Water evaporation algorithm optimized cascade controller for frequency regulation of integrated microgrid

Abstract

Integration of renewable energy sources into existing grid influence the stability of the power system. This article introduces the application of cascade controller in hybrid power system which enhance the frequency stability during power perturbations of the load and generation. For this study, a thermal power unit is considered with integration of a microgrid consist of regular diesel generator, renewable power generating units, energy storage and other power managing devices. Proportional-integral and proportional-integral-derivative (PI-PID) cascade controller is provided for this hybrid power system to reduce the frequency oscillations during system uncertainties. The optimal values of the PI-PID controller are achieved by using water evaporation optimization (WEO) algorithm with fast convergence rate. Investigations are carried out in different scenarios of the IM and results are compared with the PID controller to showcase the advantages of the cascade controller for frequency regulation. Simulations are carried out in MATLAB-SIMULINK^® software environment.

Keywords

Frequency control microgrid PI-PID cascade controller water evaporation algorithm

1 Introduction

Cost, pollution, and continuous inanition of the fossil fuels created a choice for alternative energy resources for electrical power generation. Among the available resources, wind and solar contribution is large as per statistics [1 –4]. Apart from the merits in terms of cost and pollution, nature of intermittent and time of availability impose frequency and power quality issues. Power management during peak hours is another challenge when the entire traditional sources are replaced with such renewable units. Therefore, integration of microgrid to traditional plants provides a satisfactory solution by keeping the frequency of the system as nominal value.

Few such configurations are available in literature [5 –17] in terms of systems, controllers, and tuning algorithms. The traditional mathematical tuning approaches are not flexible for hybrid power system scenarios due to integration of PV and wind. The volatile nature of wind speed and irradiance of PV panels makes this tuning procedure as complex unlike conventional interconnected power system scenarios [4]. Therefore, several intelligent control schemes were proposed from last once decade for such hybrid power and microgrid systems. Fuzzy logic (FL) [6 –8] and artificial neural network (ANN) [9 –11] based controllers with extended learning [12] and optimization algorithms [13 –22] applied for interconnected power system, isolated system and microgrid to enhance its stability during real power perturbations. For AC microgrid, hybrid fuzzy tuned PI-controller with particle swarm optimization (PSO) tuning mechanism is applied [5]. The optimal controller parameters of either PI or PID controllers, rules, or limits of membership functions of fuzzy logic and weights of ANN architectures are identified using evolutionary and swarm intelligent techniques. Further, studies are extended to intelligent hybrid energy management in presence of renewables [6]. In [6], from insolation and change in frequency signals, a fuzzy system is used to inverter control to reduce frequency oscillations. With fuzzy, controller outputs depend on scaling factor. In [7], scaling factor-based FL with PI, PD and PID controllers are designed for isolated hybrid systems and robustness of each controller verified at different disturbances. In [8], adaptive fuzzy PID controllers are used for isolated power system. In aforementioned fuzzy based controllers, tuning of parameters is achieved by quasi-oppositional harmony search (QOHS) [7] and improved sine cosine algorithm (ISCA) [8]. Apart from FL, ANN mechanisms are also used in literature as controllers and related works are reported in [9 –11]. In [9], PSO is used for tuning ANN to control isolated microgrids in presence of electric vehicles (EV) and self-tuned ANN is used in [10]. Recently, integrating layered recurrent ANN with robust control strategy is applied to control the system during diverse conditions [11]. Further, combined fuzzy and ANN schemes are also available in literature [12].

Overall, application of population search-based algorithms for tuning is a common path in AGC studies identified for the isolated and hybrid power and microgrid systems in presence of renewables irrespective of controller mechanism. Some of the available algorithms used for frequency control of different hybrid power systems (HPS) and microgrids are listed in [13 –22]. Isolated wind-diesel HPS is considered in [13] and the pitch controller parameters are optimized using genetic algorithm (GA) to minimize the power deviations. In [14], PSO algorithm helps to find parameter gains of fractional order PID controller to minimize the frequency errors of solar-diesel HPS. Invasive weed optimization (IWO) technique also applied for tuning of typical controllers in interconnected power system and corresponding outcomes are presented in [15]. For isolated microgrids, crow search algorithm (CSO) is used for PI and PID controller tuning [16]. In [17], biogeography-based optimization (BBO) algorithm used in wind-solar standalone microgrid to find optimal resonance controller parameters. 2-, 3-degree of freedom controllers are also applied in microgrid scenarios to minimize frequency changes where the optimal parameter gains are achieved by dragonfly algorithm (DA) [18, 19]. For multi microgrids, JAYA algorithm helps for tuning of PID, and results are available in [20]. Recently, selfish-herd optimization (SHO) [21], grasshopper optimization algorithm (GOA) [22] and social spider optimization (SSO) [23] algorithms are applied in hybrid, renewable and interconnected microgrid architectures. Prior to this, ANN and FL controllers are also using these algorithms for tuning their selective parameters. Apart from these intelligent approaches, several control schemes are already tested in hybrid power system scenarios known as μ-synthesis approach, H-infinity control, model predictive control, active disturbance rejection control, sliding mode control and hybrid control mechanisms are also available in literature [24 –28]. However, recent trends in HPS and microgrid models with PV and wind are available in [29 –33].

Among existing models, hybrid power system models with both conventional and renewable power units become so popular since the benefits of power management, cost and pollution can be achieved. Therefore, a thermal coordinated microgrid hybrid power system model is considered in this paper for frequency control studies. Initially, PID controller is used for providing simultaneous control for both thermal and microgrid units to minimize the frequency oscillations and to enhance the system stability during load, wind speed and PV irradiance perturbations. Later, PI-PID cascade controller is designed with solution accept policy. To achieve acceptable solutions, an amount of power change from microgrid units is taken as an additional input signal for PI-PID controller. Further, the impacts of both PID and PI-PID cascade controllers are studied in a coordinated scenario with storage elements and without storage elements. In all cases, the optimal parameters of both controllers are identified by a water evaporation algorithm (WEO) whose execution time is fast compared to other techniques.

2 System studied

Thermal plant coordinated microgrid architecture is considered in this paper to investigate the frequency stability studies with cascade controller. For thermal plant, reheat turbine and governor with dead band components are modelled whereas for the microgrid, the contributed components are wind generator (WG), PV generator, diesel generator (DG), fuel cell (FC), aqua electrolyzer (AE), ultra-capacitor (UC), flywheel energy storage system (FESS) and battery energy storage system (BESS). Among these elements, UC, FESS and BESS are the storage elements that initiate their action of charging and discharging electrical power based on frequency changes sensing. WG, PV generator inputs are random in nature therefore no control over these components. Finally, the controller simultaneously controls the AE, DG, FC and the thermal unit via secondary control mechanism. The schematic diagram of the investigated system is shown in Fig. 1.

Fig. 1

Block diagram of thermal coordinated microgrid.

The parameter values of hybrid power system are provided in Table 1. Both thermal and microgrid supplies additional change in demand to balance real power in integrated mode as shown in Equation (1) given by

Table 1

System parameters

Thermal unit		Renewable systems		Controllable DG sources		Storage units
Parameter	Value	Parameter	Value	Parameter	Value	Parameter	Value
T _sg	0.08	K _w	1	K _AE	0.02	K _FESS	–0.01
T _t	0.3	K _PV	1	K _FC	0.01	K _BESS	–0.003
T _r	10	T _w	1.5	K _DEG	0.003	K _UC	–0.7
K _r	0.3	T _PV	1.8	T _AE	0.5	T _FESS	0.1
K _ps	120			T _FC	4	T _BESS	1
T _ps	20			T _DEG	2	T _UC	0.9
R	2.4

$Δ P_{L} = Δ P_{μ g} + Δ P_{g}$ (1)

In Equation (1), ΔP_μg is the output change in power from the microgrid unit, ΔP_g is the thermal unit output change in power. As several small units are connected together in the microgrid of the hybrid power system, the total power delivered from microgrid during load changes is given by $\begin{matrix} Δ P_{μ g} = Δ P_{PV} + Δ P_{WT} + Δ P_{DG} + Δ P_{AE} \\ + Δ P_{FC} + Δ P_{UC} + Δ P_{BESS} + Δ P_{FESS} \end{matrix}$ (2)

In Equation (2), ΔP_W and ΔP_PV are the wind and solar real power perturbations, ΔP_DG, ΔP_AE and ΔP_FC are the output changes in real powers of DG, AE and FC, ΔP_UC, ΔP_BESS and ΔP_FESS are the storage components contribution in terms of charging and discharging. The individual transfer functions of all these components are clearly mentioned in Fig. 1. To design a suitable controller for this integrated hybrid power system, the reference output variable is change in frequency Δf is expressed as $Δ f = \frac{(- Δ P_{L} + Δ P_{μ g} + Δ P_{g}) K_{ps}}{(1 + {sT}_{ps})}$ (3)

The power contributed from thermal and microgrid units varies with controller performance along with PV and wind power changes. These contributions are expressed with the following equations for both units of the integrated power system. $\begin{matrix} Δ P_{g} = \frac{(\frac{- 0.2}{π} s + 0.8) (K_{r} T_{r} s + 1)}{({sT}_{sg} + 1) ({sT}_{t} + 1) ({sT}_{r} + 1)} \\ (Δ u - \frac{1}{R} Δ f) \end{matrix}$ (4) $Δ P_{w} = \frac{K_{w}}{T_{w} S + 1} Δ w$ (5) $Δ P_{PV} = \frac{K_{PV}}{T_{PV} S + 1} Δ φ$ (6)

In Equation (4), Δu is the controller output and Δw, Δφ are the cumulative input changes of wind speed and irradiance of wind and PV units. These changes are incorporated in the system with stochastic models available in [16] in order to study the system stability under such variations. According to [16], the stochastic generation of wind and PV input changes are modelled as $\begin{matrix} Δ w, Δ φ and Δ P_{L} = α_{0} H (t) + α_{1} H (t - t_{1}) \\ + α_{2} H (t - t_{2}) + \dots + α_{n} H (t - t_{n}) + ɛ \end{matrix}$ (7)

In Equation (7), α_i (i = 0, 1, …, n) represents magnitude of input parameter changes in per unit and t_i (i = 0, 1, …, n) represents time delays. H(t) represents the Heaviside step function and noise in inputs represented by ɛ. The values of the coefficients for various stochastic models are provided in Table 2. These loads and renewable power perturbations are controlled by secondary controller. The selection and design of suitable controller is discussed in section 3.

Table 2

Stochastic function values

Source	α_i	t _i
Load	0.05, 0.2, –0.6	0, 20, 40
Solar	0.475, –0.75, –0.15, –0.05, –0.2, –0.4	0, 10, 20, 30, 40, 50
Wind	0.01, –0.05, 0.1	0, 20, 40

3 Controller design and tuning procedure

In literature, PI and PID controllers are extensively used as secondary generation control. In this work also, PID controller is opted initially whose output control signal is given by $Δ u = (k_{p} + \frac{k_{i}}{S} + k_{d} s) . Δ f$ (8)

In Equation (8), k_p, k_i and k_d are the proportional, integral, and derivative gain parameters of the PID controller. The control signal generated by the PID controller directly connected to both thermal unit and other controllable sources of microgrid. This controller scheme enhances the steady state and transient stability specifications of the hybrid power system. However, there is no comparison in between thermal power generation change and change in power of microgrid components. This scenario increases the amount of power change of thermal unit which is not preferable in such coordinated power systems. Therefore, PI-PID cascade controller scheme is replaced PID to balance power in more economical way along with stability of the system during load and power perturbation. For this cascade controller, two input signals are used from the output states of the test system. One is change in frequency similar to PID controller whereas second is the change in power of the microgrid system. This selection required solution accept policy implemented in tuning mechanism. In PI-PID cascade controller, PI component is actuated by Δf and power change in microgrid (ΔP_μg) is subtracted from the output of PI and resultant component is given as input to PID part of PI-PID controller. This connection scheme is presented in Fig. 2. The final controller output signal generated from the PI-PID controller for hybrid power system is given by $\begin{matrix} u_{i} (s) = ((k_{p_{1}} + \frac{k_{i_{1}}}{S}) . Δ f - Δ P_{μ g}) \\ (k_{p_{2}} + \frac{k_{i_{2}}}{S} + k_{d_{2}} s) \end{matrix}$ (9)

Fig. 2

PI-PID cascade controller scheme adapted in the system.

In Equation (9), k_{p
₁}, k_{i
₁} are the proportional, integral gain parameters of PI and k_{p
₂}, k_{i
₂}, k_{d
₂} are the proportional, integral, and derivative gain parameters of PID in PI-PID cascade controller of the test system.

Fig. 3

Algorithm of WEO with solution accept policy (SAP).

Fig. 4

Responses of hybrid power system during 1% of load decrease case a. change in frequency, b. change in thermal power, c. change in microgrid output and d. control signal.

Figure 2 shows the schematic diagram of cascade controller set up for test hybrid power system. In each case, the solution accept policy is considered for identification of optimal parameter gains of the PI-PID controller with energy values of signals ΔP_μg and ΔP_g over a period of time (T) with the solution achieved with PID controller. Before checking these conditions, the overall objective function is framed with the help of frequency change information similar to existing mechanisms available in literature survey. Therefore, an objective function is framed to tune the controller parameter with Δf as output variable given by $J_{1} = \int_{0}^{T} Δ f {(t)}^{2} dt$ (10)

Using Equation (10) as objective function, the optimal values of PID and PI-PID controller parameters are obtained using WEO algorithm. The water drop solutions are generated within the extreme limits of controller parameters given by $k_{\min 1} ⩽ k_{p}, k_{i}, k_{d} ⩽ k_{\max 1}$ (11)

The limits described in Equation (11) are for the PID controller tuning. For PI-PID controller, the upper and lower boundaries of parameter gains are given by $k_{\min 2} ⩽ k_{p_{1}}, k_{i_{1}} ⩽ k_{\max 2}$ (12) $k_{\min 1} ⩽ k_{p_{1}}, k_{i_{1}}, k_{d_{1}} ⩽ k_{\max 1}$ (13)

Equation (12) is for PI component and Equation (13) for PID component of PI-PID cascade controller. However, minimization of J₁ with PI-PID controller is not unique objective of the paper. Along with, two more indices are using to avoid additional burdens on both conventional and renewable units with the help of power sharing described by ${\begin{matrix} J_{2} = \sum_{i = 1}^{N} {(Δ P_{g} (i))}^{2} \\ J_{3} = \sum_{i = 1}^{N} {(Δ P_{μ g} (i))}^{2} \end{matrix}}$ (14)

With these additional measures, solution accept policy is implemented in the system to allow the controllers parameters so that additional benefits are achieved discussed in simulation results section.

4 Water evaporation algorithm with solution accept policy

The optimal parameter gains values of PID and PI-PID cascade controllers are identified by using water evaporation algorithm (WEO). WEO algorithm is proposed in the year 2016 by A. Kaveh and T. Bakhshpoori by mimic the nature of water molecules evaporation from different surfaces [34, 35]. The mechanism of this optimization algorithm is similar like other population search approaches but with two parallel phases to provide fast accepted solutions. Using molecular dynamics, the nature of evaporation of tiny water particles from solid surfaces with different wettability is a motivation for WEO. The analogy with available population search-based techniques is visible in WEO since the water evaporation rate varies with surface based on biological and environmental conditions. Particles in PSO, learners in TLBO and population in other heuristic algorithms is similar to water particles in WEO algorithm. Therefore, algorithm individuals refer to water particles and their search space is solid surfaces with different wettability. The water particles possess charge and when charge q decreased from 0.7e to 0e (e refers to 1 electron charge) represents minimization of objective function towards optimal solutions. For updating individuals of WEO, evaporation flux is used as a measure for determining the probability of updating particles position. This updating mechanism is performed with two phases.

monolayer evaporation phase (MEP)

Droplet evaporation phase (DEP)

After these phases, water particles updated to new surfaces until to reach the convergence condition. Once the final convergence condition is satisfied (in terms of number of t_max or Error_min), best solution is stored. In updating mechanism, ability of search is enhanced with the usage of two phases. MEP enhance the global search ability and local search ability is enhanced by DEP. The MEP and DEP evaporation phases are provided in 4.1 and 4.2.

4.1 Monolayer evaporation phase (MEP)

Based on evaporation flux (J (q)) expression, energy of molecules is related. The equation for J (q) is given by $J (q) = e^{- E_{sub} / K_{B} T}, q ⩾ 0.4 e$ (15)

In Equation (15), E_sub represents the interaction energy from the substrate, mainly provided by the electrical charge q assigned on the substrate [35] depends on the temperature T and K_B is the Boltzman constant. As stated in Equation (15), E_sub varies when q increases leads to objective function individuals (i) fitness (Fit) change for each iteration (t) given by $E_{sub} {(i)}^{t} = \frac{(E_{\max} - E_{\min}) * ({Fit}_{i}^{t} - {Fit}_{\min})}{({Fit}_{\max} - {Fit}_{\min})} + E_{\min}$ (16)

In Equation (16), E_min (- 3.5 as per [34]) and E_max (- 0.5) are the minimum and maximum values of substrate interaction energy. Minimum and maximum fitness function values are Fit_max and Fit_min. After E_sub (i) ^t vector generation for all the individuals, MEP matrix is generated as follows: ${MEP}_{ij}^{t} = \begin{matrix} 1 if {rand}_{ij} < e^{E_{sub} {(i)}^{t}} \\ 0 if {rand}_{ij} ⩾ e^{E_{sub} {(i)}^{t}} \end{matrix}$ (17)

In Equation (17), j represents decision variable and ${MEP}_{ij}^{t}$ is the updating probability of individuals.

4.2 Droplet evaporation phase (DEP)

Based on contact angle (θ) of water particles, the DEP matrix is constructed. The selection of minimum and maximum values of θ with proper justifications are available in [34, 35]. According to updating mechanism, the contact angle of i^th individual at t^th iteration is given by $θ {(i)}^{t} = \frac{(θ_{\max} - θ_{\min}) * ({Fit}_{i}^{t} - {Fit}_{\min})}{({Fit}_{\max} - {Fit}_{\min})} + θ_{\min}$ (18)

DEP matrix is constructing using the information available after evaluation of Equation (18) is given by ${DEP}_{ij}^{t} = \begin{matrix} 1 if {rand}_{ij} < J (θ_{i}^{t}) \\ 0 if {rand}_{ij} ⩾ J (θ_{i}^{t}) \end{matrix}$ (19) where, ${DEP}_{ij}^{t}$ is the updating probability of the water molecule. After MEP and DEP phases, the water molecules set updating for next iteration (WM^t+1) using the current molecules set (WM^t) and random permutation step size (S) given by

${WM}^{t + 1} = {WM}^{t} + S * {\begin{matrix} {MEP}^{t} t ⩽ t_{\max} / 2 \\ {DEP}^{t} t > t_{\max} / 2 \end{matrix}}$ (20)

This optimization process carried out until the satisfaction of termination criteria. However, number of runs are added in the WEO algorithm for the cascade controller optimal parameter gains identification with the help of J₂ and J₃. At the end of final iteration, J₂ and J₃ are calculated with the available best solution achieved using WEO and compared with pre-defined values of J₂ and J₃ (based on prior controller) and if sum of both new measures are greater than existing measures then WEO go for next run. This increment in number of runs continue until maximum runs completed.

4.3 Application of WEO for finding optimal controller gains

The controller (both PID and PI-PID) gains are the decision variables used for calculation of main fitness function shown in Equation 10 and supportive fitness fuctnions shown in Equation 14. Randomly generated water molecules of the WEO algorithm represents the controllers gains and corresponding fitness values are evaluated using Equation 10. These solutions are updated using MEP and DEP mechanisms and optimal solutions are achived at the end of final iteration of WEO. To accept the solution, SAP is included in the algorithm with the help of additional fitness functions.

5 Simulation results

The stability enhancement of the hybrid power system with both PID and PI-PID controllers are studied with thermal and microgrid power coordination concept. The results are presented in this section are classified in four cases to show the superiority of the cascade controller to minimize frequency oscillations under different power disturbances. In first case, only change in load is taken under power disturbances and no power changes are considered in renewable sources wind and PV. In second case, the presence of storage components is neglected. In third case, small random disturbances are incorporated in the PV and solar along with large demand variations. Finally, stochastic load and power patterns are considered cumulatively as reported in section 2.

Case-1 : In this case, both PV and wind power output changes are zero. Load perturbations (either demand decrease or increase) are mitigated by thermal unit and DG, FC and AE of microgrid along with energy storage devices. During 1% decrease in demand, the change in frequency, change in thermal power and change in power shared by microgrid are presented in Fig. 4a, 4b and 4c respectively. The control signals generated by both PID and PI-PID controllers are provided in Fig. 4d. With proposed cascade controller scheme (ΔP_μg and Δf as inputs), the stability of the system is enhanced during load perturbations that is evident from Table 3 where the time domain transient and steady state parameters are reported. Similar results are presented in Fig. 5 during 1% power demand increase. In both cases, the final values of generation changes of thermal and microgrid units of hybrid power system are same. However, the responses of these components during initial time zones subjected to disturbances are improved in terms of transient specifications such as peak overshoot and signal energy (J).

Table 3
Performance specifications of simulated system under load perturbations (case 1)

Load change (p.u) PID controller Cascade controller

Δf _peak t _peak t _ss Δf _peak t _peak t _ss

0.01↓ –0.01003 0.414 20 –0.00597 0.209 16

0.1↓ –0.1062 0.362 20 –0.06359 0.172 17

0.01↑ 0.01017 0.385 22 0.00528 0.152 18

0.1↑ 0.1047 0.444 19 0.06389 0.187 15

Load change (p.u)	PID controller	Cascade controller
0.01↓	–0.01003	0.414	20	–0.00597	0.209	16
0.1↓	–0.1062	0.362	20	–0.06359	0.172	17
0.01↑	0.01017	0.385	22	0.00528	0.152	18
0.1↑	0.1047	0.444	19	0.06389	0.187	15

Fig. 5

Responses of hybrid power system during 1% of load increase case a. change in frequency, b. change in thermal power, c. change in microgrid output and d. control signal.

These improvements with PI-PID controller reduced additional power burdens on generating units since solution accept policy is incorporated in the algorithm accept such global optimal parameters of the controller with J. The presence of storage devices also helps in improving the stability of the system.

This study further extended to large load disturbances and the corresponding frequency responses are presented in Fig. 6. When –10% of load change happened in the system, the frequency changes in presence of both controllers are reported in Fig. 6a and 6b for 10% load increase. Similar observations are made in such loadings and reported in Tables 3 4. In all the four load change conditions, the optimal parameter gains of PID and PI-PID are reported in Table 4.

Fig. 6

Change in frequency of hybrid power system during a. 10% of load increase, b. 10% of load decrease.

Table 4

PID and PI-PID controller parameters of during load perturbations (case-1)

ΔP_L (p.u)	PID controller			Cascade controller
	k _p	k _i	k _d	k _p1	k _i1	k _p2	k _i2	k _d2
0.01↓	–0.8775	–0.9945	–0.9858	–2.0296	–2.7226	0.9204	0.2806	0.9922
0.01↑	–0.9761	–0.9827	–0.9468	–2.6261	–2.3908	0.8426	0.1393	0.9456
0.1↓	–0.8977	–0.9945	–0.9050	–2.0751	–2.6163	0.9650	0.8877	0.8663
0.1↑	–0.4215	–0.2272	–0.3790	–2.6825	–2.5977	0.8802	0.6487	0.8936

Case-2: Transformation of electrical generation from conventional scenario to microgrid and renewable based scenario, increase the importance of storage elements presents in order to mitigate the problems associated with transformation. In such transformation, cascade controller enhances the stability of the system than PI and PID controllers as discussed in case-1 and the proposed solution accept policy minimize the deviations of both powers in thermal and microgrid plants. However, solution accept policy significance is minimum without storage units.

Results presented in Figs. 7 (1% decrease) and 8 (1% increase) shows the corresponding information. Frequency deviations are minimized when the PID controller replaced by PI-PID cascade controller (shown in Figs. 7a 8a) but the measures.

Fig. 7

Responses of hybrid power system during 1% of load decrease without energy storage elements case a. change in frequency, b. change in thermal power, c. change in microgrid output and d. control signal.

Fig. 8

Responses of hybrid power system during 1% of load increase without energy storage elements case a. change in frequency, b. change in thermal power, c. change in microgrid output and d. control signal.

J₂ and J₃ of cascade controllers are slightly nearer to PID controller measures. The impact of storage elements in stability enhancement of such coordinated and hybrid systems also visible from these cases 1 and 2. Further, discussions are provided in comparative section.

Case-3: In the test system, both wind and solar photovoltaic generating units are presented. However, their impacts are not considered in the cases 1 and 2. But in real time, larger portion of generation is from either PV or wind or both. Integration wind and PV makes the generation as unpredictable, volatile and nature dependent. Therefore, frequency control of such systems is a challenging task and with proper control strategy, it is appreciable. The proposed PI-PID controller with ΔP_μg and f as input information provided fast response and settles the frequency deviations in minimum time. In this case, noise in wind speed and PV irradiance is considered in the test system along with load fluctuations and the responses with PID and PI-PID controllers are presented from Figs. 9 12. Figure 9 shows the frequency deviations of the system during noise and load perturbation condition provided the significance of proposed cascade controller architecture in terms of the peak and steady state stability parameters reported in Table 5. Once the frequency is controlled by either PID or PI-PID controller after initiation of load changes, the frequency is maintained as nominal value during wind and PV input noise conditions in case of cascade controller. The presence of storage elements and controller accept SAP and therefore, the additional measures are also minimum in case of PI-PID compared to PID as shown in Figs. 10 11. Figure 12 presents controllers output signals.

Fig. 9

Frequency deviation responses of test system during wind and PV power noise condition.

Fig. 10

Thermal power deviation responses of test system during wind and PV power noise condition.

Fig. 11

Responses of microgrid system during wind and PV power noise condition.

Fig. 12

Control signals generated during wind and PV power noise condition for 1% load disturbance.

Table 5

PID and PI-PID controller parameters of during load perturbations without storage units (case-2)

ΔP_L (p.u)	PID controller			Cascade controller
	k _p	k _i	k _d	k _p1	k _i1	k _p2	k _i2	k _d2
0.01↓	–0.9414	–0.9986	–0.8181	–2.5123	–1.0456	0.9225	0.1348	0.1444
0.01↑	–0.9905	–0.8762	–0.6571	–2.0296	–2.7225	0.9204	0.2806	0.9922

Case-4: Along with demand variations, considerable input power fluctuations (wind or PV) is considered to study the impact of cascade controller, configuration of thermal and microgrid and presence of storage units. Initially, load change of 0.01 p.u is considered as power disturbance and later irradiance change of 0.04 p.u is considered as nature dependent source variation. The corresponding frequency change in system in coordinated mode, generation output power changes of both thermal and microgrid plants along with controller outputs are presented in Figs. 13 , 15 and 16. Further, all the possible power disturbances on both generation and demand side are considered using the stochastic models whose information is provided in Table 2. Under such large system variations also, the proposed PI-PID cascade controller with SAP concept provided extremely better responses than PID controller. In this case, the frequency changes are presented in Fig. 17 and controller’s outputs for minimizing the frequency changes are presented in Fig. 18. The controller parameter optimal gains for all case studies are reported from Tables 6.

Fig. 13

Frequency deviation responses of test system during case 4.

Fig. 14

Thermal power deviation responses of test system during case 4.

Fig. 15

Responses of microgrid system during case 4.

Fig. 16

Control signals generated during case 4.

Fig. 17

Responses of hybrid power system during random load perturbations.

Fig.18

Control signal during random load perturbations.

Table 6

PID and PI-PID controller parameters of during stochastic variations of wind speed and irradiance (case-4)

ΔP_L (p.u)	PID controller			Cascade controller
	k _p	k _i	k _d	k _p1	k _i1	k _p2	k _i2	k _d2
0.01↓	–0.6109	–0.4482	–0.5737	–1.8236	–1.7761	0.9870	0.4465	0.8492

The objective of solution accept policy of controllers is to find an optimal solution which minimize both frequency and generation power changes. The fitness function final values after WEO execution are plotted in Fig. 19 for all four case studies shows the advantage of cascade controller than PID. All results discussed from section 4.1 to 4.4 show the enhanced specifications in terms of the transient and steady state specifications of the system and improves overall stability.

Fig. 19

Fitness function values of WEO for the test system with PID and PI-PID controllers for a. case-1, b. case-2, c. case-3 and d. case-4.

6 Conclusions

In this paper, PI-PID cascade controller scheme is designed for thermal coordinated microgrid with change in frequency and microgrid power as primary and secondary inputs. This controller structure enhances the stability of the system during load and stochastic disturbances of renewable units. It also reduces peak changes of frequency errors during speed and irradiance changes of wind and PV systems respectively. These improvements are verified and compared with PID controller. All the optimal parameter gains of PID and PI-PID controllers are identified by using WEO algorithm. Solution accept policy is integrated in the process of searching of optimal parameters to reduce the additional power peak burdens on microgrid and thermal systems during load perturbations.

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