Fig.1

Diagram of high-proportional renewable energy micro-grid

Fig.2

Diagram of load frequency control of micro-grid

Fig.3

Open loop step responses of all subsystems in micro-grid

Fig.4

Control structure of PID based on desired dynamic equation

Fig.5

Outputs and control signals versus l with ωd and k remaining unchanged

Fig.6

Outputs and control signals versus k with ωd and l remaining unchanged

Fig.7

Outputs and control signals versus ωd with l and k remaining unchanged

Fig.8

Parameter tuning procedure of the PID based on desired dynamic equation

Fig.9

Distributions of k p , k i , k din PID stability region

Fig.10

Distributions of ω d , k ,   l in PID stability region based on desired dynamic equation

Fig.11

Distributions of k p , k i , k din PID stability region with delay time

Fig.12

Distributions of ω d , k ,   l in PID stability region based on desired dynamic equation with delay time

Fig.13

Tracking performance of water level with step change

Tab.1

Parameters of PID-DDE, PID-O, and PID-OP

Fig.14

Control performance with step changes in solar power, wind power, and consumer load

Tab.2

Control performance index statistics under working Condition 1

Fig.15

Control performance with random fluctuation in solar and wind power and step changes in consumer load

Tab.3

Control performance index statistics under working Condition 2

Fig.16

Control performance with step changes in solar power, wind power, and consumer load

Tab.4

Control performance index statistics under working Condition 3

Fig.17

Monte Carlo experimental results under working Condition 1

Fig.18

Monte Carlo experimental results under working Condition 2

Fig.19

Monte Carlo experimental results under working Condition 3