## Robust frequency control in a hybrid winddiesel power system

3.1 System modeling

The basic system configuration of an isolated hybrid wind-diesel power generation system as shown in Fig. 5 (Das et.al. 1999) is used in this study. The base capacity of the system is 350 kVA. The diesel is used to supply power to system when wind power could not adequately provide power to customer. Moreover, The PPC is installed in the wind side while the governor is equipped with the diesel side. In addition to the random wind energy supply, it is assumed that loads with sudden change have been placed in this isolated system. These result in a serious problem of large frequency deviation in the system. As a result, a serious problem of large frequency deviation may occur in the isolated power system. Such power variations and frequency deviations severely affect the system stability. Furthermore, the life time of machine apparatuses on the load side affected by such large frequency deviations will be reduced.

3.2 Pitch control design in a hybrid wind-diesel power system

3.2.1 Linearized model of hybrid wind-diesel power system with PPC

For mathematical modelling, the transfer function block diagram of a hybrid wind-diesel power generation used in this study is shown in Fig. 6 (Das et.al. 1999). The PPC is a 1st order lead-lag controller with single input feedback of frequency deviation of wind side. The state equation of linearized model in Fig. 6 can be expressed as

Where the state vector AX = [AfW AfD APD1 APD AH1 AH2 APm ], the output vector AY = [AfW], AUPPC is the control output of the PPC. The proposed control is applied to design a proposed PPC K(s). The system in equation (6) is referred to as the nominal plant G.

3.2.2 Optimization problem formulation

The optimization problem can be formulated as follows,

mm _ max where Z and Zspec are the actual and desired damping ratio of the dominant mode, respectively; a and aspec are the actual and desired real part, respectively; Kmax and Kmin are the maximum and minimum controller gains, respectively; Tmax and Tmin are the maximum and minimum time constants, respectively. This optimization problem is solved by GA to search optimal or near optimal set of the controller parameters.

### 3.2.3 Designed results

In this section, simulation studies in a hybrid wind-diesel power generation are carried out. System parameters are given in (Das et.al. 1999). In the optimization, the ranges of search parameters and GA parameters are set as follows: KC e [1 100], T1 and T2 e [0.0001 1], crossover probability is 0.9, mutation probability is 0.05, population size is 200 and maximum generation is 100. As a result, "the proposed PPC" is given automatically. In simulation studies, the performance and robustness of the proposed PPC is compared with those of the PPC designed by the variable structure control (VSC) obtained from (Das et.al. 1999). Simulation results under four case studies are carried out as shown in table 1.

Cases |
Disturbances |

1 |
Step input of wind power or load change |

2 |
Random wind power input |

3 |
Random load power input |

4 |
Simultaneous random wind power and load change. |

Table 1. Operating conditions

Table 1. Operating conditions

Case 1: Step input of wind power or load change

First, a 0.01 pukW step increase in the wind power input and the load power are applied to the system at t = 5.0 s, respectively. Fig. 7 and Fig. 8 show the frequency deviation of the diesel generation side which represents the system frequency deviation. The peak frequency deviation is reduced significantly by both of the VSC PPC and the proposed PPC. However, the proposed PPC is able to damp the peak frequency deviation quickly in comparison to VSC PPC cases.

x 10"

x 10"

M |
-Proposed PPC | ||||||||||||||||||||||||||||||||||||||||||||

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1 | ||||||||||||||||||||||||||||||||||||||||||||

# # # | |||||||||||||||||||||||||||||||||||||||||||||

V, |
/ |
Time (sec) Fig. 7. System frequency deviation against a step change of wind power. x 10
## Renewable Energy Eco FriendlyRenewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. |

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