Study on the crucial element and its monotone in power grid part П: mechanism and certification

The mechanism and the related certification of crucial element and its monotone proposed in Part ? is analyzed.Based on the concepts of operating circle and limiting circle,the limiting value of active power flow in transmission elements is amended.Under a given operation mode,the crucial element’s monotone of power systems is studied from the simple to the more complex in three situations as following.Firstly,on the basis of DC power flow model,taking the sine nonlinearity into consideration,the monotone relationship between active power flow in transmission elements and injective active power,and the existence of crucial element’s monotone are proven mathematically.And then,an algorithm is proposed to find the monotone interval in which the crucial element’s monotone maintains.Secondly,taking resistance,namely power losses,into consideration,the monotone relationship between active power flow in transmission elements and injective active power,and the existence of crucial element’s monotone continue to maintain.Comparing with the no-loss situation,the monotone interval shifts according to the value of r/x when the loss is considered.Thirdly,the impact of voltage level and reactive power on the crucial element’s monotone is discussed qualitatively.A comparison test with 5-bus system is following,in which the certification about the above three situations is done.