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358 CHAPTER 11 Energy Management for PV Installations

Mode 4: The PV power is sufficient (DP ¼ 0 and P pv ¼ P load ), batteries are
completely charging so the disconnection of the batteries is necessary to protect
them.
Mode 5: The produced photovoltaic power (P pv > P load ) is sufficient to supply
the load and batteries are fully charged (SOC ¼ SOC max ), so the excess energy
will be dissipated in a derivate load or in an auxiliary source.
Mode 6: The produced photovoltaic power is insufficient to supply the load
(P pv < P load ) and the batteries are discharged (SOC < SOC min ).
Mode 7: In this case, there is no PV power production (during night or cloudy
day P pv ¼ 0) and batteries are completely discharged, so the load will be discon-
nected (P load ¼ 0).
Mode 8: The produced photovoltaic power (P pv > P load ) is sufficient to supply
the load and batteries are fully charged (SOC ¼ SOC max ), but the load is discon-
nected, so the excess energy will be dissipated in a derivate or dump load.
The different modes depend on the four switches K 1 ,K 2 ,K 3 , and K 4 . Mathemat-
4
ically, it can obtain 16 (2 ¼ 16) cases (Table 11.6). It is noticed that the four first
modes are the same than those in the first structure.
After simplifications, we obtain the Table 11.7.
The eight real modes are given in Table 11.8.

Table 11.6 Mathematically Cases Based on Four Switches of PV/Battery System
Switches Powers
P batt-
Modes
K 1 K 2 K 3 K 4 P pv discharge P batt_charge P aux P load
0 0 0 0 Mode 7 0 0 0 0 0
0 0 0 1 Mode 8 P pv 0 0 0 P pv
0 0 1 0 Mode 3 0 P batt 0 0 P pv
0 0 1 1 X X X X X X
0 1 0 0 Mode 4 P pv 0 0 0 0
0 1 0 1 Mode 5 P pv 0 0 0 P pv
0 1 1 0 Mode 2 P pv P batt 0 0 P pv þ P batt
0 1 1 1 X X X X X X
1 0 0 0 Mode 6 P pv 0 1 0 P pv
1 0 0 1 X X X X X X
1 0 1 0 X X X X X X
1 0 1 1 X X X X X X
1 1 0 0 Mode 1 P pv 0 1 0 P pv
1 1 0 1 X X X X X X
1 1 1 0 X X X X X X
1 1 1 1 X X X X X