Cascade controller based modeling of a four area thermal: gas AGC system with dependency of wind turbine generator and PEVs under restructured environment

Abstract

This paper investigates automatic generation control (AGC) of a realistic hybrid four-control area system with a distinct arrangement of thermal units, gas units and additional power generation. A proportional-integral-double derivative cascaded with proportional-integral (PIDD-PI) controller is employed as secondary controller in each control area for robust restructured AGC considering bilateral transactions and contract violations. The Harris Hawks algorithm is used to determine the optimal controller gains and system parameters under several scenarios. Electric vehicle (EV) aggregators are employed in each area to participate fully along with thermal and gas units to compensate for the unscheduled system demand in the local area. A comparison of non-cascaded controllers such as PI-PD, PD-PID and the proposed PIDD-PI proves the superiority of the last. The effect of the decline in inertia is closely examined because of the sudden outage of a generating unit while at the same time considering the change in area frequency response characteristics and area control error. EV fleets make significant contributions to improving the system dynamics during system inertia loss. The use of EVs in the presence of a wind energy-supported grid can provide a stable efficacy to the power grid. Numerous simulations with higher load demands, stochastic communication delays in presence of the WTG plant, and violations in system loadings and changes in gas turbine time constants in the absence of WTG demonstrate the robustness of the proposed control approach.

1 Introduction

A properly designed power system can deal with sudden load changes and system frequency fluctuations. It should be able to regulate system voltage and frequency within prescribed operating limits to offer satisfactory power quality [1]. However, deviations from the normal operating condition can occur because of load change and this can result in frequency and tie-power deviations from scheduled standard deviations that may be undesirable [2]. Presently, the power industry maintains vertically integrated utility (VIU) structure which constitutes generation (GENCO), transmission (TRANSCO) and distribution (DISCO) companies. One VIU always maintains the transmission voltage level when interconnected to other VIUs [3]. In the AGC regime, every particular service unit operates in its regulated region and can identify its area control error by adopting the tie-line bias control concept [4]. The open Market Scenario is a collective effort of well-designed market policies and economic benefits which leads to good quality of service. The independent entities of GENCOs, TRANSCOs, and DISCOs play a discrete function in the AGC sphere and, need to be modeled differently [5].

Many researchers have contributed toward designing a multi-area AGC model in the restructured regime. Rahman et al. [6] maintained the frequency change in a grid-associated multi-control area power system comprising hydro and thermal units under an open market scenario. AGC operation of a multi-area multi-unit thermal system is characterized by cost-based analysis which is subjected to various changes in load and contingencies [7]. Also, Shiva and Mukherjee [8] extended the restructured AGC study to five area systems which comprise conventional units with realistic constraints consideration like generation limiting (GRC), governor dead zone (GDB) and signal delay. Morsali et al. [9] designed a thyristor-controlled series capacitor to damp out the oscillations in a conventional system with GRC, GDB and delay.

Climate change, energy reliability and security needs, and environmental pollution have promoted the need for more penetration of renewable energy [10]. There has been a growing popularity of wind generation although wind generations, intermittent and hence no fixed generation can be ensured. Thus conventional plants have to provide the additional reserve for the undispatchable wind generation [11,12,13]. Also, there has to be a limit on the integration of renewable sources in the grid because of supply-generation mismatch, voltage swings and frequent instability of the grid [14, 15]. With wind power integration, the overall inertia of the system decreases because of intermittency and an increase in the regulation constant [16]. An investigation was carried out at Great Britain's electricity network to analyze the challenges of governor control with a developed stochastic modeling tool [17] while here might be compromise of the frequency regulation of the power system with high wind energy integration [18].

The presence of controllable loads or distributed energy resources such as electric vehicles can offer frequency support thereby increasing the inertia of a renewable integrated energy system. This notion has established a concept of plug-in transportation such as plug-in electric-powered vehicles or hybrid vehicles whose reliance is on fossil fuels and be able to interface to the grid for charging and discharging [19]. Debbarma and Dutta [20] introduced electric vehicles integrated with other traditional sources such as hydro, thermal, and gas turbine units in LFC studies under an open market scenario while [21] introduced a new participation factor to implement the extent of participation of plug in vehicles for primary control to improve the frequency characteristics. Similar strategies with V2G have been designed for secondary control of integrated power networks [22]. A smart charging method for electric vehicles based on the V2G strategy is proposed for secondary frequency control to remove the unbalance between demand and generation [23]. Singh et al. [24] showed V2G feasibilities in modelling a characteristic distribution network of a metropolitan area to meet maximum demand along with decreased voltage sag. Nguyen et al. [16] integrated the concept of Certainty Equivalent and Adaptive Control and an agenda to be participated by the customer for coordinating both the charging and discharging of EVs.

Most of the literature on AGC is mainly focused on the design of non-cascade controllers such as integral [23], proportional-integral-derivative [7, 13], three-degree-of-freedom proportional-integral-derivative [6], and fractional-order proportional-integral-derivative [20]. These controllers have been successfully used as secondary controllers in conventional systems with two [16], three [7] and five areas [8]. Johnson Michael and Moradi Mohammad [25] used a tuned PID controller for non-linear cascade control systems, while [26] analyzed process control data collected from one shot industry using two PID controllers. In non-cascade controllers, the number of fine-tuning knobs is fewer than those in cascade controllers. The presence of more tuning knobs in the controller can be advantageous for obtaining better results. Dash et al. [27] explored the performance of PI-PD and PD-PID [28] controllers in four and three area thermal systems respectively by subjecting the system to various disturbances and uncertainties. However, the feasibility and performance of the cascade controller have not been evaluated in multi-area open market AGC systems consisting of electric vehicles and wind generation. Thus, the application of cascade controllers in restructured AGC needs to be studied.

The main difficulty concerned with any sort of controller is the selection of the optimal parameters that reduce the changes and ensure zero area control error (ACE). With the advent of computation, optimizing multiple data is no longer a problem. Most research is now carried out with a touch of optimization algorithms [6,7,8]. The reason for this is that the entire research problem in reality is highly non-linear, and it is necessary to find the optimum solution. Several minimizations or maximization algorithms such as novel genetic algorithm, powerful particle swarm optimization [9], biogeography based optimization [7], quasi oppositional harmony search [9], have been successfully applied in two-area, three area restructured multi-area multi-source systems for tuning gains of 3DOF-PID [6] FOPID [20] controllers. A meta-heuristic algorithm based on a group of hawks trying to chase its targeted rabbit with its features of predator birds for tracing, encircling, flushing out and capturing the potential animal (rabbit) is known as the Harris Hawks Algorithm [29]. In the algorithm, the leader of the hawks attacks the prey. If it is not successful because of the dynamic nature and fast escape of the prey switching strategies are followed by other hawks in the group to hit the escaped prey until seized. The flowchart and steps can be found in [30, 31]. With puzzling and exhausting of the escaped prey, birds can find the targeted rabbit. This is a promising advantage of the combined strategy. Thus, the Harris Hawk Optimization (HHO) maintains the balance in the exploratory and exploitative phases.

The objectives of this paper are as follows:

• 1. To develop a four area hybrid AGC model of a realistic power system with six GENCOs and six DISCOS having thermal and gas generating units integrated with wind turbine generation (WTG) in all control areas.

• 2. To compare the performance of PID, PI-PD, PD-PID and PIDD-PI controllers as secondary controllers during bilateral transactions and determine the best.

• 3. To facilitate the test system with EV aggregators and evaluate the effect of discharged EV aggregators in meeting uncontracted load demand using HHO optimized best controller obtained in (2).

• 4. To demonstrate the effect of a decline in inertia for the system considered in (3) due to sudden outage of a generating unit in an area considering the change in area frequency response characteristics and area control error. To investigate the significance of EV aggregators for the above scenario.

2 Power system framework

Figure 1 shows the representation diagram of four-area multi-unit grid-connected systems in an open market environment. Each of Area 1 and 4 are employed with two thermal units while one gas unit is provided in Areas 2 and 3 respectively. Each control area is employed with WTG as additional generations. To get a realistic approach to the network, thermal generations are operational with suitable GRC and GDB of 3%/min and 0.06% respectively. The incremental power generation from WTG is fed to all control areas to maintain the power balance automatically. Also, the gas units are equipped with GRC of 20%/min. Six GENCOs and DISCOs are considered for investigation. Control Area 1 has two GENCOs and two DISCOs. Areas 2 and 3 have one GENCO and one DISCO each, and Area 4 has two GENCOs and two DISCOs. Aggregators in each control area collect EVs’ information and fetch them to the control dispatch center. The capacity ratio of Area 1, 2, 3 and 4 are considered as 1:2:2:4.

Fig.1

Schematic representation and system layout of the four- area hybrid system under restructured environment. a Schematic diagram of the four-area AGC model. b Description of DISCO participation matrix for the four-area AGC model in restructured environment. c Transfer function model and layout of Area 1 of the hybrid system under restructured environment (incorporating EV and WTG). d Transfer function model of the four area system under Restructured environment (without EV and WTG)

2.1 Designing aspects of four area restructured system model

In a restructured environment, a DISCO participation matrix (DPM) provides information on the type of transaction i.e. the liberty of a GENCO in its area or other areas to agree with DISCOs in its area or other areas too [8, 32, 33]. Thirty-six contract participation factor elements in DPM exist with six GENCOs and DISCOs in total.

$${\text{DPM}} = \left[ {\begin{array}{*{20}c} {{\text{cpf}}_{{{11}}} } & {{\text{cpf}}_{{{12}}} } & {{\text{cpf}}_{{{13}}} } & {{\text{cpf}}_{{{14}}} } & {{\text{cpf}}_{{{15}}} } & {{\text{cpf}}_{{{16}}} } \\ {{\text{cpf}}_{{{21}}} } & {{\text{cpf}}_{{{22}}} } & {{\text{cpf}}_{{{23}}} } & {{\text{cpf}}_{{{24}}} } & {{\text{cpf}}_{{{25}}} } & {{\text{cpf}}_{{{26}}} } \\ {{\text{cpf}}_{{{31}}} } & {{\text{cpf}}_{{{32}}} } & {{\text{cpf}}_{{{33}}} } & {{\text{cpf}}_{{{34}}} } & {{\text{cpf}}_{{{35}}} } & {{\text{cpf}}_{{{36}}} } \\ {{\text{cpf}}_{{{41}}} } & {{\text{cpf}}_{{{42}}} } & {{\text{cpf}}_{{{43}}} } & {{\text{cpf}}_{{{44}}} } & {{\text{cpf}}_{{{45}}} } & {{\text{cpf}}_{{{46}}} } \\ {{\text{cpf}}_{{{51}}} } & {{\text{cpf}}_{{{52}}} } & {{\text{cpf}}_{{{53}}} } & {{\text{cpf}}_{{{54}}} } & {{\text{cpf}}_{{{55}}} } & {{\text{cpf}}_{{{56}}} } \\ {{\text{cpf}}_{{{61}}} } & {{\text{cpf}}_{{{62}}} } & {{\text{cpf}}_{{{63}}} } & {{\text{cpf}}_{{{64}}} } & {{\text{cpf}}_{{{65}}} } & {{\text{cpf}}_{{{66}}} } \\ \end{array} } \right]$$

(1)

$$\Delta {\text{P}}_{{{\text{tie13}}}} = \, \left( {{\text{Power}}\,{\text{ import}}\,{\text{ from}}\,{\text{ Area}}\,{ 3}} \right) \, - \, \left( {{\text{Power }}\,{\text{export }}\,{\text{to }}\,{\text{Area 1}}} \right) \, = \, \left( {{\text{cpf}}_{{{41}}} + {\text{ cpf}}_{{{42}}} } \right) \, - \, \left( {{\text{cpf}}_{{{14}}} + {\text{ cpf}}_{{{24}}} } \right).$$

(2)

$$\Delta {\text{P}}_{{{\text{tie23}}}} = \, \left( {{\text{Power}}\,{\text{ import }}\,{\text{from}}\,{\text{ Area}}\,{ 3}} \right) \, - \, \left( {{\text{Power}}\,{\text{ export}}\,{\text{ to}}\,{\text{ Area}}\,{ 2}} \right) \, = \, \left( {{\text{cpf}}_{{{34}}} - {\text{ cpf}}_{{{43}}} } \right).$$

(3)

$$\Delta {\text{P}}_{{{\text{tie34}}}} = \, \left( {{\text{Power}}\,{\text{ import}}\,{\text{ from }}\,{\text{Area}}\,{ 4}} \right) \, - \, \left( {{\text{Power}}\,{\text{ export }}\,{\text{to }}\,{\text{Area}}\,{ 3}} \right) \, = \, \left( {{\text{cpf}}_{{{54}}} + {\text{ cpf}}_{{{64}}} } \right) \, - \, \left( {{\text{cpf}}_{{{45}}} + {\text{ cpf}}_{{{46}}} } \right).$$

(4)

$$\Delta {\text{P}}_{{{\text{tie34}}}} = \, \left( {{\text{Power}}\,{\text{ import}}\,{\text{ from }}\,{\text{Area}}\,{ 4}} \right) \, - \, \left( {{\text{Power}}\,{\text{ export}}\,{\text{ to}}\,{\text{ Area}}\,{ 3}} \right) \, = \, \left( {{\text{cpf}}_{{{54}}} + {\text{ cpf}}_{{{64}}} } \right) \, - \, \left( {{\text{cpf}}_{{{45}}} + {\text{ cpf}}_{{{46}}} } \right).$$

(5)

$$\Delta {\text{P}}_{{{\text{tie24}}}} = \, \left( {{\text{Power}}\,{\text{ import}}\,{\text{ from }}\,{\text{Area}}\,{ 4}} \right) \, - \, \left( {{\text{Power}}\,{\text{ export}}\,{\text{ to }}\,{\text{Area}}\,{ 2}} \right) \, = \, \left( {{\text{cpf}}_{{{53}}} + {\text{ cpf}}_{{{63}}} } \right) \, - \, \left( {{\text{cpf}}_{{{35}}} + {\text{ cpf}}_{{{36}}} } \right).$$

(6)

It can be observed from Fig. 1 that the exchanges of power among the control areas are given by Exch_1, Exch_2, Exch_3 and Exch_4 respectively. The tie-power flow exchanges among the control areas in terms of contracted power demand can be calculated as follows:

$${\text{Exch}}\_{1 } = \, \left[ {\left( {{\text{Demand }}\,{\text{in }}\,{\text{DISCOs }}\,{\text{in}}\,{\text{ Area}}\,{ 2}\,{\text{ from }}\,{\text{GENCOS }}\,{\text{in }}\,{\text{Area}}\,{ 1}} \right) \, - \, \left( {{\text{Demand }}\,{\text{in }}\,{\text{DISCOs }}\,{\text{in }}\,{\text{Area}}\,{ 1}\,{\text{ from }}\,{\text{GENCOS}}\,{\text{ in}}\,{\text{ Area}}\,{ 2}} \right)} \right] \, \times \, \Delta {\text{P}}_{{{\text{L1}}}} + \, \left[ {\left( {{\text{Demand}}\,{\text{ in }}\,{\text{DISCOs }}\,{\text{in}}\,{\text{ Area}}\,{ 3}\,{\text{ from}}\,{\text{ GENCOS}}\,{\text{ in}}\,{\text{ Area }}\,{1}} \right) \, - \, \left( {{\text{Demand }}\,{\text{in}}\,{\text{ DISCOs}}\,{\text{ in }}\,{\text{Area }}\,{3 }\,{\text{from}}\,{\text{ GENCOS }}\,{\text{in }}\,{\text{Area}}\,{ 1}} \right)} \right] \times \, \Delta {\text{P}}_{{{\text{L1}}}} + \, \left[ {\left( {{\text{Demand}}\,{\text{ in }}\,{\text{DISCOs }}\,{\text{in}}\,{\text{ Area}}\,{ 4 }\,{\text{from }}\,{\text{GENCOS }}\,{\text{in }}\,{\text{Area }}\,{1}} \right) \, - \left( {{\text{Demand}}\,{\text{ in }}\,{\text{DISCOs}}\,{\text{ in }}\,{\text{Area}}\,{ 1 }\,{\text{from}}\,{\text{ GENCOS}}\,{\text{ in }}\,{\text{Area}}\,{ 4}} \right)} \right] \, \times \, \Delta {\text{P}}_{{{\text{L1}}}} = \, \Delta {\text{P}}_{{{\text{tie12}}}} + \, \Delta {\text{P}}_{{{\text{tie13}}}} + \, \Delta {\text{P}}_{{{\text{tie14}}}} .$$

(7)

$${\text{Exch}}\_{2 } = \, \left[ {\left( {{\text{Demand}}\,{\text{ in }}\,{\text{DISCOs}}\,{\text{ in}}\,{\text{ Area}}\,{ 2}\,{\text{ from}}\,{\text{ GENCOS}}\,{\text{ in }}\,{\text{Area}}\,{ 1}} \right) \, - \, \left( {{\text{Demand}}\,{\text{ in}}\,{\text{ DISCOs }}\,{\text{in }}\,{\text{Area}}\,{ 1 }\,{\text{from }}\,{\text{GENCOS}}\,{\text{ in }}\,{\text{Area}}\,{ 2}} \right)} \right] \, \times \, \Delta {\text{P}}_{{{\text{L2}}}} = \, \Delta {\text{P}}_{{{\text{tie23}}}} .$$

(8)

$${\text{Exch}}\_{3 } = \, \left[ {\left( {{\text{Demand}}\,{\text{ in}}\,{\text{ DISCOs }}\,{\text{in}}\,{\text{ Area}}\,{ 2}\,{\text{ from}}\,{\text{ GENCOS}}\,{\text{ in}}\,{\text{ Area}}\,{ 1}} \right) \, - \, \left( {{\text{Demand }}\,{\text{in}}\,{\text{ DISCOs }}\,{\text{in }}\,{\text{Area }}\,{1 }\,{\text{from }}\,{\text{GENCOS }}\,{\text{in}}\,{\text{ Area}}\,{ 2}} \right)} \right] \, \times \, \Delta {\text{P}}_{{{\text{L3}}}} = \, \Delta {\text{P}}_{{{\text{tie34}}}} .$$

(9)

$${\text{Exch}}\_{4 } = \, \left[ {\left( {{\text{Demand}}\,{\text{ in}}\,{\text{ DISCOs}}\,{\text{ in}}\,{\text{ Area}}\,{ 2}\,{\text{ from}}\,{\text{ GENCOS }}\,{\text{in}}\,{\text{ Area}}\,{ 1}} \right) \, - \, \left( {{\text{Demand }}\,{\text{in}}\,{\text{ DISCOs }}\,{\text{in }}\,{\text{Area }}\,{1 }\,{\text{from }}\,{\text{GENCOS }}\,{\text{in}}\,{\text{ Area}}\,{ 2}} \right)} \right] \, \times \, \Delta {\text{P}}_{{{\text{L4}}}} = \, \Delta {\text{P}}_{{{\text{tie24}}}} .$$

(10)

The scheduled tie line power expression can be given as:

∆P_{tie, i−j (scheduled)} = [Power supplied from GENCOs of ith area to DISCOs of jth area] − [Power supplied from GENCOs of jth area to DISCOs of ith area].

The tie-line error can be depicted by:

$$\Delta {\text{P}}_{{{\text{tie}},{\text{ i }}{-}{\text{ j }}({\text{error}})}} = \, \Delta {\text{P}}_{{{\text{tie}},{\text{ i }}{-}{\text{ j }}({\text{actual}})}} + \, \Delta {\text{P}}_{{{\text{tie}},{\text{ i }}{-}{\text{ j }}({\text{scheduled}})}} .$$

(11)

2.2 Wind generator turbine

The electric power generation from WTG depends on wind velocity (V_W) which is comprised of base wind velocity (V_WB), wind gust velocity (V_WG), ramp wind velocity (V_R) and noise wind velocity (V_WN) as [21]:-

$${\text{V}}_{{\text{W}}} = {\text{V}}_{{{\text{WB}}}} + {\text{V}}_{{{\text{WG}}}} + {\text{V}}_{{{\text{WR}}}} + {\text{V}}_{{\text{N}}}$$

(12)

The mechanical power output of WTG is given by:

$${\text{P}}_{{\text{w}}} = \left( {\frac{{1}}{{2}}} \right){\rho C}_{{\text{p}}} {\text{A}}_{{\text{r}}} {\text{v}}_{{\upomega }}^{{3}}$$

(13)

where ρ (= 1.25 kg/m³), C_p, A_r (= 1735 m²) and v_w are the air-density, co-efficient of power, blade swept area and available wind speed respectively. It is a well known fact that the total system inertia decreases when there exists more intermittent source integration. The equivalent regulation constant increases thereby reducing the area frequency response characteristics [16]. Assuming R_W to be the amount of wind power participation in the grid [14], R_R is the amount of remaining conventional generation fed to the grid, and the modified inertia constant of the system can be expressed as:

$${\text{H}}_{{\text{new,i}}} = {\text{H}}_{{\text{old, i}}} \left[ {{1} + {\text{(R}}_{{\text{W}}} - {\text{R}}_{{\text{R}}} {)}} \right]$$

(14)

The modified equivalent speed regulation constant is:

$${\text{R}}_{{\text{new,i}}} = \frac{{{\text{R}}_{{\text{old,i}}} }}{{\left[ {{1} + \left( {{\text{R}}_{{\text{W}}} - {\text{R}}_{{\text{R}}} } \right)} \right]}}$$

(15)

The modified AFRC is expressed as follows:

$${\upbeta }_{{\text{new,i}}} = {\text{B}}_{{\text{new,i}}} = \frac{{1}}{{{\text{R}}_{{\text{old,i}}} }}\left[ {{1} + \left( {{\text{R}}_{{\text{W}}} - {\text{R}}_{{\text{R}}} } \right)} \right] + {\text{D}}_{{\text{i}}}$$

(16)

Changes in R_i and β_i result in a new area control error given by:

$${\text{ACE}}_{{\text{new,i}}} = {\Delta P}_{{\text{tie,i}}} + {\upbeta }_{{\text{new,i}}} {\Delta F}_{{\text{i}}} .$$

2.3 EV aggregators

EV batteries connected to the power system with battery chargers regulating the power between the DC and AC are constituent of EV aggregators. A dead band function along with droop control R is present with upper and lower bounds as primary governor control. R depends on the charge of the system (known as the state of charge) and is introduced in the system with a participation factor [34]. During the peak hours, EV gets charged from the grid while EV gets discharged during off-peak hours [23, 24]. The range of charge–discharge for the EV is considered as ± 5 kW but it is allowed to charge to 50 kW or even more with rapid charging. EV participates to reduce the area control error for secondary control of frequency.

The SOC needs to be more than 20% if the PEV battery in charging mode is introduced to primary control (Fig. 2). For SOC below 45% or above 70%, K_EVi lies between 0 < K_EVi < 1 and K_EVi = 1 between 45 and 70%. The highest and lowest amount of EV fleets’ power capacity is given by ${\Delta P}_{{{\text{AG}}}}^{{{\text{max}}}}$ and ${\Delta P}_{{{\text{AG}}}}^{{{\text{min}}}}$ as:

$${\Delta P}_{{{\text{AG}}}}^{{{\text{max}}}} = + \left[ {\frac{{1}}{{{\text{N}}_{{{\text{EVi}}}} }} \times {\Delta P}_{{{\text{EVi}}}} } \right]$$

(17)

$${\Delta P}_{{{\text{AG}}}}^{{{\text{min}}}} = - \left[ {\frac{{1}}{{{\text{N}}_{{{\text{EVi}}}} }} \times {\Delta P}_{{{\text{EVi}}}} } \right].$$

(18)

Fig. 2

Gain K_EVi versus state of charge (SOC)

2.4 Design and tuning of PIDD-PI controller

The basis behind cascade controller configuration (Fig. 1c) is that the model controlled inner loop overcomes the integral anti-windup that may saturate the inner control loop. This may result in a track mismatch of the outer loop with inner loop controllers as the output of G2 is directly fed into G1. The main functions of cascade control are: (a) in presence of external or internal disturbance, whether the inner control has any effect on the outer control and (b) outer process to ensure the output process quality. The external loop equation relating the process output Y(s), outer process, and load disturbance D(s) is given as [27, 28].

$${\text{Y}}_{{1}} \left( {\text{s}} \right) \, = {\text{ G}}_{{1}} \left( {\text{s}} \right) \, \times {\text{ X}}_{{1}} \left( {\text{s}} \right) \, + {\text{ D}}\left( {\text{s}} \right)$$

(19)

The inner control is given as:

$${\text{Y}}_{{2}} \left( {\text{s}} \right) \, = {\text{ G}}_{{2}} \left( {\text{s}} \right) \, \times {\text{ X}}_{{2}} \left( {\text{s}} \right)$$

(20)

In this paper, PIDD forms the constituent of single-loop control followed by a PI controller in cascade (Fig. 1c). Reference track and disturbance rejection are carried out with the responses. Two controllers X1(s) and X2(s) are named as the outer and the inner controllers respectively. There are chances of further disturbances due to the additional derivative parameter caused by continuous fluctuation in load demand. Thus a filter is added to minimize the undesirable effect of high-frequency noise. Here, the PI controller is made as the inner and PIDD as the outer controllers.

$${\text{X}}_{{1}} {\text{(s)}} = {\text{K}}_{{\text{P}}} + \frac{{{\text{K}}_{{\text{I}}} }}{{\text{s}}} + \frac{{{\text{Ns}}^{{2}} }}{{{\text{(N}} + {\text{s)}}}}{\text{K}}_{{\text{D}}}$$

(21)

$${\text{X}}_{{2}} {\text{(s)}} = {\text{K}}_{{{\text{PP}}}} + \frac{{{\text{K}}_{{{\text{II}}}} }}{{\text{s}}}$$

(22)

$${\text{Y(s)}} = \left[ {\frac{{{\text{G}}_{{1}} {\text{(s)G}}_{{2}} {\text{(s)C}}_{{1}} {\text{(s)}}}}{{{1} + {\text{G}}_{{2}} {\text{(s)C}}_{{2}} {\text{(s)}} + {\text{G}}_{{1}} {\text{(s)G}}_{{2}} {\text{(s)C}}_{{1}} {\text{(s)C}}_{{2}} {\text{(s)}}}}} \right]{\text{R(s)}} - \left[ {\frac{{{\text{G}}_{{1}} {\text{(s)}}}}{{{1} + {\text{G}}_{{2}} {\text{(s)C}}_{{2}} {\text{(s)}} + {\text{G}}_{{1}} {\text{(s)G}}_{{2}} {\text{(s)C}}_{{1}} {\text{(s)C}}_{{2}} {\text{(s)}}}}} \right]{\text{D(s)}}$$

(23)

G₁(s) and G₂(s) are the primary and secondary control loops respectively, while D(s) is the load disturbance. For simultaneous tuning of controller parameters of PIDD-PI controller, a recently introduced algorithm named “Harris Hawks Optimization” (HHO) is used. The formulation of the above constrained optimization problem is as follows:

$${\text{J}}_{{{\text{ITAE}}}} = \int\limits_{{0}}^{{\text{t}}} {\left\{ {\left( {{\Delta F}_{{\text{i}}} } \right) + \left( {{\Delta P}_{{\text{tie i - j}}} } \right)} \right\}} {\text{.tdt}}$$

(24)

Minimize the objective function J_ACE such that:

$${\text{K}}_{{{\text{Pi}}}}^{{{\text{min}}}} \le {\text{K}}_{{{\text{Pi}}}} \le {\text{K}}_{{{\text{Pi}}}}^{{{\text{max}}}} ;\quad {\text{K}}_{{{\text{PPi}}}}^{{{\text{min}}}} \le {\text{K}}_{{{\text{PPi}}}} \le {\text{K}}_{{{\text{PPi}}}}^{{{\text{max}}}}$$

$${\text{K}}_{{{\text{Ii}}}}^{{{\text{min}}}} \le {\text{K}}_{{{\text{Ii}}}} \le {\text{K}}_{{{\text{Ii}}}}^{{{\text{max}}}} ;\quad {\text{K}}_{{{\text{IIi}}}}^{{{\text{min}}}} \le {\text{K}}_{{{\text{IIi}}}} \le {\text{K}}_{{{\text{IIi}}}}^{{{\text{max}}}}$$

$${\text{K}}_{{{\text{Di}}}}^{{{\text{min}}}} \le {\text{K}}_{{{\text{Di}}}} \le {\text{K}}_{{{\text{Di}}}}^{{{\text{max}}}} ;\quad {\text{N}}_{{\text{i}}}^{{{\text{min}}}} \le {\text{N}}_{{\text{i}}} \le {\text{N}}_{{\text{i}}}^{{{\text{max}}}}$$

where ${\text{K}}_{{{\text{Pi}}}}^{{{\text{max}}}}$, ${\text{K}}_{{{\text{Pi}}}}^{{{\text{min}}}}$, ${\text{K}}_{{{\text{Ii}}}}^{{{\text{max}}}}$, ${\text{K}}_{{{\text{Ii}}}}^{{{\text{min}}}}$, ${\text{K}}_{{{\text{PPi}}}}^{{{\text{max}}}}$, ${\text{K}}_{{{\text{PPi}}}}^{{{\text{min}}}}$, ${\text{K}}_{{{\text{IIi}}}}^{{{\text{max}}}}$, ${\text{K}}_{{{\text{IIi}}}}^{{{\text{min}}}}$, ${\text{N}}_{{\text{i}}}^{{{\text{max}}}}$, and ${\text{N}}_{{\text{i}}}^{{{\text{min}}}}$ represent the maximum and minimum values of controller parameters, respectively. The HHO algorithm is employed to evaluate the optimum controller gains and other parameters of the proposed cascade controller in which the candidates/populations are the Harris Hawks and the optimal global solution is the intended prey that tends to escape from time to time. The HHO technique’s tuned parameters are taken with 50 search agents, and maximum number of iteration of 50. The tuned parameters are fixed by minimising the cost function over 40 trials.

3 Results and analysis

The proposed hybrid system is executed for the bilateral transaction, contract violation, outage of a generating unit and thereby decline in inertia, and robustness analysis with: (1) higher load demand (2) communication delays; (3) system loading and (4) change in time constants of the gas generating unit.

3.1 Bilateral transactions

First, a DPM is chosen to explain the case of bilateral transactions, where any GENCOs of any area can contract with any DISCOs in any area. Active power of 0.01 p.u is contracted between each DISCO and GENCO. Considering the above DPM, GENCOs in Area 1, 2, 3 and 4 should generate active power of 0.02 p.u., 0.01 p.u., 0.01 p.u. and 0.02 p.u. respectively.

$${\text{DPM}}_{{\text{A}}} = \left[ {\begin{array}{*{20}c} {{0}{\text{.2}}} & {{0}{\text{.1}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.1}}} \\ {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.1}}} & {{0}{\text{.1}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} \\ {{0}{\text{.1}}} & {{0}{\text{.2}}} & {{0}{\text{.1}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} \\ {{0}{\text{.2}}} & {{0}{\text{.1}}} & {{0}{\text{.2}}} & {{0}{\text{.1}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} \\ {{0}{\text{.1}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.1}}} & {{0}{\text{.2}}} \\ {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.2}}} & {{0}{\text{.1}}} & {{0}{\text{.1}}} \\ \end{array} } \right]$$

(25)

Again, WTG is employed in each control area, and provide active power output of 0.002 p.u. from 50–100 s and 0.0005 p.u.from 100–200 s to the grid as shown in Fig. 3d.

Fig. 3

Comparison of performance of PID, PI-PD, PD-PID and PIDD-PI during bilateral transactions. a Frequency deviation in Area 1. b Tie-power deviation in the line connecting Area 1 and 4. c Tie-power deviation in the line connecting Area 3 and 4. d Power generation in thermal plant and WTG unit in Area 1

Thus, the remaining power after considering power output from WTG, i.e. (0.02–0.002 = 0.018 p.u), (0.01–0.002 = 0.008 p.u.), (0.01–0.002 = 0.008 p.u.) and (0.02–0.002 = 0.018 p.u) accordingly should be generated by the GENCOs in each area, respectively. Using DPM, ∆P_tie1-2 = (0.2 + 0.1) − (0.1 + 0.2) = 0 p.u. Similarly, the schedule tie line power between Area 1 and 2 is: ∆P_tie1-2 = ∆P_tie1-2 = ∆P_tie1-2 = ∆P_tie1-2 = ∆P_tie1-2 = 0 p.u.

The system is equipped with a non-cascade controller such as PID and a cascade controller such as PI-PD, PD-PID and PIDD-PI. These controllers are used as secondary controllers and parameters are optimized using the HHO technique. The optimized parameters for the aforesaid controllers are shown in Table 1.The cost function J_ITAE for PID, PI-PD, PD-PID and PIDD-PI controllers are noted as 0.0718, 0.0674, 0.0370 and 0.0214, respectively. The system dynamic responses corresponding to optimum parameters of each controller are obtained and are shown in Fig. 3.

Table 1 Optimum parameters for PID, PD-PID, PI-PD and PIDD-PI controller under bilateral transactions

From the J_ITAE values and Fig. 3, the dominance of PIDD-PI over PID, PI-PD and PD-PID controller can be easily inferred for the proposed hybrid system. Figure 3d shows the change in ∆P_g(WTS) due to the change in V_w. Furthermore, the system responses of electricity generations from thermal (∆P_g11, ∆P_g12, ∆P_g41, ∆P_g42) and gas generators (∆Pg₂, ∆Pg₃) of the respective areas are evident of being regulated (only power generation in Area 1 is shown). The significant improvement of PIDD-PI controller over PID, PI-PD and PD-PID are tabulated in Table 2 and Fig. 3a–c. The settling time and peak undershoot in case of PIDD—PI controller is seen to outperform others, whereas the peak overshoot is either equal or similar with the others. Thus, it can be inferred that PIDD—PI controller is superior in terms of less time to settle and lower maximum undershoot with almost similar peak overshoot against PID and other cascade controllers.

Table 2 Comparison of Performance improvement of PIDD-PI over PID, PI-PD and PD-PID controllers

3.2 Contract violation (nominal case)

Here, DISCOs in all areas demand more power, violating the contracts and needing to be compensated by individual generators. The compensation of uncontracted load is encouraged through EV aggregators because of rapid starting characteristics of EVs. 250 discharged EVs are considered in Area 1, while 600 EVs are considered in each of the other areas. Assuming each DISCO requires excess load of 0.01 p.u. so some loads in Area 1, 2, 3 and 4 becomes 0.04 p.u., 0.02 p.u. 0.02 p.u. and 0.04 p.u. respectively. The total number of 2050 EVs will share a certain percentage of the unscheduled power by discharging. As an incremental power output of WT is provided in each area, a portion of load demand will be maintained at the same level. The PIDD—PI cascade controller is employed as secondary controller for the evaluation and the HHO technique is employed to tune the gains and other parameters of the controller. The corresponding system responses are plotted, compared and presented in Fig. 4a–d.

Fig. 4

Comparison of system dynamic responses during contract violation to show the effect of EV aggregators. a Frequency deviation (Area 1 and 4). b Tie-power deviation (in the line connecting area 1 and 3; area 1 and 2). c Power generation in absence of EV aggregators (Area 1, 3 and 4). d Power generation in presence of EV aggregators (area 1, 2 and 4)

Based on market information, area participation factors (apf’s) are considered such that the thermal units in Area 1 share 0.012 p.u and 0.011 p.u. power respectively, while EV aggregators discharges 0.012 p.u. power. Thus, (0.012 + 0.011 + 0.012 = 0.036 p.u.) along with 0.004 p.u. from WT confirm the generation of 0.04 p.u. within which the uncontracted load of 0.02 p.u. has been shared. To understand the effect of EV aggregators, the same is optimized in presence and in absence of EV aggregators, and are tabulated in Table 3.

Table 3 Optimum parameters of PIDD-PI controller during contract violation of 2% from nominal 2%

Similarly, gas units and EV aggregators in area 2 and 3 contributes and discharge 0.0145 p.u. and 0.0012 p.u. power (total power_area2 = 0.0145 + 0.0012 + 0.004 = 0.02 p.u.) 012 p.u. and 0.004 p.u. (total power_area3 = 0.012 + 0.004 + 0.004 = 0.02 p.u.MW) respectively. The thermal units and EV aggregators in area 4 contributes (0.0159 + 0.0150 = 0.030 p.u.MW) and 0.005 p.u.MW power, respectively (total power_area4 = 0.030 + 0.005 + 0.004 = 0.04 p.u.MW). The apf are taken as apf₁₁ = 0.34, apf₁₂ = 0.34, apf₁₃ = 0.32; apf₂₁ = 0.92, apf₂₂ = 0.08; apf₃₁ = 0.75, apf₃₂ = 0.25; apf₄₁ = 0.44, apf₄₂ = 0.41, apf₄₃ = 0.138. The generation schedule without EV aggregators is presented in Fig. 4d. This matches the generation profile.

3.3 Sudden outage of a thermal unit in area 1

Assume a contingency occurs in the system and there is an outage of a thermal unit in area 1 which results in reduction of inertia as well as capacity of area1. Because of the presence of a WTG unit, an analysis is carried out with inertia reduction of area 1 by 0–60% in steps of 20%. The modified R, B and T_PS are shown in Table 4. The system considered here for investigation is similar to the previous one in Sect. 3.2 apart from the fact that in Area 1, the values of H, R, B and T_PS are modified as in Table 4. The PIDD-PI controller is used as a secondary regulator in all control areas and the HHO optimized controller parameters are tabulated in Table 5. Figure 5 shows the responses when the inertia is reduced because of the penetration of renewable sources.

Table 4 Modified R, B, T_PS when inertia is reduced by 0%, 10%, 20%, 30%, 40%, 50% and 60% in area 1

Table 5 Optimum controller gains with contract violation of 2% and reduced inertia of 20%, 40% and 60%

Fig. 5

Comparison of system dynamic responses due to outage of a thermal unit considering the effect of R, B. a Frequency deviation in area 4 in presence of EV aggregators. b Tie-power deviation in the line connecting area 1 and 2 in presence of EV Aggregators. c Tie-power deviation in the line connecting area 2 and 3 in absence of EV Aggregators. d Control signal in area 1 for 20%, 40% and 60% reduction in inertia respectively in presence of EV Aggregators

From Fig. 5, it can be inferred that the governor response becomes less sensitive beause of the decrement in inertia and aptitude to control the power output of the grid connected system. It results in further frequency deviation and a long settling time. Also, the tie-power deviation experiences more oscillations when the inertia declines gradually.

3.4 Examining the proposed PIDD-PI cascade controller’s robustness

As stated in the literature, participation of EV aggregators in a smart grid requires open communication channels which may be stochastic in nature. Also, load demand in a control area may not follow the contracted demand and may violate in urging more power from any GENCO. Therefore, it is of utmost interest to ensure the toughness of the projected cascade controller. Thus, four scenarios are considered here for investigation namely (1) increase in load demand from nominal 4% (Sect. 3.2) to 8% and 10% (2) open communication channels of 50 ms, 100 ms and 300 ms time delay; (3) ± 25% change in system loading and (4) ± 25% change in gas generating unit parameters (C_i, T_f and T_cd) simultaneously.

The HHO method is again used to optimize the regulator parameters at changed conditions which are tabulated in Tables 6 and 7. The dynamic responses at changed condition are compared with dynamic responses obtained at nominal condition (Sect. 3.2) and are depicted in Fig. 6. Specifically, Fig. 6a depicts the frequency deviation in area 1 at higher violations of contract and both responses exhibit almost similar routine in terms of time to settle. But as the load demand increases, both the peak overshoot and peak undershoot increase. The uncontracted demands of 4% (4 + 4 = 8%) and 6% (4 + 6 = 10%) have been attained by the conventional generations, WTG unit and EV aggregators as shown in Fig. 6b. Moreover, the proposed controller responds well to open communication channels of ${{\tau (t)}}$ = 50 ms and 100 ms. However, the same becomes unstable when controller gains are optimized at ${{\tau (t)}}$ = 300 ms (Fig. 6d). Generation profile of 6% extra demand from Area 1 is easily mitigated by the local GENCOs as confirmed from Fig. 6b.

Table 6 Optimum regulator parameters during higher SLP of 6% and 10% and communication delays of ${{\tau (t)}}$ = 50 ms,100 ms and 300 ms

Table 7 Optimum controller gains and parameters for ± 25% change in system loading, ± 25% change in C_i, T_f and T_cd of gas generating unit

Fig. 6

Comparison of system dynamic responses during higher violation of contracted demand and different time delays in the system. a Frequency deviation in area 1 for 4% and 6% violations in contracted demand from nominal one. b Power generation in area 1 for 6% violations in contracted demand from nominal one. c Tie-power deviation in line connecting Area 1 and 3 for open communication channels of 50, 100 and 300 ms. d Frequency deviation in area 4 for open communication channel delays of 50, 100 and 300 ms

Figure 7 represents the system dynamics without consideration of additional energy from WTG. Specifically, Fig. 7a, b depict the frequency change and tie-power change for ± 25% change in system loading. Also, Fig. 7c, d depict the system responses when there is a ± 25% change in gas generating unit parameters (C_i, T_f and T_cd). The responses reveal that both changed conditions offer similar performance except peak deviations are slightly different but are within a satisfactory limit. The EV aggregators in conjunction with the proposed controller gains have shown satisfactory performance, with the robust controller settings not required to reset during change in higher contract violations, time delay of 50 ms and 100 ms, and system loading and time constants of the gas generating unit.

Fig. 7

Comparison of system dynamic responses during ± 25% change in system loading and gas generating unit parameters such as Ci, T_f and T_cd at the same time. a Frequency deviation in area 1 for ± 25% change in system loading. b Tie-power deviation in line connecting Area1 and 2 for ± 25% change in system loading. c Frequency deviation in Area 4 for ± 25% change in Ci, T_f and T_cd at the same time. d Tie-power deviation in line connecting Area 1 and 2 for ± 25% change in C_i, T_f and T at the same time

3.5 Convergence characteristics of different algorithms

It is observed that the Harris hawk algorithm has successfully optimized twenty-four parameters simultaneously in a system. In this case study, HHO is compared with other powerful algorithms such as the Quasi Oppositional Harmony Search Algorithm (QOHSA) [7, 8], Biogeography Based Optimization (BBO) [13] and the Bat Algorithm (BA) [28]. These algorithms have been successfully applied in optimizing different parameters under AGC studies in both a conventional and deregulated environment. For effective comparison, the population size and maximum generation for each algorithm are both kept the same at 50. One of the previous case studies in Sect. 3.4 where the load demand is increased from 4 to 8% is considered here for investigation and each algorithm is employed one by one to plot the convergence characteristics. The responses are compared and are shown in Fig. 8 which clearly establishes that the HHO algorithm converges at a lower J_ITAE value than the other algorithms but the time of convergence is almost the same for all (100 s). Thus, HHO outperforms others in terms of lower J_ITAE values.

Fig. 8

Convergence characteristics of HHO with BA, QOHSA and BBO

4 Conclusion

This paper investigates a cascade controller-based AGC of a four area hybrid power system with six GENCOs, six DISCOs and integrated wind power generation in a restructured environment. The system is investigated for bilateral transactions and contract violation scenarios. The following are the outcomes:

PIDD-PI as secondary controller outperforms PID, PI-PD and PD-PID in terms of fast settling time and peak undershoot. The peak overshoot remains similar to other controllers.

• (a) EV aggregators mitigate the uncontracted demand of 1% from every DISCO in each area (4% in Area 1, 2% in Area 2, 2% in Area 2 and 4% in Area 4) along with conventional units, and assist in reducing frequency and tie-power deviation.

• (b) Sudden outage of a thermal unit in Area 1 leads to decrease in the sum of total system inertia (Area 1 has only one thermal unit and WTG unit) and AFRC because the regulation constant is increased. With a decline of inertia, system oscillation increases, resulting in higher overshoot and undershoot along with prolonged time to settle down the ACE.

• (c) Further robustness of the PIDD-PI controller is exhibited against realistic non-linearity such as 4% and 6% violation of contracts, stochastic communication delays of 50 ms, 100 ms and 300 ms, ± 25% of system loading and ± 25% of variation time constants C_i, T_f and T_cd.

• (d) It is recommended to employ more EV aggregators to make the system operate in a stable condition at ${{\tau (t)}}$ = 300 ms. Thus, in the presence of EV aggregators, the nominal controller parameters obtained at contract violation (Sect. 3.2) are not required to reset except for ${{\tau (t)}}$ = 300 ms.

Appendix

Parameter	Value
F, Tgi, Tri, Kri, Tti	60 Hz, 0.08 s, 10 s, 0.5 s, 0.3 s
Tcri, Tfi, Tcdi, Kgi	0.3 s, 0.23 s, 0.2 s, 0.15
Xi, Yi, bi, Ci	0.6 s, 1 s, 0.05, 1
RAG and Ri, TEVi	2.4 Hz./p.u.MW, 1 s
TPS, KPS	20 s, 120 Hz./p.u.MW
Hi, Tw, Di	5 s, 1.5 s, 0.00833 p.u.MW/Hz