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3. Energy Management for Photovoltaic Installations 355

Table 11.2 Mathematically Cases Based on Three Switches of PV/Battery
System
Switches Powers
Modes
K 1 K 2 K 3 P pv P batt P load
0 0 0 Mode 5 0 0 0
0 0 1 Mode 3 0 P batt P batt
0 1 0 Mode 4 P pv 0 P pv
0 1 1 Mode 2 P pv P batt P pv þ P batt
1 0 0 X X X X
1 0 1 X X X X
1 1 0 Mode 1 P pv 0 P pv
1 1 1 X X X X

Table 11.3 Simplified Table in the Case of Three Switches (PV/Battery
System)
Switches Powers
Modes
K 1 K 2 K 3 P pv P batt P load
0 0 0 Mode 5 0 0 0
0 0 1 Mode 3 0 P batt P batt
0 1 0 Mode 4 P pv 0 P pv
0 1 1 Mode 2 P pv P batt P pv þ P batt
1 1 0 Mode 1 P pv 0 P pv

Table 11.4 Real Cases Based on Three Switches of PV/Battery System

Modes Sources DP SOC K1 K2 K3 P load
Mode 1 PV 0 SOC < SOC max 1 1 0 P pv
Mode 2 PV þ Battery <0 SOC > SOC min 0 1 1 P pv þ P batt
Mode 3 Battery <0 SOC > SOC min 0 0 1 P batt
Mode 4 PV 0 SOC ¼ SOC max 0 1 0 P pv
Mode 5 / <0 SOC ¼ SOC min 0 0 0 0

These equations can be minimized to:

P pv ¼ðK 2 þ K 1 Þ$P pv (11.8)
(11.9)
P batt ¼ðK 3 þ K 1 Þ$P batt