38.8.2.1 Sample Study AC-DC System

Figs. 38.11 and 38.12 show the proposed the four-wheel electric vehicle drive system scheme with the PV, FC sources, the diesel generator, and the backup battery. The DC compensator scheme developed by the first author is used to ensure stable, efficient, and minimal inrush operation of the hybrid renewable energy scheme. The novel PSO and GA self-tuned multiregulators and coordinated controller are used for the following purposes:

1. Diesel AC generator set with control regulator is based on excess generation and load dynamic matching and stabilization of the common DC collection bus using six-pulse-controlled rectifier.

2. AC/DC power converter regulator to regulate the DC voltage at the diesel engine AC/DC interface and ensure limited inrush conditions and dynamic power matching to reduce current transients and improve utilization at the diesel engine interface AC-DC bus.

3. The DC side green plug filter compensator GPFC-SPWM regulator for pulse-width switching scheme to regulate the DC bus voltage and minimize inrush current transients and load excursions and/or PV and FC nonlinear volt-ampere characteristics. The GPFC device acts as a matching DC-DC interface device between the DC load dynamic characteristics and that of the hybrid main PV, FC, and backup diesel generator set.

4. The permanent magnet DC motor drive with the speed regulator that ensures speed reference tracking with minimum inrush conditions and ensures reduced voltage transients and improved energy utilization.

The unified DC-AC utilization scheme is fully validated using the Matlab/Simulink software environment under normal conditions, DC load excursion, PMDC motor torque changes and the PV, and FC source output variations due to the inherent volt-ampere nonlinear relationship. Other excursion conditions in the diesel engine generator set are also introduced to assess the control system robustness, effective energy utilization, and speed reference tracking.

Photo voltaic PV

The equivalent circuit shown in Fig. 38.13 is used to model the PV cells used in the proposed PV array [29]. This model consists of a current source, a resistor, and a reverse parallel connected diode. The PVA model developed and used in Matlab/Simulink environment is based upon the circuit given in Fig. 38.13, in which the current produced by the solar cell is equal to that produced by the current source, minus that which flows through the diode, minus that which flows through the shunt resistor:

$I=I_L-I_D-I_{SH}$

  (38.8)

where I=output current, I_L=photo-generated current, I_D=diode current, and I_SH=shunt current. The current through these elements is governed by the voltage across them:

$V_j=V+I{R}_S$

  (38.9)

where V_j=voltage across both diode and resistor R_SH (volts), V=voltage across the output terminals (volts), I=output current (amperes), and R_S=series resistance (Ω).

The current diverted through the diode is

$I_D=I_o\left\{exp\left[\frac{q{V}_j}{nkT}\right]-1\right\}$

  (38.10)

where I₀=reverse saturation current (amperes), n=diode ideality factor (1 for an ideal diode), q=elementary charge, k=Boltzmann's constant, and T=absolute temperature.

The characteristic equation of a solar cell, which relates solar cell parameters to the output current and voltage [30]:

$I=I_L-I_o\left\{exp\left[\frac{q\left(V+I{R}_s\right)}{nkT}\right]-1\right\}-\frac{V+I{R}_s}{R_{SH}}$

  (38.11)

where R_SH=shunt resistance (Ω). The I-V curve of an illuminated PV cell has the shape shown in Fig. 38.14 as the voltage across the measuring load is swept from zero to V_OC, The power produced by the cell in watts can be easily calculated along the I-V sweep by the equation P=IV. At the I_SC and V_OC points, the power will be zero, and the maximum value for power will occur between the two.

Fuel cell energy system model

Fuel cell stacks were connected in series/parallel combination to achieve the rating desired. Fig. 38.15 shows a simplified diagram of the PEMFC system [31,32]. The FC model here is for a type of PEM, which uses the following electrochemical reaction:

${\mathrm{H}}_2+\frac{1}{2}{\mathrm{O}}_2\to {\mathrm{H}}_2\mathrm{O}+\mathrm{Heat}+\mathrm{Electrical}\mathrm{Energy}$

  (38.12)

Fig. 38.16 shows a simulated V-I (voltage versus current) polarization curve of a fuel cell [31,32]. As the cell current begins to increase from zero, a sudden drop of the output voltage of the fuel cell is seen. This drop of the cell voltage is due to activation voltage loss. Then, almost a linear decrease of the cell voltage is seen as the cell current increases beyond certain values, as shown in Fig. 38.17, which is a result of the ohmic loss. Finally, the cell voltage drops sharply to zero as the load current approaches the maximum current density that can be generated of the fuel cell. The sharp voltage drop is the effect of the concentration loss in the fuel cell. The fuel cell can be commonly modeled by simple equivalent first-order circuit shown in Fig. 38.10. The open circuit voltage is modified as follows:

$E_{oc}=N\left(E_n-Aln\left(i_o\right)\right)$

  (38.13)

where

$A=\frac{RT}{Z\alpha F}$

  (38.14)

where R=8.3145 J/(mol K); F=96,485 As/mol; z=number of moving electrons; E_n=Nernst voltage, which is the thermodynamics voltage of the cells and depends on the temperatures and partial pressures of reactants and products inside the stack; and i₀=exchange current, which is the current resulting from the continual backward and forward flow of electrons from and to the electrolyte at no load. It depends also on the temperatures and partial pressures of reactants inside the stack. α is the charge transfer coefficient, which depends on the type of electrodes and catalysts used and T is the temperature of operation. The fuel cell voltage V_FC is modeled as [31,32]

$V_{FC}=E_{oc}-V_{\mathrm{Activation}\mathrm{loss}}-V_{\mathrm{Ohmic}\mathrm{loss}}-V_{\mathrm{Concentrion}\mathrm{loss}}$

  (38.15)

where

$V_{\mathit{Activation}\mathit{Loss}}=Alog\left(\frac{I_{FC}+i_n}{i_o}\right)$

  (38.16)

$V_{\mathit{Ohmic}\mathit{Loss}}=R_m\left(I_{FC}+i_n\right)$

  (38.17)

$V_{\mathit{Concentration}\mathit{Loss}}=Blog\left(1-\frac{I_{FC}+i_n}{i_L}\right)$

  (38.18)

Fuel cell stacks were connected in series/parallel combination to achieve the rating desired. The output of the fuel cell array was connected to a DC bus through a DC/DC converter. The DC bus voltage was kept constant via a DC bus voltage controller.

Dynamic error driven control

The proposed control system developed by first author comprises four subregulators or controllers named as a diesel DC generator set value control regulator, DC side green plug filter compensator GPFC-SPWM regulator, the permanent magnet DC motor drive speed controller, and the AC/DC power converter regulator. Figs. 38.12–38.15 depict the proposed multiloop dynamic self-regulating controllers based on multiobjective optimization search and optimization technique based on soft computing PSO and GA. The global error is the summation of the three loop individual errors including voltage stability, current limiting, and synthesis dynamic power loops. Each multiloop dynamic control scheme is used to reduce a global error based on a triloop dynamic error summation signal and to mainly track a given speed reference trajectory loop error in addition to other supplementary motor current limiting, and dynamic power loops are used as auxiliary loops to generate a dynamic global total error signal that consists of not only the main loop speed error but also the current ripple, overcurrent limit, and dynamic overload power conditions.

The global error signal is input to the self-tuned controllers shown in Figs. 38.18–38.21. The (per unit) three-dimensional-error vector (e_vg, e_Ig, and e_pg) of the diesel engine controller scheme is governed by the following equations:

$e_{vg}\left(k\right)=V_g\left(k\right)\left(\frac{1}{1+S{T}_g}\right)\left(\frac{1}{1+SD}\right)-V_g\left(k\right)\left(\frac{1}{1+S{T}_g}\right)$

  (38.19)

$e_{Ig}\left(k\right)=I_g\left(k\right)\left(\frac{1}{1+S{T}_g}\right)\left(\frac{1}{1+SD}\right)-I_g\left(k\right)\left(\frac{1}{1+S{T}_g}\right)$

  (38.20)

$e_{\mathit{Pg}}\left(k\right)=I_g\left(k\right)\times V_g\left(k\right)\left(\frac{1}{1+S{T}_g}\right)\left(\frac{1}{1+SD}\right)-I_g\left(k\right)\times V_g\left(k\right)\left(\frac{1}{1+S{T}_g}\right)$

  (38.21)

The total or global error e_tg(k) at the AC side scheme at a time instant

$e_{tg}\left(k\right)={\gamma }_{vg}{e}_{vg}\left(k\right)+{\gamma }_{ig}{e}_{ig}\left(k\right)+{\gamma }_{\mathit{pg}}{e}_{\mathit{pg}}\left(k\right)$

  (38.22)

In the same manner, the (per unit) three-dimensional-error vector (e_vd, e_Id, and e_pd) of the GPFC scheme is governed by the following equations:

$e_{vd}\left(k\right)=V_d\left(k\right)\left(\frac{1}{1+S{T}_d}\right)\left(\frac{1}{1+SD}\right)-V_d\left(k\right)\left(\frac{1}{1+S{T}_d}\right)$

  (38.23)

$e_{\mathit{Id}}\left(k\right)=I_d\left(k\right)\left(\frac{1}{1+S{T}_d}\right)\left(\frac{1}{1+SD}\right)-I_d\left(k\right)\left(\frac{1}{1+S{T}_d}\right)$

  (38.24)

$e_{Pd}\left(k\right)=I_d\left(k\right)\times V_d\left(k\right)\left(\frac{1}{1+S{T}_d}\right)\left(\frac{1}{1+SD}\right)-I_d\left(k\right)\times V_d\left(k\right)\left(\frac{1}{1+S{T}_d}\right)$

  (38.25)

and the total or global error e_td(k) for the DC side green plug filter compensator GPFC scheme at a time instant

$e_{td}\left(k\right)={\gamma }_{vd}{e}_{vd}\left(k\right)+{\gamma }_{\mathit{id}}{e}_{\mathit{id}}\left(k\right)+{\gamma }_{pd}{e}_{pd}\left(k\right)$

  (38.26)

In addition, The (per unit) three-dimensional-error vector (e_vR, e_IR, and e_pR) of the three-phase-controlled rectifier scheme is governed by the following equations:

$e_{vR}\left(k\right)=V_R\left(k\right)\left(\frac{1}{1+S{T}_R}\right)\left(\frac{1}{1+SD}\right)-V_R\left(k\right)\left(\frac{1}{1+S{T}_R}\right)$

  (38.27)

$e_{IR}\left(k\right)=I_R\left(k\right)\left(\frac{1}{1+S{T}_R}\right)\left(\frac{1}{1+SD}\right)-I_R\left(k\right)\left(\frac{1}{1+S{T}_R}\right)$

  (38.28)

$e_{PR}\left(k\right)=I_R\left(k\right)\times V_R\left(k\right)\left(\frac{1}{1+S{T}_R}\right)\left(\frac{1}{1+SD}\right)-I_R\left(k\right)\times V_R\left(k\right)\left(\frac{1}{1+S{T}_R}\right)$

  (38.29)

The total or global error e_tR(k) for the three-phase-controlled converter rectifier scheme at a time instant:

$e_{tR}\left(k\right)={\gamma }_{vR}{e}_{vR}\left(k\right)+{\gamma }_{iR}{e}_{iR}\left(k\right)+{\gamma }_{pR}{e}_{pR}\left(k\right)$

  (38.30)

Finally, the (per unit) three-dimensional-error vector (e_ωm, e_Im, and e_pm) of the PMDC motor scheme is governed by the following equations:

$e_{\omega m}\left(k\right)={\omega }_m\left(k\right)\left(\frac{1}{1+S{T}_m}\right)\left(\frac{1}{1+SD}\right)-{\omega }_m\left(k\right)\left(\frac{1}{1+S{T}_m}\right)$

  (38.31)

$e_{\mathrm{I}\mathrm{m}}\left(k\right)=I_m\left(k\right)\left(\frac{1}{1+S{T}_m}\right)\left(\frac{1}{1+SD}\right)-I_m\left(k\right)\left(\frac{1}{1+S{T}_m}\right)$

  (38.32)

$e_{\mathit{Pm}}\left(k\right)=I_m\left(k\right)\times {\omega }_m\left(k\right)\left(\frac{1}{1+S{T}_m}\right)\left(\frac{1}{1+SD}\right)-I_m\left(k\right)\times {\omega }_m\left(k\right)\left(\frac{1}{1+S{T}_m}\right)$

  (38.33)

and the total or global error e_tm(k) for the MPFC scheme at a time instant

$e_{tm}\left(k\right)={\gamma }_{\omega m}{e}_{\omega m}\left(k\right)+{\gamma }_{im}{e}_{im}\left(k\right)+{\gamma }_{\mathit{pm}}{e}_{\mathit{pm}}\left(k\right)$

  (38.34)

A number of conflicting objective functions are selected to optimize using the PSO algorithm. These functions are defined by the following:

$J_1=\mathrm{Minimize}\left\{\left|e_{tg}\right|,\left|e_{tR}\right|,\left|e_{td}\right|,\left|e_{tm}\right|\right\}$

  (38.35)

$J_2=\mathrm{Steady}\mathrm{state}\mathrm{error}=\left|e_{\omega }\left(k\right)\right|=\left|{\omega }_{ref}\left(k\right)-{\omega }_m\left(k\right)\right|$

  (38.36)

$J_3=\mathrm{Settling}\mathrm{time}$

  (38.37)

$J_4=\mathrm{Maximum}\mathrm{over}\mathrm{shoot}$

  (38.38)

$J_5=\mathrm{Rise}\mathrm{time}$

  (38.39)

In general, to solve this multiobjective complex optimality search problem, there are two possible optimization techniques based on particle swarm optimization (PSO): single aggregate selected objective optimization (SOO), which is explained, and multiobjective optimization (MOO). The main procedure of the SOO is based on selecting a single aggregate objective function with weighted single-objective parameters scaled by a number of weighting factors. The objective function is optimized (either minimized or maximized) using either GA or particle swarm optimization search algorithm (PSO) methods to obtain a single global or near-optimal solution. On the other hand, the main objective of the multiobjective (MO) problem is finding the set of acceptable (trade-off) optimal solutions. This set of accepted solutions is called Pareto front. These acceptable trade-off multilevel solutions give more ability to the user to make an informed decision by seeing a wide range of near-optimal selected solutions that are feasible and acceptable from an “overall” standpoint. Single-objective (SO) optimization may ignore this trade-off viewpoint, which is crucial. The main advantages of the proposed MOO method are the following: It doesn't require a priori knowledge of the relative importance of the objective functions, and it provides a set of acceptable trade-off near-optimal solutions. This set is called Pareto front or optimality trade-off surfaces. Both SOO and MOO searching algorithms are tested, validated, and compared. The dynamic error-driven controller regulates the controllers' gains using the particle swarm optimization (PSO) and GA to minimize the system total error, the settling time, the rising time, and the maximum overshoot. The proposed dynamic triloop error-driven controller, developed by the first author, is a novel advanced regulation concept that operates as an adaptive dynamic-type multipurpose controller capable of handling sudden parametric changes, load and/or DC source excursions. By using the triloop error-driven controller, it is expected to have a smoother, less dynamic overshoot and fast and more robust speed controller when compared with those of classical control schemes. The proposed general PMDC motor drive model with the novel triloop error-driven controller is fully validated in this application for effective reference speed trajectory tracking under different loading conditions and parametric variations, such as temperature changes, while driving a complex mechanical load with nonlinear parameters and/or torque-speed characteristics.

Self tuned variable structure sliding mode bang-bang VSC/SMC/B-B controller

In the variable structure sliding mode controller scheme, an optimally adaptive and self-tuned variable structure sliding mode controller for PMDC motor drive systems using particle swarm optimization technique (PSO) and GA is shown in Fig. 38.22. The slope of the sliding surface is designed as

$\sigma =\beta e_t+K_{\alpha }\frac{d{e}_t}{dt}$

  (38.40)

With adaptive adjustable error scaling gain,

$\beta ={\beta }_0+{\beta }_1\left|e_t\right|$

  (38.41)

where

$\left|e_t\right|=\sqrt{{\left({\gamma }_I{e}_I\right)}^2+{\left({\gamma }_{\omega }{e}_{\omega }\right)}^2+{\left({\gamma }_V{e}_V\right)}^2+{\left({\gamma }_p{e}_p\right)}^2}$

  (38.42)

The system control voltage has the following form in the time domain [33]: the control is an on-off logic; that is, when $\sigma >0,V_c=1,\mathrm{and}\mathrm{when}\sigma <0,V_c=-1$

The PSO and GA search and optimization are implemented for tuning the various gains β₀, β₁, and α to minimize the selected five conflicting objective functions (J₁−J₅). This test is to verify that the proposed VSC/B-B with adaptive β can maintain the motor speed with nonlinear J(ω_m) and B(ω_m) even if the load changes; accordingly, the robustness can be confirmed.

Self tuned artificial neural network controller ANN

The neural network used in this application is the simplest one that uses three layers, which is widely used in the control of the electric machines. Each layer is composed of neurons. Each neuron is connected via weights to the previous layer. The first layer is connected to the input variables. The second one is connected via weights to all the neurons of the previous layer, and the last one is composed of one neuron given the output value. The weights and the biases of the ANN network's are updated to provide that the global error of the system is minimized. The proposed ANN regulator is tuned online using the back-propagation algorithm. The online ANN rule-based algorithm is used to update the ANN network weights and biases to ensure continuous effective dynamic response while keeping the motor inrush current under specified tolerable limits. The input vector with three-layer ANN as shown in Fig. 38.23 is

$\overline{X}=\left\{e_t\left(k\right),e_t\left(k-1\right),e_t\left(k-2\right),e_t\left(k-3\right),\mathrm{\Delta }{V}_c\left(k-1\right)\right\}$

  (38.43)

Self tuned fuzzy logic controller (FLC)

As shown in Fig. 38.24, the FLC system consists of three subsystems, which are the fuzzification, rule base, and defuzzification. Fuzzification subsystem converts the exact inputs to fuzzy values using five membership functions: positive big (PB), positive small (PS), zero (ZZ), negative small (NS), and negative big (NB). The rule base unit processes these fuzzy values with fuzzy rules. The defuzzification unit converts the fuzzy results to exact values. The FLC input values are the global error, e_t, and change in global error, de_t. According to these variables, a rule table is produced in the FLC rule base unit as shown in Table 38.4.

Table 38.4

Fuzzy rule decision table

et	det
	NB	NS	ZZ	PS	PB
NB	NB	NB	NS	NS	ZZ
NS	NB	NS	NS	ZZ	PS
ZZ	NS	NS	ZZ	PS	PS
PS	NS	ZZ	PS	PS	PB
PB	ZZ	PS	PS	PB	PB

38.8.2.2 Digital Simulation Results

The integrated microgrid for PMDC-driven electric vehicle scheme using the photovoltaic (PV), fuel cell (FC), and backup diesel generation with battery backup renewable generation system performance is compared for two cases, with fixed and self-tuned-type controllers using either GA or PSO. The second case is to compare the performance with artificial neural network (ANN) controller and fuzzy logic controller (FLC) with the self-tuned-type controllers using either GA or PSO. The tuned variable structure sliding mode controller VSC/SMC/B-B has been applied to the speed tracking control of the same EV for performance comparison. There are three different speed references. In the first speed track, the speed increases linearly and reaches the 1 pu at the end of the first 5 s, and then, the reference speed remains speed constant during 5 s. At tenth second, the reference speed decreases with same slope as at the first 5 s. After 15 s, the motor changes the direction and EV increases its speed through the reverse direction. At twentieth second, the reference speed reaches the −1 pu and remains constant speed at the end of twenty-fifth second, and then, the reference speed decreases and becomes zero at thirtieth second. The second reference speed waveform is sinusoidal, and its magnitude is 1 pu, and the period is 12 s. The third reference track is constant speed reference starting with an exponential track. In all references, the system responses have been observed. Matlab/Simulink software was used to design, test, and validate the effectiveness of the integrated microgrid for PMDC-driven electric vehicle scheme using photovoltaic (PV), fuel cell (FC), and backup diesel generation with battery backup renewable generation system with the FACTS devices. The digital dynamic simulation model using Matlab/Simulink software environment allows for low-cost assessment and prototyping, system parameter selection, and optimization of control settings. The use of PSO search algorithm is utilized in online gain adjusting to minimize controller absolute value of total error. This is required before full-scale prototyping that is both expensive and time-consuming. The effectiveness of dynamic simulators brings on detailed submodels selections and tested submodels Matlab library of power system components already tested and validated. The common DC bus voltage reference is set at 1 pu. Digital simulations are obtained with sampling interval Ts=20 μs. Dynamic responses obtained with GA are compared with the ones resulting from the PSO for the seven proposed self-tuned controllers. The dynamic simulation conditions are identical for all tuned controllers. To compare the global performances of all controllers, the normalized mean-square-error (NMSE) deviations between output plant variables and desired values and is defined as

$NMS{E}_{V_{\mathrm{D}\mathrm{C}-\mathrm{bus}}}=\frac{{\displaystyle \sum {\left(V_{\mathrm{D}\mathrm{C}-\mathrm{bus}}-V_{\mathrm{D}\mathrm{C}-\mathrm{bus}-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}{{\displaystyle \sum {\left(V_{\mathrm{D}\mathrm{C}-\mathrm{bus}-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}$

$NMS{E}_{{\omega }_m}=\frac{{\displaystyle \sum {\left({\omega }_m-{\omega }_{m-ref}\right)}^2}}{{\displaystyle \sum {\left({\omega }_{m-ref}\right)}^2}}$

The digital simulation results validated the effectiveness of both GA- and PSO-based tuned controllers in providing effective speed tracking minimal steady-state errors. Transients are also damped with minimal overshoot, settling time, and fall time. The GA- and PSO-based self-tuned controllers are more effective and dynamically advantageous in comparison with the artificial neural network (ANN) controller, the fuzzy logic controller (FLC), and fixed-type controllers. The self-regulation is based on minimal value of absolute total/global error of each regulator shown in Figs. 38.18–38.21. The control system comprising the three dynamic multiloop error-driven regulators is coordinated to minimize the selected objective functions. SOO obtains a single global or near-optimal solution based on a single-weighted objective function. The weighted single-objective function combines several objective functions using specified or selected weighting factors as follows:

$\mathrm{weighted}\mathrm{objective}\mathrm{function}={\alpha }_1{J}_1+{\alpha }_2{J}_2+{\alpha }_3{J}_3+{\alpha }_4{J}_4+{\alpha }_5{J}_5$

where α₁=0.20, α₂=0.20, α₃=0.20, α₄=0.20, and α₅=0.20 are selected weighting factors. J₁, J₂, J₃, J₄, and J₅ are the selected objective functions. On the other hand, the MO finds the set of acceptable (trade-off) optimal solutions. This set of accepted solutions is called Pareto front. These acceptable trade-off multilevel solutions give more ability to the user to make an informed decision by seeing a wide range of near-optimal selected solutions.

Table 38.5 shows the optimal solutions of the main objective functions versus the tuned variable structure sliding mode controller gain-based SOGA and MOGA control schemes. On the other hand, Table 38.6 shows the optimal solutions of the main objective functions versus the tuned variable structure sliding mode controller gain-based SOPSO and MOPSO control schemes. Table 38.7 shows the DC bus behavior comparison using the GA-based tuned variable structure sliding mode controller for the three selected reference tracks. In addition, Table 38.8 shows the system behavior using the PSO-based tuned variable structure sliding mode controller. Figs. 38.25–38.30 show the effectiveness of MOPSO and MOGA search and optimized control gains in tracking the PMDC-EV motor three reference speed trajectories. Comparing the PMDC-EV dynamic response results of the two study cases, with GA and PSO tuning algorithms and traditional controllers with constant controller gain results shown in Table 38.9, ANN controller in Table 38.10 (Figs. 38.31–38.33) and FLC in Table 38.11 (Figs. 38.34–38.36), it is quite apparent that the GA and PSO tuning algorithms highly improved the PMDC-EV system dynamic performance from a general power quality point of view. The GA and PSO tuning algorithms had a great impact on the system efficiency improving it from 0.906631 (constant gains controller), 0.928253 (ANN controller), and 0.937334 (FLC) to around 0.948156 (GA-based tuned controller) and 0.930708 (PSO-based tuned controller) that is highly desired. Moreover, the normalized mean square error (NMSE-V_DC-Bus) of the DC bus voltage is reduced from 0.08443 (constant gains controller), 0.04827 (ANN controller), and 0.03022 (FLC) to around 0.007304 (GA-based tuned controller) and 0.005854 (PSO-based tuned controller). In addition, the normalized mean square error (NMSE_ω_m) of the PMDC motor is reduced from 0.053548 (constant gains controller), 0.02627 (ANN controller), and 0.02016 (FLC) to around 0.0076308 (GA-based tuned controller) and 0.006309 (PSO-based tuned controller). Maximum transient DC voltage over/undershoot (pu) is reduced from 0.054604 (constant gains controller), 0.04186 (ANN controller), and 0.03126 (FLC) to around 0.009302 (GA-based tuned controller) and 0.007259 (PSO-based tuned controller). Maximum transient DC current—over/undershoot (pu) is reduced from 0.087336 (constant gains controller), 0.07355 (ANN controller), and 0.04383 (FLC) to around 0.00292 (GA-based tuned controller) and 0.005987 (PSO-based tuned controller). DC bus voltage (pu) is improved from 0.917020 (constant gains controller), 0.932736 (ANN controller), and 0.94745 (FLC) to around 0.97417 (GA-based tuned controller) and 0.974602 (PSO-based tuned controller). DC bus current (pu) is reduced from 0.769594 (constant gains controller), 0.67464 (ANN controller), and 0.64712 (FLC) to around 0.614695 (GA-based tuned controller) and 0.607674 (PSO-based tuned controller). PMDCM total controller Error (e_tm) is reduced from 0.095145 (constant gains controller), 0.04200 (ANN controller), and 0.02154 (FLC) to around 0.009167 (GA-based tuned controller) and 0.0048638 (PSO-based tuned controller). DC side GPFC Error (e_td) is reduced from 0.70746 (constant gains controller), 0.03416 (ANN controller), and 0.02416 (FLC) to around 0.004618 (GA-based tuned controller) and 0.0074294 (PSO-based tuned controller). The diesel engine gen set total controller error (e_tg) is reduced from 0.067513 (constant gains controller), 0.04507 (ANN controller), and 0.02964 (FLC) to around 0.005121 (GA-based tuned controller) and 0.007013 (PSO-based tuned controller). The diesel engine converter total controller error (e_tR) is reduced from 0.086233 (constant gains controller), 0.03978 (ANN controller), and 0.0260 (FLC) to around 0.003265 (GA-based tuned controller) and 0.0053836 (PSO-based tuned controller).

Table 38.5

Selected objective functions versus the tuned variable structure sliding mode controller-based SOGA and MOGA control schemes

	The diesel generator regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_g\hfill \\ \hfill {\beta }_{0g}\hfill \\ \hfill {\beta }_{1g}\hfill \end{array}\right]$	The GPFC-DC side regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_d\hfill \\ \hfill {\beta }_{0d}\hfill \\ \hfill {\beta }_{1d}\hfill \end{array}\right]$	The PMDC motor regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_m\hfill \\ \hfill {\beta }_{0m}\hfill \\ \hfill {\beta }_{1m}\hfill \end{array}\right]$	The α- controller for the converter regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_R\hfill \\ \hfill {\beta }_{0R}\hfill \\ \hfill {\beta }_{1R}\hfill \end{array}\right]$	J1 Minimize the (total error) ×10−2	J2 Minimize the (steady-state error) (pu) ×10−2	J3 Minimize the (settling time) (pu) ×10−2	J4 Minimize the (maximum overshoot) ×10−2	J5 Minimize the (rise time) ×10−2
SOGA	0.4111	0.6814	0.5376	0.0775	0.4262	0.9659	0.3315	0.6058	0.4274
	7.6052	7.2686	3.7351	2.3320
	34.4595	18.0903	20.3967	49.4889
MOGA	0.2438	0.1278	0.5250	0.7085	0.3359	0.1214	0.1330	0.6465	0.5219
	6.7638	9.9706	4.6294	2.0195
	39.6771	41.6427	29.9333	31.7174
	0.4171	0.7711	0.0017	0.8023	0.6439	0. 5840	0.8680	0.5505	0.4381
	9.9078	7.3238	7.2307	6.6139
	42.8415	30.3825	41.9151	33.9013
	0.0796	0.5655	0.9480	0.5227	0.9325	0.7425	0.1286	0.4502	0.1956
	4.6150	9.8655	8.5251	9.5619
	14.8331	27.3988	20.8308	27.8837
	0.5943	0.8238	0.8155	0.3747	0. 6220	0.8159	0.7435	0.3811	0.8706
	2.5467	9.8989	2.4722	5.2401
	14.8681	13.7004	37.7790	42.9201
	0.8499	0.9512	0.2953	0.4528	0.8135	0.2985	0.1727	0.4810	0. 7690
	5.2918	2.8911	6.2706	8.2844
	40.0583	30.3251	45.0299	22.0045
	0.7103	0.0042	0.3397	0.3788	0.6970	0.7092	0.4680	0.3245	0.8129
	5.8841	9.0935	8.5068	7.4244
	13.7034	26.9887	27.6030	33.5903

Table 38.6

Selected objective functions versus the tuned variable structure sliding mode controller gains based SOPSO and MOPSO control schemes

	The Diesel generator Regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_g\hfill \\ \hfill {\beta }_{0g}\hfill \\ \hfill {\beta }_{1g}\hfill \end{array}\right]$	The GPFC – DC side Regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_d\hfill \\ \hfill {\beta }_{0d}\hfill \\ \hfill {\beta }_{1d}\hfill \end{array}\right]$	The PMDC motor Regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_m\hfill \\ \hfill {\beta }_{0m}\hfill \\ \hfill {\beta }_{1m}\hfill \end{array}\right]$	the α- controller for the converter Regulator $\left[\begin{array}{c}\hfill {K_{\alpha }}_R\hfill \\ \hfill {\beta }_{0R}\hfill \\ \hfill {\beta }_{1R}\hfill \end{array}\right]$	J1 Minimize the (Total Error) ×10−2	J2 Minimize the (Steady State Error) (PU) ×10−2	J3 Minimize the (Settling Time) (PU) ×10−2	J4 Minimize the (Maximum Overshoot) ×10−2	J5 Minimize the (Rise Time) ×10−2
SOPSO	0.6420	0.8224	0.4837	0.9958	0.6430	0.5063	0.3271	0.2178	0.1942
	3.5994	4.5435	1.5718	4.7632
	15.9501	45.8496	30.2713	38.4880
MOPSO	0.9180	0.1091	0.9511	0.2032	0.1188	0.4657	0.8187	0.7850	0.6490
	6.8088	7.1060	5.3405	3.3284
	41.9628	26.4457	33.8367	26.9778
	0.7877	0.6885	0.4439	0.4364	0.6431	0.6374	0.4381	0.3956	0.1433
	8.2403	6.4446	9.0896	5.2320
	33.1334	45.6199	26.3367	19.1299
	0.2735	0.5283	0.4714	0.6509	0.7553	0.1289	0.5451	0.7768	0.3175
	8.0252	9.0582	4.1808	5.1085
	25.5645	47.8210	19.7245	49.4370
	0.6223	0.2945	0.0753	0.5513	0.7700	0.5610	0.5095	0.3739	0.5064
	6.1631	3.5565	5.5806	5.3880
	35.5179	44.9276	33.6105	40.9104
	0.7421	0.5091	0.8113	0.5772	0.8056	0.2506	0.4081	0.7742	0.2081
	8.5694	4.4184	3.9733	5.9874
	17.4213	35.7326	46.4878	27.2446
	0.8711	0.0135	0.5838	0.7024	0.5603	0.3070	0.6489	0.1938	0.3129
	7.2711	4.0452	8.5443	1.7882
	17.0029	26.1268	30.2219	17.1486

38.8.3.1 Sample Study Motorized System

Fig. 38.37 depicts the block diagram of the utilization (single-phase induction motor SPIM) and the connection of switched smart filter compensated device using green plug/energy management/energy economizer GP-EM-EE devices and the speed control drive system to the SPIM load. Figs. 38.38 and 38.39 show the proposed triloop dynamic tracking controller to ensure both objectives of (energy/power) saving and power quality enhancement of the supply system current and load bus voltage. The novel PSO and GA self-tuned multiregulators and coordinated controller are used for the following purposes: (1) green plug filter compensator GPFC-SPWM regulator for pulse-width switching scheme to regulate the DC bus voltage and minimize inrush current transients and load excursions and (2) the SPIM drive with the speed regulator that ensures speed reference tracking with minimum inrush conditions and ensure reduced voltage transients and improved energy utilization. Figs. 38.40–38.44 depict the proposed family of switched smart filter compensated devices using green plug/energy management/energy economizer GP-EM-EE devices. All filters objectives can be either (a) harmonic reduction and power quality (PQ) enhancement or (b) electric power/energy savings and dynamic reactive compensation for the single-phase induction motor loads. The proposed utilization scheme is fully validated using the Matlab/Simulink software environment under normal conditions, load excursion, SPIM motor torque changes to assess the control system robustness, effective energy utilization, and speed reference tracking.

The common concerns of power quality are the long-duration voltage variations (overvoltage, undervoltage, and sustained interruptions), short-duration voltage variations (interruption, sags, and swells), voltage imbalance (voltage unbalance), waveform distortion (DC offset, harmonics, interharmonics, notching, and noise), voltage fluctuation (voltage flicker), and power frequency variations. To prevent the undesirable states and to reduce the power consumption, a GPF scheme is used to stabilize the system.

Self tuned conventional PID controller

Fundamentally, the conventional PID controller comprises three basic control actions. They are simple to implement and they provide good performance. The tuning process of the gains of PID controllers can be complex because it is iterative: first, it is necessary to tune the “proportional” mode, then the “integral,” and then add the “derivative” mode to stabilize the overshoot, then add more “proportional,” and so on. The PID controller has the following form in the time domain as shown in Fig. 38.45:

$u\left(t\right)=K_{p}e\left(t\right)+K_i{\displaystyle \underset{0}{\overset{t}{\int }}e\left(t\right)dt}+K_d\frac{de\left(t\right)}{dt}$

  (38.60)

where e(t) is the selected system error, u(t) the control variable, K_p the proportional gain, K_i the integral gain, and K_d is the derivative gain. Each coefficient of the PID controller adds some special characteristics to the output response of the system. Because of this, choosing the right parameters becomes a crucial decision. In this scheme, the triloop error-driven controller is utilized with traditional PID controller. PID controller gains (K_P, K_I, and K_D) are dynamically self-tuned using the PSO and GA dynamic search and optimization criterion based on total error minimization, steady-state error, maximum overshoot, and settling time and rising time.

38.8.3.2 Digital Simulation Results

The family of (GP-EM-EE) devices system performance is compared for two cases; with (as shown in Table 38.12) and without the (GP-EM-EE) devices, the second case is studied with fixed (as shown in Table 38.13) and self-tuned-type controllers using either GA or PSO. In addition, the second case is studied to compare the performance with artificial neural network (ANN) controller (as shown in Table 38.14) and fuzzy logic controller (FLC) (as shown in Table 38.15) with the self-tuned-type controllers using either GA or PSO. The self-tuned-type controllers based either GA or PSO is tuned conventional PID controller and has been applied to the speed tracking control of the same system parameters for performance comparison. Matlab/Simulink software was used to design, test, and validate the effectiveness of the (GP-EM-EE) devices for small motors used in household appliances, washers, dryers, fans, water pumps, ventilation systems, air conditions, and other applications in dispersing machines, actuators, and small converters with induction motor size from 5 to 25 kVA. The digital dynamic simulation model using Matlab/Simulink software environment allows for low-cost assessment and prototyping, system parameter selection, and optimization of control settings. The use of GA and PSO search algorithms is utilized in online gain adjusting to minimize controller absolute value of total error. This is required before full-scale prototyping that is both expensive and time-consuming. The effectiveness of dynamic simulators brings on detailed submodels selections and tested submodels Matlab library of power system components already tested and validated. The dynamic simulation conditions are identical for all tuned controllers. To compare the global performances of tuned conventional PID controller, the normalized mean-square-error (NMSE) deviations between output plant variables and desired values and is defined as

${\mathrm{NMSE}}_{V_S}=\frac{{\displaystyle \sum {\left(V_S-V_{S-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}{{\displaystyle \sum {\left(V_{S-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}$

${\mathrm{NMSE}}_{{\omega }_m}=\frac{{\displaystyle \sum {\left({\omega }_m-{\omega }_{m-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}{{\displaystyle \sum {\left({\omega }_{m-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}$

${\mathrm{NMSE}}_{I_s}=\frac{{\displaystyle \sum {\left(I_S-I_{S-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}{{\displaystyle \sum {\left(I_{S-\mathrm{r}\mathrm{e}\mathrm{f}}\right)}^2}}$

The control system comprises the three dynamic multiloop error-driven regulator is coordinated to minimize the selected objective functions. SOO obtains a single global or near-optimal solution based on a single-weighted-objective function. The weighted single-objective function combines several objective functions using specified or selected weighting factors as follows:

$\mathrm{weighted}\mathrm{objective}\mathrm{function}={\alpha }_1{J}_1+{\alpha }_2{J}_2+{\alpha }_3{J}_3+{\alpha }_4{J}_4+{\alpha }_5{J}_5$

where α₁=0.20, α₂=0.20, α₃=0.20, α₄=0.20, and α₅=0.20 are selected weighting factors. J₁, J₂, J₃, J₄, and J₅ are the selected objective functions. On the other hand, the MO finds the set of acceptable (trade-off) optimal solutions. This set of accepted solutions is called Pareto front. These acceptable trade-off multilevel solutions give more ability to the user to make an informed decision by seeing a wide range of near-optimal selected solutions. Table 38.16 shows the system behavior using traditional controllers with constant controller gains for the (GP-EM-EE) schemes. In addition, Table 38.10 shows system behavior comparison using the SOGA-based tuned conventional PID controller, and Table 38.17 shows the system behavior comparison using the MOGA-based tuned conventional PID controller. Finally, Tables 38.18 and 38.19) show system behavior comparison using the SOPSO- and MOPSO-based tuned conventional PID controller, respectively. Comparing the system dynamic response results of the two study cases, with GA and PSO tuning algorithms and traditional controllers with constant controller gain results, ANN controller and FLC, it is quite apparent that the GA and PSO tuning algorithms highly improved the system dynamic performance from a general power quality point of view. The GA and PSO tuning algorithms had a great impact on motor RMS voltage (pu) improving it from 0.8578 (without the (GP-EM-EE) device), 0.9762 (constant gains controller), 0.9790 (ANN controller), and 0.9598 (FLC) to around 0.9804 (SOGA-based tuned controller), 0.9865 (MOGA-based tuned controller), 0.9887 (SOPSO)-based tuned controller, and 0.9852 (MOPSO-based tuned controller). Motor RMS current (pu) is reduced from 0.8724 (without the (GP-EM-EE) device), 0.7029 (constant gains controller), 0.6837 (ANN controller), and 0.6863 (FLC) to around 0.6247 (SOGA-based tuned controller), 0.6304 (MOGA-based tuned controller), 0.6358 (SOPSO)-based tuned controller, and 0.6471 (MOPSO-based tuned controller). Maximum transient motor voltage over/undershoot (pu) is reduced from 0.1797 (without the (GP-EM-EE) device), 0.0905 (constant gains controller), 0.0769 (ANN controller), and 0.0788 (FLC) to around 0.0472 (SOGA-based tuned controller), 0.0394 (MOGA-based tuned controller), 0.0441 (SOPSO)-based tuned controller, and 0.0365 (MOPSO-based tuned controller). Maximum transient motor current – over/undershoot (pu) is reduced from 0.1875 (without the (GP-EM-EE) device), 0.0701 (constant gains controller), 0.0871 (ANN controller), and 0.0828 (FLC) to around 0.0431 (SOGA-based tuned controller), 0.0533 (MOGA-based tuned controller), 0.0412 (SOPSO)-based tuned controller, and 0.0563 (MOPSO-based tuned controller). Moreover, the normalized mean square error (NMSE_V) of the motor voltage is reduced from 0.4672 (without the (GP-EM-EE) device), 0.0828 (constant gains controller), 0.0790 (ANN controller), and 0.0844 (FLC) to around 0.00396 (SOGA-based tuned controller), 0.00429 (MOGA-based tuned controller), 0.00489 (SOPSO)-based tuned controller, and 0.00440 (MOPSO-based tuned controller). In addition, the (NMSE_ω_m) of the SPIM motor is reduced from 0.6476 (without the (GP-EM-EE) device), 0.0809 (constant gains controller), 0.0715 (ANN controller), and 0.0838 (FLC) to around 0.00458 (SOGA-based tuned controller), 0.00608 (MOGA-based tuned controller), 0.00608 (SOPSO)-based tuned controller, and 0.00513 (MOPSO-based tuned controller). The (NMSE_I) of the motor current is reduced from 0.4238 (without the (GP-EM-EE) device), 0.0722 (constant gains controller), 0.0837 (ANN controller), and 0.0860 (FLC) to around 0.00361 (SOGA-based tuned controller), 0.00499 (MOGA-based tuned controller), 0.00602 (SOPSO)-based tuned controller, and 0.00465 (MOPSO-based tuned controller). Total harmonic distortion (THD) (%) of the supply voltage is reduced from 19.647 (without the (GP-EM-EE) device), 7.8228 (constant gains controller), 10.4023 (ANN controller), and 8.2175 (FLC) to around 6.2535 (SOGA-based tuned controller), 4.8408 (MOGA-based tuned controller), 4.2581 (SOPSO)-based tuned controller, and 4.1081 (MOPSO-based tuned controller). THD (%) of the supply current is reduced from 20.346 (without the (GP-EM-EE) device), 7.3532 (constant gains controller), 9.3573 (ANN controller), and 7.5181 (FLC) to around 4.1530 (SOGA-based tuned controller), 4.0103 (MOGA-based tuned controller), 5.2433 (SOPSO)-based tuned controller, and 5.1378 (MOPSO-based tuned controller). THD (%) of the motor voltage is reduced from 21.675 (without the (GP-EM-EE) device), 8.0566 (constant gains controller), 8.5408 (ANN controller), and 9.9806 (FLC) to around 5.7887 (SOGA-based tuned controller), 4.9313 (MOGA-based tuned controller), 4.5873 (SOPSO)-based tuned controller, and 4.3629 (MOPSO-based tuned controller). THD (%) of the motor current is reduced from 21.675 (without the (GP-EM-EE) device), 10.8589 (constant gains controller), 9.3120 (ANN controller), and 11.0353 (FLC) to around 3.9572 (SOGA-based tuned controller), 3.9998 (MOGA-based tuned controller), 5.1673 (SOPSO)-based tuned controller, and 5.1216 (MOPSO-based tuned controller). The system efficiency is improved from 0.7853 (without the (GP-EM-EE) device), 0.8577 (constant gains controller), 0.8943 (ANN controller), and 0.9195 (FLC) to around 95.4132 (SOGA-based tuned controller), 95.4882 (MOGA-based tuned controller), 95.4999 (SOPSO)-based tuned controller, and 90.7467 (MOPSO-based tuned controller). Motor power factor is improved from 0.7167 (without the (GP-EM-EE) device), 0.9082 (constant gains controller), 0.8609 (ANN controller), and 0.9169 (FLC) to around 95.1040 (SOGA-based tuned controller), 90.8137 (MOGA-based tuned controller), 91.7450 (SOPSO)-based tuned controller, and 91.4433 (MOPSO-based tuned controller). Reduction in kWh consumption (%) is reduced from 0.000 (without the (GP-EM-EE) device), 14.4937 (constant gains controller), 12.3129 (ANN controller), and 11.4634 (FLC) to around 18.3913 (SOGA-based tuned controller), 16.5388 (MOGA-based tuned controller), 15.9691 (SOPSO)-based tuned controller, and 16.5328 (MOPSO-based tuned controller).

The application validated the operation of a novel wind-driven squirrel cage induction generator fed from single-phase supply. The scheme utilizes a simple but effective series-parallel switched capacitor filter to ensure dynamic terminal voltage stabilization, effective energy utilization, and minimal impact of electric load switching and dynamic excursions and wind velocity changes. The novel error-driven self-regulating multiloop dynamic controller utilizes random search optimization algorithms using particle swarm optimization (PSO) and GA to continuously search for effective and optimized controllers gains that can cope with specified objective function restrictions of minimum voltage deviations, limited generated current and power excursions due to terminal load changes, and wind velocity excursions and gusting. The application presents a family of novel low-cost green plug electricity saving devices/energy management/energy economizer (GP-EM-EE) devices equipped with a dynamic online error-driven optimally tuned controller. The (GP-EM-EE) are small low-cost energy conservation devices in the form add-on dynamic switched capacitor filter compensator schemes for low horsepower motors used in household appliances, washers, dryers, fans, water pumps, ventilation systems, air conditioners, and other cyclic motorized loads used in dispersing machines, actuators, and small converters with induction motor size from 5 to 25 kVA. The (GP-EM-EE) devices family can be used with all types of small horsepower motors with billions of small motors used in multitude of applications that consumes over 50%–60% of total electric energy generated in the world. The (GP-EM-EE) device can save 10–20% of the electricity cost of operating the small motor over the estimated motor life span of 7–10 years. This translates into millions of dollars in daily electricity savings, reduced electric utility overloading conditions, blackouts, brownouts, and enhanced, secure, and reliable operation with additional sizable power capacity release due to reduced electric demand and feeder losses.