To prevent the bus voltage at renewable energy nodes in distributed renewable energy distribution networks from failing to achieve safe ride-through after a fault occurs, and to avoid large-scale unit disconnection that could lead to more severe voltage collapse accidents, China has established corresponding transient voltage safety ride-through standards for renewable energy units. These standards specify the continuous grid-connected conditions for renewable energy units, which are described as follows: After a fault occurs in the power system, the bus voltage at renewable energy nodes must satisfy the upper and lower voltage boundary requirements within specified time intervals during different periods, ensuring continuous grid connection and transitioning to a new operational level. Currently, China has established transient voltage ride-through requirements for photovoltaic power plants based on the “Code for Security and Stability Calculation of Electric Power Systems” (Suo et al., 2025), as illustrated in Figure 1.

The bus voltage at renewable energy nodes after a fault must meet the specified ride-through standards. The low-voltage ride-through requirement stipulates that when the per-unit value of the bus voltage drops to 0.2, it must remain grid-connected for 0.625 s and recover above the low-voltage ride-through boundary to 0.9 within 2 s. The high-voltage ride-through requirement specifies that the per-unit value of the bus voltage should be below 1.3 within 0.5 s after the fault, below 1.25 between 0.5 and 1.0 s, and below 1.2 between 1.0 and 10 s. The blue dashed line represents the low-voltage safety ride-through boundary, while the red dashed line represents the high-voltage safety ride-through boundary. After a disturbance, the continuous grid-connected voltage of all renewable energy node buses must transition to a new operational level within the safety region depicted in the diagram.

The transient voltage safety ride-through requirement is a hard constraint on the safety of bus voltages at renewable energy unit nodes, restricting the allowable transitional evolution process after a disturbance. The voltage must transition to a new operational level within specified limits. Based on this, this section will use the transient voltage safety ride-through standard as a benchmark to quantify the trajectory deviation during the time-domain transient voltage process of the bus after a fault occurs at renewable energy nodes. Taking into account the cumulative degree of bus voltage offset, a time-section-based transient voltage safety evaluation index is established. K VSI = 1 H L ∑ i = 1 H ∑ j = 1 L Δ V i j (1)

Where, L represents the number of time sections in the transient voltage trajectory curve, H is the total number of renewable energy nodes in the system, and Δ V i j is the voltage deviation of the i − th renewable energy node at time section j . Δ V i j = V max − V i j , V max > V i j V i j − V min , V i j > V max 0 , V min < V i j < V max (2)

Where, V max represents the high-voltage ride-through boundary specified in the transient voltage safety ride-through standard, and V min represents the low-voltage ride-through boundary specified in the same standard.

The aforementioned K VSI represents the transient voltage safety level of renewable energy integration nodes in the distribution network. By using time sections as the basis for establishing standards, it effectively captures data at specific time points, facilitating the analysis of instantaneous states and simplifying the dynamic processes of complex systems. When the voltage of the renewable energy unit meets the transient voltage safety ride-through standard, K VSI = 0 ; when the voltage exceeds the upper or lower boundaries specified in the standard, K VSI > 0 ; and the larger the value of K VSI , the greater the extent to which the fault disrupts the transient voltage safety of the entire system.

To optimize the distributed allocation of synchronous condensers, the first step is to determine their appropriate installation locations within the entire distributed renewable energy distribution network. This process is guided by the transient voltage safety evaluation index defined in Section 1.2, with the aim of enhancing the transient voltage safety ride-through capability of renewable energy node buses. The specific process is described as follows.

The optimal selection of installation nodes for distributed synchronous condensers requires consideration of the overall applicability of the distributed renewable energy distribution network under various operating conditions. Multiple renewable energy output scenarios are predefined in the constructed system to form a set of operational scenarios, and multiple fault conditions are predefined to form a fault set.

Where, C represents the number of operational scenarios, F represents the number of fault disturbances, K VSI i j , k is the transient voltage safety evaluation index for the node at the k − th position after connecting a synchronous condenser in the i − th operational scenario and the j − th fault disturbance, K VSI i j , 0 is the transient voltage safety evaluation index for the node without connecting a synchronous condenser in the i − th operational scenario and the j − th fault disturbance, S g is the capacity of the system for sequentially connecting synchronous condensers.

Rank the transient voltage safety level improvement effects E k or each installation position. Larger values indicate better overall transient voltage safety level improvements for the distributed renewable energy distribution network after connecting a synchronous condenser. Select the top N positions from this ranking as the installation nodes for the synchronous condensers.

To optimize the allocation of synchronous condenser capacity, it is first necessary to consider the transmission supply capability of the outbound channels. This ensures that the distributed renewable energy distribution network meets the transient voltage safety ride-through requirements for renewable energy while minimizing the configured capacity of synchronous condensers and reducing the transmission power deviation in outbound channels as much as possible. The objective function of the constructed optimization model is as follows: J = min 1 F C ∑ i = 1 C ∑ j = 1 F ∑ r N S r + ρ i j + ∑ z Z P i j , z − P i 0 , z (4)

Where, S r represents the capacity of the synchronous condenser at the r − th renewable energy node to be optimized, ρ i j is the penalty function set for the transient voltage safety requirement under the i − th operational scenario and the j − th fault disturbance, Z is the number of outbound transmission channels in the power grid, P i j , z is the transmission power of the z − th outbound channel under the i − th operational scenario and the j − th fault disturbance, P i 0 , z is the transmission power of the z − th outbound channel under the i − th operational scenario without any fault disturbance, C is the number of operational scenarios, F is the number of fault disturbances. ρ i j = 0 , K VSI i j = 0 M 1 + K VSI i j , K VSI i j > 0 (5)

Where, M represents a positive constant.

Constraint 1: the configured distributed synchronous condensers must satisfy the power flow balance constraint during system steady-state operation. P i = V i ∑ j = 1 n V j G i j ⁡ cos ⁡ θ i j + B i j ⁡ sin ⁡ θ i j Q i = V i ∑ j = 1 n V j G i j ⁡ sin ⁡ θ i j − B i j ⁡ cos ⁡ θ i j i = 1 , 2 , ⋯ , n (6)

Where, V i and V j are the voltages at nodes i and j , G i j is the real part of the admittance matrix at position i , j , B i j is the imaginary part of the admittance matrix at position i , j , θ i j is the phase angle difference between nodes i and j , n is the total number of nodes in the network, P i and Q i represent the active power and reactive power injected at the node, respectively.

Constraint 2: the system must satisfy the numerical solvability constraints of differential-algebraic equations during transient processes. d x d t = f x , y , t 0 = g x , y (7)

Where, x represents the element state variable (i.e., generator rotor speed), y represents the system algebraic variable (i.e., bus voltage and transmission power of outbound channels), and t represents the time in the dynamic process. This formula is used to calculate the voltage trajectory of renewable energy node buses and the transmission power of outbound channels during the time-domain process.

Constraint3: capacity constraints of synchronous condensers. S r , ⁡ min ≤ S r ≤ S r , ⁡ max (8)

Where, S r , ⁡ min represents the lower bound of the synchronous condenser capacity at node, and S r , ⁡ max represents the upper bound of the synchronous condenser capacity at node r .

Regarding the objective function constructed in Section B, the model is a complex dynamic differential-algebraic equation that represents a nonlinear parameter optimization problem considering the grid. It involves the optimization of synchronous condenser capacities at multiple nodes, which is difficult to solve using classical mathematical programming methods. Taking into account computational efficiency and accuracy, as well as ensuring the globality of the search, this paper adopts the Beetle Swarm Optimization (BSO) algorithm to solve the objective function.

The Beetle Swarm Optimization (BSO) algorithm is a novel optimization algorithm that maximally combines the advantages of the beetle antennae search and particle swarm optimization, complementing each other to achieve high search efficiency and global search capabilities (Jiang et al., 2021; Yang et al., 2021). In this algorithm, the initial particles of the beetles are obtained through Monte Carlo random sampling. By incorporating an adaptive inertia weight adjustment strategy into the optimization iteration process, the BSO algorithm improves the search process for a population of N p beetles. In this population, the capacity of the synchronous condensers corresponds to the positions of the beetles. Therefore, in the k + 1 − th iteration, the velocity V i , j k + 1 and position X i , j k + 1 of the j − th element corresponding to the i − th beetle are as follows: V i , j k + 1 = ω k V i , j k + c 1 k r 1 p i , j k − X i , j k + c 2 k r 2 g j k − X i , j k (9) X i , j k + 1 = X i , j k + λ V i , j k + 1 + 1 − λ ξ i , j k (10)

Where, p i , j k represents the j − th element of the best position in the history of the i − th beetle at the k − th iteration, g j k represents the j − th element of the global best position at the k − th iteration, r 1 and r 2 are random numbers within the range 0 , 1 , ω k is the inertia weight, λ is a positive constant, ξ i , j k is the position increment factor. ω k + 1 = ω max − k + 1 k max ω max − ω min (11) c 1 k + 1 = 2 ⁡ sin 2 π k max − k + 1 2 k max (12) c 2 k + 1 = 2 ⁡ sin 2 π k + 1 2 k max (13)

Where, ω max is the maximum inertia weight, ω min is the minimum inertia weight, c 1 k + 1 is the self-learning factor, c 2 k + 1 is the swarm learning factor, k max is the maximum allowed number of iterations. ξ i , j k + 1 = δ k V i , j k sign f X r , i , j k − f X l , i , j k (14) δ k = η δ δ k − 1 (15) X r , i , j k = X i , j k − 1 + d 2 × V i , j k − 1 (16) X l , i , j k = X i , j k − 1 − d 2 × V i , j k − 1 (17)

Where, δ k is the search step size at the k th iteration, sign * is the sign function, X l , i , j k is the position of the left antenna of the beetle, X r , i , j k is the position of the right antenna of the beetle, f X l , i , j k is the fitness value of the left antenna of the beetle, f X r , i , j k is the fitness value of the right antenna of the beetle, η δ is the variable step size factor, d is the distance between the left and right antennae of the beetle.

The flowchart of the Beetle Swarm Optimization (BSO) algorithm is shown in Figure 2.

Referring to the standard IEEE 33-bus power system, a schematic diagram of the distributed new energy distribution network is designed as shown in Figure 3. The entire distribution network involves two voltage levels: 10 kV and 35 kV, with a total of 10 new energy generator units and two external transmission channels. Each generator unit operates at a 10 kV voltage level and is connected to the 35 kV distribution network via step-up transformers. Based on this configuration, three basic operational scenarios are considered sequentially: high new energy generation (generator output at 100%), medium new energy generation (generator output at 60%), and low new energy generation (generator output at 20%). Furthermore, contingency analysis is conducted by considering anticipated faults. Since three-phase short-circuit faults cause the most severe transient voltage instability and significantly impact the power transmission capacity of the external channels, this paper selects three-phase short-circuit faults occurring at the two external transmission channels for analysis.

The renewable energy power station includes both photovoltaic and wind power generation, which not only ensures diversity in renewable energy types but also effectively mitigates the intermittency issues associated with single-source generation through their complementary operation.

By combining the considered operational scenario set with the fault set, a total of six operating conditions are formulated. A three-phase short-circuit fault occurring in Transmission Channel 01 is denoted as Fault a, and a three-phase short-circuit fault in Transmission Channel 02 is denoted as Fault b. Optimization for the siting and sizing of synchronous condensers is then performed under these conditions. The case study simulation is conducted on the MATLAB simulation platform.

Based on the distributed synchronous condenser installation node selection method proposed in Section 3A, synchronous condensers with a capacity of 1 Mvar are sequentially connected at the busbars of each new energy generator unit in the distributed new energy distribution network. The transient voltage safety evaluation index is calculated for all six operating conditions with the introduction of fixed-capacity synchronous condensers. Using Equation (3), the voltage safety improvement effect index at the new energy integration points is obtained, as shown in Table 1.

The determination of the installation nodes for distributed synchronous condensers requires consideration of multiple factors. On one hand, it is necessary to consider the impact of the installation location on the transient voltage regulation capability under multiple operating conditions of the transmission grid, ensuring that the transient voltage at new energy nodes meets safety ride-through requirements. On the other hand, the economic cost of installation must be considered; insufficient installation can lead to inadequate regulation effects and longer recovery times, while excessive installation can result in economic waste. The enhancement effect index E k is calculated and sorted in descending order. The top five positions from this sorting are selected as the installation nodes for the synchronous condensers, specifically at nodes 1, 3, 4, 6, and 7.

Next, the capacity allocation for the synchronous condensers at each installation node is performed using the BSO algorithm to optimize the objective function. The parameters used are: the total number of individuals in the beetle swarm N p = 20 , the maximum number of iterations k max = 200 , the maximum inertia weight ω max = 0.95 , the minimum inertia weight ω min = 0.45 , the distance between the left and right antennae of the beetles d = 0.5 , and all positive constants are set to 0.5. The resulting capacities for the distributed synchronous condensers at each new energy bus are as follows: a capacity of 35 Mvar at Node 1, 5 Mvar at Node 3, 8 Mvar at Node 4, 47 Mvar at Node 6, and 33 Mvar at Node 7.

Without synchronous condensers, three-phase short circuits occur at the buses of Transmission Channel 01 and Transmission Channel 02 under three operating scenarios, with a fault duration of 0.2s. Considering the transient voltage ride-through standards for renewable energy power plants, the bus voltage waveforms of the renewable energy units are shown in Figure 4, where the vertical axis U * represents the per-unit value of the renewable energy unit bus voltage. The transmission power waveforms of the outgoing channels are shown in Figure 5, where the vertical axis P * represents the per-unit value of the transmission power.

The simulation waveforms indicate that under different operating conditions, faults in the outgoing transmission channels cause transient voltage issues at the renewable energy integration buses of the distribution network, leading to unsafe voltage ride-through phenomena. This increases the risk of renewable energy units disconnecting from the grid. Under fault scenario (a), the maximum overvoltage peak exceeds the safety limit by 14%. Under fault scenario (b), the maximum voltage peak exceeds the limit by 8.4%, while the minimum voltage drops to 85% of the safety threshold. Even after fault clearance, voltage fluctuations persist at the renewable energy nodes, affecting the stable operation of the sending-end grid. In particular, under fault scenario (b), the voltage fluctuation is most severe, exhibiting a voltage oscillation of 0.1 p.u. relative to the pre-fault steady-state nominal voltage. During certain intervals, the grid-connected bus voltage even falls below the safety threshold by 0.2 p.u. Moreover, during three-phase short-circuit faults, the transmission power of the affected channel drops to zero, while the transmission power of the unaffected channels deviates significantly from their normal scheduled values. The peak value reaches as high as 0.62 p.u. After fault clearance, the transmitted power still exhibits fluctuations in the range of 0.1–0.22 p.u., which not only causes power surges in the receiving-end grid but also affects the normal operation of equipment within the power system.

When a fault occurs in Transmission Channel 01, the surrounding area contains a higher number of renewable energy units, and the connected transmission lines are relatively short. This results in significant post-fault transmission power spikes. The smaller the output of the renewable energy units, the more pronounced the transmission power spikes become. In contrast, Transmission Channel 02 has fewer nearby photovoltaic units and is connected to longer transmission lines. Consequently, no significant transmission power spikes occur after fault clearance in this channel, and changes in renewable energy output only cause fluctuations in steady-state transmission power.

The transient overvoltage phenomenon is mainly caused by the increased reactive current from renewable energy units. After fault clearance, even though the grid voltage recovers rapidly, the time-delay characteristics of the control system cause the units to continue providing reactive power support, resulting in transient overvoltage issues. By installing synchronous condensers at the point of interconnection and utilizing their fast response characteristics, instantaneous reactive power support can be provided during faults, and the system’s reactive power can be quickly adjusted after fault clearance to ensure safe transient voltage ride-through.

After optimizing the placement of distributed synchronous condensers at the corresponding renewable energy buses, the optimized bus voltage waveforms of the renewable energy units are shown in Figure 6, where the vertical axis U * represents the per-unit value of the renewable energy unit bus voltage. The transmission power waveforms of the outgoing channels are shown in Figure 7, where the vertical axis P * represents the per-unit value of the transmission power.

The simulation waveforms indicate that, after configuring distributed synchronous condensers in the distributed renewable energy grid, the bus voltages of renewable energy units under six operating conditions all meet the specified transient voltage safety ride-through standards and transition to new steady-state operating levels within a reasonable voltage fluctuation range. Compared to before the introduction of distributed synchronous condensers, the voltage sag depth is significantly mitigated: the sag range is reduced from 0.29 to 0.95 p.u. before optimization to 0.20–0.46 p.u. after optimization. Under the two fault scenarios, the maximum voltage sags are reduced by 21.5% and 81.8%, respectively, effectively preventing generator tripping incidents. Furthermore, overvoltage peaks are markedly suppressed. The average peak voltage across all operating conditions is approximately 1.16 p.u., providing a margin of 10.8% below the safety limit of 1.3 p.u. The maximum overvoltage peaks under the two fault scenarios are reduced by 23.8% and 19.2%, respectively, thereby effectively eliminating the risk of voltage violations.

After the optimized configuration of distributed synchronous condensers, the elimination of faults in Transmission Channel 01 significantly mitigates power spikes and power transmission fluctuations in both transmission channels, only occuring a 0.98% power peak violation and maintaining consistency with the pre-fault scheduled values. After fault clearance in Transmission Channel 02, the power curves of both channels transition more smoothly to a new operational level, further enhancing the stability of power delivery. This significantly reduces the deviation between post-fault transmission power and the originally scheduled values while diminishing power transmission fluctuations. As a result, the transmission power of the two outgoing channels remains nearly constant, reducing power surges caused by significant deviations on the receiving grid. This greatly improves the stability of power supply through the outgoing channels and is of great significance for enhancing transient voltage support and facilitating the friendly grid integration of high-proportion renewable energy systems.