
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)11279-0
10.1016/j.heliyon.2024.e35248
e35248
Research Article
Design and experimentation of a simple fuzzy pi-based ac chopper electronic load controller for pico hydropower system
Ndukwe Samuel C. samuel_21001605@utp.edu.my
ndukwesamuelc123@gmail.com
⁎
Kannan Ramani
Wei Ho Tatt
Dept of Electrical & Electronics Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750, Tronoh, Perak, Malaysia
⁎ Corresponding author. samuel_21001605@utp.edu.myndukwesamuelc123@gmail.com
27 7 2024
15 9 2024
27 7 2024
10 17 e3524820 3 2024
18 6 2024
25 7 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
The use of electronic load controllers (ELCrs) is widely adopted in pico hydropower systems to maintain output power supplied to the consumer load, regardless of changes in consumer demand. This is due to the absence of moving mechanical parts, affordability, prevention of the hammer effect in pipes, and being more efficient than the governor systems. However, implementing existing ELCrs in a pico hydropower system can pose challenges related to power quality, efficiency, or costs. In this paper, a fuzzy PI-based single-switch bidirectional AC chopper electronic load controller (FP-SSBAC ELCr) is proposed. This configuration reduces the number of insulated gate bipolar transistors (IGBTs) from two, typically found in the conventional bidirectional AC choppers, to one per phase, resulting in cost reduction. A hybrid controller, comprising fuzzy and PI controllers, is designed to quickly maintain a constant output voltage and frequency when consumer load abruptly changes. The gains of the PI controller are updated by the fuzzy logic controller based on the voltage error and its derivative. The proposed model is simulated in MATLAB/Simulink and validated experimentally under sudden changes in consumer load. The results achieved with the FP-SSBAC ELCr demonstrate improved dynamic performance without overshoot compared to PI-based ELCrs. The highest recorded voltage and current total harmonic distortions (THDs) are 2.8 % and 2.1 %, respectively, meeting the IEEE 519 standard. Therefore, the proposed model has the potential to enhance performance and efficiency and can be implemented cost-effectively in pico hydropower systems.

Keywords

Electronic load controller (ELCr)
Fuzzy logic controller
Harmonics
Pico hydropower plant (PHP)
IGBT
==== Body
pmc1 Introduction

Many alternative and renewable energy sources (RES) are presently the subject of extensive global exploration. RES are sought after because they are environmentally friendly, produce no pollution and are naturally replenished. RES contribute about 30 % of global energy production [1]. Amongst the RES, hydropower holds the top position for conversion efficiency [2,3] and has a low cost of operation and maintenance. Hydropower stands as the most widely utilized renewable energy source, making up approximately 15 % of the total global energy production [4]. Pico hydropower (PHP) is the smallest-scale hydropower with a capacity of up to 5 kW. It is considered a family hydropower in some countries because it can be owned and installed by one household [[5], [6], [7]]. PHP can be seamlessly integrated into the environment without the need for significant considerations such as large-scale resource storage or population resettlement. As a result, the energy capacity of the pico-hydro source exhibits substantial promise in addressing the energy demands of rural and remote regions.

The generator stands out as a key component within the framework of the pico hydropower system. Therefore, choosing the right generator is crucial when setting up a PHP. Several factors are considered before selecting a generator for pico-hydro. These factors include estimated power, type of consumer loads, the availability of generators in the market, and cost [8]. AC generators namely – induction and permanent magnet synchronous generators are mainly used in pico hydro. Additionally, DC generators can also be used. However, if the generators are 2 kW and above, they are considered costly and involve brush gears, requiring significant maintenance [9]. The use of a self-excited induction generator (SEIG) is preferred in situations where the cost is a significant factor [10,11]. The SEIG exhibits impressive dynamic response, demands low maintenance, incorporates inherent protection against overloads and short circuits, and can generate power across different speeds [10]. Nevertheless, it faces challenges in voltage regulation and consumes reactive power [10,12]. Excitation capacitors provide the SEIG with the necessary reactive power. Controlling the reactive power supply allows for the regulation of the SEIG's output voltage. Efforts have been made using different semiconductor devices to manage the reactive power delivered to the SEIG. The use of a switched capacitor network and static VAR schemes for the provision of reactive power is analysed in Ref. [13]. The switched capacitors are arranged in a binary manner and switched to provide reactive power based on demand. The static VAR compensator is made up of a combination of a fixed-shunt capacitor and a thyristor-controlled reactor. The reactor and the capacitor can be arranged in different topologies as proposed in Refs. [14,15]. However, its slow transient response to the application of a heavy load and injection of harmonics are the major drawbacks [16].

Aside from reactive power control for SEIG, the power generated can be kept at maximum, and a special controller is used to switch excess power not needed by the consumer loads to dummy loads. This special controller is known as an electronic load controller. The generator operates at its highest power output, with the electronic load controller tracking and controlling the power supplied to the load. The voltage and frequency are in turn kept at the desired specifications. The first generation ELCr made use of SCR to control power dumped to the ballast load [17,18]. The SCR is triggered at a conduction angle determined by the error signal. This is known as the phase angle control method. However, it suffers from high harmonic current injections, unequal distribution of current per phase, and shift of the magnetizing curve [19]. A PWM rectifier-chopper-based ELCr for SEIG is designed and implemented in Refs. [20,21]. The controller provides good control but suffers from distortion in the current waveform because of the presence of a bridge rectifier and a big filter capacitor connected across it. In the case of three-phase SEIG, there is an unbalanced current distribution per phase under dynamic and steady-state conditions. Another regulation technique, the binary regulation involves switching individual dummy loads arranged in weight of ascending order [22]. However, due to its size, the number of switches, and complexity, it is not recommended for pico hydro systems. Bidirectional AC chopper ELCr was first proposed by Ref. [23]. The voltage harmonic distortion in this technique is low compared to that of the phase regulation, and PWM rectifier techniques. A synchronized bidirectional AC chopper is reported by Ref. [19]. Other researchers took a different approach replacing the ELCr with STATCOM to solve power quality problems associated with the application of nonlinear loads [[24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35]]. The STATCOM has a voltage source converter (VSC) that provides reactive power, harmonic elimination, and terminal voltage and frequency regulation. When there is excess power, the power is used for charging batteries [26]. On the other hand, when there is power demand, the VSC converts the stored DC voltage to AC voltage thereby keeping the voltage and frequency at the desired values [36]. A decoupled voltage and frequency controller (DVFC) is reported in Refs. [[37], [38], [39]]. The DVFC comprises the three-pulse rectifier bridge ELCr and VSC. The conventional ELCr controls the frequency and voltage while the VSC handles harmonic elimination and load balancing [40]. The active power only flows through the DVFC during unbalanced load conditions; whereas, in the VSC-based ELCr, active power flows continuously [40].

Various control techniques have been reported in the literature. Classical control techniques such as PI and PID are used in Refs. [18,38,41,42] because they are simple and easy to implement. However, these classical controllers prove insufficient in handling transient or continuous disturbances during system operation [43]. Additionally, the fixed gain values of the PI and PID controllers exhibit a slow dynamic response, significant overshoot, and oscillations under varying operating conditions. To address the issues encountered by traditional PI and PID controllers, intelligent controllers such as neural networks, and fuzzy logic controllers have been employed in various ELCr [[44], [45], [46], [47], [48], [49]]. Nevertheless, the real-world implementation of these artificial intelligence (AI) techniques requires substantial training data to understand the system's behaviour, making it a demanding and time-consuming task. Deploying them in practical applications can sometimes be challenging due to computational burdens.

In this work, a simple and efficient model is proposed to improve the performance of the ELCr. The proposed topology uses a bridge rectifier and a single IGBT per phase configured as a bidirectional switch to redirect excess power to a dummy load. This is a continuation of the work reported by Ref. [50]. Utilizing voltage as a control parameter results in a substantial decrease in the circuit's design complexity and the number of components when compared to the bidirectional AC chopper ELCr reported in Ref. [19]. Incorporating a fuzzy PI controller improves the effectiveness of the ELCr. Unlike certain advanced control methods, designing and implementing a fuzzy PI controller is comparatively straightforward, striking a balance between complexity and performance. The controller swiftly controls the voltage in a shorter duration while maintaining V/F ratio of the induction generator. The remaining parts of this paper are structured as follows: Section 2 elaborates on the FP-SSBAC electronic load controller. Section 3 focuses on the controller design. Section 4 presents the Simulink simulation. Section 5 focuses on experimental analysis and discussion. In conclusion, Section 6 summarizes key findings and suggests potential areas for future research.

2 FP-SSBAC electronic load controller

Fig. 1 presents the proposed electronic load controller model. The system comprises the SEIG, consumer load, dump load, and electronic load controller. The electronic load controller maintains a constant power output from the generator. The controller redirects the surplus power the consumer load does not use to the dummy load.Fig. 1 Block diagram of FP-SSBAC electronic load controlled for a pico hydropower plant.

Fig. 1

The total power in the system is given by Eq. (1).(1) PG=PCL+PD

where PG is the power provided by the generator, PCL is consumed by the consumer load, and PD is the power of the dummy load. The proposed electronic load controller consists of one IGBT connected with a bridge rectifier in a bidirectional mode. In the positive half-cycle, solely two diodes (D2 and D4) are in a forward-biased state, as depicted in Fig. 2. The remaining pair of diodes (D1 and D3) are in a reverse-biased state. During the negative half-cycle, D1 and D3 become forward-biased, while D2 and D4 are reverse-biased. The AC power modulation is achieved by applying pulse width modulation signals to the IGBTs' gates, with a defined duty cycle. This topology offers an advantage over the two IGBT bidirectional AC choppers because it reduces the number of IGBTs and driver circuits by 50 %. A hybrid fuzzy PI controller is employed, combining the advantages of a PI controller and a fuzzy logic controller. This controller receives two inputs—the voltage error signal and its derivative. Within the fuzzy PI controller, the fuzzy logic component generates two gains (Kp and Ki), which are utilized by the PI controller to calculate the output value. This resultant output from the fuzzy PI controller is then directed to a PWM generator, which generates an equivalent PWM signal for the IGBT gate.Fig. 2 Direction of current flow (a) positive cycle (b) negative half cycle.

Fig. 2

2.1 Control strategy

The electronic load controller maintains the power in the system as long as the consumer load doesn't exceed the rated power. For the SEIG, care must be taken when selecting the excitation capacitor. A fixed capacitor is selected to provide the needed reactive power. To guarantee stable operation and maximum magnetic flux in the generator, it is essential to uphold a steady voltage-to-frequency ratio in the V/F relationship for an asynchronous generator. In this work, an improved ELCr with a hybrid controller is employed to stabilize the V/F ratio under balanced loading conditions. Based on the error voltage and change in error, a resultant PWM with a specific duty cycle is generated to switch the IGBTs. The proposed system can be modified for a single-phase system with just one controller, one bidirectional switch, and a dummy load. By controlling the terminal voltage, the power is simultaneously regulated.

2.2 Modeling of SEIG

The dynamic model for the three-phase SEIG is formulated by utilizing stationary d-q axes within the reference frame [51]. The voltage-current equations are formulated as follows:(2) [v]=[R][i]+[L]p[i]+ωr[G][i]

where [v], [i], [R], [L], [G], ωr, and p represent the voltage, current, resistance, transformer inductance, rotational inductance, rotor speed, and time derivative, respectively. The SEIG functions in the saturation area with a nonlinear magnetizing characteristic. Hence, the calculation of the magnetizing current needs to be performed at every integration level concerning stator and rotor currents, as demonstrated in Eq. (3).(3) Im=(ids+idr)2+(iqs+iqr)2

where Im is the magnetizing current, ids, and idr are the stator current and rotor current in the d-frame, respectively. The iqs and iqr are the stator and rotor currents in the q-frame, respectively. The magnetizing inductance Lm is represented as:(4) Lm=w+xIm+yIm2+zIm3

The coefficients w, x, y, and z are determined by executing a synchronous speed test on the SEIG. The formulated expressions for the electromagnetic torque and the shaft torque are as follows:(5) Temag=(3P4)×Lm(idsidr−iqsiqr)

(6) Ts=Temag+J(2P)ω˙rotor

where Temag is the developed electromagnetic torque, P is the number of poles, Ts is the shaft torque, ω˙rotor is the rotor speed derivative, and J is the inertia of the load and rotor.

Two requirements must be met for an induction machine to function as an independent generator. Firstly, a suitable capacitor bank must be linked to the stator winding terminals to provide reactive power. Secondly, the machine is rotated by a prime mover at a speed exceeding the synchronous speed to produce electricity through interaction with the residual magnetism present in the rotor. The SEIG's excitation capacitance can be determined through three methods: steady-state analysis, dynamic modeling, and using the nameplate data [52]. The minimum capacitance needed by the SEIG is given by Eq. (7).(7) Cmin=12πfXc

where Cmin, f, and Xc represent minimum capacitance, frequency, and capacitive reactance respectively.

2.3 AC chopper analysis

The resultant waveform of the dump load voltage by AC chopping is represented in Fig. 3. The modulated voltage can be represented by the product of the sinusoidal supply voltage and switching signal s(t).Fig. 3 PWM chopping of AC voltage.

Fig. 3

The switching function s(t) can be obtained by expanding the pulse into a Fourier series for a single switching period, as described in Eq. (8).(8) s(t)=C0+∑n=1∞Cncosnωst+∑n=1∞Dnsinnωst

where C0 represents the DC component, Cn and Dn are the Fourier coefficients, n is the harmonic order, and ωs is the angular switching frequency.(9) C0=tONtON+tOFF=tONT=D

(10) Cn=1π∫02πs(t)cos(nωt)dωt=1nπsin(n2πD)

(11) Dn=1π∫02πs(t)sin(nωt)dωt=1nπ[1−cos(n2πD)]

The dump load voltage VD(t) is obtained by the product of switching function s(t) with the supply voltage vs(t).(12) vs(t)=Vpsinωt

(13) VD(t)=vs(t)⋅s(t)=Vpsinωt⋅s(t)

(14) VD(t)=C0Vpsinωt+∑n=1∞CnVp(cosnωst⋅sinnωt)+∑n=1∞DnVp(sinnωst.sinnωt)

where Vp represents the peak voltage and VD(t) denotes the dump load voltage. From Eq. (14), the second and third terms are high-frequency elements. These high-frequency elements are filtered off using a low-pass filter. After filtering, the dummy load voltage can be described in terms of the primary component of the supply frequency.(15) VD=C0Vpsinωt=D.Vpsinωt

where D represents the duty cycle. The instantaneous power equation is represented in Eq. (16) given that consumer loads and dump loads are resistive (pf = 1).(16) PG(t)=(Vsinωt)2RCL+(D⋅Vpsinωt)2RD

The RMS value of the dump load voltage can be expressed as:(17) Vrms_D=0.707D⋅Vp

2.4 Controller board

The detailed circuit diagram of the controller is shown in Fig. 4. The basic parts of the setup for 1 kW ELCr are as follows.Fig. 4 Detailed circuit diagram of the FP-SSBAC electronic load controller for PHP.

Fig. 4

2.4.1 ESP32

This is a low-power microcontroller developed by Expressif Systems. It has a dual-core processor that supports multitasking and efficiently handles complex tasks. This microcontroller has integrated WiFi and Bluetooth. The ESP32 serves as the controller's brain. It handles voltage sensing, runs the control algorithm, and produces the actuating signal as PWM for controlling the IGBTs.

2.4.2 Voltage feedback transformer

Three 220/12 V step-down transformers provide voltage feedback to the controller. The purpose of the sense transformer is to step down the higher AC voltage from the generator to a lower level. The lower AC voltage is further rectified and filtered with a low capacitor of 10 μF. The DC voltage is scaled down using a resistor divider for the microcontroller. The voltage transformers provide galvanic isolation between the power and control circuits, preventing electric shock.

2.4.3 Bridge rectifiers

Each IGBT is connected to a single bridge rectifier in bidirectional mode. The current and voltage ratings of the controller are factors to be considered when selecting a bridge rectifier. The line current is calculated using Eq. (18).(18) IL=P3VLcosϕ

where P, IL, VL, and cos ϕ represent the generated power, line current, line voltage, and power factor, respectively.

Using the induction generator parameters: P = 750 W, VL = 400 V, pf = 0.823, IL is obtained as 1.32 A. The phase current is equivalent to the line current in a SEIG whose stator windings are connected in star form. The rating of the rectifier is obtained using Eq. (19).(19) Bcurr=Ip×sf

where Bcurr is the current rating of the bridge rectifier, Ip is the phase current, and sf is the safety factor. Using Ip as 1.32 A and sf as 7, Bcurr is calculated as 9.24 A. A KBPC1010 rectifier is selected, which has an average rectified output current rating of 10 A and a peak repetitive reverse voltage of 1000 V.

2.4.4 IGBTs and drivers

An isolated power supply is used to power the individual IGBT drivers. The individual power supply is connected so the ground is tied to a single IGBT emitter. The dedicated IGBT driver used is TLP250, the input and output of which are optoisolated. Selecting the suitable IGBT requires ensuring that its VDS rating surpasses the peak voltage of each phase, measured at 325.2 V. Similarly, the continuous drain current of the IGBT needs to be a minimum of seven times larger than the phase current. IRFP40N60 N-channel IGBT meets the stated requirements.

2.4.5 Consumer loads and dump loads

A linear load in the form of a resistive load is used for the consumer load and a dummy load for this setup. A safety factor of 30 % is incorporated into the design.

2.4.6 Ripple filter

A ripple filter is employed to absorb high-frequency signals generated by the switching operation of the AC chopper controller. It utilizes a low resistance of value 2 Ω and a capacitor of 2 μF.

2.4.7 Prime mover

A 7 hp, 3000 rpm, 4 stroke petrol engine is used as a prime mover to drive the SEIG. The petrol engine's speed is regulated by adjusting the throttle until it reaches the desired level necessary for the generator to operate at full load.

3 Controller design

3.1 PI controller design

The PI controller is the most used controller for industrial applications. However, the non-linear nature of the SEIG makes it ineffective in achieving optimal control across various loading conditions using a conventional PI controller. In order to maintain a steady power output, it is crucial to continuously update the PI parameters by considering the error signal and previous errors. A PI controller is represented by Eq. (20).(20) u(t)=Kp⋅e(t)+Ki⋅∫0te(t)⋅dt

where Kp is the proportional gain, Ki is the integral gain, and error is e(t). The conventional PI controller operates with a single input parameter, e(t), making it unsuitable for managing complex systems with multiple inputs. Likewise, its fixed gains make it inadaptable to system changes. To overcome these challenges, a fuzzy PI controller is adopted. Because of its complex nature, obtaining the transfer function of an induction machine can be quite challenging. The system's representation can be estimated by a first-order plus dead time (FOPDT) equation, outlined in Eq. (21) [53].(21) G(s)=Ke−sLsτ+1

where L is the dead time, K is the static gain, and τ is the time constant of the system. The following steps are taken to derive the system transfer function.• Step 1: Firstly, the generator is run without connecting the electronic load controller, dummy loads, and consumer loads. The generator's response curve is shown in Fig. 5.Fig. 5 Open loop response curve of the SEIG without load and electronic load controller.(22) G(s)=1.24e−0.96s0.25s+1

Fig. 5

• Step 2: The values of K, L, τ, and slope (M) are obtained.

• Step 3: The transfer function of the SEIG is formulated from the values obtained from step 2.

The time constant τ = 0.25, gain K = 1.24, dead time L = 0.96 s, and M = 5.10.

The PI controller is tuned utilizing the OLTR (open-loop transient response) and EPI (error performance index) techniques. The system is subjected to a unit step input, and various controllers' performances are evaluated. This procedure seeks to identify the most suitable Kp and Ki values for configuring the fuzzy PI controller.

Fig. 6 represents the various OLTR and EPI tuning methods. The gains are calculated using the formula in Ref. [54]. The values of the gains obtained are tested with the transfer function, and the responses are plotted, as shown in Fig. 7. The values obtained using different tuning methods are listed in Table 1.Fig. 6 OLTR and EPI classification of PI tuning methods.

Fig. 6

Fig. 7 Combined responses (a) OLTR methods (b) EPI methods.

Fig. 7

Table 1 PI gains calculated with different tuning methods.

Table 1S/N	Method	Kp	Ki	
1	ZN	0.184	0.058	
2	WJC	0.423	0.579	
3	CHR	0.072	0.062	
4	CC	0.240	0.127	
5	ISE	0.253	−0.220	
6	ISTSE	0.231	0.005	
7	ISTE	0.251	0.073	
8	ITAE	0.248	0.232	

From Table 2., the WJC outperforms in delay time, settling time, and rise time, but it has an overshoot of 12.2 %. While other tuning methods do not produce overshoot. The ISE is unstable because the curve is in the opposite direction. The ISTSE is the least responsive among the tuning methods, with a settling time of 740 s. The second-best tuning method is ITAE, which has a settling time of 13.5 s and no overshoot. The Kp and Ki gains obtained from various tuning methods provide knowledge for the fuzzy PI controller design.Table 2 Performance index.

Table 2Method	Delay time (s)	Rise time (s)	Settling time (s)	Peak overshoot (%)	
ZN	8.60	33.4	60.0	0.0	
WJC	1.31	0.74	5.60	12.2	
CHR	9.00	28.50	50.80	0.0	
CC	3.86	14.43	27.20	0.0	
ISE	Unstable	Unstable	Unstable	Unstable	
ISTSE	90.00	414.90	740.00	0.0	
ISTE	6.35	26.93	49.60	0.0	
ITAE	1.91	6.79	13.50	0.0	
Superior	WJC	WJC	WJC	All except WJC, ISE	

3.2 Fuzzy PI controller

The block of the fuzzy PI controller is shown in Fig. 8. The controller consists of a fuzzy logic controller (FLC) and a PI controller. The FLC updates the gains of the PI controller based on the error and change in error. The PI controller is connected to a gain block and a limiter before linking to the PWM generator. The limiter prevents the value from surpassing 1 (the maximum duty ratio) due to the cumulative action of the PI controller. The duty ratio value sent to the PWM generator block switches the IGBTs S1–S3. The FLC has three major stages: fuzzification, inference system, and defuzzification. The fuzzification stage is responsible for converting raw input data to crisp value. The inference system makes decisions using logical linguistic rules from the rule base and relevant data from the database in a linguistic format. The output from the inference system is passed to the defuzzifier, which converts the fuzzy output back to crisp values. The inputs of the fuzzy PI controller are voltage error and its derivative and are expressed as Eqs. (23), (24), respectively.(23) e(t)=Vref−Vm

(24) ce(t)=e(t)−e(t−1)

where Vm is the measured voltage, Vref is the reference voltage, e(t) is the error, e(t-1) is the previous error, and ce(t) is the change in error. The raw input values are individually transformed into distinct fuzzy sets, each encompassing five memberships: negative big (NB), negative small (NS), zero (Z), positive small (PS), and positive big (PB).Fig. 8 Control block diagram of the fuzzy PI controller.

Fig. 8

The line voltage of the reference voltage (Vref) is 400 V. The measured voltage and reference voltage are expressed in per-unit values. The range of the fuzzy sets for the input variables is −0.15 to 1 pu for error and −0.3 to 1 pu for change in error, as shown in Fig. 9. The formation of a fuzzy PI controller's rule base is shaped by the count of membership functions and the expert's practical experience along with data interpretation. The membership table is formulated to show the degree of membership of each input value in linguistic terms. For simplicity, the degree of membership of inputs is represented by a triangular membership function. Meanwhile, the output membership functions are depicted as singletons. The Sugeno-Takagi model is represented in the form as:If a is A1 and b is B1 THEN h is h = f (a, b)

where a and b are input values, A1 and B1 are fuzzy sets in the antecedent, whereas h = f (a, b) is a crisp function in the consequent. The crisp function is expressed as a polynomial in Eq. (25).(25) h=pa+qb+r

In this study, a constant is adopted for the consequent. Hence p = q = 0, h = f (a, b) = r. This is known as a zero-order Sugeno fuzzy model. Fig. 10 shows the output membership functions. Where, very small (VS), small (S), medium (M), big (B), and very big (VB) are the output variables' memberships. The output memberships are developed around these values. The Kp is effective in controlling systems when error is big, while Ki is effective for systems close to the set point. Thus the fuzzy rules for Kp and Ki are formulated in Table 3, Table 4, respectively.Fig. 9 Input membership functions (a) error (b) change in error.

Fig. 9

Fig. 10 Output membership functions (a)Kp(b)Ki.

Fig. 10

Table 3 Fuzzy rule base table for Kp.

Table 3			e			
ce	NB	NS	Z	PS	PB	
NB	VS	S	VS	S	M	
NS	VS	M	S	M	M	
Z	S	B	S	B	B	
PS	S	B	M	B	VB	
PB	M	VB	B	VB	VB	

Table 4 Fuzzy rule base table for Ki.

Table 4			e			
ce	NB	NS	Z	PS	PB	
NB	VS	S	B	S	M	
NS	VS	M	B	M	M	
Z	S	B	B	B	B	
PS	S	B	VB	B	VB	
PB	M	VB	VB	VB	VB	

A total of 25 rules are formulated from two inputs, each of five membership functions. The format of the rule is given as follows:

IF e is NB AND ce is NB, THEN Kp is VS AND Ki is VS.

The Sugeno-Takagi fuzzy inference is preferred for precise control and decision-making using algebraic functions. It offers lower computational complexity and effectively manages non-linear systems, expressing outcomes as linear or nonlinear functions. The linguistic output data are converted into crisp output data, and this transformation is achieved using the weighted average method. The equation of the weighted average method is expressed in Eq. (26) [55]:(26) h*=∑μC˜(h‾).h‾∑μC˜(h‾)

where h* is the crisp value, Σ is the algebraic sum, and h‾ represents the centroid of each symmetric membership function.

4 Simulation results

The FP-SSBAC ELCr has been evaluated to determine the output waveform and the extent of harmonic distortions introduced into the system. The details of the generator for this simulation are given in the Appendix. The simulation is carried out using linear loads (resistive). Fig. 11 illustrates the steady-state performance of the system at 70 % loading (2800 W).Fig. .11 Steady-state performance at 70 % loading.

Fig. .11

The terminal voltage (Vg) and load current (IL) are sinusoidal and in phase. The dump load's voltage (Vd) and current (Id) waveforms are modulated. The generator's current (Ig) exhibits a high-frequency component that overlaps with the original current because of the controller's switching action. The output voltage is measured at 230 Vrms with a consistent frequency of 50 Hz. The SEIG voltage THD and load current THD are 2.98 % and 3.45 %, respectively, as shown in Fig. 12.Fig. 12 Harmonic spectrum and THD (a) Output voltage (b) Load current.

Fig. 12

Fig. 13 shows the system's dynamic performance when 70 % of the consumer load is applied at 2 s. The controller quickly regulates the system after two complete cycles. This is achieved by the fast control action of the fuzzy PI controller. The duty of the signal sent to the IGBTs is reduced when consumer load is applied. This ensures that the system's power is constant and at the rated value. The output frequency is maintained at 50 Hz throughout the simulation.Fig. 13 Dynamic performance under 70 % loading at 2 s.

Fig. 13

5 Experimental results and validation

The setup for the experiment is shown in Fig. 14. A three-phase, 1 hp, 400 V, 50 Hz, 4-pole induction machine operates as the generator. Excitation is provided by a fixed capacitance of 20 μF connected in star fashion. The induction generator is coupled to a prime mover whose speed is kept constant to deliver maximum power to the induction machine. A fluke meter 434 power quality & energy analyzer is used for power quality analysis. The program is written in C language and then uploaded onto the microcontroller. The photograph of the developed SSBAC-ELCr board is shown in Fig. 15.Fig. 14 Photograph of the experimental setup for the proposed FP-SSBAC ELCr for pico hydropower in the laboratory.

Fig. 14

Fig. 15 Photograph of the developed FP-SSBAC ELCr board.

Fig. 15

Fig. 16a), 16b), and 16c) depict the steady-state response of voltage and current across a 40 W resistive load in each phase. The voltage and current waveforms are in phase with each other. The FP-SSBAC ELCr maintains the terminal voltage and frequency at the desired values of 236 V and 50 Hz, respectively, as shown in Fig. 16a–d. Fig. 16e) and f) give information on the power factor, reactive power, and apparent power when a 100 W load is applied to the system. The total harmonic distortions of the terminal voltage (THD VG), load current (THD IL), and generator current (THD IG) when 180 W load is applied to the system are presented in Fig. 16g), h), and 16i), respectively. The recorded harmonics are 2.5 % for THD VG, 2.1 % for THD IL, and 3.6 % for THD IG. The uniform harmonic spectrum in each phase indicates that the system is balanced. The dump load voltage and current are in modulated sinusoidal waveform with THD values of 20.2 % and 29.4 %, respectively, as shown in Fig. 16j).Fig. 16 Experimental results (a) phase A voltage and current of consumer load (b) phase B voltage and current of consumer load (c) phase C voltage and current of consumer load (d) voltage, current and frequency of each phase at 300 W consumer load (e) power and power factor of each phase at 300 W consumer load (f) energy consumed per phase at 300 W consumer load (g) terminal voltage harmonics at 180 W (h) load current harmonics at 180 W (i) generator current harmonics (j) dummy load voltage and current for phase C when 300 W load is applied (k) voltage harmonics of dummy load (l) current harmonics of dummy load.

Fig. 16

Fig. 17, Fig. 18 represent transient responses of the system when subjected to load changes. In Fig. 17, Fig. 140 W consumer load is applied to the system. After 3 cycles, the output voltage was maintained at the reference voltage. The frequency is also kept at 50 Hz. The system response is captured when 100 W is removed, as shown in Fig. 18. The terminal voltage is restored to reference voltage after 3 cycles. The controller showed impressive performance in voltage regulation and maintaining the rated frequency.Fig. 17 Transient response at the application of 140 W consumer load.

Fig. 17

Fig. 18 Transient response at the removal of 100 W from the system.

Fig. 18

Fig. 19 illustrates the terminal voltage when various consumer loads are connected to the system. The FP-SSBAC ELCr maintained the terminal voltage at 236 V within a range of ±2.5 % for phases A, B, and C. The frequency of the system at various consumer loads is presented in Fig. 20. The frequency recorded is within ±1 % of the rated frequency 50 Hz. The experimental results are presented in Table 5. The controller demonstrated excellent performance in voltage and frequency regulation. The reference voltage is set at 236 V to maintain a constant frequency of 50 Hz, following the V/F ratio of the induction machine. In addition, the controller demonstrated good power quality as the recorded harmonic distortions were less than 5 %. The highest recorded harmonic distortion is at 120 W loading, with THD VG at 2.8 % and THD IG at 3.7 %. Fig. 21 compares THD VG and THD IL in simulation and experimentation at 70 % loading. The harmonic distortion observed during experimentation is lower than in the simulation. This reduction is due to the introduction of a ripple filter, which blocks high-order harmonics. Only the 3rd harmonics were significantly recorded.Fig. 19 Output voltage of the system at different loads.

Fig. 19

Fig. 20 Frequency of the system at different loads.

Fig. 20

Table 5 Experimental data.

Table 5Load (W)	THD VG (%)	THD IL (%)	THD IG (%)	Phase A (Vrms)	Phase B (Vrms)	Phase C (Vrms)	Frequency (Hz)	
120	2.8	2.0	3.7	236.27	238.82	235.72	49.76	
180	2.5	2.1	3.6	236.54	237.52	236.31	50.10	
300	2.2	2.1	2.5	235.03	238.82	236.84	50.00	
420	2.0	1.8	2.3	236.43	237.10	236.45	49.98	
540	2.0	1.9	2.1	235.50	236.15	235.70	49.70	

Fig. 21 Comparison of THD of voltage and current in simulation and experiment at 70 % loading.

Fig. 21

A detailed comparison of various existing electronic load controllers in pico hydropower and the proposed model is presented in Table 6. The proposed controller can be readily deployable in rural areas and has minimal maintenance costs. This can replace the phase regulation and bridge rectifier with IGBT-based electronic load controllers, which suffer from harmonic distortions and an unequal distribution of current per phase. The STATCOM and DVFC have good power quality features and are suitable for micro/small hydropower systems since implementing them in a household PHP would be prohibitively expensive.Table 6 Comparison between existing ELCr in pico hydropower and the proposed model.

Table 6Performance measure	[18]	[56]	[28,29]	[38,39]	Proposed Model	
Regulation method	Phase regulation	Bridge Rectifier with IGBT	STATCOM	DVFC	FP-SSBAC	
Switch type	SCR/Triac	IGBT	IGBT	IGBT	IGBT	
Number of switches	3	1	6	7	3	
Cost of hardware components	Cheap	Cheap	Expensive	Expensive	Cheap	
Switching technique	Pulse fired signal	PWM	PWM	PWM	PWM	
Injected harmonics by the dump load	High	High	Low	Low	Low	
Control variable	Frequency	Voltage	Voltage and current	Voltage and current	Voltage	
Complexity	Firing accuracy is dependent on the frequency sensor (complex)	Easy to implement	Complex (involves the extraction of active current)	Complex (involves the extraction of active current)	Easy to implement	
Distribution of current per phase	Current is not distributed per phase	Current is not distributed per phase	There is a balanced distribution of current per phase	There is a balanced distribution of current per phase	There is a balanced distribution of current per phase	
Control technique	PID	PID	PI	PI	Fuzzy PI	

The proposed controller is compared with an existing bidirectional AC chopper ELCr [19]. The proposed FP-SSBAC ELCr is simple to design and has fewer component counts than in Ref. [19]. The drivers and IGBT used in the proposed model are half the number used in the existing model. Hence, this leads to a decrease in cost. In terms of harmonic distortion, the two controllers have similar THD values. The comparison of the SYnACC and FP-SSBAC electronic load controllers in terms of THD is illustrated in Fig. 22. The THDVG and THDIL of the SynACC ELCr are slightly lower than the FP-SSBAC controller. Meanwhile, the THDIG of the FP-SSBAC is lower than that of SynACC ELCr. Both controllers have THD values that are compliant with the IEEE 519 standard.Fig. 22 Comparison of THDs obtained by different bidirectional AC chopper controllers.

Fig. 22

6 Conclusion

A fuzzy PI-controlled single-switch bidirectional AC chopper-based ELCr has been designed to regulate voltage and frequency in a pico hydropower system. The proposed controller has been modeled and simulated using Simulink. A prototype has been successfully produced. The findings from the physical prototype experiments and the simulated results obtained using a MATLAB model of the system support the claims presented in this article. The voltage and the frequency of the SEIG system were maintained at 236 V and 50 Hz, respectively. These references were maintained regardless of the consumer load applied to the system as long as the power ratings were not exceeded.

The proposed linear electronic load controller is simple and easy to implement, making it suitable for pico hydropower applications. It offers a fitting substitute for both the electronic load controller of the first generation and the PWM rectifier-chopper ELCr, effectively resolving the related problems. A ripple filter was introduced at the PCC to block high-frequency current components from interfering with the consumer load current. Consequently, only the third harmonic was captured in the power quality analysis. The highest THDs of the load voltage and current were 2.8 % and 2.1 %, respectively, and they comply with the IEEE 519 standard. The fuzzy PI controller demonstrated exceptional responsiveness, with PI gains updated according to the error and its derivative, resulting in minimal overshoot and rapid system stabilization. Hence, torque fluctuation in the generator was significantly reduced.

In addition, comparing FP-SSBAC ELCr with the conventional bidirectional AC chopper ELCr yielded a decrease in component count and cost. This controller can be readily deployed to manage power in pico hydropower systems. Moreover, the circuit size can be reduced further by replacing the sense transformers with linear optocouplers and resistors, resulting in a more compact and simplified design. Therefore, the proposed FP-SSBAC ELCr is a perfect choice for pico hydropower systems where cost and performance are critical. Further research can be conducted on the implementation of predictive control techniques on electronic load controllers. Intelligent technologies such as the Internet of Things (IoT) can be integrated to remotely monitor, control, and analyze data, enabling a more sophisticated and adaptable approach to load management.

Data availability statement

Data will be provided upon request.

CRediT authorship contribution statement

Samuel C. Ndukwe: Writing – original draft, Validation, Software, Methodology, Investigation, Conceptualization. Ramani Kannan: Writing – review & editing, Resources, Project administration, Funding acquisition. Ho Tatt Wei: Resources, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix Induction machine 5.4hp, 400 V, 50 Hz, speed 1430 rpm, stator resistance 1.405 Ω, rotor resistance 1.395 Ω, stator inductance | rotor inductance = 0.005839 H, mutual inductance 0.1722 H, Excitation capacitance 78 μF.

Acknowledgment

The research paper was supported by the 10.13039/501100016152 Yayasan Universiti Teknologi PETRONAS (YUTP) grant YUTP-FRG 1/2021:015LC0-349 , the Center of Graduate Studies UTP, and the 10.13039/501100009614 Petroleum Technology Development Fund (PTDF) . The authors are grateful to Madam Khairul Nisak Md Hasan for her invaluable support.
==== Refs
References

1 The-Sustainable-Development-Goals-Report https://unstats.un.org/sdgs/report/2023/ 2023
2 Kumar K. Saini R.P. A review on operation and maintenance of hydropower plants Sustain. Energy Technol. Assessments 49 2022 101704 10.1016/j.seta.2021.101704
3 Kadier A. Kalil M.S. Pudukudy M. Hasan H.A. Mohamed A. Hamid A.A. Pico hydropower (PHP) development in Malaysia: potential, present status, barriers and future perspectives Renew. Sustain. Energy Rev. 81 2018 2796 2805 10.1016/j.rser.2017.06.084
4 World Energy Outlook 2023 – Analysis - IEA, (n.d.). https://www.iea.org/reports/world-energy-outlook-2023 (accessed January 24, 2024).
5 Green J. Fuentes M. Rai K. Taylor S. Stimulating the Picohydropower Market for Low-Income Households in Ecuador 2005
6 Meier T. Fischer G. Assessment of the Pico and Micro-hydropower Market in Rwanda, Nairobi (Kenya): GVEP 2011
7 Paish O. Green J. The Pico Hydro Market in Vietnam 2001 Retrieved on September 16
8 Zainuddin H. Yahaya M.S. Lazi J.M. Basar M.F.M. Ibrahim Z. Design and development of pico-hydro generation systems for energy storage using consuming water distributed to houses World Academy of Science, Engineering and Technology 59 2009 154
9 Harvey A. Brown A. Hettiarachi P. Inversin A. Micro-hydro Design Manual 1993
10 Krishna V.B.M. Sandeep V. Murthy S.S. Yadlapati K. Experimental investigation on performance comparison of self excited induction generator and permanent magnet synchronous generator for small scale renewable energy applications Renew. Energy 195 2022 431 441 10.1016/j.renene.2022.06.051
11 Pandey Y. Iqbal A. Singh S.P. Husain M.A. Micro/pico hydropower generation system using self-excited induction generators and applications of AI for its performance improvement Computer Science, Technology and Applications 2022 51
12 Duvvuri S.S. Sandeep V. Yadlapati K. Krishna V.B.M. Research on induction generators for isolated rural applications: state of art and experimental demonstration, Measurement Sensors 24 2022 10.1016/j.measen.2022.100541
13 Murthy S.S. Singh B. Capacitive VAr controllers for induction generators for autonomous power generation Proceedings of International Conference on Power Electronics, Drives and Energy Systems for Industrial Growth 1996 IEEE 679 686 10.1109/PEDES.1996.535862
14 Çalgan H. Ilten E. Demirtas M. Thyristor controlled reactor‐based voltage and frequency regulation of a three‐phase self‐excited induction generator feeding unbalanced load International Transactions on Electrical Energy Systems 30 2020 1 17 10.1002/2050-7038.12387
15 Ahmed T. Noro O. Hiraki E. Nakaoka M. Static VAR compensator-based voltage regulation for variable-speed prime mover coupled single-phase self-excited induction generator IEEE Trans. Ind. Appl. 125 2005 355 365 10.1541/ieejias.125.355
16 Chilipi R.R. Singh B. Murthy S.S. Madishetti S. Bhuvaneswari G. Design and implementation of dynamic electronic load controller for three‐phase self‐excited induction generator in remote small‐hydro power generation IET Renew. Power Gener. 8 2014 269 280 10.1049/iet-rpg.2013.0087
17 Murthy S.S. Singh B. Kulkarni A. Sivarajan R. Gupta S. Field experience on a novel pico-hydel system using self excited induction generator and electronic load controller The Fifth International Conference on Power Electronics and Drive Systems, 2003. PEDS 2003 2003 IEEE 842 847 10.1109/PEDS.2003.1283076
18 Praptodiyono S. Maghfiroh H. Nizam M. Hermanu C. Wibowo A. Design and prototyping of electronic load controller for pico hydropower system Jurnal Ilmiah Teknik Elektro Komputer Dan Informatika 7 2021 461 10.26555/jiteki.v7i3.22271
19 Kumar P. Kalla U. Bhati N. Agarwal K.L. Performance investigation of synchronized three-phase AC chopper-based controller for small hydrogeneration systems IEEE Trans. Ind. Appl. 58 2022 2217 2228 10.1109/TIA.2022.3140285
20 Kathirvel C. Porkumaran K. Jaganathan S. Design and implementation of improved electronic load controller for self-excited induction generator for rural electrification Sci. World J. 2015 2015 1 8 10.1155/2015/340619
21 Singh B. Murthy S.S. Gupta S. Analysis and design of electronic load controller for self-excited induction generators IEEE Trans. Energy Convers. 21 2006 285 293 10.1109/TEC.2005.847950
22 Ali A. Arshad Akhtar H. Siddiqi M.U.R. Kamran M. An efficient and novel technique for electronic load controller to compensate the current and voltage harmonics Engineering Science and Technology, an International Journal 23 2020 1042 1057 10.1016/j.jestch.2019.11.009
23 Ramirez J.M. Torres M.E. An electronic load controller for self-excited induction generators 2007 IEEE Power Engineering Society General Meeting 2007 IEEE 1 8 10.1109/PES.2007.385540
24 Singh B. Murthy S.S. Gupta S. STATCOM-based voltage regulator for self-excited induction generator feeding nonlinear loads IEEE Trans. Ind. Electron. 53 2006 1437 1452 10.1109/TIE.2006.882008
25 Kalla U.K. Singh B. Murthy S.S. Jain C. Kant K. Adaptive sliding mode control of standalone single-phase microgrid using hydro, wind, and solar PV array-based generation IEEE Trans. Smart Grid 9 2018 6806 6814 10.1109/TSG.2017.2723845
26 Tyagi S. Singh B. Das S. ELD-OSG control of a battery-based electronic load controller for a small hydro energy conversion system IEEE Trans. Ind. Appl. 58 2022 3142 3152 10.1109/TIA.2022.3149846
27 Kalla U.K. Singh B. Murthy S.S. Slide mode control of microgrid using small hydro driven single‐phase SEIG integrated with solar PV array IET Renew. Power Gener. 11 2017 1464 1472 10.1049/iet-rpg.2016.0089
28 Giri A.K.K. Arya S.R. Maurya R. Babu B.C. Power quality improvement in stand-alone SEIG-based distributed generation system using lorentzian norm adaptive filter IEEE Trans. Ind. Appl. 54 2018 5256 5266 10.1109/TIA.2018.2812867
29 Meena D.C. Singh M. Giri A.K. Leaky-momentum control algorithm for voltage and frequency control of three-phase SEIG feeding isolated load Journal of Engineering Research 2021 109 120 10.36909/jer.ICARI.15335
30 Giri A.K. Arya S.R. Maurya R. Babu B.C. VCO‐less PLL control‐based voltage‐source converter for power quality improvement in distributed generation system IET Electr. Power Appl. 13 2019 1114 1124 10.1049/iet-epa.2018.5827
31 Qureshi A. Giri A.K. Arya S.R. Padmanaban S. Power conditioning using DSTATCOM in a single-phase SEIG-based isolated system Electr. Eng. 104 2022 111 127 10.1007/s00202-021-01423-1
32 Kundu S. Singh M. Giri A.K. Adaptive control approach-based isolated microgrid system with alleviating power quality problems, electric power components and Systems 52 2024 1219 1234 10.1080/15325008.2023.2239222
33 Kundu S. Singh M. Giri A.K. Control algorithm for coordinated operation of wind-solar microgrid standalone generation system Energy Sources, Part A Recovery, Util. Environ. Eff. 44 2022 10024 10044 10.1080/15567036.2022.2143943
34 Kundu S. Singh M. Giri A.K. Kadiyan S. Chittora P. Shailly D. Robust and fast control approach for islanded microgrid system and EV charging station applications Electr. Eng. 2024 10.1007/s00202-024-02291-1
35 Kundu S. Singh M. Giri A.K. Synchronization and control of WECS-SPV-BSS-based distributed generation system using ICCF-PLL control approach Elec. Power Syst. Res. 226 2024 10.1016/j.epsr.2023.109919
36 Kalla U.K. Singh B. Murthy S.S. Jain C. Kant K. Adaptive sliding mode control of standalone single-phase microgrid using hydro, wind, and solar PV array-based generation IEEE Trans. Smart Grid 9 2018 6806 6814 10.1109/TSG.2017.2723845
37 Kalla U.K. Singh B. Murthy S.S. Kant K. Chilipi R.R. Adaptive harmonic cancellation scheme for voltage and frequency control of a single-phase two-winding SEIG 2015 IEEE Industry Applications Society Annual Meeting 2015 1 7 10.1109/IAS.2015.7356930 IEEE
38 Chandran V.P. Murshid S. Singh B. Improved TOGI-based voltage and frequency control for PMSG feeding single-phase loads in isolated pico-hydro generation IETE J. Res. 67 2021 882 898 10.1080/03772063.2019.1571953
39 Chandran V.P. Murshid S. Singh B. Voltage and frequency controller with power quality improvement for PMSG based pico-hydro system 2018 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES) 2018 1 6 10.1109/PEDES.2018.8707810 IEEE
40 Rathore U.C. Singh S. Designing of electronic load controller for 3-ϕ SEIG used in constant power prime-mover driven Pico/Micro hydro power generation system 2016 IEEE 7th Power India International Conference (PIICON) 2016 IEEE 1 6 10.1109/POWERI.2016.8077179
41 Yadav A. Appan A. Steady-state analysis of Electronic Load Controller for three phase alternator 2015 Annual IEEE India Conference (INDICON) 2015 IEEE 1 6 10.1109/INDICON.2015.7443654
42 Mhlambi B.A. Kusakana K. Raath J. Voltage and frequency control of isolated pico-hydro system 2018 Open Innovations Conference (OI) 2018 IEEE 246 250 10.1109/OI.2018.8535603
43 Ahmed K.Y. Bin Yahaya N.Z. Asirvadam V.S. Saad N. Kannan R. Ibrahim O. Development of power electronic distribution transformer based on adaptive PI controller IEEE Access 6 2018 44970 44980 10.1109/ACCESS.2018.2861420
44 Singh B. Rajagopal V. Neural-network-based integrated electronic load controller for isolated asynchronous generators in small hydro generation IEEE Trans. Ind. Electron. 58 2011 4264 4274 10.1109/TIE.2010.2102313
45 Karmakar S. Artificial neural network-built electronic load controller for three-phase self-excited induction generator feeding single-phase load Michael Faraday IET International Summit 2020 (MFIIS 2020) 2021 Institution of Engineering and Technology 185 190 10.1049/icp.2021.1073
46 Karmakar S. Mahato S.N. EasyChair Preprint Artificial Neural Network-Based Electronic Load Controller for Self-Excited Induction Generator Artificial Neural Network-Based Electronic Load Controller for Self- Excited Induction Generator 2019
47 Palwalia D.K. Singh S.P. Digital signal processor based fuzzy voltage and frequency regulator for self-excited induction generator Elec. Power Compon. Syst. 38 2010 309 324 10.1080/15325000903273411
48 Ofosu R.A. Kaberere K.K. Nderu J.N. Kamau S.I. Design of BFA-optimized fuzzy electronic load controller for micro hydro power plants Energy for Sustainable Development 51 2019 13 20 10.1016/j.esd.2019.04.003
49 Kesler S. Doser T.L. A voltage regulation system for independent load operation of stand alone self-excited induction generators Journal of Power Electronics 16 2016 1869 1883 10.6113/JPE.2016.16.5.1869
50 Ndukwe S.C. Kannan R. Wei H.T. A single-switch bidirectional AC chopper-based electronic load controller for pico hydropower system 2023 IEEE Symposium on Industrial Electronics and Applications, ISIEA 2023 2023 Institute of Electrical and Electronics Engineers Inc. 10.1109/ISIEA58478.2023.10212213
51 Singh B. Murthy S.S. Gupta S. Transient analysis of self-excited induction generator with electronic load controller (ELC) supplying static and dynamic loads Proceedings of the International Conference on Power Electronics and Drive Systems 1 2003 771 776 10.1109/PEDS.2003.1283000
52 Krishna V.B.M. Duvvuri S.S. Sobhan P.V.S. Yadlapati K. Sandeep V. Narendra B.K. Experimental study on excitation phenomena of renewable energy source driven induction generator for isolated rural community loads Results in Engineering 21 2024 10.1016/j.rineng.2024.101761
53 Karl J. Hagglund T. PID controllers:theory, design, and tuning The Instrumentation, Systems and Automation Society 1995 North Carolina Research Triangle Park
54 Pavan Kumar Y.V. Bhimasingu R. Design of voltage and current controller parameters using small signal model-based pole-zero cancellation method for improved transient response in microgrids SN Appl. Sci. 3 2021 10.1007/s42452-021-04815-x
55 Ross T.J. Fuzzy Logic with Engineering Applications 2010 John Wiley
56 Rana K. Meena D.C. Self excited induction generator for isolated pico hydro station in remote areas 2018 2nd IEEE International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES) 2018 821 826 10.1109/ICPEICES.2018.8897329 IEEE
