Multi-Criteria Decision Analysis Approach for DC Microgrid Bus Selection

DC microgrids can use unipolar or bipolar topologies. The unipolar DC bus is cost-effective but loses power delivery during faults, while the bipolar DC bus improves reliability by ensuring power delivery even during faults. The schematic of each microgrid topology is given in Figure 1, and the key bus characteristics are summarised in Table 1.

Figure 1.

Unipolar (a) and bipolar (b) DC microgrid.

The resilience of a microgrid can be evaluated according to three main elements. First, the resilience to source failure, which measures the system’s ability to maintain power supply in the event of a power source failure. The second element is resilience to load variations, which evaluates the system’s ability to adapt to fluctuations in energy demand. Finally, the resilience to disruptive events, such as short circuits, can lead to blackouts in certain configurations. This classification is provided in Figure 2.

Figure 2.

Microgrid resilience classification.

Power system resilience can be evaluated through distinct phases, as shown in Figure 3. While the specific terminology used might vary across studies, the core concept of the resilience trapezoid represents two key phases: the disruption transition (td–ts) refers to the period from the start of the event to the end of its disruptive impact. The recovery transition phase (ts–tr) represents the duration from the beginning of restoration activities until the system fully regains functionality (Kiptoo et al., 2023).

Figure 3.

Resilience curve.

Invulnerability refers to the microgrid’s ability to maintain operation during disturbances, as given by Eq. (1) (Beyza and Yusta, 2021; Wang et al., 2025). (1) invulnerability=PmicrogridtsPmicrogridtd \text{invulnerability}=\frac{{{P}_{\text{microgri}{{\text{d}}_{{{t}_{s}}}}}}}{{{P}_{\text{microgri}{{\text{d}}_{td}}}}} where Pmicrogridts=Pbat+Ppv+Pwind {{P}_{\text{microgri}{{\text{d}}_{{{t}_{s}}}}}}={{P}_{\text{bat}}}+{{P}_{\text{pv}}}+{{P}_{\text{wind}}} represents the rated power of the microgrid after a power disruption, and Pmicrogridtd {{P}_{\text{microgri}{{\text{d}}_{td}}}} is the power of the microgrid before disruption.

Recoverability indicates how quickly a microgrid can recover and resume full operation after a disruption, as represented by Eq. (2) (Yodo and Wang, 2016). (2) recoverability=1−∑t=tdt=tr(Pload−Pren)t∑t=tdt=trP1oadt \text{recoverability}=1-\frac{\mathop{\sum }_{t={{t}_{d}}}^{t={{\text{t}}_{r}}}({{P}_{\text{load}}}-{{P}_{\text{ren}}})\left( t \right)}{\mathop{\sum }_{t={{t}_{d}}}^{t={{t}_{r}}}{{P}_{1oad}}\left( t \right)} where P_load is the power demand and P_ren is the power generated by the PV (photovoltaic panel) and wind generators.

The overall resilience of the microgrid (MG) can be represented by Eq. (3) (Chang et al., 2021). (3) Resilience=invulnerability+recoverability/2 \[\text{Resilience}=\left( \text{invulnerability}+\text{recoverability} \right)/2\]

To assess the resilience of the microgrid under short-circuit fault conditions, it is assumed that power generation remains constant and the load capacity is sufficient. By simulating a pole-to-ground fault on the bus, the investigation can evaluate the impact on each microgrid’s invulnerability and recoverability (Rocchetta et al., 2018). (4) invulnerability=0<invulnerability<1healthy bus0short circuit bus \text{invulnerability}=\left\{ \begin{matrix} 0<\text{invulnerability}<1 & \text{healthy}\,\text{bus} \\ 0 & \text{short}\,\text{circuit}\,\text{bus} \\\end{matrix} \right.

During a short-circuit fault, no power is delivered to the faulted branch, and recoverability is zero. (5) recoverability=1−∑t=tdt=tr(Ploadt)∑t=tdt=trPloadt=1−1=0 \text{recoverability}=1-\frac{\mathop{\sum }_{t={{t}_{d}}}^{t={{t}_{r}}}({{P}_{\text{1oa}{{\text{d}}_{\text{t}}}}})}{\mathop{\sum }_{t={{t}_{d}}}^{t={{t}_{r}}}{{P}_{\text{1oa}{{\text{d}}_{\text{t}}}}}}=1-1=0

In normal operating conditions, power is distributed efficiently and recoverability remains at its maximum. (6) recoverability=recoverability=1healthy bus0short circuit bus \text{recoverability}=\left\{ \begin{matrix} \text{recoverability = }1 & \text{healthy}\,\text{bus} \\ 0 & \text{short}\,\text{circuit}\,\text{bus} \\\end{matrix} \right.

In a system with two buses, such as a bipolar DC microgrid, the resilience can be expressed as: (7) Rbipolar MG=Rbus1+Rbus2/2 {{R}_{\text{bipolar MG}}}=\left( {{R}_{\text{bus1}+}}{{R}_{\text{bus}2}} \right)/2

Bipolar DC microgrid architecture is more fault-resilient than unipolar DC microgrids, making it the superior choice between the two configurations.

Table 2 compares the components, costs, and system specifications of unipolar and bipolar DC microgrids.

The annual cost of all components in the unipolar and bipolar DC microgrid is presented by Eqs. (8) and (9). (8) Ctannualunipolar=∑pv=1npvpv+∑wind=1nwind(wind)+∑c=1nc(conv)+∑b=1nb(bat)+∑i=12costcable+∑i=11breaker {{C}_{t\left( annual \right)unipolar}}=\mathop{\sum }_{pv=1}^{{{n}_{pv}}}\left( pv \right)+\mathop{\sum }_{wind=1}^{{{n}_{wind}}}(wind)+\mathop{\sum }_{c=1}^{{{n}_{c}}}(conv)+\mathop{\sum }_{b=1}^{{{n}_{b}}}(bat)+\mathop{\sum }_{i=1}^{2}\text{cos}{{\text{t}}_{\text{cable}}}+\mathop{\sum }_{i=1}^{1}\left( \text{breaker} \right) (9) Ctannualbipolar=∑pv=1npvpv+∑wind=1nwind(wind)+∑c=1nc(conv)+∑b=1nb(bat)+∑i=13costcable+∑i=12breaker+Costcircuit balancer {{C}_{t\left( \text{annual} \right)\text{bipolar}}}=\mathop{\sum }_{pv=1}^{{{n}_{pv}}}\left( pv \right)+\mathop{\sum }_{wind=1}^{{{n}_{wind}}}(\text{wind})+\mathop{\sum }_{c=1}^{{{n}_{c}}}(\text{conv})+\mathop{\sum }_{b=1}^{{{n}_{b}}}(\text{bat})+\mathop{\sum }_{i=1}^{3}\text{cos}{{\text{t}}_{\text{cable}}}+\mathop{\sum }_{i=1}^{2}\left( \text{breaker} \right)+\text{Cos}{{\text{t}}_{\text{circuit}\,\,\text{balancer}}}

By calculating the ratio of the two annual costs, the relative economic performance of the unipolar and bipolar DC microgrids can be determinate by Eq. (10). (10) CtannualbipolarCtannualunipolar=1+CostcableCtannualunipolar+Costcircuit balancerCtannualunipolar+Costone breakerCtannualunipolar \frac{{{C}_{t\left( \text{annual} \right)\text{bipolar}}}}{{{C}_{t\left( \text{annual} \right)\text{unipolar}}}}=1+\frac{\text{Cos}{{\text{t}}_{\text{cable}}}}{{{C}_{t\left( \text{annual} \right)\text{unipolar}}}}+\frac{\text{Cos}{{\text{t}}_{\text{circuit}\,\,\text{balancer}}}}{{{C}_{t\left( \text{annual} \right)\text{unipolar}}}}+\frac{\text{Cos}{{\text{t}}_{\text{one}\,\,\text{breaker}}}}{{{C}_{t\left( \text{annual} \right)\text{unipolar}}}}

It is notable that the cost ratio is greater than one and can even reach two, depending on the specific technologies chosen for cables, breakers, and circuit balancers. A ratio approaching two indicates that bipolar DC microgrids are approximately twice as expensive to implement as unipolar ones.

The previous results were evaluated using HOMER (Hybrid Optimization of Multiple Energy Resources) software, UL Solutions (Formerly developed by HOMER Energy), which performs analysis based on net present cost (NPC) and cost of energy (COE). The analysis shows that the most cost-efficient configuration is a DC microgrid with only DC loads, as it achieves the lowest NPC and COE, as presented in Figure 4.

Figure 4.

NPC and COE comparison. COE, cost of energy; NPC, net present cost.

In conclusion, choosing the best microgrid configuration involves a trade-off between resilience and cost. If resilience is the priority, the bipolar DC microgrid is the optimal choice due to its ability to isolate faults and maintain partial functionality during short-circuit events. However, when cost is the primary concern, the unipolar DC microgrid becomes a more attractive option. The decision on which microgrid to adopt should be based on an analytical approach that balances these conflicting criteria. In this context, advanced methods such as the AHP can offer valuable insights.

Table 3 presents a comparison of key DC and AC microgrid topologies, describing their characteristics, usage frequency. This comparison helps to identify the most appropriate topologies for the current evaluation. Six major microgrid topologies (AC, unipolar DC, bipolar DC, multi-terminal DC, multi-bus DC and ring DC) are selected for comparison based on their significance in existing literature and real-world applications. The remaining three topologies (radial DC, mesh DC and star DC) are excluded due to their limited usage and minimal practical relevance in contemporary microgrid systems (Saaty, 2008).

The AHP hierarchy foundation is composed of three phases, the initial phase defines the overall problem or decision goal at the top of the hierarchy. Below this, relevant criteria are identified and arranged in a hierarchical structure. The last step presents the different alternatives, as presented in Figure 6 (Kiptoo et al., 2023; Parvaneh and Hammad, 2024).

Figure 6.

AHP technique (Siksnelyte et al., 2018; Yildiz et al., 2025). AHP, analytic hierarchy process.

Table 4 defines the various options (alternatives) being considered for the decision and the relevant criteria that will be used to evaluate them. For example, if the decision involves choosing the best type of DC microgrid topology, the alternatives might be single-bus, bipolar-bus, ring configurations, multi-bus and multi-terminal topology. The criteria considered in the analysis include protection, resilience, and cost.

Table 5 outlines potential scenarios which consumers classified their individual preferences related to the criteria established in Table 4. These scenarios directly reflect consumer priorities and how they might weigh the different criteria

The AHP avoids directly assigning weights by utilizing pair-wise comparisons. Consumers compare these factors pair-wise, judging which holds more weight for their specific needs. These comparison data are then structured in a matrix, where each cell indicates how much more important one criterion is compared to another, as shown in Table 6.

The pairwise comparison matrix for the criteria, C, is: (11) C=c11⋯c13⋮⋱⋮c31⋯c33 C=\left[ \begin{matrix} {{c}_{11}} & \cdots & {{c}_{13}} \\ \vdots & \ddots & \vdots \\ {{c}_{31}} & \cdots & {{c}_{33}} \\\end{matrix} \right]

Each element of the ‘C’ matrix is normalised: (12) C^=C^ij=Cij∑k=1nCkj \text{\hat{C}}=\left[ {{{\hat{C}}}_{ij}} \right]=\left[ \frac{{{C}_{ij}}}{\mathop{\sum }_{k=1}^{n}{{C}_{kj}}} \right]

The weight for each criterion is calculated by taking the means of the rows of Ĉ : (13) Wi=1n∑j=1nC^ij pour i=1,…n with∑i=1nwi=1 {{W}_{i}}=\frac{1}{n}\mathop{\sum }_{j=1}^{n}{{\hat{C}}_{ij}}\,\,\,\,\text{pour}\,\,i=1,\ldots n\,\,\text{with}\,\sum\nolimits_{i=1}^{n}{{{w}_{i}}}=1

Finally, the AHP method analyses this matrix to calculate weights for each criterion, reflecting their relative influence in the consumer’s decision-making, ultimately leading to a DC microgrid selection that prioritises the criteria that matter most to them. The pair-wise comparison matrix (criterion × criterion) considering scenario S5 is defined by Figure 7.

Figure 7.

Criteria’s pair-wise comparison from the expert.

The consistency index and the consistency ratio are calculated by Eqs. (16) and (17). (14) CI=λmax−nn−1;n=number of criteria \text{CI}=\frac{{{\lambda }_{\text{ }\!\!~\!\!\text{ max }\!\!~\!\!\text{ }}}-n}{n-1};n=\text{number}\,\text{of}\,\text{criteria} (15) CR=CIrandom indexRI, If CR < 0.1,pairwise comparison matrix is reasonably consistent. \text{CR}=\frac{\text{CI}}{\text{random}\,\,\text{index}\left( RI \right)},\,\,\text{If CR}\,<\,0.1\text{, pairwise comparison matrix is reasonably consistent}\text{.}

The pairwise comparison matrix A for the alternatives is: (16) A=a11⋯a16⋮⋱⋮a61⋯a66 A=\left[ \begin{matrix} {{a}_{11}} & \cdots & {{a}_{16}} \\ \vdots & \ddots & \vdots \\ {{a}_{61}} & \cdots & {{a}_{66}} \\\end{matrix} \right]

Each element of the ‘A’ matrix is normalised by: (17) a^ij(k)=aij(k)∑r=1maij(k) \[\hat{a}_{ij}^{(k)}=\frac{a_{ij}^{(k)}}{\mathop{\sum }_{r=1}^{m}a_{ij}^{(k)}}\]

The weight for each alternative is defined by the following relation: (18) wik=1m∑j=1ma^ij(k) w_{i}^{\left( k \right)}=\frac{1}{m}\mathop{\sum }_{j=1}^{m}\hat{a}_{ij}^{(k)}

The pairwise comparison of alternatives for each criterion is presented in Figures 8–10.

Figure 8.

Cost pair-wise comparisons from all alternatives.

Figure 9.

Protection pair-wise comparisons from all alternatives.

Figure 10.

Resilience pair-wise comparisons from all alternatives.

The analysis shows clear differences in performance between the alternatives. A2 is the best option, while A3 is the weakest. The other alternatives fall between these two, as demonstrated in Figure 11.

Figure 11.

Microgrid scores for scenario 5.

For scenarios 1, 2, 3, 6 and 7, the unipolar DC microgrid consistently ranked first, while the bipolar DC microgrid consistently held the second position. However, a notable shift occurred in scenarios 4 and 5, where the bipolar DC microgrid surpassed the unipolar DC microgrid to claim the top position. When considering the overall score across all scenarios, the bipolar DC microgrid ultimately secured the second-place ranking, demonstrating its strong overall performance despite the unipolar DC microgrid’s dominance in specific scenarios. The multi-terminal topology consistently maintained the lowest ranking across all scenarios, as presented in Figure 12.

Figure 12.

All scenario results.

When considering all seven scenarios and applying the same approach, the AHP results differ for each scenario. This classification is influenced by the types and number of criteria considered. The bipolar topology emerges as the top choice, followed by unipolar in second place, and AC microgrid in third. It is clear that these rankings are shaped by the specific criteria selected for evaluation. By introducing additional criteria, the rankings could change, potentially leading to a different classification, as presented in Figure 13.

Figure 13.

Overall score for each microgrid topology.

The initial pairwise comparison matrix C be an 3 × 3 matrix, and the initial weight vector is 3 × 1 as given by the next Eq. (19). (19) C=c11⋯c13⋮⋱⋮c31⋯c33, and wc=w1w2w3 C=\left[ \begin{matrix} {{c}_{11}} & \cdots & {{c}_{13}} \\ \vdots & \ddots & \vdots \\ {{c}_{31}} & \cdots & {{c}_{33}} \\\end{matrix} \right],\,\,\text{and}\,\,{{w}_{c}}=\left[ \begin{array}{*{35}{l}} {{w}_{1}} \\ {{w}_{2}} \\ {{w}_{3}} \\\end{array} \right]

Let a small perturbation δc_ij be applied to some elements of the judgement matrix C. The perturbed matrix C′ is:

C′ = C + ΔC ; where ΔC represents the matrix of perturbations.

The perturbation in the weight vector will affect the alternative decision matrix D.

The Jacobian matrix, J of partial derivatives, is given by Eq. (20). (20) J=∂D∂C=D1/C1D1/C2D1/C3D2/C1D2/C2D2/C3D3/C1D3/C2D3/C3D4/C1D4/C2D4/C3D5/C1D5/C2D5/C3D6/C1D6/C2D6/C3 J=\frac{\partial D}{\partial C}=\left[ \begin{array}{*{35}{l}} {{D}_{1/C1}} & {{D}_{1/C2}} & {{D}_{1/C3}} \\ {{D}_{2/C1}} & {{D}_{2/C2}} & {{D}_{2/C3}} \\ {{D}_{3/C1}} & {{D}_{3/C2}} & {{D}_{3/C3}} \\ {{D}_{4/C1}} & {{D}_{4/C2}} & {{D}_{4/C3}} \\ {{D}_{5/C1}} & {{D}_{5/C2}} & {{D}_{5/C3}} \\ {{D}_{6/C1}} & {{D}_{6/C2}} & {{D}_{6/C3}} \\\end{array} \right] where: ∂Di∂Cj \frac{\partial {{D}_{i}}}{\partial {{C}_{j}}} is the partial derivative of the decision with respect to the pairwise comparison judgement between alternatives i and criteria j.

A large value for ∂Di∂Cj \frac{\partial {{D}_{i}}}{\partial {{C}_{j}}} indicates that a small change in the criteria (j) can greatly affect the alternative (i) rank. On the contrary, a small value means that the decision is less sensitive to changes in the criteria (j)weight.

To improve the quality of the research, a dual-source data acquisition strategy is employed. The first dataset is based on expert evaluations, informed by their specialised knowledge. The second dataset is derived from established scientific literature. By integrating these complementary data sources, a more comprehensive and reliable assessment is achieved. Table 7 provides a review of microgrid criteria and their importance across different topologies (Al Dawsari et al., 2024; Cabana-Jiménez et al., 2022; Gerber et al., 2023; Kiptoo et al., 2023).

The analysis of Table 7 indicates that DC microgrid research places the highest priority on resilience (40%), underscoring the critical need for systems capable of withstanding disruptions. Protection ranks second at 30%, emphasizing the importance of safeguarding equipment and ensuring safety. Cost, while still a key factor, holds a lower priority (20%), suggesting that it is optimised within the constraints defined by resilience and protection requirements (Bouchekara et al., 2023; Chandra et al., 2020). The pairwise comparison matrix is presented in Figure 18.

Figure 18.

Pairwise comparison matrix from scientific articles.

The second criterion has the highest weight, which is also observed in the expert judgement. However, the first and last criteria change in the expert judgement results. The results of both tables are closely comparable, though variations may occur if more criteria are introduced. The method used to improve the sensitivity of the decision matrix is illustrated in Figure 19.

Figure 19.

Flowchart of sensitivity improvement. AHP, analytic hierarchy process.

The decision matrix based on scientific data can be determined using expert choice software results. (23) Dsc=0.17x+0.150.10x+0.16−0.26x+0.290.21−0.02x+0.210.03x+0.190.13−0.04x+0.150.02x+0.14−0.12x+0.18−0.15x+0.220.17x+0.06−0.02x+0.18−0.11x+0.17−0.23x+0.280.200.21x+0.11−0.23x+0.29 \[{{D}_{sc}}=\left[ \begin{array}{*{35}{l}} 0.17x+0.15 & 0.10x+0.16 & -0.26x+0.29 \\ 0.21 & -0.02x+0.21 & 0.03x+0.19 \\ 0.13 & -0.04x+0.15 & 0.02x+0.14 \\ -0.12x+0.18 & -0.15x+0.22 & 0.17x+0.06 \\ -0.02x+0.18 & -0.11x+0.17 & -0.23x+0.28 \\ 0.20 & 0.21x+0.11 & -0.23x+0.29 \\\end{array} \right]\]

Then, the Jacobian matrix from scientific data J_sc will be equal to: (24) Jsc=∂Dsc∂Ci=0.170.10−0.260−0.020.030−0.040.02−0.12−0.150.17−0.02−0.11−0.2300.21−0.23 {{J}_{sc}}=\frac{\partial {{D}_{sc}}}{\partial {{C}_{i}}}=\left\{ \begin{array}{*{35}{l}} 0.17 & 0.10 & -0.26 \\ 0 & -0.02 & 0.03 \\ 0 & -0.04 & 0.02 \\ -0.12 & -0.15 & 0.17 \\ -0.02 & -0.11 & -0.23 \\ 0 & 0.21 & -0.23 \\\end{array} \right\}

The global Jacobian matrix from all data will be equal to: (25) J=a∂Dexp∂Ci+b∂Dsc∂Ci=0.26a+0.17b0.13a+0.10b−0.20a−0.26b0.01a−0.02a−0.11a−0.12b−0.18a−0.02b−0.09a−0.01a−0.02b−0.07a−0.06a−0.15b−0.06a−0.11b0.25a+0.21b0.03a+0.03b0.13a+0.02b0.12a+0.17b0.20a−0.23b−0.16a−0.23b J=a\frac{\partial {{D}_{exp}}}{\partial {{C}_{i}}}+b\frac{\partial {{D}_{sc}}}{\partial {{C}_{i}}}=\left\{ \begin{array}{*{35}{l}} 0.26a+0.17b & 0.13a+0.10b & -0.20a-0.26b \\ 0.01a & -0.02a & -0.11a-0.12b \\ -0.18a-0.02b & -0.09a & -0.01a-0.02b \\ -0.07a & -0.06a-0.15b & -0.06a-0.11b \\ 0.25a+0.21b & 0.03a+0.03b & 0.13a+0.02b \\ 0.12a+0.17b & 0.20a-0.23b & -0.16a-0.23b \\\end{array} \right\}

Given that a and b are weighting coefficients that represent the relative importance of expert judgements and scientific data in assessing the impact of a change on the sensitivity of a decision, a sensitivity analysis can be conducted. The goal is to determine a and b while minimizing the elements of the global Jacobian matrix. To achieve this, the Frobenius norm of the matrix is used. The Frobenius norm is given by: (26) ‖J‖F=∑i,jJij2 \[\|J{{\|}_{F}}=\sqrt{\sum\limits_{i,j}{{{\left| {{J}_{ij}} \right|}^{2}}}}\] where J_ij are the elements of the matrix J. The Frobenius norm squared is: (27) ‖J‖F2=0.8376a2+ab+0.8048b2 \|J\|_{F}^{2}=0.8376{{a}^{2}}+ab+0.8048{{b}^{2}}

The objective function to minimise is: fa,b=0.8376a2+ab+0.8048b2 f\left( a,b \right)=0.8376{{a}^{2}}+ab+0.8048{{b}^{2}}

Subject to the constraint: (28) ga,b=a+b−1=0 g\left( a,b \right)=a+b-1=0

The evolution of the norm of Frobenius is presented by Figure 20.

Figure 20.

Frobenius norm evolution.

These values that minimise the Frobenius norm of the matrix J under the constraint are: a≈0.4745, b≈0.5255 a\approx 0.4745,\,\,\,\,b\approx 0.5255

This approach reflects the understanding that scientific data, often gathered through rigorous research and analysis, tends to be more consistent and objective compared to expert judgement, which may be influenced by personal biases or limited experience.

By prioritizing scientific data, we are reducing the risk of decisions being overly influenced by subjective factors. This adjustment ensures that the results of the AHP model are more robust and less sensitive to variations in expert opinions. Moreover, this approach plays a key role in improving the sensitivity of the final decision.

Figure 21 presents the ranking of six alternatives (A1–A6) under three conditions: initial ranking, after criteria weight perturbation, and after optimisation. It visually compares how the ranks shift across these scenarios.

Figure 21.

Rank of decision vector.

The initial ranking shows A2 as the top alternative and A3 as the lowest. After criteria weight perturbation, all alternatives shift in rank, with A1 falling to first place, indicating high sensitivity. Alternatives A4 and A5 show a decrease, indicating that the new weight setup is less favourable for them. The optimisation process restores rank stability, with most alternatives returning to positions close to the initial scenario. A2 regains the top position, and A1, A3, and A5 also align with their original ranks. Only A4 and A6 switch places, showing minor impact and confirming the optimisation’s effectiveness in stabilizing the decision.