CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '91368478eb16604d',cH: 'zo30p_bkLIbUtu_figouENfv8tyr2OtjbPOV2edANj0-1739803068-1.2.1.1-FhbUHqGj3XH.B1iNEFBLX4nEdglueD.SwnY.lN8zvM65v9KvCgwiv1SwI6DbW8ZO',cUPMDTk: "\/abstracts\/search?q=line%20voltage%20stability%20indices%20%28LVSI%29&__cf_chl_tk=_jZUsrARYL1sG_vGGP6X14gRkCfEJJIojecchLnNC7g-1739803068-1.0.1.1-F8Hz_VwYtcsB5jzQQjVaQ_XB3_5_CbJhfkjxMIR6tjg",cFPWv: 'g',cITimeS: '1739803068',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=line%20voltage%20stability%20indices%20%28LVSI%29&__cf_chl_f_tk=_jZUsrARYL1sG_vGGP6X14gRkCfEJJIojecchLnNC7g-1739803068-1.0.1.1-F8Hz_VwYtcsB5jzQQjVaQ_XB3_5_CbJhfkjxMIR6tjg",md: "tUrAvkCQo5bGL_oA28MtDQ2DQoYA6sB8M379tH2enKw-1739803068-1.2.1.1-AyumYXM43lNBjSm_xZ7g8YtKXMkBapNn_AnVvRhpuDWPoItMeO1qKbCqx_xgHKrIn4piB5DBCp65imnEfXrW8g6P8GxtNQmfgR5l1K6_uLZ71B6XLY8N72m28I.FJ.UokIfajFC0YdCXU7SxidE.cGuheifkLKZrLZDsqwToTEMP.W9_dh5hCclJW6U448VMbqcN7xM4.kvyerCDFJvqcIApz3eTp5rQNC2FuBPM6ycNPYfDTpEODDxsRkrqb7D4XkjQZkIF0teeufGqfESlTZGJnIRy67N8RHkCnzYUwatPksFzDE99JOUBop8jCXaiBFNHQdV1woz4TPTFw20QnqJB7p5MUT9racoNRWhxeEGv.8SN.ueJM59Ui37uoOhoD2cIJqMipVv1Wn6fzSQmoBEaCRNPIM4ey6fhpzRzAfHCOHLE2nqi_61.UE506FkVSjTP8T_soF.D8nNwsePVZ8LMGQdaLUbLKyW3WtHvMeeDuKpRhhJDcAiDtx3IWIre246_Qjrc3.wu6cHPdoVEde48mYt96OsARFEMirBuhTZvinxypuuTn7S35nJT5.NpCrwwZXYTBUdJm.VzcwdTS7TooSYMowuG0TjpYa77Xicls05vWBjNwCsg5zVRL2lnhZGIGb7uv5532qErkBt16A1DZlJ4rauKWjNJ3GIp342hY_y6te3xNAk7Vw2q_YpxFFbzzd0LcnjON_FJtku.4tRoc1FZEuL4PxsPkoNFAEjMtUqOXWnWAh2TV3fCcNqHQXCHheS3PSgJ0vRkdK_vn2W8on5h.qMElalSWXMrh76HBcwTGWl7DVqyG5nzqpyLk5BQeVaGdd.mTML_1NaxAXL_iBDVFzgIZU2wdz64PQaIzZPaiplzYv45hSgSywikw_MFkPJzeO_YFw1_Qqi8MYQTeSCMT6Ijfb.9RJ10yCrDtubLJhirovwy02pluQCM84lfuChqR7g7pOOBPR6N8oKPwHj7uxP.7dC7za_MC4zZH2dt8yuOXmGm__wN.E7d4tF4B2GvLiM3mWr_5SisO0gw.z5jBq4Ni1zxnNOhTGrZWV_WlnqjPP4lwO97o2436gkCJB1i64YDf7Sb08E9pK_nT0Qk0bk5_DWccBzbJxIzRFek8k_aOGzAvXaBt_PxqM3j7isFKPJx0_mesADj2Gp14ksesQiL7JPzpH7MO2YlgRykcY8cEWMh8X0ML1yq.bVIBYFiwqEl216IopkMwGwcbAC4asCrkfNwgNkPVvd.wW9jnbyB5iLnIUC6CqpsUpLj2_TWzlShKNAAxSbLQ6fSnlSwidgE6o9y_pnNyrMlcHuhYxWf832NZwTe93JJt7x.zYW5KdR8WNMseFjn4JPRjb4CrjsfbUlrI.iPOACtiur1PIE3wyJiy5d9CrlU.hVo37J4sOD7YtDcZbo1bGV2hiupTN_GV8bdqdn4ElgGCeUhWdEpkwRJYzTSFK7Ftb2FBs_8u3hk1GzdFX2SBIesHk0ea_ZRPbwN9aKOvLfXV17c_wfqmGYtUtVqZ4QDXMOESVPJApJDilwk07RUtjBMUSj35Bx3GG3ckUhg2ytfPDl2_LK42YnDgM0CYckZIlsNXZofwDtYFMC7CceNUysWNpoBWgdHp6UopIjaZPz_6hy5yXVmgUGmzIp_LfoSt1YZO9flIb.m3rC1K9D1VjZaSS975E7_Z0k6JTWSfNT54BDtzkE1ZtKso.idobkE7MKLXeKBumsj2WeNUBGDYEMifaUYDQQcl0Un_olKnhJuiwQSsGFct2G5kAwMzf1dQUCMR3Wynu0kuGzWbICwN68J7H3nW7kzMXks6CrY8tdyWM33V_CQUCGvMIYn6YE4ysjeLc63PXjsC72.74Tg3_QIo7b1.7EhRG._yw5nkgONyimLZAsNwBfwlTc7RODUF596fEXoVqMeIVr_jvYO07h_c4puEdaFNT5f2vLdOOXJ1cdGyYK6Grre39FjJeWIKgerbnf12dB8o8DEihw.n748mL0RwXy6rBsYKAb4tyvRIH91onBOSxquSdWL1i2O",mdrd: "vASX0IeoBlYiE0M5CMwVD6H1MH8guWhyjLmVwy2wBCY-1739803068-1.2.1.1-.Dk7iSIiDPlJIigxqZG6TFGvFjXJSCLLi03l5sFNQuMkLBXz9lp.7D2Q2eFrsGYc._OUh8ZTPPIhpnBoHXUQrGl7XqsniDoo6MJtaA1knEngMVvuZxvvQf8xctY1Lx1OH5vI14gr28LJPT7_vEfroryd2.rDgLOoDFHLgnt_VQ6GNm3wThkxrJ4WWsaVAshmq6RKux_Jr1ucEsypLMF0EWmH_oNF4fIEIMjtPA7hF.a4UZje8liNOAELPQZS_1su_uxwSuBy4cfmyi4wPc2286k09WVbGCtAWfFoTuwHH5gb9KEAsgezoFDx.CGP6IMh93Lx0vEgRGOXiLv996sblFyOTidc0gMPDq37e7ZoOOoPBrdBaaWxW_3_FBJYDtwAXdqvm_TB5lKH.mP6eDg5FKwh49HXM5y4EjTopilKYmIQYOQ_fIfFrxo7lUCYXKkzvFpwYL_rafSwufPsyl5pGwi7ecM4mgexiRX4fvfDC9djilzArm3L4kLBB9s5mPU4.ieZ34rBwn2bnTOClL19b55IYDVcwR1d4PZtmBznFis97w7LYmzKDJv6XnAQbGgIIr8BkcslsZoXvunvkjA6zaAw_Wlm4rbs1vVovmW2BmEssyywntUQUn_mQdxtTTVIDGq9_63daYUAiczjdSwehDVZHHris9ohhR3zTb_OMARLEMks61T_tgy.PIC7E4LpG8gB9TPZKdZ2E5MFLg_GDjnQMNQo2h0K2nCTsGP5Z0097FBtUR2vmIJMcY9R.ALofDzqqxDBHSsSQKVixdN78pS87gEZJTYHpRzzHPaR.yrqZueHJSZ0euionV2hiW4iBg_TH_uw_eKRu0Edq.RnO0pvnxuuY47858xNRZU0OY2xoIYCew6QfKq9NtjhFFbA2UeKFzrjIez7S3AzVzGT1jgqGI7l0ZIeFeORYbpEpdamAb9JW6GmCxDo8meoJaa3Z0tPSAlrFBcRM1EcKhzGRW.ZebnGUw4i4KI8kSNA8pJlRN7NHY6MnVmQb.uZXbkdxWSYPGgBffqT1sfns4E_jiyP658WLbKtUUDMfZdUk09lg9hPwx9DXh7XbhViyGXMsCuQDoVuCPgOrtUPBHnXGLNgDqZKE.2nGpqvCVTTnB3xnIf804ndZWZWC7czzSPnEeUTglS1_Z2uY3rPGhHoBREmZ0zMvk_VQPVI8llr_KnwJC9cfKFzjnFT8Y8uS_tThX0VbHsQDXMIvAsK8T3tDGfVnKQHaUl2YfW.I3XD9H43_8RegXmXC2ar7WJy7WiLOj7n8vZft6mxFxazp7FuE4FRBdUdd82hPZHfZ9KHrL1ePkmsisaCllxTGnqdiYjJ9W7_HyKhQj3tKB.lA0rvvplZ7KbeVSQ6rwxnMGGnRjrUa6KM1VFCXvpzUMK9MUGX.MF6ki6CBvUjLsL5Qk.8kIvMm84oviORhDIIPlWL4MmwJVtbiLwYINNfHlgwIFkF8zUdEl21Jk_tEsjyIUgDiaLQy_hqVHQq0E11rAPtnYSvkuVcHsHAcCWQiOup.HkL04frCdrfXyibZYf5DBY.2ZlGQZ6zyM4FmyHDfcZV0sdF2BHrTo6qnGoIGFbluFCWdAUKu.fXOxySCI9uov7hsTRVZInI3Tunf6DBt0ncBtOrqKU15.zRl2j51yUbyQY4ILy5WlYYDP9jfCBoscmQHf0Zc9Nbbz8LvZXs0bHQ3I2lsHf77D.1RQvNy43NCsGnRN8AEWJcXQJ_geG6iBMTwRbsxmro90b6psY.MEOh3bayKru83qnhj1NzO2dvr_rWyvyYY1dwyHKdtbgh.AL70QcpkXkkN6A7KoX_AIsVZ.6FQrZTBQXQb.fS3FMsMWYfYrRqxuClI0J7mtKt1NrK1teNzr_8rVuEZRQtsXslMVq.YZOSElEtJCX3F8BIpchV2A8M5x2YKigF7vPbdSnEEuzGfKIUwBGUP6JkxOJAquOp7rUdU3U9B_mu7c7x2iq5fdTGskbQk5jgwC7sKJ8cvw"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/g/orchestrate/chl_page/v1?ray=91368478eb16604d';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=line%20voltage%20stability%20indices%20%28LVSI%29&__cf_chl_rt_tk=_jZUsrARYL1sG_vGGP6X14gRkCfEJJIojecchLnNC7g-1739803068-1.0.1.1-F8Hz_VwYtcsB5jzQQjVaQ_XB3_5_CbJhfkjxMIR6tjg" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>