## 1 Introduction  
The modern grid has a large number of controllers in the measurement of electricity that are widespread in different parts of the world, such as generation, transmission, and distribution, for which control and construction often lead to delays in communication [1]. As the system becomes more complicated, new technology phasor measuring units (PMUs) are created to measure dynamic data from the power system, such as voltage, flow, demand angles, frequency, and power factor. Global positioning system (GPS) satellites synchronize all the collected information with PMUs. Signals such as voltage response, speed response, rotor angle, and so on are evaluated and transmitted to the control center. Because the PMUs must send signals to the control center, they depend on various communication infrastructure [2], which introduces time delays. Delays between the moment of measurement and the signal reaching the controller are generally in the nanoseconds to seconds range, depending on location, structures, and various other parameters [3, 4]. The quality of the electricity supplied to a customer is referred to as power quality [5]. In order to maintain the reliability and cost of electrical machinery, it is necessary to maintain and improve the comfortable energy of the machine. In this article, we use a combination of a thyristor switch capacitor (TSC) and a thyristor-controlled reactor (TCR) [6, 7, 8] to make an energy-friendly improvement for a hybrid machine. The total voltage deviation (TVD) at the point of common coupling (PCC) is sent to the TSC and TCR controllers. All of these measurements are collected and delivered via the PMU. This causes a delay and delays the controller input. Previously, several studies on the effects of time on the control mechanism and feeding system have been performed [5; 9; 10; 11; 12]. Furthermore, several studies have been performed with the aim of minimizing the negative impact of delays on system performance [13; 14; 15; 16; 17]. All of these available solutions to mitigate the effects of delays are considered to be ongoing delays, time-varying delays, or random delays [4]. The inter-area oscillations of a multiarea-linked power system could be successfully suppressed under the impact of time-varying delays on a wide-area communication network, according to [PERSON] et al. [18]. Bilinear transforms were used to obtain a discrete-time model of a long-range attenuation controller. [PERSON] et al. proposed a new approach to power control for wireless networks [19]. This approach optimized both the energy efficiency and the latency of the communication together, taking into account the quality of the service constraints associated with the maximum bit error rate or the minimum achievable bit error rate [19]. [PERSON] et al. concentrated on time delays introduced into the control system by hackers to destabilize the system, and a time delay estimator was modified using an indirect supervisor and a modified minimum average. A squared minimization technique that tracked the time delay introduced by an attacker used model reference control [20]. [PERSON] et al. proposed an enhanced time delay compensator (ETDC) approach that managed varying time delays, introducing the perspective of network latency instead of dead time; also, the ETDC took advantage of real signals and measurement transmission procedures in WAMS, building a closed-loop memory control for the power system [21]. The authors of [22] addressed the time delay effect of wide-area monitoring and control systems (WAMCS) in smart power grids, which can have a significant impact on system stability. The main purpose was to perform a detailed WAMCS delay analysis in the event of a network failure. In addition, [23] addressed the issue of delay minimization for wireless sensor network (WSN) relay-based delay minimization routing (DMR) and cooperative delay minimization routing (CoDMR) issues.