To enable standardized and performance-oriented selection of converter topologies in VSC-HVDC systems, a quantitative indicator framework is established to characterize the relationship between engineering scenarios and topology adaptability (Damanik et al., 2022).

Based on the requirements of renewable integration, urban distribution, and traction-power systems, seven key indicators are defined as the feature vector X = [x ₁ , x ₂ , … , x ₇ ]. Each indicator corresponds to a practical engineering constraint, and its value is obtained through typical parameter ranges in converter design or, when direct measurement is not applicable, through structured expert assessment. The normalization follows min–max bounds derived from standard equipment ratings and planning specifications, ensuring that the feature representation maintains physical meaning and comparability across scenarios rather than being based on arbitrary scaling.

AC/DC Voltage Difference Ratio (x₁): Describes the matching degree between AC and DC voltages and is obtained by normalizing the typical voltage ratio limits used in VSC-HVDC design. Series-connected topologies adapt better to large voltage differences without transformers, whereas parallel configurations are more suitable for compact low-voltage systems.

Tolerance to Control Complexity (x₂): Represents the complexity of modulation and circulating current suppression control, where higher values indicate that the control platform and protection coordination allow for more advanced hybrid control strategies based on standard HVDC control architectures.

Spatial Compactness Requirement (x₃): Reflects the constraints of installation footprint, where the value corresponds to typical equipment layout limits in urban substations and rail traction power stations.

Reliability Requirement (x₄): Characterizes the need for continuous operation under faults. Topologies possessing self-clearing ability maintain stability during short-circuits, whereas those depending on external breakers score lower in high-reliability scenarios. Topologies incorporating full-bridge or hybrid submodules inherently provide stronger fault ride-through capability according to HVDC reliability criteria.

Power Quality Requirement (x₅): Reflects the constraint on harmonic distortion and waveform quality, indicating how strictly a topology must control THD to satisfy grid codes.

Cost Sensitivity (x₆): Corresponds to investment and operating cost constraints, where normalized device count and auxiliary circuit complexity reflect relative cost contributions in typical engineering budgeting.

Engineering Complexity Tolerance (x₇): Represents the acceptable installation and construction complexity, based on standard construction and commissioning conditions for HVDC converter stations.

These seven indicators quantitatively transform scenario-specific requirements into a comprehensive characteristic vector X, serving as the input feature set for subsequent response-function modeling and multi-criteria evaluation. The formulation allows consistent comparison of topologies across diverse operating environments while preserving engineering meaning and traceability.

Traditional converter evaluation approaches often rely on linear normalization and static weighting, which fail to reflect the nonlinear relationship between engineering indicators and topology adaptability (He and Cheng, 2024). In practical converter design, each topology exhibits a distinct performance response pattern under varying operational conditions. To capture these nonlinear dependencies, a response-function-based mapping framework is introduced, which transforms physical indicators into adaptability scores through topology-specific response curves.

For an engineering indicator x, the corresponding adaptability value y is normalized within [0,1] via a mapping function f(x). Three response function forms are used according to the indicator’s physical variation pattern: linear for monotonic trends, saturating for diminishing returns, and inverted U-shaped when an optimal operating range exists.

The Analytic Hierarchy Process (AHP) (Mbuli, 2024) is applied to quantify the relative importance of evaluation indicators and model subjective preferences in converter topology scoring. A seven-order judgment matrix is constructed for the engineering feature indicators. To enhance consistency and reduce subjective bias, several strong preference relationships are defined based on expert consensus. For instance, the AC/DC voltage difference ratio (x ₁ ) is considered more important than reliability (x ₄ ), and tolerance to engineering complexity (x ₇ ) slightly more critical than power quality (x ₅ ). Undefined adjacent pairs are completed through an adjacency mechanism to ensure smooth weighting continuity.

After constructing the judgment matrix A , the weight vector w _AHP of each characteristic indicator is calculated using the eigenvector method. To verify the consistency of the judgment matrix, the maximum eigenvalue λ _max is further calculated, and the consistency index CI and consistency ratio CR are calculated based on this. The consistency ratio threshold set in this paper is 0.1. When CR < 0.1, the judgment matrix is considered to have good logical consistency.

Although the AHP method mentioned above relies on expert judgment to set indicator weights, and has the advantages of a clear structure and expression of subjective experience, it is still inevitable that there will be some human bias. In order to improve the objectivity of the evaluation system, this paper further introduces the entropy weight method (Li et al., 2020), which measures the dispersion of each feature dimension in the topological scoring results to construct a weight distribution that reflects the actual discrimination ability.

This method analyzes the output results of a family of topological performance response functions. For each engineering operating condition input vector, all candidate topological structures output a standardized scoring vector, which represents their adaptability performance under various indicators. The scoring vectors of all candidate topologies under this operating condition are stacked to form a scoring matrix F .

In order to ensure that all indicators are on a uniform scale and can accurately reflect the relative differences between scores, the scoring matrix F needs to be column normalized to obtain matrix P : P = P i j = F i j ∑ i = 1 n ∑ j = 1 n F i j (5)

If P _ij = 0, then assign a very small positive number to ensure that the logarithmic function is defined. This step ensures that the score distribution of each indicator is within the same range, which facilitates subsequent information analysis. Next, the entropy value is calculated, which reflects the uniformity of the indicator value distribution. For the jth indicator, its information entropy E _j is defined as: E j = − 1 lnn ∑ i = 1 n P ij ⁡ ln ⁡ P ij (6)

If the score difference of a certain indicator is small in all schemes, its entropy value tends to be close to the maximum value, indicating that the information is less discriminative; conversely, it indicates that the indicator is more effective in distinguishing between schemes. Based on the information entropy E _j of each indicator, its entropy weight vector w _{entropy y} can be calculated: W entropy j = 1 − E j ∑ j = 1 m 1 − E j (7)

The final weight vector represents the importance of each characteristic indicator reflected in the output of the topological response function under the current operating conditions. Compared to subjective weighting methods, the entropy weighting method relies more on the scoring data itself, thereby enhancing the sensitivity of the evaluation system to differences in operating conditions and scoring outputs. The normalization procedure, entropy calculation and entropy-based weight vector are mathematically described in Equations 5–7.

Figure 1 illustrates the integrated topology scoring process, based on the defined indicators, response functions, and hybrid weights. This process takes engineering feature vectors as input, undergoes a series of function calculations and weight fusion, and ultimately outputs the comprehensive scores and ranking results of each candidate topological structure, which are used to guide structural selection decisions.

Specifically, the feature vector X is input based on actual operating conditions, serving as the input for the topological performance response function. Each candidate topological structure outputs a set of feature response scores through its predefined response function family. Subsequently, two sets of weight vectors are calculated using the AHP method and the entropy weight method, respectively. The former reflects expert knowledge, while the latter reflects the variability of the scores.

Considering the complementarity of the two methods in terms of information sources and modeling objectives, this paper adopts a linear weighting approach to construct the combined weight vector w _combined: w c o m b i n e d = η w A H P + 1 − η w e n t r o p y (8) where η is the fusion coefficient in the range [0,1], determining the balance between subjective preference (AHP) and objective variability (entropy weighting). The fusion of subjective AHP weights and objective entropy weights is formulated in Equation 8. In engineering practice, η is selected within a moderate interval to avoid overweighting either expert judgment or data dispersion; therefore, η is chosen in the range of 0.4–0.6 in this study. We further verified that varying η within this interval does not change the ranking order of the candidate topologies, indicating that the evaluation results remain stable and do not rely on fine-tuning of η.

Finally, the score vectors corresponding to each topological structure are weighted by the combination weight vector to obtain their comprehensive score values: T i = w combined F i (9)

The unified decision score for each topology is computed using Equation 9. Through this scoring process, a unified and scalable scoring mechanism is provided for the selection of flexible DC system topologies in multiple scenarios.