Long-term　Energy　Contracts　(LECs)　are　formal　agreements　signed　for　several　years　by　energy　sellers　and　buyers　at　a　guaranteed　purchase　price.　However,　unexpected　events　(e.g.,　pandemics,　trade　disputes　and　regional　wars)　are　exacerbating　Energy　Market　Price　(EMP)　volatility,　resulting　in　psychological　biases　in　gains　and　losses　between　energy　sellers　and　buyers　and　disruptions　to　the　execution　of　LECs.　To　ensure　the　effective　execution　of　LECs,　we　propose　a　Prospect-Theory　Evolutionary　Game　Model　(PTEGM),　which　characterizes　different　risk　preferences　and　loss　aversions　of　energy　sellers　and　buyers　under　EMP　volatility　through　the　prospect　theory.　After　deriving　EMP　ranges　of　cooperation　and　non-cooperation　(i.e.,　significant　reference　values　for　energy　price　terms　in　LECs)　by　replicator　dynamic　equations,　the　cooperation　evolution　of　LECs　can　be　investigated.　Extensive　numerical　experiments　are　conducted　to　simulate　the　cooperation　evolution　of　LECs　under　EMP　volatility.　Research　results　reveal　nonlinear　relationships　between　EMP　volatility　and　cooperation　and　highlight　that　EMP　volatility　does　not　necessarily　cause　non-cooperation　of　LECs.　EMP　ranges　of　cooperation　and　non-cooperation　can　be　measured　as　energy　price　terms　in　LECs　to　improve　energy　sustainability,　because　the　enactment　of　energy　price　terms　considering　psychological　factors　can　mitigate　energy　supply　disruptions　caused　by　EMP　volatility.