Takagi-Sugeno Fuzzy Gain Controller for Vehicle-to-Grid (V2G) Load
Frequency Control
Marayati Mersadek1, Farrukh Nagi1, Navinesshani Permal2, Agileswari A/P Ramasamy1, Aidil Azwin1
1. Universiti Tenaga Nasional, Institute of Power Engineering (IPE)
2. Faculty of Engineering and Built Environment (FETBE), UCSI University, Kuala Lumpur, Malaysia
Abstract
Load Frequency Control (LFC) has gained more importance with the introduction of
deregulated Renewable Energy Sources (RES) connectivity with the grid. Electrical Vehicles
(EVs) can feed electricity back into the grid in Vehicle-to-Grid (V2G) mode to maintain
stability. However, the increasing number of EVs penetrating the grid causes frequency
instability in the power system. If required, EVs may utilize bi-directional chargers to transfer
power back to the grid in the V2G mode while they are charging or in a grid-connected state,
restoring the frequency instability of the grid. The frequency restoration response time is
important to reset the grid frequency fluctuations in the shortest time possible to avoid shutting
down the power system. This paper presents a Takagi-Sugeno (T-S) fuzzy linear output
controller for LFC in two-area systems with tie-line control. This work models EV batteries as
a single lump of large-capacity battery energy storage systems. The EV's battery system
provides ancillary power to the two-area power system to reset it to a steady state after a load
disturbance. The T-S fuzzy controller's linear output dependency on its inputs enables it to
respond efficiently to load variations in the nonlinear two-area power systems. The proposed
controller parameters are evaluated from stability analyses and its robustness is tested with
sensitivity analysis. It is compared with other fuzzy controllers, and it demonstrates a fastsettling time and reduced frequency deviation response.
Keywords: Takagi-Sugeno fuzzy controller, load frequency control, Tie-line control, Vehicleto-Grid (V2G), Batteries lumped model, Implicit Euler solver.
1.0 Introduction
RES can provide a respite to alarming global warming. Photo-voltaic (PV) systems are
expected to play a major role in providing efficient and zero-emission energy together with
wind energy. The PV system can add power to the unregulated power system in the daytime to
be stored in large pools of EV batteries. However, charging EV batteries also causes frequency
instability of the grid. Unlike PV power, EV batteries' power is always available and the V2G
strategy enables the batteries' power to flow back to the grid and maintain power stability [1].
Shortly, most of the EVs will be plugged in for charging at any time of the day as the charging
stations in parking lots, and residential and commercial areas will be readily available [2].
However, there should be a limit on EV battery power to contribute back to the grid and keep
a safe charge margin in EVs for driving trips. The charging stations are programmed to handle
the connected batteries charging and discharging limitations based on the batteries' State of
Charge (SOC).
Frequency control of the grid is an important aspect of power system operation. It ensures a
reliable supply to meet the demand under uncertainties and varying loads. With deregulated
power systems to cater to renewable energy sources, the load uncertainties are more recurrent
[3]. In two or more interconnected power system areas, the fluctuations in the load demand led
to frequency fluctuations [1]. The generators under primary generation control (AGC) increase
the generation to restore the frequency under ±0.5Hz and reset the tie-line parameters between
the areas to a steady state in the shortest time [4]. In an interconnected area power system,
secondary control, also called Load Frequency Control (LFC) comes into action if the primary
control is insufficient to stabilize the frequency [5]. The dynamic of a power system is timevariant and non-linear, linearizing the non-linear time-invariant systems is not effective if the
load variations are high and require changes in the operating point [6,7].
The fuzzy system plays an important role in modeling and controlling nonlinear systems by
using a priori knowledge about the system or available measurements as linguistic rules [8].
Traditionally, LFC PID gain-scheduling controller design requires many empirical test runs to
evaluate the PID parameters, which is time-consuming and tedious work [9]. Among the
various LFC fuzzy controllers, Fuzzy PI controllers [10,11], Fuzzy Gain scheduled
Proportional and Integral (FGPI) [6,12,13], Scaled-Fuzzy with GA [14], Neuro-fuzzy
controllers [15, 16] are widely used. In multi-area systems, [12,16,17,18] presents two areas,
[19] presents three areas, and [6] presents four-area LFC systems. In [20] T-S fuzzy controller
is presented with constant output contrary to the linear output proposed in this research work.
Fuzzy controllers in unregulated V2G power systems can be employed in various ways. In three
area power systems, Datta in [1] uses a fuzzy controller to command the distributed PV system
to reduce the frequency fluctuations, and Saber et.al in [21] use a fuzzy controller to control the
charging/discharging EV battery. Recently, Fractional Order (FO) controllers have gained
attention due to their increased flexibility and extra tuning of the fractional order of the
integrator and fractional order of the differentiator. Arya in [22] presents two-loop cascade V2G
fuzzy fractional order structured controllers with robust non-linear performance. Others took
advantage of Fractional Order Controller (FOC) flexibility in FLC, termed it FOFLC, and tuned
it with self-adaptive and optimization techniques [23-25].
The major problem concerned with FOFLC types of controllers is the optimum selection of the
parameters that minimize the deviations and guarantee zero area control error (ACE). Further,
the constraint optimization problems are highly nonlinear, and finding the optimal solution is a
challenging task [26]. Other fuzzy LFC controllers discussed above have many rules and are
based on the Mamdani Fuzzy Inference System (FIS) [8] which has defuzzified output and adds
a computational burden. LFC fuzzy controllers with PID control require an operational gains
setting. The above problems are the motivation behind this work to contribute by devising a
simple and robust load frequency controller that has a low settling time and less overshoot.
Takagi-Sugeno (T-S) controllers with few linear control rules are nonlinear variable gain
controllers [27], which enable the T-S fuzzy controller to adjust its output to nonlinear system
inputs and are easier to implement in real-time [20,28]. T-S fuzzy controller offers embedded
gains setting, instead of external PID control, it guarantees smooth interpolated output in linear
relation with the inputs. When used in a two-area V2G power system, it shows fast convergence
of ACE to zero error with less frequency deviation in comparison to its predecessors.
2. EVs Batteries modeling
Modeling of a large number of EV battery penetrations, and scheduling with associated SOC,
charging times, and capacities empirically/probabilistically [29-30] are not considered in this
work. However, Koichiro [2] presented lumped modeling of EVs with user convenience and
uncertainty. The lumped EV batteries model is based on three EV states of ‘Driving’,
‘Charging’, and ‘Controllable’ with three transitions ‘Plug-in’, ‘Control-in’, and ‘Plug-out’
connecting the three states as shown in Figure 1.
Driving
State
Plug-in
Plug-out
Charging
State
Control-in
Controllabl
e
State
Figure 1. EVS states and transition [2]
During driving, the EVs are not connected to the grid; but, during charging, they are. In a
controllable state, the EVs are available for V2G transfer command. All the while when EVs
are connected to the grid the charging station monitors the batteries' SOCs and keeping the
customer convenience a priority, it only allows the EVs to serve the grid between 90% - 80%
of SOC. The charging station is connected to the Distribution Management System (DMS) and
exchanges information every 30 seconds regarding the sum of the inverter capacity of EVs,
their states, and SOCs. DMS with charging station information and grid frequency fluctuation
calculates the LFC signal and sends it back to the charging station for V2G transfer.
It is expected that charging stations will be readily available at workplaces, and commercial
and residential parking lots, and most of the EVs will be in controllable states with closed to
full SOC. Modeled EV data for the initial 100EVs/station is shown in Figure 2. EVs between
Plug-out and control-in transitions are in driving and charging states, represented as dotted
shades in Figure 1, and are not available for V2G transfer. All other EVs are in a controllable
state and available for V2G transfer, as shown in Figure 2. Then controllable EVs NNC which
are available for V2G transfer computed as in eqn. (1).
𝑁𝑁𝐶 (𝑡) = 𝑁𝑖𝑛𝑖 − (𝑁𝑃𝑂 (𝑡) − 𝑁𝐶𝐼 (𝑡))
(1)
𝐵𝑘𝑊 (𝑡) = 𝑁𝑁𝐶 (𝑡). 𝐶𝑘𝑊 (𝑡)
(2)
Where Nini is the initial 100 EVs, NPO and NCI are Plug-out and Control-In EVs respectively.
EV batteries lumped model for one charging station with 100 EVs in Simulink environment is
shown in Figure 3. LFC signal is generated by DMS for charging/discharging instructions to
the charging station. The output average EV power outputs and SOCs remain the same for all
other stations as long as the EVs modeled data in Figure 2 is statistically unchanged. Battery
charging is limited to inverter capacity CkW = ±3kW as:
EVs in driving and charging
states. Not available for V2G
Figure 2. EV charging and discharging data model for one charging station (EVData)
Figure 3. EV batteries Simulink lumped Model [2] of 10 charging station. At top is batteries
charging/ discharging inverter model, in middle is batteries V2G transfer limitations and at
bottom is charging station energy storage. ‘EVData’ is modeled in Figure 2.
Each EV is equipped with a CkW = 3kW and CkWh = 15kWh battery power and energy
respectively. The battery capacity BkWh limits EVS to participate in V2G for customer
convenience is kept between SOC limits of 90% - 80% and regulates the charging and
discharging power of EV PEV as
𝑈
𝐵𝑘𝑊ℎ
= 𝑁𝑁𝐶 . 𝐶𝑘𝑊ℎ . (0.9)
(3)
𝐿
𝐵𝑘𝑊ℎ
= 𝑁𝑁𝐶 . 𝐶𝑘𝑊ℎ . (0.8)
(4)
The controllable EVs NCN in eqn. (1) are batteries' total stored energy EEV in Figure 3 as
𝐸𝑐𝑜𝑛 (𝑡) = 𝐸𝑁𝑖𝑛𝑖 − 𝐸𝐸𝑉 (𝑡) + 𝐸𝑁𝐶𝐼 (𝑡) − 𝐸𝑁𝑃𝑂 (𝑡)
(5)
Initial EVS energy 𝐸𝑁𝑖𝑛𝑖 and control-in energy 𝐸𝑁𝐶𝐼 are obtained by multiplying with 85% to
maintain 85% of the average SOC in the batteries, such that batteries above 85% respond to
V2G command and discharge while below 85% start to charge. The 𝐸𝑁𝐶𝐼 depends upon the NCI
data in Figure 2 and is in eqn. (6).
(6)
𝐸𝑁𝐶𝐼 (𝑡) = 0.85 . 𝐶𝑘𝑊ℎ . 𝑁𝐶𝐼 (𝑡)
The plug-out energy 𝐸𝑁𝑃𝑂 does not participate in V2G transfer and depends on differential
change 𝐷𝑃𝑂 of plug-out EVs NPO in time interval τ is computed using eqn. (7)
𝐷𝑃𝑂 (𝜏) =
∆𝑁𝑃𝑂
(7)
∆𝜏
from which the total plug-out energy 𝐸𝑁𝑃𝑂 (𝑡) can be calculated using eqn. (8)
𝑡
𝐸
(𝜏)
𝐸𝑁𝑃𝑂 (𝑡) = ∫0 𝐷𝑃𝑂 (𝜏) . 𝑁𝑐𝑜𝑛(𝜏) . 𝑑𝜏
(8)
𝑁𝐶
3. Two-area power system model
A general linearized two-area power system with a tie-line is adopted from [5] for LFC is shown
in Figure 4. Other relevant parameters are given in Table 1.
Table 1. Two Area System Parameters [2]
Area
1
2
Base power
Freq.- sens. load coeff.
D1 = 0.5
D2 = 0.9
Inertia constant
H1 = 5
H2 = 4
Speed regulation Hz/MW
R1 =0.05
R2 =0.0626
Governor time constant
τg1 =0.2 sec τg2 =0.3 sec
Turbine time constant
τT1 =0.5 sec τT1 =0.6 sec
Synchronous power coeff.
Nominal frequency
Random load change pu
∆PL1 = ±0.3 ∆PL2 = ±0.3
General
1000 MVA
Ps =2
60 Hz
-
1
2
Figure 4. Two area LFC model [5] with T-S controller and EV lumped models.
The system in simple state equations form can be expressed as:
𝑥̇ (𝑡) = 𝐴𝑥(𝑡) + 𝐻𝑢(𝑡) + 𝐿𝑑(𝑡)
(9)
and
𝒖(𝑡) = [𝑢1 𝑢2]𝑇
(10)
𝐝(𝑡) = [∆𝑃𝑑1 ∆𝑃𝑑2 ]
(11)
where A, H, and L are the system state matrix, input matrix, and disturbance matrix respectively.
x(t), u(t), and d(t) are the state vector, control vector, and load change vector respectively. The
state vector x(t) is defined as:
𝒙(𝑡) = [∆𝑓1, ∆𝑃𝑔1 , ∆𝑃𝑣1 , ∆𝑃𝑡𝑖𝑒12 , ∆𝑓2 , ∆𝑃𝑔2 , , ∆𝑃𝑣2 ]
(12)
where ∆f denotes frequency deviation from the nominal value, ∆Pg, ∆Pv and ∆Ptie12 are
governor, valve change settings, and change in tie-line power respectively. The system output
depends on area control error (ACE1, ACE2) and is given as:
𝑦 (𝑡 )
𝐴𝐶𝐸1
𝑦 (𝑡 ) = [ 1
]=[
]
𝐴𝐶𝐸2
𝑦2 (𝑡)
(13)
[
∆𝑃
+ 𝐵1 ∆𝑓1
𝐴𝐶𝐸1
] = [ 𝑡𝑖𝑒12
]
𝐴𝐶𝐸2
𝐵2 ∆𝑓2 − ∆𝑃𝑡𝑖𝑒12
(14)
where ∆Ptie12 is the variation in line power between area 1 to area 2. B =[B1 B2] is the
frequency bias factor and is given as:
𝟏
𝑩= 𝑹+𝑫
(15)
where D= [D1 D2 ] and R= [R1 R2] are given in Table 1.
4. T-S Fuzzy Linear Controller
Most of the industrial processes are currently controlled by the PID. The controller nth output
z(n. ∆T) in positional form sampled at ∆T sampling interval is:
𝒛(𝑛) = 𝐾𝑝 𝒆(𝑛) + 𝐾𝑖 ∑𝑛𝑖=0 𝒆(𝑖 ) + 𝐾𝑑 (𝒆(𝑛) + 𝒆(𝑛 − 1)
(16)
Kp, Ki, Kd and are proportional, integral, and derivative gains respectively, and index i is
integral step time, e = [ACE1 ACE2] is the Area Control Error in Figure 4.
In this work, the PI controller is used for forcing the steady state frequency deviation from the
primary loop by integration action of the secondary loop, so Kd =0, reducing eqn. (16) to eqn.
(17).
𝒛𝑷𝑰 (𝑛) = 𝐾𝑝 𝒆(𝑛) + 𝐾𝑖 ∑𝑛𝑖=0 𝒆(𝑖 )
(17)
4.1. Input Membership functions
The T-S fuzzy controller proposed in this study has Gaussian input membership functions (MF),
which are known to provide a smooth transition and wide widths overlap among the adjacent
Gaussian memberships function. They increase the number of firing rules and consequently
reduce the number of membership functions [31]. Two inputs error e and error rate 𝒆̇ are used
with five Gaussian membership functions [A1, A2] = [err, edot] = [‘NB’ ‘NS’ ‘Z’ ‘PS’ ‘PB’]
are shown in Figure 5. The limits of the input e = [-1 1] as per the two-area power system are
scaled to pu =[-1 1]. Similarly 𝒆̇ = [-1 1] also has the same range.
Figure 5. Gaussian inputs membership function (a) A1(e) error (b) A2(𝒆̇ ) error dot.
4.2. Output Membership function (MF)
Two T-S fuzzy controller variants are implemented with constant and linear output MFs, the
input MFs are kept the same for comparison purposes as shown in Figure 5. T-S fuzzy one
output inference system uses three singleton outputs B(1,1:3)= [‘P’, ‘Z’ ‘N’] membership
functions, that are either constant or linear. Since ACE (e) signals range between [-1 1] pu the
fuzzy output ranges need to be [-1 1] as well. Then the output MFs are defined as:
B(1,1) = 1
B(1,2)= 14e+12𝒆̇ +0
B(1,3)= -1
(‘P’, mf - constant)
(‘Z’, mf- linear)
(‘N’, mf - constant)
(18)
Where ki =14 and kp =12 for linear Z mf from eqn. (17) and will be discussed later.
The rule firing strength wr is derived from AND () logic between two inputs membership
functions A1 =  (e) and A2 =  (𝒆̇ ) for rth rule is given as
wr= A1r (e)  A2r (𝒆̇ )
(19)
The T-S output is a weighted sum of input data points. The final output u of the system is the
weighted average over all r-fired rules [32]:
∑𝑅𝑟=1 𝑤𝑟 𝐵𝑟
𝑢= 𝑅
∑𝑟=1 𝑤𝑟
(20)
Where R are the fuzzy rules described in Table 2.
4.2.1. Linear Output
Based on [27] the linear MF ‘Z’ in eqn. (18) acts non-linear variable PI gains controller for kp,
ki, and kd =0 in eqn. (17) with ACE magnitude as
𝑘𝑝 (𝑒, 𝑒̇ )
= [𝑨1 (𝒆)  𝑨2 (𝒆̇ )]
𝑘𝐼 (𝑒, 𝑒̇ )
= [𝑨1 (𝒆)  𝑨2 (𝒆̇ )]
(21)
𝑘𝑐 (𝑒, 𝑒̇ ) = (1 + [𝑨1 (𝒆)  𝑨2 (𝒆̇ )])
Where kc = 0 in eqn. (18) is the constant bias for MF ‘z2’ for the controller output u. The bias
helps to reduce the overshoot in the initial response. The 𝑘𝑝 (𝑒, 𝑒̇ ) = 12 controls the amplitude
of output and 𝑘𝐼 (𝑒, 𝑒̇ ) =14 affects the steady state error of the controller output the other two
output MF are constants [‘P’ = 1, ‘N’ = -1]. The linear PI controller in eqn. (17) is then
converted to a non-linear fuzzy PI controller as eqn. (22).
𝐵(1,2) (𝑛) = [14 ∑𝑛𝑖=0(𝑒(𝑖), 𝑒̇ (𝑖))] + [12(𝑒𝑖 (𝑛), 𝑒̇ (𝑛))] + 0
(22)
The fuzzy rules are given in Table 2 to drive the frequency deviation to zero. The rules output
MF matches the input MF signs i.e. e=’NB’ and edot =’ NB’ then u=’N’ are in the same sense
of ACE signal. The purpose of the T-S fuzzy LFC controller is to adjust the gain of ACE in the
primary loop in Figure 4. T-S fuzzy linear in this study is acting as a gain controller.
Table 2. T-S Fuzzy Logic Rule Table
e
edot
NB
NS
Z
PS
PB
NB
NS
Z
PS
PB
N
N
N
N
Z
N
N
N
Z
P
N
N
Z
P
P
N
Z
P
P
P
Z
P
P
P
P
4.2.2. Constant Output
T-S controller with constant ‘Z’ MF is given as:
𝑘𝑝 (𝑒, 𝑒̇ )
=0
𝑘𝐼 (𝑒, 𝑒̇ )
=0
(23)
𝑘𝑐 (𝑒, 𝑒̇ ) = (1 + [𝑨𝟏 (𝒆) 𝑨𝟐 (𝒆̇ )])
The two T-S fuzzy controllers’ outputs are summarized in Table 3. T-S fuzzy output rules
surface plots are shown in Figure 6. The linear ‘Z’ fuzzy partition surfaces in Figure 6(a) are
smaller in comparison to the constant ‘Z’ fuzzy space [20] in Figure 6(b). Further, the linear
surface in Figure 6(a) has a bumpy surface between the flat top and drop surface due to the
interpolation property.
Table 3. T-S fuzzy variants output MF
Output MF, zr
‘P’
‘Z’
‘N’
(a)
T-S Linear
-1
[14 12 0]
1
T-S Constant
1
1
-1
(b)
Figure 6. T-S rules surface plot. (a) With linear ‘Z’ MF. (b) With constant ‘Z’ MF.
5. T-S Fuzzy Controller Analysis
Two controller analyses, stability, and sensitivity are conducted here to show the usefulness of
the proposed controller. Stability analysis of the T-S fuzzy controller determines the parameters
ki and kp in eqn. (22) to reset the frequency deviation in the two-area system for step input
disturbance ∆𝑃𝐿 = 1 pu. The sensitivity analysis assesses the robustness of the controller to
maintain its operation with varying system parameters.
5.1. Stability Analysis
The stability is evaluated for settling time of frequency deviation ∆f in eqn. (12) with respect
∆𝑓
∆𝑓
to ki and kp as partial derivatives 𝑚𝑖𝑛[∆𝑘𝑖 ∆𝑘𝑝 ] with respect to settling time. The plot of partial
derivatives is shown in Figure 7(a) and the minimum selected settling time values are shown
in the inset as ki =14 and kp =12. The frequency deviation (∆f) step response for Mamdani and
TS fuzzy controller at selected ki and kp is shown in Figure 7(b). Linear TS fuzzy controller
characteristics are smaller than Mamdani as shown in the inset box, Figure 7(b).
Figure 7. Stability Analyses . (a) kp and ki gains selection for minimum settling time
(b) Frequency deviation for step input disturbance ∆PL =1pu at selected gains in (a).
5.2. Sensitivity Analysis
To test the robustness of the T-S fuzzy controller the turbine and load parameters nominal time
constants of turbine τT1 =0.5 sec and load 2*H1=10 sec respectively are perturbed by ±50%
of nominal values. The perturbation effect on frequency (∆f) and power deviation (∆Ptie) with
step ∆𝑃𝐿 = 1 pu and random ∆𝑃𝐿 = 0.3 pu disturbances are shown in Figure 8-9. The aboveselected T-S fuzzy controller parameters ki = 14 and kp = 12 are used for the test. The T-S fuzzy
controller transient response closely matches the nominal values both with random and step
∆PL. The sensitivity test indicates that re-tuning the controller parameters for small variations
of process variables is not necessary.
Figure 8. Effect of changing turbine parameters, step ∆𝑃𝐿 = 1 pu.
(a) Effect on frequency deviation(b) Effect on tie-line power ∆Ptie.
Figure 9. Effect of changing turbine parameters, random ∆𝑃𝐿 = 0.3 pu. (a)
Effect on frequency deviation(b) Effect on tie-line power ∆Ptie.
6. Two-Area Network Simulation
Two-area power system [5] used for simulation is shown in Figure 4. Turbine power output is
limited to 0.4 pu to enable the V2G power PEV1 and PEV2 contribution. The secondary controller
(LFC) generates Area Requirements (AR) based on the load fluctuation ∆PL. Which represents
the LFC signal generated by DMS for charging/discharging instructions to the charging station.
The AR signal is fed to the EV battery lumped model for V2G transfer. The ∆PL is modeled as
a random signal at 30-second intervals for the two areas with ±0.3 pu amplitude as shown in
Figure 10. A total of 1000 EVs are simulated in each area with 10 charging stations each with
100 EVs/station. The EV number can be changed with the ‘Station’ block. The AR signal is
scaled to MW [2] in the EV lumped model for the EV charging/discharging circuit and output
PEV is reduced back to per unit values before feedback to the area power system. For
MATLAB/SIMULINK simulation, a fixed step with a step size of ‘1’ and ode1be (Backward
Euler) solver is used.
Figure 10. Uniform random per unit load disturbance ∆PL, representing
distributed management system (DMS) to LFC.
7. Results and Analysis.
A comparison of two T-S fuzzy variants, linear and constant is shown in Figure 11. Only one
area of power analysis is considered for conciseness. It can be seen in Figure 11(a) that the TS fuzzy linear variant due to output interpolation and non-linear gain capabilities has a
comparatively low frequency response in comparison to constant T-S fuzzy LFC. The results
show the suitability of T-S linear FLC in V2G mode has the lowest frequency deviation
overshoot in the range of ±10-3 pu than its counterpart LFC controllers with a range of ±10-2
pu, due to its non-linear variable gain PI properties. The low overshoot capability of T-S fuzzy
LFC is due to the quick settling time of tie-line parameters to zero steady state for LFC signal
disturbances. The tie-line power comparison is shown in Figure 11(b). T-S fuzzy linear and
constant controllers have the same tie-line power. For customer convenience, the battery's SOC
is kept between 90% - 80% SOC, and PEV is cut off as per the model in Figure 3.
EV charging and discharging are shown in Figure 12. EVs charge/discharge within 90%-80%
of battery capacity with the average SOC set to 85%, as in eqn. (6). Between 90% - 85% SOC,
the batteries discharge with +PEV in V2G mode as per AR signal for frequency stabilization,
and between 85% - 80% SOC the batteries are charged with -PEV. EV power contribution to the
grid for LFC is shown in Figure 13.
Figure 11. (a)T-S fuzzy frequency deviation comparison between linear and constant
LFC. (b) Tie-line power comparison between T-S fuzzy constant and linear. The ∆Ptie
line is obscured in the image.
Figure 12. EV V2G analysis. (a) EV pu power output to the two-area power
system. (b) EV SOC variations due to the AR signal from the two-area power
system.
𝐿
Figure 13. V2G contribution to assist Turbine 0.4 pu at 𝐵𝑘𝑊ℎ
= 80% for LFC.
T-S linear fuzzy LF is compared with three other fuzzy controllers Mamdani [18] and gain
scheduling techniques [6, 12] in Figure 14. For all the comparison techniques, the input MFs
are kept the same as in Figure 5. The output fuzzy rules of the Mamdani technique are the same
as in Table 2 and output MFs are given in Appendix-Figure 1 (a). The other two gain scheduling
techniques' output MFs are given in Appendix-Figure 1 (b, c), and the fuzzy rules in Appendix
Tables 1 and 2. Two gain scheduling techniques' fuzzy rule surfaces are shown in AppendixFigure 2.
A comparison of T-S Linear LFC with other techniques is shown in Figure 14. The Mamdani
frequency deviation in Figure 14(a) is compared with T-S fuzzy. The gain scheduling
techniques in Figures 14(b) and 14(c) and Mamdani don’t perform well in reducing the
frequency deviations as compared to the T-S fuzzy controller. The drawback of Mamdani and,
gain scheduling techniques is that they require more rules, in order of 49 instead of 25 rules
used in this work for greater choices of kp and ki gains. Further, these techniques lack the gain
interpolation capabilities of T-S fuzzy linear controllers. The surface plots of the three
compared techniques are shown in Appendix-Figure 2. The partition surfaces are not smooth
to give the progressive choices of outputs in comparison to the T-S fuzzy linear controller which
has the capability of variable kp and ki gains depending upon the inputs.
Figure 14. T-S linear fuzzy LFC frequency deviation comparison with other
fuzzy techniques. (a) Mamdani [18], the trace in middle is T-S linear fuzzy LFC
(b) Fuzzy gain scheduling 1 [6] (c) Fuzzy gain scheduling 2 [12].
8. Conclusion
In this work, the effectiveness of T-S linear fuzzy LFC in a V2G power system is demonstrated
with a two-area power system. EVs data is assumed for 10 charging stations each with 100
EVs. The T-S linear fuzzy controller design and properties were discussed in detail. Although
1000 EVs were modeled in this work, the EVs can be increased with a lower variance of
SOC. The sensitivity and stability analysis proved the robustness of the T-S fuzzy LFC
controller with fast resetting of frequency deviation in two area networks. Distributed Control
Systems (DCS) systems are responsible for the integration of various power plant operations,
allowing centralized control and monitoring. Real-time implementation and tuning of T-S fuzzy
controllers can be easily implemented through DCS in the absence of a defuzzification process.
Model-based direct and non-model-based in-direct adaptive T-S load frequency fuzzy
controllers can be further explored. Only one output membership function is linear in this work
while the others are constant, the effect of linearizing all output membership functions and
tuning of TS fuzzy inputs and output membership functions can be further explored.
Appendix
Fig Figure 1 App. Output Mfs of comparison fuzzy controllers, (a) Mamdani [18]. (b) Gain
schescheduling 1 [6]. (c) Gain Scheduling 2 [12].
Table 1 App. Gain Sched. 1 [6]
KP, KI Fuzzy Rules
e
Table 2 App. Gain Sched. 2 [12] KP, KI
Fuzzy Rules
edot
N
B
NS
Z
PS
PB
e
edot
NB
NS
Z
PS
PB
NB
NS
Z
PS
PB
S
S
B
S
S
S
B
B
B
S
S
B
B
B
S
S
B
B
B
S
S
S
B
S
S
NB
S
S
M
M
B
NS
S
M
M
B
VB
Z
M
M
B
VB
VB
PS
M
B
VB
VB
VVB
PB
B
VB
VB
VVB
VVB
Figure 2 App. Fuzzy surface plot. (a) Mamdani [18] (b) Gain sched. 1 [6]. (c) Gain sched. 2 [12]
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