetrical fault on the AC transmission line, the three-phase voltage on the PV plant side can be expressed as follows:

$$\begin{array}{cc}\hfill \stackrel{•}{U_{\eta }}=& \stackrel{•}{U_{\eta }^{+}}+\stackrel{•}{U_{\eta }^{-}}+\stackrel{•}{U^0}\hfill \\ \hfill =& U^{+}\angle ({\delta }^{+}+{\phi }_{\eta })+U^{-}\angle ({\delta }^{-}-{\phi }_{\eta })+k_0{U}^0\angle {\delta }^0\hfill \end{array}$$

(1)

where U represents the voltage magnitude; δ represents the initial phase angle of the voltage; superscripts +, − and 0 are positive, negative, and zero sequence components, respectively; η = a, b, c indicates the phase, φ_a = 0, φ_b = π2/3, and φ_c = π4/3; k₀ indicates the grounding coefficient; k₀ = 1 indicates that the fault type is a grounding fault; and k₀ = 0 is a non-grounding fault

The dual-vector control method is commonly used in engineering. Consequently, the transient time of the fault current is only a few milliseconds. It can be considered that the fault current quickly follows its reference value. By combining Equation (1) and the basic formulas presented in reference [19] for derivation and analysis, the expression for the fault current on the PV power station side of the transmission line can be derived as follows:

$$\stackrel{•}{I_{N\eta }}=I_{Nm}\angle ({\delta }^{+}+{\theta }^{+}+{\phi }_{\eta })+\left|k_{\chi }\right|k_{\rho }{I}_{Nm}\angle ({\delta }^{-}+{\theta }^{-}+{\phi }_{\eta })+k_0{I}_0\angle {\phi }_0$$

(2)

here:

$$\begin{array}{c}\{\begin{array}{c}{I}_{Nm}={\displaystyle \frac{2}{3U^{+}}}\sqrt{{({\displaystyle \frac{P^{*}}{1-k_{\chi }{k}_{\rho }^2}})}^2+{({\displaystyle \frac{Q^{*}}{1+k_{\chi }{k}_{\rho }^2}})}^2}\\ {\theta }^{+}=\arctan {\displaystyle \frac{-Q^{*}/(1+k_{\chi }{k}_{\rho }^2)}{P^{*}/(1-k_{\chi }{k}_{\rho }^2)}}\\ {\theta }^{-}=\arctan {\displaystyle \frac{k_{\chi }{Q}^{*}/(1+k_{\chi }{k}_{\rho }^2)}{-k_{\chi }{P}^{*}/(1-k_{\chi }{k}_{\rho }^2)}}\end{array}\end{array}$$

(3)

Here, k_χ represents the control objective of the control strategy. When k_χ = 1, it suppresses active power fluctuations; when k_χ = 0, it suppresses negative sequence currents; and when k_χ = −1, it suppresses reactive power fluctuations [20]. P* and Q* represent the active and reactive power commands during the fault period in the PV array. k_ρ = U⁻/U⁺ represents the voltage unbalance of the grid. I_Nm is the amplitude of the positive sequence current component of the fault current. I₀ and φ₀ represent the amplitude and initial phase angle of the zero-sequence current, respectively, which are determined by the zero-sequence voltage and the impedance in the zero-sequence network.

Based on Equations (2) and (3) and the vulnerability of power electronic devices (poor overcurrent capability), the following conclusions can be drawn:

(1)

The fault current characteristics on the PV power station side are significantly different from those of traditional transmission line faults, influenced by various factors such as control objectives, active and reactive power references, and grid unbalance.

(2)

Due to the limited overcurrent capability of power electronic devices and the controllability of grid-connected inverters, the maximum amplitudes of positive and negative sequence currents in the fault current generally do not exceed 1.5 times the rated value.

(3)

If a grounded fault occurs, the fault current is dominated by the zero-sequence current; because of that, the following takes place: ① grid-connected transformer typically adopts a YNd11 connection; ② the PV power station exhibits weakly fed characteristics for positive and negative sequence components.

2.2. Adaptive Analysis of Traditional Directional Components

When a forward fault occurs in the transmission line, the criterion for judging the forward fault direction corresponding to the sequence fault component direction element is the following:

$$0^{\circ }\le {\alpha }^j=\arg (-{\displaystyle \frac{\mathrm{\Delta }\stackrel{•}{U^j}}{\mathrm{\Delta }\stackrel{•}{I^j}}})\le {180}^{\circ }$$

(4)

Here, j represents +, −, 0, which indicates the positive sequence, negative sequence, and zero sequences, respectively; α⁺, α⁻, and α⁰ represent the positive sequence impedance angle, negative sequence impedance angle, and zero sequence impedance angle, respectively; $\mathrm{\Delta }\stackrel{•}{U^j}$ represents the voltage phasor of the corresponding sequence component; and $\mathrm{\Delta }\stackrel{•}{I^j}$ represents the current phasor of the corresponding sequence component.

When a fault occurs, it may cause the phase jump of the grid voltage. However, under normal operating conditions, PV power plants usually operate at a unity power factor. Therefore, the positive sequence voltage and current of the PV power plant side should be in the same phase. The specific expressions for the positive sequence voltage and current phasors on the PV power plant side before and after the fault are as follows:

$$\{\begin{array}{c}\stackrel{•}{U_{[1]}^{+}}=U^{+}\angle ({\delta }^{+}+{\phi }_{\eta })\hfill \\ \stackrel{•}{I_{[1]}^{+}}=I_{Nm}\angle ({\delta }^{+}+{\theta }^{+}+{\phi }_{\eta })\hfill \\ \stackrel{•}{U_{[0]}^{+}}={\displaystyle \frac{U^{+}}{k_{\lambda }}}\angle ({\delta }^{+}+{\phi }_{\eta }-\mathrm{\Delta }\delta )\hfill \\ \stackrel{•}{I_{[0]}^{+}}={\displaystyle \frac{2k_{\lambda }{P}_0}{3U^{+}}}\angle ({\delta }^{+}+{\phi }_{\eta }-\mathrm{\Delta }\delta )\hfill \\ \stackrel{•}{\mathrm{\Delta }{U}^{+}}=\stackrel{•}{U_{[1]}^{+}}-\stackrel{•}{U_{[0]}^{+}}\hfill \\ \stackrel{•}{\mathrm{\Delta }{I}^{+}}=\stackrel{•}{I_{[1]}^{+}}-\stackrel{•}{I_{[0]}^{+}}\hfill \end{array}$$

(5)

Here, ∆δ represents the positive sequence voltage angle jump; k_λ represents the positive sequence voltage drop coefficient; P₀ represents the power of the PV power plant during normal operation; $\stackrel{•}{U_{[1]}^{+}}$ and $\stackrel{•}{U_{[0]}^{+}}$ represent the positive sequence voltage after and before the fault, respectively; $\stackrel{•}{I_{[1]}^{+}}$ and $\stackrel{•}{I_{[0]}^{+}}$ represent the positive sequence current after and before the fault, respectively; φ_[1] and φ_[0] represent the phase angles of the positive sequence current after and before the fault, respectively; and δ_[1] and δ_[0] represent the phase angles of the positive sequence voltage after and before the fault, respectively. Combining Equations (1)–(5), the following can be obtained:

$$\begin{array}{cc}\hfill {\alpha }^{+}=& \arg (-{\displaystyle \frac{\mathrm{\Delta }\stackrel{•}{U^{+}}}{\mathrm{\Delta }\stackrel{•}{I^{+}}}})\hfill \\ \hfill =& \arctan [{\displaystyle \frac{k_{\lambda }(\sin \mathrm{\Delta }\delta +k_{\nu }\sin {\theta }^{+})-k_{\nu }\sin ({\theta }^{+}+\mathrm{\Delta }\delta )}{k_{\lambda }(\cos \mathrm{\Delta }\delta -k_{\nu }\cos {\theta }^{+})+k_{\nu }\cos ({\theta }^{+}+\mathrm{\Delta }\delta )-1}}]\hfill \end{array}$$

(6)

Here,

$$k_{\nu }={\displaystyle \frac{1}{k_{\lambda }{P}_0}}\sqrt{{({\displaystyle \frac{P^{*}}{1-k_{\chi }{k}_{\rho }^2}})}^2+{({\displaystyle \frac{Q^{*}}{1+k_{\chi }{k}_{\rho }^2}})}^2}$$

(7)

According to Equations (3) and (6), α⁺ is related to variables such as ∆δ, P*, Q*, k_χ, k_ρ, and k_λ. However, when a fault occurs in the system, these variable factors are all fixed values. To facilitate subsequent analysis, the following assumptions are made for specific analysis:

(1)

Reactive power command during the fault at 0 ≤ Q*(pu) ≤ 0.6;

(2)

Positive sequence voltage drops at 0.3 < k_λ < 0.7.

It can be assumed that P* = 0.7 pu, ∆δ ≈ π/9, k_χ = 1, and k_ρ = 0.6, regardless of the variations in the reactive power command Q* and the positive sequence voltage drop k_λ. Based on (6) and (7), it can be calculated that the range of the positive sequence incremental impedance angle α⁺ falls between −150° and 0°. These results do not satisfy the forward fault criterion described in Equation (4). Consequently, the positive sequence directional element fails to operate correctly. Similarly, the analysis process for the other two control objectives follows the same logic and is not elaborated upon further here.

When k_χ = 0, the PV power plants suppress the negative-sequence current. Therefore, there is no negative-sequence current in the transmission line, which causes the negative-sequence directional element to fail to work. When k_χ is 1 or −1, combining Equations (1)–(4) can lead to the following:

$$\begin{array}{cc}\hfill {\alpha }^{-}=& \arg (-{\displaystyle \frac{\mathrm{\Delta }\stackrel{•}{U^{-}}}{\mathrm{\Delta }\stackrel{•}{I^{-}}}})\hfill \\ \hfill =& \arctan [{\displaystyle \frac{k_{\chi }{Q}^{*}/(1+k_{\chi }{k}_{\rho }^2)}{-k_{\chi }{P}^{*}/(1-k_{\chi }{k}_{\rho }^2)}}]\hfill \end{array}$$

(8)

According to Equation (7), when k_χ = 1, α⁻∈(0°,90°) under any fault condition; when k_χ = −1, α⁻∈(−180°, −90°) under any fault condition. Therefore, the negative sequence directional element may fail to operate correctly.

The main transformer of a PV power plant typically adopts the YNd11 connection. When a ground fault occurs at the fault point, the zero-sequence impedance in the zero-sequence network is mainly composed of the transformer’s zero-sequence impedance and the line’s zero-sequence impedance. The impedance angle of the zero-sequence directional element is not affected by the PV power plant and can accurately judge the forward direction fault.

In summary, based on the analysis in this section, when a forward direction fault occurs at the fault point on the transmission line of a PV power plant, the positive-sequence fault component directional element on the side of the PV power station is related to factors such as active and reactive power commands, control objectives, and fault conditions. The traditional positive-sequence directional element’s judgment basis is no longer applicable to the directional element on the PV power station side.

Due to the weak-feed characteristics of PV inverters, among traditional directional elements, only the zero-sequence directional components remain unaffected.

With the expansion of PV development, the grid-connected voltage levels range from 10 to 220 kV, encompassing both neutral isolated systems and neutral grounded systems. This paper mainly focuses on neutral grounded systems. For the neutral isolated systems, despite the absence of a zero-sequence current path, the zero-sequence current generated by the distributed capacitance of the cables is sufficient to trigger the criterion.

3. Traveling Wave Direction Analysis of Hybrid OHLs–Cable

3.1. Polarity Analysis of VTW and CTW

Defining the voltage traveling wave generated by the fault as u_F, and the distributed capacitance of the line as C, the discharge quantity of the distributed capacitance of the line can be expressed as follows:

$$\mathrm{\Delta }Q=C{u}_F\mathrm{\Delta }x$$

(9)

Here, ∆Q represents the discharge quantity of the distributed capacitance of the line, and ∆x represents the distance from the fault point. When ∆x is small enough, according to Equation (1), it can be derived as follows:

$$i_F=\underset{\mathrm{\Delta }t\to 0}{\lim }{\displaystyle \frac{\mathrm{\Delta }Q}{\mathrm{\Delta }t}}=\underset{\mathrm{\Delta }t\to 0}{\lim }{\displaystyle \frac{C{u}_F\mathrm{\Delta }x}{\mathrm{\Delta }t}}=C{u}_{F}v$$

(10)

Here, i_F represents the CTW; ∆t represents the traveling wave propagation time; and v represents the wave velocity of the traveling wave. Then, the change in magnetic field within the line can be expressed as follows:

$$\mathrm{\Delta }\mathrm{\Phi }=L{i}_F\mathrm{\Delta }x=LC{u}_{F}v\mathrm{\Delta }x$$

(11)

Here, ∆Φ represents the magnetic field change within the line; L is the distributed inductance of the line. According to Equation (11), the electric field within the line can be expressed as follows:

$$E_M=\underset{\mathrm{\Delta }t\to 0}{\lim }{\displaystyle \frac{\mathrm{\Delta }\mathrm{\Phi }}{\mathrm{\Delta }t}}=\underset{\mathrm{\Delta }t\to 0}{\lim }{\displaystyle \frac{LC{u}_{F}v\mathrm{\Delta }x}{\mathrm{\Delta }t}}=LC{u}_F{v}^2$$

(12)

Similarly, when ∆x is sufficiently small, it can be determined that $E\approx u_F$. Then, combining this with the definition of wave velocity of the traveling wave, the relationship between the voltage and current traveling waves can be derived as follows:

$${\displaystyle \frac{u_F}{i_F}}=\sqrt{{\displaystyle \frac{L}{C}}}$$

(13)

Based on Equation (13), it can be seen that the polarities of the CTW and VTW generated by the fault are the same, and the ratio between them is determined by the distributed parameters of the line.

3.2. Analysis of the Traveling Wave Refraction and Reflection in Hybrid Line

When a traveling wave propagates along a line, and if the line parameters suddenly change at a certain point (i.e., the wave impedance changes), the refraction and reflection of the wave will occur at that point. After multiple refractions and reflections, the wave will enter a new steady state. This process is illustrated in Figure 3 [21].

As shown in Figure 3, the traveling wave after refraction and reflection satisfies the following equation:

$$\{\begin{array}{c}{u}_1+u_2=u_3\\ i_1-i_2=i_3\\ u_2=i_2{Z}_1\\ u_3=i_3{Z}_2\end{array}$$

(14)

From Equation (14) and Figure 3, it can be seen that the refraction and reflection coefficients for CTW and VTW are as follows:

$$\{\begin{array}{c}{\lambda }_u={\displaystyle \frac{u_2}{u_1}}={\displaystyle \frac{Z_2-Z_1}{Z_2+Z_1}}\in \left(-1,1\right)\\ {\lambda }_i={\displaystyle \frac{i_2}{i_1}}={\displaystyle \frac{Z_2-Z_1}{Z_2+Z_1}}\in \left(-1,1\right)\\ {\beta }_u={\displaystyle \frac{u_3}{u_1}}={\displaystyle \frac{2Z_2}{Z_2+Z_1}}\in \left(0,+\infty \right)\\ {\beta }_i={\displaystyle \frac{i_3}{i_1}}={\displaystyle \frac{2Z_1}{Z_2+Z_1}}\in \left(0,+\infty \right)\end{array}$$

(15)

Here, λ_u, λ_i, β_u, and β_i represent the reflection and refraction coefficients for VTW and CTW at the impedance discontinuity point, respectively.

Therefore, the corresponding VTW and CTW at the impedance discontinuity point are as follows:

$$\{\begin{array}{c}u=\left(1+{\lambda }_u\right)u_f=\left(1+{\displaystyle \frac{Z_2-Z_1}{Z_2+Z_1}}\right)u_f={\displaystyle \frac{2Z_2}{Z_2+Z_1}}{u}_f\\ i=\left(1+{\lambda }_i\right)i_f=\left(1+{\displaystyle \frac{Z_2-Z_1}{Z_2+Z_1}}\right)i_f=-{\displaystyle \frac{2Z_2}{Z_2+Z_1}}{i}_f\end{array}$$

(16)

Here, u and i represent the VTW and CTW measured by the detection equipment, respectively; u_f and i_f represent the fault traveling wave voltage and current, respectively.

Figure 4a,b illustrate the traveling wave propagation processes for OHL faults and cable faults, respectively, in a hybrid line. M and N represent the bus on the OHL side and cable side, respectively. J₁, J₂, J₃, and J₄ are the mutation points of VTW and CTW at the connection points between the OHL and cable. N₁, N₂, N₃, M₁, M₂, and M₃ are the mutation points of VTW and CTW on the bus on the N and M sides, respectively.

Table 1. Traveling wave mutations with cable fault.

	J			M
	VTW	CTW		VTW	CTW
J1	${\beta }_{Ju}^{\prime }$uF	${\beta }_{Ji}^{\prime }$iF	M1	${\beta }_{Lu}^{\prime }$(1 + ${\lambda }_{Nu}^{\prime }$)uF	${-\beta }_{Lu}^{\prime }$(1 −${\lambda }_{Nu}^{\prime }$)iF
J2	${\lambda }_{Ju}^{\prime }$${\lambda }_{Fu}^{\prime }$${\beta }_{Ju}^{\prime }$uF	${\lambda }_{Ji}^{\prime }$${\lambda }_{Fi}^{\prime }$${\beta }_{Ji}^{\prime }$iF	M2	λLuβFu(1 + λNu)uF	−λLuβFu(1 − λNu)iF
J3	(${\lambda }_{Ju}^{\prime }$${\lambda }_{Fu}^{\prime }$)2${\beta }_{Ju}^{\prime }$uF	(${\lambda }_{Ji}^{\prime }$${\lambda }_{Fi}^{\prime }$)2${\beta }_{Ji}^{\prime }$iF	M3	${\lambda }_{Lu}^2$λFuβFu(1 + λNu)uF	${-\lambda }_{Lu}^2$λFuβFu(1 − λNu)iF
	……	……		……	……

and

Table 2. Traveling wave mutations with transmission line fault.

	N			J
	VTW	CTW		VTW	CTW
N1	${\beta }_{Ju}^{\prime }$uF	${\beta }_{Ji}^{\prime }$iF	J1	${\beta }_{Ju}^{\prime }$(1 + ${\lambda }_{Mu}^{\prime }$)uF	−${\beta }_{Ji}^{\prime }$(1 −${\lambda }_{Mi}^{\prime }$)iF
N2	${\lambda }_{Ju}^{\prime }$${\lambda }_{Fu}^{\prime }$${\beta }_{Ju}^{\prime }$uF	${\lambda }_{Ji}^{\prime }$${\lambda }_{Fi}^{\prime }$${\beta }_{Ji}^{\prime }$iF	J2	${\lambda }_{Ju}^{\prime }$${\lambda }_{Fu}^{\prime }$${\beta }_{Ju}^{\prime }$(1 + ${\lambda }_{Mu}^{\prime }$)uF	${-\lambda }_{Ji}^{\prime }$${\lambda }_{Fi}^{\prime }$${\beta }_{Ji}^{\prime }$(1 −${\lambda }_{Mi}^{\prime }$)iF
N3	(${\lambda }_{Ju}^{\prime }$${\lambda }_{Fu}^{\prime }$)2${\beta }_{Ju}^{\prime }$uF	(${\lambda }_{Ji}^{\prime }$${\lambda }_{fi}^{\prime }$)2${\beta }_{Ji}^{\prime }$iF	J3	(${\lambda }_{Ju}^{\prime }$${\lambda }_{Fu}^{\prime }$)2${\beta }_{Ju}^{\prime }$(1 + ${\lambda }_{Mu}^{\prime }$)uF	−(${\lambda }_{Ji}^{\prime }$${\lambda }_{Fi}^{\prime }$)2${\beta }_{Ji}^{\prime }$(1 −${\lambda }_{Mi}^{\prime }$)iF
	……	……		……	……

outline the evolution of fault-traveling waves at various points when the fault occurs on the cable and OHL, respectively. In these tables, λ_Ju and λ_Ji represent the reflection coefficients for VTW and CTW at the connection points, respectively; λ_Fu and λ_Fi represent the reflection coefficients for VTW and CTW at the fault location, respectively; λ_Nu, λ_Ni, λ_Mu, and λ_Mi represent the reflection coefficients for VTW and CTW on the N and M sides, respectively; β_Fu and β_Fi represent the refraction coefficients for VTW and CTW at the fault location, respectively; and β_Ju and β_Ji represent the refraction coefficients for VTW and CTW at the connection points, respectively.

Based on Table 1 and Table 2, the traveling wave propagation processes in a hybrid line do not change their polarity. Therefore, when the positive direction of CTW is defined, the fault section of the hybrid line can be judged based on the polarity of the traveling wave.

3.3. Fault Direction Criterion Based on Traveling Wave Energy

The fault direction discrimination coefficient based on traveling wave energy is defined as follows:

$$E={\displaystyle {\int }_{t_s}^{t_s+t_d}{u}_F}(t)i_F(t)dt$$

(17)

where t_s and t_d are, respectively, the start time and duration of the data window; u_F(t) and i_F(t) are the voltage traveling wave value and current traveling wave value.

Based on the results from Table 1 and Table 2, the fault direction discrimination criterion for different fault sections is analyzed, taking a single-phase-to-ground fault as an example.

(1)

Cable-side single-phase-to-ground fault:

$$\begin{array}{cc}\hfill E=& {\beta }_{Ju}{\beta }_{Ji}(1+{\lambda }_{Ju}{\lambda }_{Fu}{\lambda }_{Ji}{\lambda }_{Fi}+{\lambda }_{Ju}^2{\lambda }_{Fu}^2{\lambda }_{Ji}^2{\lambda }_{Fi}^2+\cdots )\hfill \\ \hfill & \times {\displaystyle {\int }_{t_s}^{t_s+t_d}{u}_F}(t)i_F(t)dt>0\hfill \end{array}$$

(18)

(2)

Transmission line side single-phase-to-ground fault:

$$\begin{array}{cc}\hfill E=& -{\beta }_{Ju}{\beta }_{Ji}(1+{\lambda }_{Mu})(1-{\lambda }_{Mi})(1+{\lambda }_{Ju}{\lambda }_{Fu}{\lambda }_{Ji}{\lambda }_{Fi}\hfill \\ \hfill & +{\lambda }_{Ju}^2{\lambda }_{Fu}^2{\lambda }_{Ji}^2{\lambda }_{Fi}^2+\cdots ) \hfill \\ \hfill & \times {\displaystyle {\int }_{t_s}^{t_s+t_d}{u}_F}(t)i_F(t)dt<0\hfill \end{array}$$

(19)

It can be seen that after defining the positive direction of the traveling wave current, the traveling wave energy values for faults occurring in different sections are opposite. Therefore, this characteristic can be used to discriminate between different fault sections.

4. Fault Section Judge Strategy Based on the Mixed Criterion

Based on the above analysis, the traveling wave energy criterion can be used to judge the fault section of hybrid lines by adding measuring equipment at the connection point of the cable and transmission line. However, if the fault phase voltage is near zero when a single-phase ground fault occurs, the generated traveling wave energy will be extremely small, and the traveling wave energy criterion may not be able to determine the fault section.

On the other hand, the zero-sequence directional components are not affected by the fault weakly fed characteristics and, as a result, are suitable for the single-phase fault. Therefore, by combining the traveling wave energy criterion with the zero-sequence directional criterion, all fault sections of the hybrid line under all the fault types can be judged.

4.1. Fault Section Judgement Process Based on Traveling Wave Energy and Zero-Sequence Directional Criterion

Based on Equations (18) and (19), after defining the positive direction of sampling at point J (taking M to N as the positive direction), the fault section can be determined based on Equation (20):

$$\{\begin{array}{cc}E<0\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} & Cable\\ E>0\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}& \mathrm{Trasmission} \mathrm{line}\end{array}$$

(20)

When other types of faults occur in the system, such as the two-phase short circuit, two-phase ground fault, three-phase short circuit, etc., traveling wave voltages and currents can be measured on multiple phases, and corresponding EA, EB, and EC values can be calculated. Considering that when the AC voltage fails near the zero-crossing, the generated traveling wave voltage and current amplitudes are relatively small, there is a possibility of misjudgment. To avoid contradictions in the judgments of each phase, when fault traveling waves are detected simultaneously on multiple phases, only the E with the largest absolute value is used as the basis for determining the fault section. If a single-phase ground fault occurs and the fault phase voltage is near the zero-crossing, the resulting traveling wave voltage and current power may be small, which may make it impossible for the traveling wave power direction criterion to make a judgment. Therefore, the zero-sequence direction criterion can be used as a supplementary judgment at this time.

Taking the OHL–hybrid line system shown in Figure 5 as an example, the following is the process for identifying the fault section in a hybrid line. The flowchart for this process is shown in Figure 6.

(1)

Measure the voltage and current with high frequency and record the data measured in the latest 0.5 s

(2)

After the line is powered off, the traveling wave is locked in accordance with Equation (21) and the recorded measurement data. Based on the transmission characteristics of traveling waves, the initial peak of the traveling wave in the early stage of a fault contains the richest fault information. This process is very brief, typically measured in microseconds. Therefore, this paper selects td = 10 μs as the initial time window. During the identification process, the selection of the time window is flexible and can be updated as the fault characteristics change.

$$\{\begin{array}{c}\left|{\displaystyle \frac{du}{dt}}\right|>{\mathrm{\Delta }}_{set1}\\ \left|\mathrm{\Delta }u\right|>{\mathrm{\Delta }}_{set2}\end{array}$$

(21)

(3)

After locking the traveling wave head, based on the arrival time of the traveling wave, high-frequency components of voltage and current are extracted through wavelet transform. Then, EA, EB, and EC are calculated using the method proposed in this paper. By comparing the absolute values of the three-phase EA, EB, and EC, the fault section is determined by selecting the quantity with the largest absolute value.

(4)

If the traveling wave head cannot be detected in the recorded waveform data, the fault section is judged based on the negative sequence direction criterion.

(5)

Based on the results of the fault section judgment, a decision is made on whether to send a signal to block the reclosing mechanism to the breakers on the M and N sides.

4.2. Application of the Proposed Method Based on FTU

To apply the method proposed in this paper to the transmission lines of floating PV power stations, it was necessary to add measurement points at the connection points between the OHLs and cables. Consequently, the utilization of feeder terminal units (FTUs) is considered for implementing the application of this method. FTUs are intelligent terminal devices installed in distribution rooms or on feeders. They can communicate with remote distribution substations, transmit operational data of distribution equipment to the substations, and receive control commands from them to control and regulate the distribution equipment. FTUs are small in size and numerous in quantity, allowing them to be placed on outdoor feeders. They are capable of achieving the three-phase synchronous sampling of current and voltage.

To meet the requirements of the fault section identification method proposed in this paper, the FTU needs to be modified to have a high-frequency sampling capability of 100 kHz and installed at the connection points between the OHLs and cables, as shown in Figure 7. Since the method in this paper only requires fault section identification to be completed before reclosing, the calculation can be based on the recorded waveform data after detecting the traveling wave, which has relatively low requirements for computational power. After the fault section is identified, the signal can be uploaded through the communication capability between the FTU and the distribution substation.

5. Simulation Analysis

This paper utilizes PSCAD/EMTDC to build a PV power generation system, as shown in Figure 5, which transmits power via a 10 kV hybrid line. Both the OHL and the cable line adopt the distributed parameter model, with the OHL spanning 20 km and the cable extending 5 km.

5.1. Verification of Criterions

To verify the correctness of the theoretical analysis of the fault current characteristics at the N-side of the hybrid line, an A-phase ground fault is initiated at location F of the outgoing line at t = 1 s, and the fault is cleared at t = 1.3 s. The measurement point is J.

Figure 8 illustrates the system voltage and fault current waveforms during an A-phase ground fault. Figure 8a,b show the three-phase voltages of the grid and the fault current at the N-side of the hybrid line, respectively. Figure 8c,d represent the positive-sequence and zero-sequence currents, respectively, when separated from the fault current at the N-side. As evident from Figure 8b–d, due to the control objective of suppressing negative-sequence currents, the fault current at the PV power station side of the hybrid line is primarily composed of the superposition of positive-sequence and zero-sequence currents, with the zero-sequence component being dominant. This observation aligns with the conclusion derived from Section 2. In the case of a ground fault, the characteristics of the three-phase fault currents at the PV power station side of the hybrid line are approximately the same in magnitude and phase, which differs significantly from the traditional characteristics of ground fault currents.

Based on the theoretical derivation and analysis in Section 2, the impedance angle of the positive-sequence directional element is influenced by five variables: ∆δ, P*, Q*, k_ξ, k_λ, and k_ρ. For these directional elements, multiple sets of simulation data are utilized to analyze how the impedance angle is affected by k_λ and k_ρ, as well as the patterns of impedance angle variation. This analysis further validates the correctness of the theoretical analysis.

Figure 9 illustrates the variation in the impedance angles of directional elements under different combinations of k_λ and k_ρ. Specifically, Figure 9 shows the impedance angle variation waveforms of the positive-sequence directional element under various combinations of k_λ and k_ρ. As seen in Figure 9, for the PV power station model established with the control objective of suppressing negative-sequence currents, the impedance angle of the positive-sequence directional element varies with changes in k_λ and k_ρ, potentially falling within the range of −180° to 0°, leading to a misjudgment in the fault section’s identification.

Through extensive simulation data, it was found that for the positive-sequence directional element, the correct operation can be achieved when k_λ lies within the range of (0.69, 1) and k_ρ varies within (0, 0.46). Based on this data analysis, it can be concluded that the directional element is likely to operate correctly when the voltage sag depth k_λ is relatively large and the voltage imbalance k_ρ is small. In most cases of severe faults, the directional element faces a significant risk of failing to operate.

Figure 10 and Figure 11 show the current and voltage waveforms recorded during an OHL fault and a cable fault, respectively. After applying wavelet transform to the current and voltage waveforms in Figure 10 and Figure 11, the resulting high-frequency components can be seen in Figure 12.

As can be seen in Figure 12, the high-frequency components of voltage and current obtained through wavelet transform are both oscillating. However, for the OHL fault, the oscillation directions of the high-frequency components of the voltage and current are the same, meaning their amplitudes are either both positive or both negative, resulting in a positive product. In contrast, during a cable fault, the amplitudes of the high-frequency components of the voltage and current are opposite, leading to a negative product. This observation confirms the previous analysis, and it is possible to identify the fault section of the hybrid line.

5.2. Verification of Fault Section Judging Method

Table 3. Simulation results of phase A single-phase ground fault.

Rg/Ω	OHL			Cable
	EA	EB	EC	EA	EB	EC
0	388.94	0.1811	−0.0169	−1693.7	59.022	57.144
100	63.017	0.021	−0.0049	−25.264	0.2150	−0.0750
200	26.475	0.0103	−0.0001	−7.1866	0.1143	−0.0548
300	14.778	0.0073	−0.0001	−3.3990	0.0855	−0.0355

,

Table 4. Simulation results of phase A to B two-phase ground fault.

Rg/Ω	OHL			Cable
	EA	EB	EC	EA	EB	EC
0	594.17	587.48	0.0101	−1612.9	−1597.4	0.1351
100	247.66	133.29	−0.0103	−187.50	−93.369	−0.0304
200	132.06	65.507	−0.0042	−58.174	−28.330	−0.034
300	82.716	39.656	−0.0016	−28.434	−13.575	−0.0239

,

Table 5. Simulation results of phase A to B two-phase fault.

Rg/Ω	OHL			Cable
	EA	EB	EC	EA	EB	EC
0	594.72	586.96	0.0028	−1605.5	−1604.8	0.0277
100	163.48	160.44	0.0028	−96.020	−94.381	0.0279
200	78.284	76.400	0.0028	−29.030	−27.997	0.0230
300	46.482	45.124	0.0028	−14.018	−13.251	0.0280

and

Table 6. Simulation results of three-phase fault.

Rg/Ω	OHL			Cable
	EA	EB	EC	EA	EB	EC
0	593.89	587.79	−0.0109	−1612.3	−1598.2	−0.3448
100	228.18	223.87	−0.0975	−188.16	−184.60	0.5562
200	123.70	120.72	−0.0805	−59.081	−57.334	0.1471
300	78.423	76.195	−0.0654	−29.079	−27.887	0.1258

show the results of A-phase short-circuits, A to B two-phase short-circuits, A to B two-phase to ground short-circuits, and three-phase short-circuit faults with different transition resistances occurring separately on the OHL and the cable at a distance of 1 km from point J, with the positive direction defined as M to N. The fault direction discrimination coefficients with the largest absolute values are highlighted in blue for each table.

It can be observed that the calculated E values for OHL faults are all positive, while the E values for cable short-circuit faults are all negative, indicating that the criterion based on Equation (19) can correctly identify the fault section. As the fault transition resistance increases, the amplitude of the traveling wave current decreases, leading to a decrease in the absolute values of E for both fault sections, but the sign of E (positive or negative) remains unchanged.

By analyzing Table 1, Table 2, Table 3 and Table 4 and their corresponding fault types, it is evident that under various fault types, the E value of the faulted phase is much larger than that of the non-faulted phases. Therefore, regardless of the fault type, the method proposed in this paper can be used to determine the fault section.

From Table 3, Table 4, Table 5 and Table 6, the absolute value of E in phase A is the largest under different faults. This is because the voltage amplitude of phase A is the highest at the instant fault occurrence, resulting in stronger CTW and VTW. As shown in Table 4, for three-phase faults with different transition resistances, the absolute value of E follows the order of phase A > phase B > phase C. Notably, the absolute value of EC is extremely small because the voltage phase C is near the zero-crossing point at the fault instant. This situation makes the criterion unreliable for fault section discrimination. This indicates that the phase angle at the fault instant significantly affects the fault characteristics. In three-phase short-circuits, two-phase short-circuits, and two-phase-to-ground short-circuits, it is impossible for multiple phases to simultaneously be near their zero-crossing points. Therefore, taking the E value with the largest absolute value as the discrimination criterion can avoid the influence of phase angles. However, for single-phase-to-ground faults, a fault occurring near the voltage zero-crossing point may affect the discrimination of the fault section.

Table 7. Simulation results of phase A single-phase ground fault under different phases.

Phase/	OHL			Cable
	EA	EB	EC	EA	EB	EC
2π/3	26.475	1.03 × 10−2	−1 × 10−4	−7.1866	1.143 × 10−2	−5.48 × 10−2
5π/6	9.1932	9 × 10−4	3.6 × 10−3	−2.520	6.8 × 10−3	1.28 × 10−2
0	−0.0405	2 × 10−3	4.3 × 10−3	0.0787	−1.97 × 10−3	4.34 × 10−2
π/6	8.0081	4.5 × 10−3	−1 × 10−4	−1.9890	4.5 × 10−3	9× 10−4
π/3	25.2905	1.39 × 10−2	−3.2 × 10−3	−6.6555	1.689 × 10−2	−6.11 × 10−2
π/2	34.5241	1.68 × 10−2	−3.9 × 10−3	−9.2543	1.954 × 10−2	−9.17 × 10−2

presents the simulation results for high-resistance faults with a transition resistance of 200 Ω under different voltage phase angles. It can be seen that as the voltage phase angle changes, the voltage amplitude at the fault instant varies, resulting in changes in the E_A value. Notably, the method proposed in this paper has a discrimination dead zone within ±5 degrees of the voltage zero-crossing point, where misjudgment may occur. In this case, the zero-sequence resistance angle criterion is needed.

When a single-phase grounding fault occurs near the zero-crossing point of the faulty phase, the traveling wave voltage generated by the fault is excessively small. At this time, although the system detects a power outage, it is unable to lock onto the traveling wave, thus triggering the detection of the zero-sequence impedance direction. Figure 13 presents the results of the zero-sequence impedance direction detection for single-phase grounding faults occurring at the zero-crossing point of the faulty phase voltage, with varying fault locations. The data used for this analysis are from before the line power outage in the recorded waveform data, ensuring the accuracy of the action. It can be seen that in such cases, the detection of the zero-sequence impedance direction exhibits high sensitivity and is not affected by the weakly fed characteristics of PV power stations. Therefore, it can serve as an effective supplement to the traveling wave energy criterion.

6. Conclusions

This paper proposes a method for fault section identification based on a hybrid criterion combining the traveling wave power and zero-sequence impedance direction, specifically addressing the issue of whether to lock out the reclosing mechanism after a fault occurs in the OHL–cable hybrid transmission line used for the delivery of power from floating PV power stations. The study begins by analyzing the adaptability of traditional sequence component direction detection under the weak-feed characteristics of PV power generation systems. Subsequently, it delves into the polarity changes in traveling waves during refraction and reflection in hybrid lines, presenting a criterion for fault section identification in OHL–cable hybrid lines based on the energy characteristics of traveling waves. Finally, a comprehensive criterion integrating traveling wave power and zero-sequence impedance direction is proposed, along with the consideration of field deployment at the connection points of hybrid lines through FTUs. The following conclusions are drawn:

(1)

Due to the dual-vector control and weak-feed characteristics of PV inverters, both positive-sequence and negative-sequence impedance direction criteria struggle to accurately determine fault directions. In contrast, the zero-sequence impedance in the zero-sequence network, primarily comprising the transformer’s zero-sequence impedance and the line’s zero-sequence impedance, is unaffected by the PV power station.

(2)

In hybrid lines, the polarity of traveling wave currents and voltages remain unaffected by refraction and reflection. The constructed criterion for the traveling wave energy direction is adept at adapting to the alternating voltage and current in AC transmission, unaffected by the weak-feed characteristics of PV power generation systems. It can accurately determine the occurrence of sections of faults, excluding single-phase ground faults.

(3)

By integrating the criteria for the traveling wave energy direction and zero-sequence impedance direction, the proposed fault section identification method in this paper can accommodate the weak-feed characteristics of photovoltaic power generation systems, is applicable to all types of faults and can be easily deployed on existing delivery lines of floating PV power generation systems through FTUs.