## 1 Introduction  
Proper coordination between the amounts of power generation and demand and losses is essential for better power system performance. This balance may be disrupted during periods of heavy load demand. If this balance is not maintained or observed at the right time, it may lead to huge damage by providing huge aberration in frequency and tie-line power from the base values. These disproportions were subdued by the conception of AGC [1, 2, 3]. [PERSON] et al. [4] provided the basic mathematical formulation of AGC in the case of a two-area thermal system. In the past, works on AGC were mainly confined to a single area system [5, 6, 7]. Later, studies included two-area [8, 9], three-area [9, 10, 11], four-area [12],and five-area [13] systems with the inclusion of non-linearity, such as the generation rate constraint, and also sometimes the governor dead band. Most of the works used thermal as generating units. [PERSON] et al. [14] have performed an analysis for a system having hydrothermal sources. [PERSON] et al. [15] assessed a two-area hydrothermal system. [PERSON] [16] considered the AGC system of varied generating sources, such as thermal power, hydropower and diesel. [PERSON] et al. [17] analyzed a hydropower-dominating system. [PERSON] et al. [18] considered the AGC system of varied generating sources, such as thermal power, hydropower, and gas. Very few papers in the literature [19] reflected on the usage of non-linearity time delay along with other forms of non-linearity. The presence of time delay in a three-area hydrothermal system has not yet been discussed in the literature. Hence, it can be carried out for analysis. Excessive use of one energy source for every purpose rigorously depletes resources. Overall, besides depletion, it also releases toxic gases which are hazardous to the environment. Thus, it is essential to combine conventional and renewable energy sources. The utmost communal forms of readily available inexhaustible bases are solar and wind energy. Numerous articles have described the contribution of solar and wind energy with respect to AGC knowledge, both in a sole arena and with unified arrangements. Moreover, geothermal and biodiesel energy sources have also been researched. Geothermal energy is a kind of thermal energy which is stored in the earth. Consequently, this category of energy can be extracted from the earth's shell. Biodiesel plants employ biodiesel to drive generators. [PERSON] et al. [20] emphasized the practice of geothermal power plants (GPPt) in AGC learning along with conventional sources. [PERSON] et al. [21] analyzed a photovoltaic-incorporated thermal system. Biodiesel is formed from oil that has been pulled out from varied plants, such as sunflower, palm, or soybean. Most commonly, palm oil is used for biodiesel. Biodiesel is a type of renewable fuel. The authors in [22] reported the usage of biodiesel in the case of an isolated scheme. The combination of GPPt and biodiesel plants in AGC knowledge has not yet been replicated in literature. Thus, the hydrothermal system incorporated with GPPt and biodiesel in time delay calls for further extensive assessments. In a unified scheme, the arrangement can be steaded with diminished alteration in glitches with the assistance of numerous energy storage devices (ESD), such as battery energy storage devices (BESDs) [23] and ultra-capactics [24]. There are many types of BESDs, such as lead-acid, lithium-ion, sodium sulfur, metal-air, and redox flow batteries (RFBs). RFB can be employed when there is a need for large storage facilities. Among all these types of BESDs, in light of AGC, RFBs show much potential [25; 26]. It has a lengthier running duration and enables great power capacity. Moreover, it even has guaranteed profits, such as swift slight-interval surplus capability, huge effectiveness, exposure from own-expulsion matters, low-priced, and not being cluttered up by unforeseen charging/discharging.