Automatic Power Factor Controller Essay

ABSTRACT
In this study, the probabilistic analysis of an automatic power factor controller (APFC) system working in industry or factory is investigated. All the industrial companies face a common problem of power factor correction of electrical loads and energy losses due to poor power factor. Hence, the study of APFC is of great importance. We assume that initially the system is operative with controlled power factor. Then it may move to a state with power factor not controlled. An inspection is carried out on the failure of the system in order to detect the type of failure. Transformer burnt, Fuse blown off, Output relay faulty and programming problem are the four types of failure due to which a system may fail. The components are replaced

The epochs of entry into the states 0,1,2,3,4,5,6,7 are regenerative points and hence these states are called regenerative states. The transition probabilities from regenerative state to regenerative state are given as follows: q_01(t) = η_1 e^(-(λ+ η_1 )t) q_27(t) = p_4i(t) q_02(t) = λe^(-(λ+ η_1 )t) q_32(t) = η_2 e^(-η_2 t) q_10(t) = η_2 e^(-(λ+ η_2 )t) q_40(t) =

q_13(t) = λe^(-(λ+ η_2 )t) q_50(t) = f_2(t) q_24(t) = p_1i(t) q_60(t) = f_3(t) q_25(t) = p_2i(t) q_70(t) = f_4(t) q_26(t) = p_3i(t)
Now by applying Laplace transformation, we get, q_01^* (s) = η_1/(s+λ+η_1 ) q_26^* (s) = L{q_26 (t)} q_02^* (s) = λ/(s+λ+η_1 ) q_27^* (s) = L{q_27 (t)} q_10^* (s) = η_2/(s+λ+η_2 ) q_40^* (s) = L{q_40 (t)} q_13^* (s) = λ/(s+λ+η_2 ) q_50^* (s) = L{q_50 (t)} q_32^* (s) = η_2/(s+η_2 ) q_60^* (s) = L{q_60 (t)} q_24^* (s) = L{q_24(t)} q_70^* (s) = L{q_70 (t)} q_25^* (s) = L{q_25 (t)}
Now, we have
P_ij = lim┬(s→0)⁡〖q_ij^* (s)〗
Therefore,
P_01 = η_1/(λ+η_1 )
P_02 = λ/(λ+η_1 )
P_10 = η_2/(λ+η_2 )
P_13 = λ/(λ+η_2 )
P_32 =