## 4 Multi-Energy Microgrid Reliability Assessment
### FMEA Analysis for Reliability Evaluation  
Due to space limitations, this study report here only analyses the impact of CCHP failure as well as quantitative analysis of the complementary coupling relationship between different energy types. CCHP failure influences the supply of cold, heat, and power energy. Power loads are mainly supplied by the PV, with a backup supplement from ES devices and PG; cold loads are supplied by CAC under the condition that there is extra power energy and that CAC output constraints are satisfied. Heat loads are supplied by the GHP under the condition that the GHP output constraints are satisfied with backup support from HS devices. Based on the evaluation indexes introduced in Section 4.2, the LOEE can be calculated by Equations (33) and (34):  
\[LOEE^{\text{elec}}_{\text{CCHP}}=\sum_{k_{\text{e}}\times\text{CCHP}}\left( \lambda_{\text{CCHP}}\cdot LOEE^{\text{elec}}_{k_{\text{e}}\times\text{CCHP}}\right) \tag{33}\]\[LOEE_{k_{\text{e,CCHP}}}^{\text{elec}}=\begin{cases} \begin{array}{cc}0&P_{\text{Load}}^{ \text{elec}}(t)\leq P_{\text{output}}^{\text{ES}}(t)+P_{\text{output}}^{\text{ PV}}(t)+P_{\text{output}}^{\text{EN}}(t)\\ \int\limits_{\text{$\tau_{\text{CCHP}}$}}[P_{\text{Load}}^{\text{PV}}(t)-P_{ \text{output}}^{\text{EN}}(t))dt&P_{\text{Load}}^{\text{elec}}(t)>P_{\text{output }}^{\text{ES}}(t)+P_{\text{output}}^{\text{PV}}(t)+P_{\text{output}}^{\text{EN}}( t)\end{array}  \tag{34}\]  
SAIDI can be calculated by Equations (35) and (36):  
\[SAIDI_{\text{CCHP}}^{\text{elec}}=\sum_{k_{\text{e,CCHP}}}(\lambda_{\text{CCHP }}\cdot SAIDI_{k_{\text{e,CCHP}}}^{\text{elec}}) \tag{35}\]  
\[SAIDI_{k_{\text{e,CCHP}}}^{\text{elec}}= \begin{cases}\begin{array}{cc}0&P_{ \text{Load}}^{\text{elec}}(t)\leq P_{\text{output}}^{\text{PES}}(t)+P_{\text{ output}}^{\text{PV}}(t)+P_{\text{output}}^{\text{EN}}(t)\\ r_{\text{CCHP}}&P_{\text{Load}}^{\text{elec}}(t)>P_{\text{output}}^{\text{ES}}(t)+P _{\text{output}}^{\text{PV}}(t)+P_{\text{output}}^{\text{EN}}(t)\end{array}\end{cases}  \tag{36}\]  
where \(k_{\text{e,CCHP}}\) is the power supply area affected by the fault of the CCHP system. Likewise, the relevant reliability indexes of heat and cold energy types can be calculated by Equations (37)-(40):  
\[LOEE_{k_{\text{h,CCHP}}}^{\text{heat}}= \begin{cases}\begin{array}{cc}0&P_{ \text{Load}}^{\text{heat}}(t)\leq P_{\text{output}}^{\text{GHP}}(t)+P_{\text{ output}}^{\text{HS}}(t)\\ \int\limits_{\text{$\tau_{\text{CCHP}}$}}[P_{\text{Load}}^{\text{heat}}(t)-P_{ \text{output}}^{\text{GHP}}(t)+\\ P_{\text{output}}^{\text{HS}}(t))\end{array}\end{cases}  \tag{37}\]  
\[LOEE_{k_{\text{e,CCHP}}}^{\text{GOH}}= \begin{cases}\begin{array}{cc}0&\Big{\{} P_{\text{Load}}^{\text{elec}}(t)<P_{\text{output}}^{\text{PS}}(t)+P_{\text{output}}^{\text{ PP}}(t)+P_{\text{output}}^{\text{EN}}(t)\Big{\}}\&\&\Big{\{}P_{\text{Load}}^{\text{cold}}(t)<P_{\text{output}}^{\text{CAC}}(t)\Big{\}}\\ \int\limits_{\text{$\tau_{\text{CCHP}}$}}[P_{\text{Load}}^{\text{cold}}(t)-P_{ \text{output}}^{\text{CAC}}(t)]dt&\{P_{\text{Load}}^{\text{elec}}(t)<P_{\text{ output}}^{\text{PS}}(t)+P_{\text{output}}^{\text{PV}}(t)+P_{\text{output}}^{\text{EN}}(t)\}\&\&\{P_{\text{Load}}^{\text{cold}}(t)\geq P_{\text{output}}^{\text{CAC}}(t)\}\\ \int\limits_{\text{$\tau_{\text{CCHP}}$}}[P_{\text{Load}}^{\text{cold}}(t)]dt&P_{ \text{Load}}^{\text{elec}}(t)\geq P_{\text{output}}^{\text{PS}}(t)+P_{\text{ output}}^{\text{PV}}(t)+P_{\text{output}}^{\text{EN}}(t)\end{array}\end{cases}  \tag{38}\]  
\[SAIDI_{k_{\text{h,CCHP}}}^{\text{heat}}= \begin{cases}\begin{array}{cc}0&P_{ \text{Load}}^{\text{heat}}(t)\leq P_{\text{output}}^{\text{GHP}}(t)+P_{\text{ output}}^{\text{HS}}(t)\\ r_{\text{CCHP}}&P_{\text{Load}}^{\text{heat}}(t)>P_{\text{output}}^{\text{GHP}}(t)+P_{ \text{output}}^{\text{HS}}(t)\end{array}\end{cases}  \tag{39}\]  
\[SAIDI_{k_{\text{e,CCHP}}}^{\text{cold}}=