In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research proposal, frequency oscillations are suppressed by implementing the proportional integral derivative (PID) controller-based control design strategy for an islanded microgrid. The modeling of the islanded microgrid is firstly presented in the form of a linearized transfer function. Further, the derived transfer function is approximated into its equivalent first-order plus dead time (FOPDT) form. The approximated FOPDT transfer function is obtained by employing the reaction curve method to calculate the parameters of the FOPDT transfer function. Furthermore, the desired frequency regulation is achieved for the manifested FOPDT transfer function by incorporating PID control design. For PID controller tuning, different rule-based methods are implemented. Additionally, comparative analysis is also performed to ensure the applicability of the comparatively better rule-based tuning method. The Wang–Chan–Juang (WCJ) method is found effective over other rule-based tuning methods. The efficacy of the WCJ method is proved in terms of transient response and frequency deviation. The tabulated data of tuning parameters, time domain specifications, and error indices along with responses are provided in support of the presented control strategy.

In this research proposal, diminution of higher order (HO) discrete interval system (DIS) is accomplished by utilizing Kharitonov polynomials. The DIS is firstly, transformed into continuous interval system (CIS). The Markov-parameters (MPs) and time-moments (TMs) are exploited for determination of approximated models. The ascertainment of model order diminution (MOD) of DISs is done by Routh-Padé approximation. The Routh table is utilized to obtain the denominator of approximated model. The unknown numerator coefficients of desired approximated model are determined by matching MPs and TMs of DISs and desired model. This whole procedure of MOD is elucidated with the help of one test illustration in which third order system is reduced to first order model as well as second order model. To prove applicability of the proposed method, impulse, step and Bode responses are plotted for both system and model. For relative comparison, time-domain specifications of proposed model are tabulated for both upper and lower limits. Further, performance indices are specified for dissimilarities between responses of system and model. The obtained results depict the effectiveness and efficacy for the proposed method.

In this research work, proportional-integral-derivative (PID) controller design is presented by utilizing reduced order modelling for interval modelled Zeta converter. The optimal values for PID controller are determined using grey wolf optimization (GWO) algorithm with specified gain cross-over frequency ( $\omega_{gc}$ ) and phase margin ( $\phi_{pm}$ ). The reduction of interval modelled higher order (HO) Zeta converter into first order model is done with the help of Routh-Padé approximation and direct truncation method. The denominator of desired reduced order model (ROM) is determined by exploiting Routh-Padé approximation. The direct truncation method is used to obtain the numerator of desired ROM. The step response and Bode diagram are provided in the support of proposed methodology. The time domain specifications and error indices are also presented to prove the effectiveness of proposed method.

The presented research proposal focuses on the approximation of higher-order (HO) multi-input multi-output (MIMO) interconnected power system model (IPSM) by employing systematic approach of proximity index value (PIV) based weight ascertainment method. The approximation of HO MIMO IPSM is accomplished by utilizing expansion parameters of HO MIMO IPSM and its desired lower-order model (LOM). The expansion parameters of HO MIMO IPSM and its LOM are exploited to construct the fitness-function. In the fitness-function weights are assigned to achieve better LOM by improving the steady-state and transient responses with respect to HO MIMO IPSM. The weights of constructed fitness-function are determined with the help of PIV method. Then obtained weighted fitness-function is optimized by satisfying the two prime constraints i.e. matching of steady-state response and preservation of stability of IPSM. To demonstrate the efficacy of the proposed systematic approximation methodology, nineteenth order IPSM is approximated to LOM of second order IPSM. Additionally, specifications of time-domain and error-indices along with responses of the proposed LOM are compared with other LOMs obtained using different approximation approaches, with respect to HO IPSM to depict the effectiveness and applicability of the proposed approach.