A hybrid control technique for small signal stability analysis for microgrids under uncertainty

Abstract

Distributed generators (DG) with inverter based on renewable sources are generally utilized in microgrids. Most of these sources work in droop control mode to effectively share the load. Higher droop is chosen on these systems to recover dynamic power sharing. This paper proposes a Hybrid Control Technique for Small Signal Stability Analysis for Microgrids under Uncertainty. The proposed topology is to recover the capacity of power system is used to restore the normal operating condition. The proposed hybrid technique is the combination of chaotic Henry gas solubility optimization (CHGSO) and recalling-enhanced recurrent neural network (RENNN) and therefore called the CHGSO-RENNN technique. The proposed technique is used to optimally predict the internal and external current loop control parameters in light and the variety of power and current parameters. The small stability is revealed through the working conditions of the whole machine. The overall stability of the small signal is investigated in a linear model so that both source and load are used to characterize the state matrix of the frame that is used for eigenvalue examination. The PI controller gain parameters are optimally tuned and the controller offers reliable frame operation. The proposed technique is performed on MATLAB/Simulink work platform.

Keywords

Fuel cell battery storage system ultra capacitor diesel generator flywheel storage system chaotic henry gas solubility optimization and recalling-enhanced recurrent neural network

Nomenclature and Abbreviations
$P_{o / p}^{PV}$ - output power of PV arrays	η_PV- efficiency of PV modules
P_rate- rated power of every unit	Irad- global irradiance incident on tilted plane
Irad_stc- standard irradiance	s- optimal size of PV units
t_fc and k_fc- constant of FC gain and time	C- capacitance on Farad
v_FINAL and v_IN- last voltages and initial voltages of UC	Δp_uc- incremental change as UC
t_uc and k_uc- time constant and gain of UC	J- moment of inertia
Δp_fess- incremental change of output power	k_fess and t_fess- gain and time constant
$E_{t}^{RES}$ - whole energy created by RESs	$E_{t}^{Load}$ - total necessary energy on MG system

Nomenclature and Abbreviations
η_ch- battery charging efficiency	K_P, K_I and K_D- gain, integral and derivative time constant
E(T)- error input	Δp_deg- incremental change of DEG
k_DEG and t_DEG- gain and time constant	RN- diagonal matrix of size (2 N×2 N)
CHGSO- Chaotic Henry Gas Solubility Optimization	RENNN- Recalling Enhanced Recurrent Neural Network
PI- proportional integral	FESS- Flywheel energy storage system
BESS- Battery energy storage system	UC- Ultra capacitor
PV- Photo Voltaic	FC- Fuel cell
HGSO- Henry Gas Solubility Optimization	SCA- Sine Cosine Algorithm
QOSCA- Quasi-Oppositional Sine Cosine Algorithm	GWO- Grey Wolf Optimizer
HSS- Hyper-spherical Search

1 Introduction

Competitive energy policies have led to decentralization of power generation due to the growing environmental conditions. It is expected to increase worldwide, because DGs are installed over the next decade. Due to the close location to the consumer, DGs deliver excellent power based on reliability and quality. Controllable DGs and controllable loads are presented to the upstream network as a microgrid [1]. Microgrid is an advanced operational management for the use of DG that is independent control unit consisting of a group of DGs [2]. This administration may preserve the reliability of the network and solve the ongoing issues caused by large-scale DG [3]. In microgrids, operating in grid-connected mode delivers energy consumption depends on internal supply/demand. At island mode, microgrids function as an independent power system [4 –8].

In recent years, system stability problems at microgrid have become well-known and explored by numerous researchers. Microgrid stability problems can often be separated into small signal as well as large disturbance stability [9, 10]. Microgrid stability research has mostly focused on mathematical modeling of microgrid stability analysis and microgrid stability enhancement systems [11, 12]. Among the several sorts of stability issues, one of the significant concerns over reliability of MG is stability of the small signal [13, 14]. It is necessary to evaluate the small signal model and choose diverse controller or filter parameters [15, 16]. Stability analysis is well recognized on conventional power system and network dynamics is generally ignored; Though, in MGs, modeling the complete small-signal dynamic equation for MGs can be hard to get due to the complexity and heterogeneity of DG control approach [17]. Consequently, small-signal performance model and analysis for microgrids has slowly become one of the most pressing problems [18, 19].

For small signal stability [20 –22], the effects of droop control gains, line resistance on MG voltage and frequency characteristics are mostly analyzed on recent works [23, 24]. The Particle swarm optimization (PSO) algorithms are employed for DG drop controllers with inverter interface by dynamic model [25]. Furthermore, the control approaches for the MG are different and have its own small-signal model [26]. By analyzing small-signal model, the appropriate parameters will be selected to achieve better stability and dynamics [27].

1.1 Objectives and contribution

A hybrid control system for small signal stability analysis for MGs under uncertainty is proposed. The proposed hybrid method is combined execution of chaotic Henry gas solubility optimization (CHGSO) and recalling-enhanced recurrent neural network (RERNN) and hence it is named as CHGSO-RERNN system.

The key innovation of the proposed work is to obtain the overall optimal solution is collected as search space of these operators.

The proposed technique is utilized to optimally predict the control parameters of internal and external current loop in light and the variety of the power and current parameters.

The gain parameters of PI controller are optimally modified and controller proposals dependable framework operation.

Section 1 and 2 shows that introduction and literature survey. A section 3 shows System Description, Section 4 demonstrates that Proposed Methodologies, Section 5 exhibits result and discussion. Section 6 finishes the manuscript.

2 Recent research works: A brief review

Previously, several research works were presented in literature depend on the detection and classification of small-signal stability on microgrid with several methods and features. Some of the current works are revised here.

Krishnan et al., [28] have presented an approach to recover the performance of droop control system by linking virtual resistance, dynamic droop gains and sliding mode control. The control parameters were optimally tuned by PSO, make sure stability. Such parameters were enhanced to attain maximum power distribution capacity in the absence of affecting stability. He et al., [29] have executed a typical two-port small-signal model of multi-stage cascaded DC-DC converters as well as calculated their equivalent small-loop gain was used to assess system stability. Altaf et al., [30] have illustrated the adaptive rate of change of frequency (ROCOF) to overwhelm the non-detection zone (NDZ) problem. The ROCOF-fed passive IDT depend on the Phase Locked Loop (PLL) closed-loop control system settings, ROCOF, and ROCOF threshold value. Therefore, PLL outcomes an alternative frequency and ROCOF output value regarding with modification of PLL configuration. Thus, the ROCOF-fed Adaptive IDT delivers a common solution for island detection uses for secure and dependable operation of dissimilar MG systems.

Pan and Mandal [31] have provided a new detection system to restore detection accuracy and diminish unnecessary false triggers. It was attained by exploring the physical properties of DC arc. This model allows a correct simulation of DC interactions among arc faults were carried out of CC and two usual control approaches. A novel detection system depends on time domain and time-frequency domain arc signatures through multilayer perceptron neural networks (MLPNN) on numeric simulations. Chen et al., [32] have elucidated a resilient distributed control depends on average consensus algorithm and PI consensus algorithm against DOS attacks and recover microgrid stability. The control turns the average voltage restoration issue caused by malicious DoS attacks. Furthermore, small-signal stability model of DC MG using distributed energy stores as well as constant power loads was recognized. Dong et al., [33] have presented a secondary frequency stabilization and regulation system for multi-parallel droop inverter system with island dependence of static frequency error. The component connection method (CCM) was recognized by state space model of multi-parallel drooped inverter MG system. A charge state space model was also recognized along with the transfer function state space mapping system.

Li and Shahidehpour [34] have performed small-signal stability of islanded hybrid AC/DC microgrids and suggest a droop-based control mechanism to organize the process of AC and DC sections.

2.1 Motivation for the research work

Review of current research work portrays that system stability on MG is important contributing factor on power distribution system. It is very difficult to preserve the stability of grid and energy balance of system occurs based on low physical inertia of the micro grid. One of the most significant concerns on reliable MG operation is small signal stability. Microgrid stability research mostly focuses on modeling MG stability enhancement systems for MGs. Several issues related to microgrid resilience are concerned, such as inclusion of non-linear communication time delay (CTD) capability, fault-ride through (FRT), advanced microgrid power flow methods and shared power. To control VSCs in microgrids, several strategies have been reported. It has numerous restrictions, such as a lack of stability when load dynamics are deemed as a lack of black start capability and weak transient performance. Centralized control demands high-bandwidth communication, and therefore failure in the communication system. A master-slave control approach has been described that is flexible for connection/disconnection of distributed energy resource (DER) units. The robust servomechanism and multivariable controllers deliver certain enhancements for robustness against MG uncertainties. The microgrids have been studied depends on small-signal modeling for normal conditions. To overwhelmed these challenges, optimal detection with advanced technology is essential. In related works, few control techniques are presented to resolve small signal disturbances; The aforementioned limitations have inspired this research work.

3 Description of the system

Hybrid power system containing a Photovoltaic array, Diesel Generator, Aqua electrolyzer, Fuel Cell and storage device as Flywheel energy storage system (FESS), Battery energy storage system (BESS) and Ultra capacitor (UC) for assessing the proposed system performance [35]. Figure 1 shows HEPS model for Single line diagram.

Fig. 1

HEPS model for Single line diagram.

RERs are connected to the MG by a power conversion system. By calculating the control domain, the dynamic stability of the HEPS is estimated, which integrates the inherent linear properties of the power system.

3.1 Mathematical modelling of system

3.1.1 Modelling of photo voltaic (PV)

The major renewable energy source is solar PV energy system, which is taken from the sunlight and changes it into energy. The equivalent circuit of PV system displays on Fig. 2.

Fig. 2

Equivalent Circuit of PV system.

The outcomes of PV unit is based on the radiation of solar which is elaborated in Equation (1), $P_{o / p}^{PV} = \frac{Irad}{{Irad}_{stc}} \times η_{PV} \times s \times P_{rate}$ (1)

While, the $P_{o / p}^{PV}$ denoted as output power of PV arrays, efficiency of PV modules are denoted as η_PV, P_rate is represented as the rated power of every unit, Irad explained a global irradiance incident on tilted plane, Irad_stc illustrated a standard irradiance and s is significance the optimal size of PV units. In standard condition the temperature of the system is 25⁰ C and irradiance is 1000 W/m2.

3.1.2 Modelling of fuel cell (FC) and aqua-electrolyzer (AE)

Fuel cell is a electrochemical devices create DC electricity by the reaction of hydrogen and oxygen. FC has (i) a reformer, (ii) a layer or unit of cells and (iii) a unit of power conversion. $g_{fc} (S) = \frac{Δ p_{fc} (Q)}{U_{2}} = \frac{k_{fc}}{1 + {Qt}_{fc}}$ (2) here the constant of FC gain and time is denoted as t_fc and k_fc, the incremental change of output power as FC is denoted as Δp_fc.

The aqua electrolyzer absorb quickly and fluctuating the output of PV and produce the hydrogen on FC [36, 37]. The model of aqua electrolyzer for small signal stability is described at Equation (3). $g_{ae} (S) = \frac{Δ p_{ae} (Q)}{U_{2}} = \frac{k_{ae}}{1 + {Qt}_{ae}}$ (3)

While, k_ae and t_ae refers gain and time constant of AE, correspondingly.

3.1.3 Ultra capacitor modelling

The electric double-layer capacitor is also called Super capacitors. The super capacitor is electrochemical capacitors that have high energy density and it compared to conventional capacitors. Smoothing out transients and matching UC load probes is the other option. The advantages of UC are high flexibility, the rate of fast charging and discharging, simple structure and high efficiency. The charge stored on UC designed with (4). $e_{uc} (S) = 0.5 c (v_{IN}^{2} v_{FINAL}^{2})$ (4) here c implies capacitance on Farad; v_FINAL and v_IN are last voltages and initial voltages of UC. Modelling of Ultra Capacitor is shown in Fig. 3.

Fig. 3

Modelling of Ultra Capacitor.

g_{uc} (S) = \frac{Δ p_{uc} (S)}{U} = \frac{k_{uc}}{1 + {St}_{uc}}

(5)

In Equation (5), Δp_uc refers incremental change as UC; t_uc and k_uc refers time constant and gain of UC.

3.1.4 Fly wheel modeling

FESS stores electric energy under kinetic energy thus the stored energy may be released through energy crisis. The benefits of FESS are high energy density, and sensitivity. This is done with the energy stored in the FESS (6). $g_{fess} (S) = \frac{Δ p_{fess} (S)}{U} = \frac{k_{fess}}{1 + {St}_{fess}}$ (6) here Δp_fess refers incremental change of output power; k_fess and t_fess refers gain and time constant.

3.1.5 Modelling of Battery Energy Storage System (BESS)

The power productions of RES extremely based on condition of weather. By saving excess power of RES and when PV, WT, DG loads are inadequate or both the micro sources and the main phase fail to fulfil the overall load requirement or MG load change then the BESS is used. The fluctuation of WT and PV is smoothed by BESS. The generated power of RES is higher than the load for the future use and the extra power is saved in Bess system. The factor such as RES generated power, state of charge (SOC) and overall demand of loads are used for store the energy in BESS at time of t. It is elaborated in Equation (7), $E_{t}^{B} = E_{t 1}^{B} + (\frac{E_{t}^{RES} E_{t}^{Load}}{η_{DC / AC}}) \times η_{ch}$ (7)

While, $E_{t}^{RES}$ is represents as whole energy created by RESs, $E_{t}^{Load}$ is signifies as total necessary energy on MG system and battery charging efficiency is denoted as η_ch.

3.1.6 Proportional-Integral-Derivative (PID) Controller

The conventional PID controller model is integrated on HEPS recover the disturbance rejection capability of system. The control law equivalent to the PID controller is described at (8) $u (Q) = K_{P} [1 + \frac{1}{{Qt}_{I}} + {Qt}_{D}] e (S)$ (8)

While, the K_P, K_I and K_D refers gain, integral and derivative time constant and E(T) denoted as error input.

If controller has an input step function, the operated signal indicates a boost function, thus causing a stability issue. This event is called the fixed point kick. The received block located on feedback path. Again, the difference method is very sensitive to high frequency noise.

3.1.7 Diesel engine modelling

The PV line does not match the load requirement to supply the power shortage on diesel engine modeling HEPS. The model of diesel generator portrays on Equation (9). $g_{deg} (Q) = \frac{Δ p_{deg} (Q)}{U} = \frac{k_{deg}}{1 + {Qt}_{deg}}$ (9)

While, Δp_deg denoted as incremental change of DEG; k_DEG and t_DEG refers gain and time constant.

3.1.8 General microgrid model

The full network, inverter, and load model are combined to signify the microgrid model. The node voltage is input of every sample. To make sure node voltage, large virtual resistors are assumed at every network node as well as ground [38]. Node voltage based on inverter load current output, current and line current may be described, $Δ V_{B} {dq}_{I} = Rn (Δ I_{OdqI} Δ I_{Load dqI} + Δ I_{NetdqI})$ (10)

The node voltage of microgrid model is provided: $[Δ V_{B dqI}] = r_{n} (\begin{matrix} m_{INV} [Δ I_{OdqI}] + \\ m_{load} [Δ I_{Load dqI}] + \\ m_{Net} [Δ I_{Net dqI}] \end{matrix})$ (11)

While, RN refers diagonal matrix of size (2 N×2 N).

3.2 Small signal stability

The stability of small signal on MG is evaluated using linearized model of the source and load of microgrid. The converter model is represented using converter current, output current states, and converter capacitor voltage. The actual and reactive power output at the output voltage angle, power control, voltage control and current control stages. Every converter is made individually in its own reference frame (dq). The load and network designed using its position-space equations. The state space equations are combined to express the total state space equation of the microgrid on common reference frame (DQ). To recover the system stability, the diverse supplementary control loops may be included.

3.2.1 Assessment of small-signal stability

A straightforward way to evaluate small-signal stability is eigenvalue of a power system model. “Small-signal” perturbations are deemed small enough to allow the equations, which represent the system to be linear. The operating condition and the controller parameter are influenced by the dynamic performance and they are demonstrated by observing the eigenvalues. The eigenvalues has most important influence on network dynamic performance [39 –42]. $\overset{\cdot}{X} = aX + bU$ (12)

Here, the eigenvalues of state matrix deliver essential information on small-signal stability of system.

(A) Power Controller

System frequency and voltage controlled using standard PI controllers depend on real-time self-tuning system with proposed technique. The controller denotes the external control loop that is used to create reference current vectors $I_{D}^{*}$ and $I_{Q}^{*}$ . The block diagram of current controller portrays on Fig. 4.

Fig. 4

Block diagram of current controller.

The equivalent state space equations may be worked out as: $\begin{matrix} \frac{D γ_{D}}{DT} = v^{*} v, \\ \frac{D γ_{D}}{DT} = F^{*} F \end{matrix}$ (13)

The output equations are specified by, $I_{E}^{*} = k_{PV} (v^{*} v) + k_{IV γ E}$ (14) ${Is}^{*} = k_{PF} (F^{*} F) + k_{IF γ s}$ (15)

The input to the power controller may be separated into two terms, which can be described as linear small-signal state space equations: reference input and feedback input: $\begin{matrix} [Δ_{γ DQ}^{*}] = a_{P} [Δ γ_{DQ}] + \\ b_{P 1} {[Δ v^{*} Δ F^{*}]}^{t} + \\ b_{P 2} {[Δ v^{*} Δ F^{*}]}^{t} \end{matrix}$ (16) here $\begin{matrix} Δ γ_{DQ} = {[Δ γ_{D} Δ γ_{Q}]}^{t}, \\ a_{P} = [0], b_{P 1} = [\begin{matrix} 1 0 \\ 0 1 \end{matrix}], \\ b_{P 2} = [\begin{matrix} 1 0 \\ 0 1 \end{matrix}] \end{matrix}$ (17)

$\begin{matrix} [Δ_{γ DQ}^{*}] = c_{P} [Δ γ_{DQ}] + d_{P 1} {[Δ v^{*} Δ F^{*}]}^{t} \\ + d_{P 2} {[Δ v^{*} Δ F^{*}]}^{t} \end{matrix}$ (18) here $\begin{matrix} Δ I_{DQ}^{*} = c_{P} [Δ γ_{DQ}] + \\ d_{P 1} {[Δ v^{*} Δ F^{*}]}^{t} + \\ d_{P 2} {[Δ v^{*} Δ F^{*}]}^{t} \end{matrix}$ (19) $\begin{matrix} d_{P 1} = [\begin{matrix} K_{PV} 0 \\ 0 K_{PF} \end{matrix}], \\ d_{P 2} = [\begin{matrix} K_{PV} 0 \\ 0 K_{PF} \end{matrix}] \end{matrix}$ (20)

(B) Current Controller

The current controller is utilized to make sure short transient and accurate monitoring of the inverter output current. The controller is regularly on these ways so that voltage used to the induction resistor R-L is such that one impulse current on inductor takes the minimal error. The two PI regulators utilized to remove current error to gain voltage forward loop and the inverter current control loop. Inductance coupling is not deemed as (Vb = Vo). The equivalent state space equation is described, $\frac{E φ_{E}}{ET} = I_{E}^{*} - I_{LE}, \frac{E φ_{Q}}{ET} = I_{Q}^{*} - I_{LQ}$ (21)

The output equation given by, $\begin{matrix} V_{D}^{*} - V_{OD} ω_{N} l_{S} I_{LQ} + \\ k_{PC} (I_{D}^{*} - I_{LQ}) + k_{IC} φ_{D} \end{matrix}$ (22) $\begin{matrix} V_{Q}^{*} - V_{OQ} + ω_{N} l_{S} I_{LQ} + \\ k_{PC} (I_{Q}^{*} - I_{LQ}) + k_{IC} φ_{Q} \end{matrix}$ (23)

The Linearized small signal state space equations:

$\begin{matrix} [\overset{•}{Δ φ_{Dφ}}] = a_{C} [Δ φ_{DQ}] \\ + b_{C 1} [I_{DQ}^{*}] + b_{C 2} [\begin{matrix} Δ I_{LDQ} \\ Δ V_{ODQ} \\ Δ I_{ODQ} \end{matrix}] \end{matrix}$ (24) here $\begin{matrix} Δ φ_{DQ} = {[Δ φ_{D} Δ φ_{Q}]}^{t}, \\ a_{C} = [0], b_{C 1} = [\begin{matrix} 1 0 \\ 0 1 \end{matrix}] \end{matrix}$ (25) $b_{C 2} = [\begin{matrix} 1 0 0 0 0 0 \\ 0 1 0 0 0 0 \end{matrix}]$ (26) $\begin{matrix} [Δ V_{DQ}^{*}] = c_{C} [Δ φ_{DQ}] + d_{C 1} [Δ I_{DQ}^{*}] + \\ d_{C 2} [\begin{matrix} Δ I_{LDQ} \\ Δ V_{ODQ} \\ Δ I_{ODQ} \end{matrix}] \end{matrix}$ (27) $\begin{matrix} c_{C} = [\begin{matrix} K_{IC} 0 \\ 0 K_{IC} \end{matrix}], \\ d_{C 1} = [\begin{matrix} K_{PC} 0 \\ 0 K_{PC} \end{matrix}] \end{matrix}$ (28) $d_{C} = [\begin{matrix} K_{PC} ω_{N} l_{S} 1 0 0 0 \\ ω_{N} l_{S} K_{PC} 0 1 0 0 \end{matrix}]$ (29)

4 Proposed system

CHGSO is a new metaheuristic based on the integration of chaotic maps in the Henry Gas Solubility Optimization (HGSO) algorithm [43]. RERNN has selective memory properties. An improved conjugate algorithm enhanced by a generalized Armijo search system is used to train the RERNN model [44].

4.1 CHGSO approach

One of the physics based approach is the Henry gas solubility optimization (HGSO) which is inspired based on the characteristics of Henry’s law [41]. The important gas law is the Henry’s law which is related based on the volume of a given gas dissolved in a given type and volume of liquid at a constant temperature. HGSO follows the huddling characteristics of the gas to balance exploitation and exploration in the search area and to avoid local optimization. In this paper proposed the integrating the chaotic map to HGSO for improve convergence rate of the HGSO. There are varies chaotic maps like chebyshev map, circle map, gauss/mouse map, iterative map, logistic map, piecewise map, sine map, singer map, sinusoidal map, tent map. Different chaotic maps have different ergodic properties. Therefore, this is one of the main reasons why different chatic maps can lead to different search formats based on convergence rate, algorithm speed and accuracy. The step wise procedure of CHGSO is described below.

4.1.1 Stepwise procedure of CHGSO approach

Step 1: Initialization with Random Generation

The Fuel cell, aqua electrolyzer, photovoltaic, ultra-capacitor, Diesel generator, fly wheel energy storage system and PI controllers K_p and K_i are initialized. The initialized parameters generated randomly in the given matrix Y_i, $Y_{i} = [\begin{matrix} Y_{1}^{1} Y_{1}^{1} \land Y_{N_{L 1}}^{1} \\ Y_{1}^{2} v Y_{1}^{2} \land Y_{N_{L 1}}^{2} \\ M M M M \\ Y_{1}^{M} Y_{1}^{M} \land Y_{N_{L 1}}^{M} \end{matrix}]$ (30)

Step 2: Fitness (objective) function evaluation

The initialized parameters based, the current best position is determined. $O_{i} = Min (e (t))$ (31)

Step 3: Generate New Position

The newly position generates via the CHGSO at the search space. Sometimes, a newly position generates via the CHGSOⁱwhich selects randomly a best CHGSO (CHGSO^j) and imitates it to find out the position (m^j). The generated new position of CHGSOⁱ is exhibited as,

$\begin{matrix} Y_{i, iter + 1} \\ = {\begin{matrix} Y_{i, iter} + r_{i} \times {fl}_{i, iter} \times {(m_{i, iter} Y_{i, iter})}_{i, iter} \\ + r_{i} \times {fl}_{i, iter} \times (m_{i, iter} Y_{i, iter}) r_{j} ⩾ {AP}_{i, iter} \\ arandompositionotherwise \end{matrix} \end{matrix}$ (32)

The random number r_j is created amid the 0 and 1 uniform distributions. Flowchart of chaotic Henry gas solubility optimization (CHGSO) is displayed in Fig. 5.

Fig. 5

Flowchart of CHGSO.

Step 4: Verify the possibility of novel positions

Here, the possibility of each CHGSO new position is verified. When the novel position of a CHGSO is possible, the location is updated, or CHGSO stays at current position not shift the newly generated position. Then, the objective function is calculated to newly position of every CHGSO.

Step 5: Updating

The CHGSO’s best position is efficient through, $Y_{i, iter + 1} = {\begin{matrix} Y_{i, iter + 1} \\ f (Y_{i, iter}) isbetterthanf (m_{i, iter}) \\ m_{i, iter} otherwise \end{matrix}$ (33)

At beyond equation, term Y_i,iter+1 indicates the value of objective function.

Step 6: Termination

Once the procedure of CHGSO is done, the procedure repeats as 3 to 5 till the maximal iteration is attained.

4.2 RERNN

The RERNN structure includes five layers as Input, State, Hidden, Output, and Delay Layer. The RERNN structure with multiple inputs and outputs are displayed in Fig. 6. The steps involved in RERNN are explained given below,

Fig. 6

Architecture of Recurrent Neural Network (RERNN).

Step 1: Initialization

Initially, Fuel cell, aqua electrolyzer, photovoltaic, ultra-capacitor, Diesel generator, fly wheel energy storage system and PI controllers K_p and K_i initialized in this step.

Step 2: Random Generation

After initialization process the input vectors are randomly created. Simultaneously, the input parameter of EV system such as SOC of battery, Engine speed and torque, the power of the battery, EM speed and torque are randomly created.

Step 3: Check the iteration

The iteration of the process is fewer when compared with maximal iteration then the data process will stop.

Step 4: Find learning rate via Armijo search

According to Armijo search, learning rate is determined and the equation is expressed as, $e (W^{K} + l_{r} P^{K}) ⩽ e (W^{K}) + α_{1} l_{r} e_{W}^{K} (P^{K})^{T}, α_{1} ⩾ 0$ (34)

Step 5: Compute the novel weight

The gradient descent algorithm is used to find out novel weight and it is calculated based on the below equation, $w^{k + 1} = w^{k} + L_{R} P^{k}$ (35)

Step 6: Check maximal iteration

Once maximum iteration is gotten the process will end. On other hand the iteration value will increase and it goes to step 6. Flowchart of RERNN portrays on Fig. 7.

Fig. 7

Flowchart of RERNN.

Step 7: Compute the direction

The calculation of learning process of the direction takes place, $P^{k} = E_{w}^{k} + β P^{k 1}$ (36) $β = \frac{α E_{w}^{k} (P^{k - 1})^{t}}{P^{k - 1} (P^{k - 1} - E_{W}^{k})}, α \in (0, 1)$ (37)

Then, it goes to step 4 and the process will repeat again. Figure 7 shows the flow chart of RERNN approach.

5 Result and discussion

In this section, a hybrid control system for small-signal stability for MGs under uncertainty with CHGSO-RENNN system. The proposed controller is performed on MATLAB/Simulink work platform and its performances are evaluated. The existing systems are Sine Cosine Algorithm (SCA), Quasi-Oppositional Sine Cosine Algorithm (QOSCA), Gray Wolf Optimizer (GWO), and Hyper-spherical Search (HSS).

Figure 8 displays convergence properties of (a) proposed by energy storage devices (b) Comparison of ITAE for proposed and existing system. The converge characteristic of prosed with energy is shown in Fig. 8(a). Without storage system, when the value of fitness is 0.7405 then the number of generator value is 4. When the value of fitness is 0.607 then the number of generator value is 10. When the value of fitness is 0.6603 then the number of generator value is from 20 to 80. When the value of fitness is 0.6601 then the number of generator value is from 90 to 100. With FESS and BESS, when the value of fitness is 0.7405 then the number of generator value is 0. When the value of fitness is 0.0605 then the number of generator value is 10. When the value of fitness is 0.6603 then the number of generator value is from 20 to 30. When the value of fitness is 0.66 then the number of generator value is from 40 to 60. When the value of fitness is 0.6507 then the number of generator value is from 70 to 80. When the value of fitness is 0.6403 then the number of generator value is from 90 to 100. With FESS and UC, when the value of fitness is 0.7405 then the number of generator value is 4. When the value of fitness is 0.7 then the number of generator value is 10. When the value of fitness is 0.69 then the number of generator value is 20. When the value of fitness is 0.6804 then the number of generator value is from 30 to 40. When the value of fitness is 0.6403 then the number of generator value is 50. When the value of fitness is 0.6402 then the number of generator value is from 60 to 100. Comparison of ITAE for proposed and existing system shown in Fig. 8(b). The existing techniques are SCA, HSS and GWO then the proposed techniques are CHGSO-RERNN.

Fig. 8

Convergence properties of (a) Proposed by energy storage devices (b) Comparison of ITAE for proposed and existing technique.

The HEPS analysis (a) Frequency variant using ΔP_d = 0.01 pu, (b) Frequency variant using Δφ = 0.01 pu is shown in Fig. 9. With FESS+BESS, if frequency offset value is –10, the time value is 0.5. If frequency offset is –1, then time value is 1. When the frequency offset value is –1.7, the time value is 1.5. When the frequency offset value is –1.8, the time value is 2. If frequency offset value is 0, then time value is 2.5. If frequency offset is 1, then time is 3. If frequency offset value is 1.2, then time value is 3.5. When the value of frequency deviation is 1.3 then value of the time is 4. If frequency deviation is 1.4 then the time is 4.5. If frequency deviation is 1.5 then the time is 5. With FESS+UC, If frequency deviation is –9 then the time is 0.5. If frequency deviation is –1 then the time is 1. If frequency deviation is –1.05 then the time is 1.5. If frequency deviation is –1.07, then time is 2. If frequency deviation value is 0, then time is 2.5. If frequency deviation value is 1.2, then time is 3.5. If frequency offset value is 1.3, then time value is 4. If frequency offset value is 1.4, then time value is 4.5. If frequency offset value is 1.5, then time value is 5. Without storage device, if frequency deviation value is 0, then time is 0. If frequency deviation value is 0, then time is 0. When the value of frequency deviation is –13, the value of time is 0.5. If frequency offset value is 3, then time value is 1. When the frequency offset value is –1.07, then time value is 1.5. When the frequency offset value is –2, the time value is 2. When the frequency offset value is 1.7, the time value is 2.5. When the frequency offset value is 1.2, the time value is 3. If frequency value is 0, then time value is 3.5. If frequency offset value is 1.7, the time value is 4. If frequency value is 0, then time value is 4.5. When the frequency offset value is 0, then time is 5. The HEPS performance for frequency offset with pu is shown in Fig. 9(b). Without storage system, if frequency value is 0, then time value is 0. When the frequency value is 0.5, the time value is –3.5. If frequency offset value is 1, then time value is –5.5. When the frequency offset value is –4.5, the time value is 1.5. When the frequency offset is –2, then time is 2. If frequency offset value is –0.6, the time value is 2.5. If frequency deviation is 0.7, then time is 3. If frequency deviation value is 0.704, then time is 3.5. When the value of frequency deviation is 0.7, then time is 4 to 5. With FESS+BESS, when the value of frequency deviation is 0, then time is 0. When frequency deviation is - 3.5 so the time value is 0.5. If frequency offset value is –5.7, the time value is 1. If frequency offset value is –4, then time value is 1.5. If frequency offset value is –4, the time value is 1.5. When the frequency offset is –2.3, then time is 2. If frequency offset is –0.7, then time is 2.5. If frequency value is –0.7, then time is 3 to 5. With FESS+UC, if frequency value is 0, then time value is 0. of the frequency deviation is –3.5 the time value is 0.5. If frequency offset value is –6, the time value is 1. If frequency offset value is –4, the time value is 1.5. If frequency offset value is 0.4, then time is 2.5. If frequency deviation is 3, then time is 0.7. If frequency deviation is 3.5, then time is 0.6. If frequency deviation is 4, then time is 0.7. If frequency deviation is 4.5, then time is 0.8. When the frequency deviation value is 5, then time is 0.8.

Fig. 9

Analysis of HEPS (a) Frequency variant using ΔP_d = 0.01pu, (b) Frequency variant using Δφ = 0.01pu.

Comparison of proposed HEPS (a) frequency variant using ΔP_d = 0.01 pu, (b) frequency variant using Δφ = 0.01 pu is shown in Fig. 10. The comparison of proposed for frequency variant using ΔP_d = 0.01 pu is displayed in Fig. 10(a). With FESS and BESS, when the value of the fitness is 0.7403 then the number of generation value is 1. When the value of the fitness is 0.6803 the value of then the number of generation value is 10. When the value of the fitness is 0.6604 then the number of generation value is from 20 to 30. When the value of the fitness is 0.66 then the number of generation value is from 40 to 50. When the value of the fitness is 0.6601 then the number of generation value is from 60 to 100. With FESS and UC, when the value of the fitness is 0.7404 then the number of generation value is 2. When the value of the fitness is 0.7 then the number of generation value is 10. When the value of the fitness is 0.6905 then the number of generation value is 20. When the value of the fitness is 0.6804 then the number of generation value is from 30 to 40. When the value of the fitness is 0.6404 then the number of generation value is 50. When the value of the fitness is 0.6402 then the number of generation value is from 60 to 100. Without storage system, when the value of the fitness is 0.74 then the number of generation value is 2. Without storage system, when the value of the fitness is 0.6707 then the number of generation value is 10. Without storage system, when the value of the fitness is 0.6604 then the number of generation value is from 20 to 80. Without storage system, when the value of the fitness is 0.6602 then the number of generation value is from 90 to 100.

Fig. 10

Comparison of proposed HEPS (a) frequency variant using ΔP_d = 0.01 pu, (b) frequency variant using Δφ = 0.01pu.

Performance of output power (a) DGs, (b) AE, (c) FC (p.u) and DEG (p.u) is shown in Fig. 11. The performance of DGs output power is shown in Fig. 11(a). If DGs output power is –1 then the time is 0. If DGs output power is –5 then the time is 2. If DGs output power is –4.5 then the time is 4. If DGs output power is –2.4 then the time is 6. If DGs output power is –1.5 then the time is 8. If DGs output power –1.6 then the time is 10. If DGs output power –1.7 then the time is 12. If DGs output power –1.604 then the value of time is 14. When the value of DGs output power –1.8 then the value of time is from 16 to 20. The performance of Output power of AE(p.u) is shown on Fig. 11(b). When the value of output power of AE is 6.5 then the value of time is 1. When the value of output power of AE is 4 then the value of time is 2. When the value of output power of AE is 4.5 then the value of time is 4. When the value of output power of AE is 3.5 then the value of time is 6. When the value of output power of AE is 2.6 then the value of time is 8. When the value of output power of AE is 2.5 then the value of time is 10. When the AE output power value is 2.4, the time value is 12. When the AE output power value is 2.5, the time value is 14. When the AE output power value is 2.404, the time value is 16. When the AE output power value is 2.3, the time value is 18 to 20. The performance of the FC output power (p.u) is shown in Fig. 11(c). When the FC output power value is 0, the time value is 0.8. When the FC output power value is 12, the time value is 0.8. When the FC output power value is 12, the time value is 2. When the FC output power value is 17, then the time value is 4. When the FC output power value is 16, then the time value is 6. When the FC output power value is 15.9, the time value is 8. When the FC output power value is 15, the time value is 10 When the HR output power value is 14.3, then the time value is 12. When the HR output power value is 14.1, then the time value is 14. When the power value When the FC output power value is 13.9, then the time value is 16. When the FC output power value is 13.8, then the time value is 18. When the FC output power value is 13.6, the time value is 20. The output power performance of DEG (p.u) portrays on Fig. 11(d). When the DEG output power value (p.u) is 0, then the time value is 0. When the DEG output power value (p.u) is 4, then the time value is 2. When the value of DEG output power (p.u) is 5.7, then the value of time is 4. When the value of DEG output power (p.u) is 5.5, then the value of time is 6. When the value of output power of DEG (p.u) is 4.7 then the value of time is 8. When the output power of DEG (p.u) is 4.5 then the value of time is 10. When the output power of DEG (p.u) is 4.4 then the value of time is 12. When the value of output power of DEG (p.u) is 4.3 then the value of time is 14. When the output power of DEG (p.u) is 4.1 then the value of time is 16. When the output power of DEG (p.u) is 4 then the value of time is from 18 to 20.

Fig. 11

Performance of output power (a) DGs, (b) AE, (c) FC (p.u) and DEG (p.u).

The performance of output power (a) DGs (p.u), (b) AE (p.u), (c) FC (p.u) and (d) DEG (p.u) is shown in Fig. 12. The Performance of DGs output power is shown in Fig. 12(a). If DGs output power is 1 then the time is –4.6. If DGs output power is 2 then the time is –7.2. If DGs output power is 3 then the time is –8.4. When the DG output power value is 4. When the DG output power value is 5, the time value is –9.3. When the DG output power value is 6, time value is –9.5. If DGs output power is 7 then the time is –9.7. If DGs output power is 8 then the time is –9.8. When the value of DGs output power is from 9 to 10 then the value of time is –9.8. The Performance of output power of AE is shown at Fig. 12(b). When the value of Output power of AE is 5 then the value of time is 2.7. When the value of Output power of AE is 10 then the value of time is 2.5. When the value of Output power of AE is 15 then the value of time is 2.3. When the value of Output power of AE is 20 then the time is 2.2. When the value of Output power of AE is 25 then the value of time is 2.1. The Performance of output power of FC (p.u) is shown in Fig. 12(c). When the HR Power Output (p.u) value is 9.8, the time value is 5. When the HR Power Output (p.u) value is 11.1, the time value is 10. HR Power Output (p.u) value is 10.2, and then the time value is 15. When the HR Power Output (p.u) value is 9.9, then the time value is 20. FC Output Power (p.u) value is 9.7, so the time value is 25. The output power performance of DEG (p.u) is shown in Fig. 12(d). When the HR output power (p.u) value is 3.5, the time value is 5. When the HR output power (p.u) value is 3.7, then the time value is 10 When the HR output power (p.u) value is 3.3, the time value is 15. When the HR output power (p.u) value is 3.1, then the time value is 20. When the value of FC output power (p.u) is 3, the value of time is 25.

Fig. 12

Performance of output power (a) DGs (p.u), (b) AE (p.u), (c) FC (p.u) and (d) DEG (p.u).

The dynamic analysis of HEPS with the proposed frequency offset and variation is shown on Fig. 13. The dynamic performance of HEPS with the proposed frequency deviation portrays on Fig. 13(a). In Study Case 1, if frequency offset value is –11, then the time value is 0.1. If frequency deviation is –3, then time is 1. When the frequency offset value is –0.9, the time value is 2. When the frequency offset value is 0.4, the time value is 3. When the frequency offset value is 0.1, the time value is 4. If frequency value is 0.2, the time value is 5. If frequency value is 0.4, then time value is 6 to 10 In Case Study 2, when the frequency offset value is 0, the time value is 0. When the frequency offset value is –3, the time value is 1. When the frequency offset value is –1.7, the time value is 2. If frequency value is 0.1, then time value is 4. If frequency value is 0.2, the time value is 5. The frequency value is 0.4, the time value is from 6 to 10. At nominal value, when the frequency offset value is –11.4, the time value is 0.5. When the frequency offset value is –3, the time value is 1. When the frequency offset value is 0, the time value is 2. When the frequency offset value is 1, the time value is 3. When the frequency value is 0.1, the time value is 4. When the frequency value is 0.2, the time value is 5. When the frequency value is 0, 4, the time value is from 6 to 10. The dynamic performance of HEPS with the proposed variation is shown in Fig. 13(b). In Study Case 1, if frequency offset value is 1.7, then time value is 0.1. If frequency offset value is 0.2, then time value is 0.5. When the frequency offset value is 1 to 3, the time value is 0.1. In Study Case 2, if frequency offset value is 3.7, then time value is 0.5. If frequency offset value is –0.7, then time value is 0.5. When the frequency offset value is 0.4, then time value is 1. When the frequency offset value is 1 to 3, the time value is 0.1. At nominal, when the frequency deviation value is 2.3, the time value is 0.5. When the frequency offset value is 1, the time value is 1.4. When the frequency offset value is 1.5 to 3, the time value is 1.

Fig. 13

Analysis of (a) frequency deviation for case studies (b) ΔP_e variation for case studies.

The frequency deviation of HEPS with RLP portrays on Fig. 14. If frequency deviation value is 0, then time value is 0. When the frequency value is –1.03, the time value is 10. If frequency offset value is 1.03, the time value is 20. If frequency offset value is –1.09, the time value is 30. If frequency offset value is –3.05, the time value is 40. When the frequency deviation value is 3.05, the time value is 50. If frequency offset value is –1.01, the time value is 60. When the frequency deviation value is 1.01, the time value is 70. If frequency offset value is 2.04, the time value is 80. If frequency offset value is –2.04, the time value is 90. When the frequency deviation value is 1.02, the time value is 100.

Fig. 14

Frequency deviation of HEPS with RLP.

Dynamic analysis of HEPS using proposed (a) frequency deviation, (b) ΔP_e variation is shown on Fig. 15. Dynamic performance of HEPS with proposed for frequency deviation portrays on Fig. 15 (a). If frequency offset value is 0, the time value is 0. If frequency offset value is –0.01, then time value is 2. If frequency offset value is 0, then time value is 4 If frequency offset value is 0.001, then the time value is 6. If frequency offset value is 0.004, the time value is 8. If frequency offset value is 0.002, then time value is 10 to 20. Dynamic performance of HEPS with proposed in ΔP_e variation is shown in Fig. 15(b). When the value of frequency is 0.007 then time is 1. When frequency is 0.003 then the time is 2. When the value of frequency is 0.002 then time is 4. If frequency is 0.001 then the time is from 6 to 20.

Fig. 15

Analysis of (a) frequency deviation (b) power variation using proposed technique with typical variation.

Dynamic analysis of HEPS using proposed (a) frequency deviation, (b) ΔP_evariation is shown on Fig. 16. Dynamic performance of HEPS with proposed for frequency deviation is shown on Fig. 16 (a). The value of time is 0. If frequency offset value is 0.006, the time value is 1. When the frequency value is 0.001, the time is 5. If frequency offset value is 0.002, the time value is 10. When the frequency value is 0.003, then the time value is 15. If frequency value is 0, the time value is 20 to 40. Dynamic performance of HEPS with proposed in ΔP_e variation is shown in Fig. 16(b). When the value of frequency is 0.007 then the time is 1. When the value of frequency is 0.002 then the time is 5. When the value of frequency is 0.001 then the value of time is 10. When the value of frequency is 0 then the value of time is from 15 to 30.

Fig. 16

Analysis of (a) frequency deviation (b) power variation using proposed technique when –0.03 to 0.005 Hz.

Dynamic analysis of HEPS using proposed (a) frequency deviation, (b) ΔP_e variation is shown in Fig. 17. Dynamic performance of HEPS with Proposed in frequency variation is displayed in Fig. 17(a). When the value of frequency is 0.006 then time is 1. When the frequency is 0.007 then time is 5. When the value of frequency is 0.005 then the value of time is 10. If frequency is 0.004 then time is 15. When the value of frequency is 0.003 then the time is 20. If frequency is 0.002 then the time is 25. When the value of frequency is 0.0024 then the time is 30. If frequency is 0.00024 then the time is 35. If frequency is 0.0001 then the time is 40. Dynamic performance of HEPS with Proposed in ΔP_e variation is displayed in 17(b). When the value of frequency is –0.037 then the time is 1. If frequency value is 0.007, then time value is 5. If frequency value is 0.004, then time is 10. If frequency value is 0.003, then time is 15. If frequency value is 0.003, then time is 15. If frequency value is 0.002, then time is 20. If frequency value is 0.001, then time is 25. When the frequency value is 0.001, the time value is 30 to 40. Robustness of the solution techniques is shown in Fig. 18.

Fig. 17

Analysis of (a) frequency deviation (b) power variation using proposed technique when –0.035 to 0.01 Hz.

Fig. 18

Robustness of the solution techniques.

6 Conclusion

In this manuscript, a hybrid control system for small-signal stability analysis for microgrids under uncertainty. The CHGSO methodology is used to recognize the optimal data’s from the open search space in the context of the objective function and creates the possible sensible data sets. By using the completed data set, the RERNN is carried out through whole machine operating condition. The proposed controller is performed on MATLAB/Simulink work platform and their performance is related with existing methods. The performance of proposed and existing systems is graphically illustrated. The existing systems are sine cosine algorithm (SCA), quasi-oppositional sine cosine algorithm (QOSCA), gray wolf optimizer (GWO), hyper-spherical search (HSS). The proposed hybrid system is the combination of Chaotic Henry Gas Solubility Optimization (CHGSO) and Recalling Enhanced Recurrent Neural Network (RERNN) therefore it is known as CHGSO-RERNN technique. Robustness of the proposed technique is 92%. This work can also be modified to fit other sorts of distributed control for power systems that use other communication and control disciplines.

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