One　of　the　most　important　issues　that　must　be　taken　into　consideration　during　the　planning　of　energy　storage　systems　(ESSs)　is　improving　distribution　network　economy,　reliability,　and　stability.　This　paper　presents　a　two-layer　optimization　model　to　determine　the　optimal　siting　and　sizing　of　ESSs　in　the　distribution　network　and　their　best　compromise　between　the　real　power　loss,　voltage　stability　margin,　and　the　application　cost　of　ESSs.　Thereinto,　an　improved　bat　algorithm　based　on　non-dominated　sorting　(NSIBA),　as　an　outer　layer　optimization　model,　is　employed　to　obtain　the　Pareto　optimal　solution　set　to　offer　a　group　of　feasible　plans　for　an　internal　optimization　model.　According　to　these　feasible　plans,　the　method　of　fuzzy　entropy　weight　of　vague　set,　as　an　internal　optimization　model,　is　applied　to　obtain　the　synthetic　priority　of　Pareto　solutions　for　planning　the　optimal　siting　and　sizing　of　ESSs.　By　this　means,　the　adopted　fuzzy　entropy　weight　method　is　used　to　obtain　the　objective　function＇s　weights　and　vague　set　method　to　choose　the　solution　of　planning　ESSs＇　optimal　siting　and　sizing.　The　proposed　method　is　tested　on　a　real　26-bus　distribution　system,　and　the　results　prove　that　the　proposed　method　exhibits　higher　capability　and　efficiency　in　finding　optimum　solutions.　©　2020　by　the　authors.　Licensee　MDPI,　Basel,　Switzerland.