Approximations for the dynamic security region of network-reduction power system

Abstract

Based on the explicit analytical equation for the stable manifold of the post fault stability region determined by the controlling unstable equilibrium points, this paper develops the explicit analytical equation for the local dynamic security region of network-reduction power systems. It presents the linear (QL method) and quadratic (QQ method) approximations for the dynamic security region based on the quadratic approximation for stable manifold and sensitivities. Furthermore, this paper compares the proposed methods to the linear approximation (LL method) of the dynamic security region based on the linear approximation for the stability region. The simulations in SMIB and IEEE 9-bus systems show that in the small-scale power systems, the LL method is robust but it may result in relative serious deviation. It is also shown that the QQ method may display fairly accurate estimation but it is sensitive to the initial parameters, and fortunately, the QL method is robust and it may meet the engineering requirements.

基于故障后主導不穩定平衡點所決定的穩定域邊界的顯式方程及其二次近似,并結合靈敏度分析法,給出了基于網絡約化模型的電力系統在給定故障下動態安全域的顯式形式及其線性近似(稱為“Q線性近似”)和擬二次近似。進一步,與基于穩定域邊界線性近似的動態安全域線性近似(稱為“L線性近似”)進行了比較分析,所得仿真結果表明:L線性近似精確度較低;擬二次近似局部精確度較高,但依賴于初始參數的選擇;Q線性近似不僅精確度高,而且對初始參數選擇的變化不敏感,能夠滿足工程要求,具有較強的適用性。