Two-Stage DEA-AHP Framework for Solar PV Power Plant Site Selection in Taiwan

1. Introduction

This paper addresses the critical challenge of selecting optimal sites for solar photovoltaic (PV) power plants, a task of paramount importance for energy security and sustainable development, particularly in the context of global efforts to transition from fossil fuels. Using Taiwan as a case study, the research highlights the urgency of this issue for nations reliant on imported energy and vulnerable to climate change.

2. Methodology: Two-Stage MCDM Framework

The core contribution of this paper is a novel two-stage Multiple Criteria Decision Making (MCDM) approach that combines Data Envelopment Analysis (DEA) and the Analytic Hierarchy Process (AHP).

3. Case Study: Taiwan

The methodology is applied to evaluate 20 potential cities and counties in Taiwan for large-scale solar PV farm construction.

4. Results and Discussion

5. Technical Details & Mathematical Formulation

DEA CCR Model (Charnes, Cooper, Rhodes): The basic DEA model used to calculate efficiency score $\theta_k$ for DMU $k$ is formulated as a linear programming problem: $$ \begin{aligned} \text{Max } & \theta_k = \sum_{r=1}^{s} u_r y_{rk} \\ \text{s.t. } & \sum_{i=1}^{m} v_i x_{ik} = 1 \\ & \sum_{r=1}^{s} u_r y_{rj} - \sum_{i=1}^{m} v_i x_{ij} \leq 0, \quad j = 1, \ldots, n \\ & u_r, v_i \geq \epsilon > 0 \end{aligned} $$ Where:

• $x_{ij}$: amount of input $i$ for DMU $j$.
• $y_{rj}$: amount of output $r$ for DMU $j$.
• $v_i$, $u_r$: virtual weights for inputs and outputs.
• $\epsilon$: a small non-Archimedean number.
• $\theta_k = 1$ indicates DEA efficiency.

AHP Pairwise Comparison & Consistency: Criteria are compared in pairs on a scale of 1-9. The priority vector $w$ (weights) is derived from the principal eigenvector of the comparison matrix $A$, where $Aw = \lambda_{max}w$. Consistency Ratio ($CR$) must be less than 0.1: $$ CR = \frac{CI}{RI}, \quad CI = \frac{\lambda_{max} - n}{n - 1} $$ where $RI$ is the Random Index.

6. Results & Chart Description

Conceptual Chart 1: Two-Stage MCDM Process Flow
A flowchart depicting: (1) 20 Candidate Locations input into (2) DEA Model (Climatic Inputs/Solar Outputs) which filters to (3) Efficient Locations (Score=1). These are then input into (4) AHP Model (5 Criteria & Sub-criteria) leading to (5) Final Weighted Ranking of Locations.

Conceptual Chart 2: AHP Criteria Weight Hierarchy
A horizontal bar chart showing the relative weights of the top-level criteria (Site, Technical, Economic, Social, Environmental) and a drill-down for the Economic criterion showing the dominant weight of the "Support Mechanisms" sub-criterion (0.332).

Conceptual Chart 3: Final Location Ranking Map
A thematic map of Taiwan with the 20 candidate locations marked. The top-ranked locations (Tainan, Changhua, Kaohsiung) are highlighted in the primary color (#FF9800), with other locations shaded in gradients based on their final AHP score.

7. Analytical Framework: Example Case

Scenario: Evaluating two hypothetical locations, "City A" and "City B," after the DEA stage.

Step 1 - AHP Pairwise Comparison (Economic Criterion):
Decision-maker compares sub-criteria:
"Support Mechanisms" is judged to be 'Moderately more important' (value 3) than "Investment Cost."
"Investment Cost" is judged to be 'Equally to moderately more important' (value 2) than "O&M Cost."
This forms a comparison matrix for the Economic sub-criteria.

Step 2 - Scoring Locations:
For the "Support Mechanisms" sub-criterion, City A (strong government subsidies) is rated 'Strongly preferred' (score 5) over City B (weak subsidies). These scores are normalized and aggregated using the criteria weights to produce a final composite score for each location.

Outcome: Even if City B has slightly better solar insolation, City A's superior policy support (high weight) leads to a higher final ranking, demonstrating the framework's ability to balance multiple, often conflicting, objectives.

8. Application Outlook & Future Directions

• Integration with GIS: Future work should tightly integrate this MCDM framework with Geographic Information Systems (GIS) for spatial analysis, constraint mapping (e.g., protected areas, slope), and visualization, creating a powerful decision support system (DSS).
• Dynamic & Probabilistic Modeling: Incorporate climate change projections to assess long-term site viability. Use stochastic DEA or fuzzy AHP to handle uncertainties in input data and expert judgments.
• Broader Technology Assessment: Adapt the framework for other renewable technologies (offshore wind, geothermal) or hybrid systems, using technology-specific criteria.
• Lifecycle Sustainability Integration: Expand the environmental criterion to a full Life Cycle Assessment (LCA) covering manufacturing, deployment, and decommissioning, aligning with circular economy principles.
• Machine Learning Enhancement: Use ML algorithms to analyze historical siting success/failure data, potentially refining the AHP weightings or suggesting new sub-criteria.

9. References

1. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444.
2. Saaty, T. L. (1980). The analytic hierarchy process. McGraw-Hill.
3. International Energy Agency (IEA). (2020). World Energy Outlook 2020. OECD/IEA.
4. IRENA. (2021). Renewable Power Generation Costs in 2020. International Renewable Energy Agency.
5. Zhu, J., et al. (2020). A comprehensive review of hybrid DEA methods. Omega, 102, 102308.
6. Isola, P., Zhu, J., Zhou, T., & Efros, A. A. (2017). Image-to-image translation with conditional adversarial networks. Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 1125-1134). (Cited as an example of a structured, two-stage framework in a different domain).

10. Original Analysis & Expert Commentary