CHAPTER 4 ON LINE LOAD FREQUENCY CONTROL The main objective of Automatic Load Frequency Control (LFC) is to maintain the frequency and active power change over lines at their scheduled values. As frequency is a common factor throughout the system, any change in active power demand/ generation at power systems is reflected throughout the system by change in frequency. Also, LFC problem is very important in interconnected power system because load perturbation in one area may disturb the frequency of others [97]. The first part of the chapter deals with modeling of a two area thermal power system taking into account the boiler system effects, generation rate constraint and the governor dead band effects and doing the analysis of dynamic responses such as frequency deviation in area one (ΔF1), area 2 (ΔF2) and tie line power deviation (ΔPtie), considering 1% step load perturbation in area 1 of system, with different controllers. The response of different controllers analysed are Proportional and Integral (PI), on-line Neural (NN) and on-line neuro-fuzzy (NF) controller. In literature many neural networks and fuzzy logic investigations for load frequency control have been presented [98]. Mostly, the boiler system effects and the governor dead band effects are neglected in load frequency studies for simplicity and also these investigations are mostly offline. But, in the realistic analysis of system performance these non-linearities have considerable effects on amplitude and settling time of oscillation and are thus included in this study. The novelty of the work is that we are using on-line neural and neuro-fuzzy controllers taking most of the system non-linearities into account. Parameters of the controllers are trained on-line using the embedded block of MATLAB SIMULINK. MATLAB program has been written for the controller and then this program is called in SIMULINK using the embedded block. In offline or fixed gain controllers a huge set of data is required to train the NN or NF controller so as to track the set point while in on-line controller, training of the parameters of membership function and weights of neural network used in defuzzification is done online while controller is in use.. Fixed gain controllers are designed at nominal operating conditions and fail to provide best control over wide range of operating conditions. The active and reactive power demands are never steady and they continuously change with load demand. The PI controllers can take care of 51
small changes in load demand without frequency and voltage exceeding the prescribed limit. In PI controller, proportionality constant provides simplicity, reliability, directness etc. But it does not provide adequate control performance when system non-linearities and boiler dynamics are considered [97,98, and 99] or if some kind of disturbance acts upon the system. To overcome all these difficulties the conventional PI controller is replaced by a neural and then by a neuro- fuzzy controller whose parameters are trained on-line. Another difference in our proposed controller is that unlike the standard ANFIS command in MATLAB toolbox which uses a hybrid learning algorithm (combination of least-squares and backpropagation gradient descent methods) to train only Fuzzy Inference Structure (FIS) here training of the weights of neural network and training of membership functions of fuzzy sets are being done simultaneously. To make the controller more adaptable to change in system parameters and more robust to noise, training of neuro fuzzy controller is made in embedded block of simulink which incorporates training of input membership functions as well as weights of neural network. The benefits of NN i.e. it’s ability to learn and that of fuzzy logic utilizing human experience are incorporated in the neuro fuzzy network. A comparative study of dynamic response of frequency deviation for 1% step load perturbation in area one of the system are done for different type of controllers. Simulated results show superiority of neuro fuzzy controller over other two controllers in terms of peak overshoot, settling time and steady state error. Part one of the chapter discusses that the transfer function approach is applicable for small fluctuations only about the operating point which is good for analysis purposes. In the second part of the chapter more practical approach is presented. After testing the superiority of neuro fuzzy controller, the PI block in Electronic Load Controller (ELC) is replaced by the neuro fuzzy embedded block thereby making it an intelligent ELC. The proposed intelligent ELC(using on line neuro-fuzzy controller) is simulated for active power control for parallel operated isolated generators feeding three wire three phase loads in SIMULINK environment using power system Blockset (PSB). The chapter is divided in two parts. Part I is organized as follows: Section 4.1 briefs the modeling of the system under study and section 4.2 discusses about the basic neuro-fuzzy controller. Section 4.3 gives the simulated results and discussion. In part II of the chapter Section 4.4 and 4.5 describe the proposed electronic load controller and the system under study respectively. Section 4.6 gives the simulated results. Section 4.7 concludes the chapter. 52
PART I
4.1. THE SYSTEM UNDER STUDY
A two area system consists of two single area thermal systems, connected through a power tie line as shown in figure 4.1. Each area feeds its user pool and tie line allows electric power to flow between the areas. The system is modeled incorporating governor dead band, generation rate constraint (GRC) non-linearities and boiler dynamics [99]. Each component of the power system is reduced to it’s transfer function as shown in figure 4.1. In earlier studies, boiler system effects and the governor dead band effects are neglected for simplicity, but they have considerable effects on dynamic response and are thus included in this study. Dynamic response for frequency control is simulated and compared in the stated model with PI, on line Neural, and on line Neuro-Fuzzy controllers. A comparative study of dynamic response such as frequency deviation in area one (ΔF1), area 2 (ΔF2), tie line power deviation (ΔPtie), for 1% step load perturbation in area 1 of the system are done with different type of controllers. The various nonlinearities considered are discussed as follows:
4.1.1 Governor Dead Band
Governor Dead Band (GDB) is defined as the total magnitude of a sustained speed change within which there is no resulting change in valve position. Describing function approach is used to incorporate the governor dead band non-linearity [99,100]. The hysteresis type of non-linearities is expressed as, rather than as y=F(x)
(4.1)
where: y=output of governor dead band F= describing function, x= sinusoidal input to governor dead band Assuming x to be sufficiently close to a sinusoidal, the above equation can be expanded using Fourier series as follows: 53
(4.2) As the backlash nonlinearity is symmetrical about the origin, F0 is zero. In this work, backlash of approximately
0.05%
is
chosen
[97].
From
the
above
equation,
for [delf 1nf]
Boiler Dynamics 1
Goto
Gain 2 -KIn1
Gain 1 -K-
Neurofuzzy 1
Step
1
5s+1
.08s+1
10s+1
Out1
In1
Out1
Backlash Governor 1
Reheater 1
KGain 3
1
120
s
20s+1
Saturation Transfer Fcn 9
Load 1 Transfer Fcn 8 .54 s
[ptienf ]
Gain 4 -K-
Gain 7 -K-
Goto 2 In1
Out1
Neurofuzzy 2
5s+1
1
10s+1
.08s+1 Backlash1
Reheater 2
Governor 2
1
KGain 8
s Saturation 1Transfer Fcn 10
120 20s+1 Load 2 [delf 2nf]
In2
-K- Gain 5
Out2
Goto 1
-K- Gain 6 Boiler Dynamics 2
Clock [delf 1nf] From [delf 2nf]
neurofzy
From 1
To Workspace
[ptienf ] From 2
Fig. 4.1 Transfer Function Modeling of a two area thermal system. simplification, neglect higher order terms, the fourier co-efficients are derived as N1=0.8 & N2=0.2. By substituting the values in (2) the transfer function for GDB is expressed as follows: (4.3)
54
4.1.2 Generation Rate Constraint (GRC)
In practice, there exists a maximum limit on the rate of change in the generating power. For thermal system a generating rate limitation of 0.1 p.u. MW per minute is considered [101].
4.1.3 Boiler Dynamics An oil or gas fired drum type boiler system is modeled in this study. The boiler receives feed water which has been preheated in the economizer and provides saturated steam outflow. Recirculation boiler make use of a drum to separate steam flow from the recirculation water so that it can proceed to the super heater as a heatable vapour; hence recirculation boiler is referred to as drum type boiler[102]. The changes in generations are initiated by turbine control valves and the boiler controls respond with necessary control action i.e. changes in steam flow and changes in throttle pressure, the combustion rate and hence the boiler output. Figure 4.2 shows the simulink model of boiler dynamics. Numerical values of various constants are mentioned in appendix B.
Fig 4.2 Boiler dynamics.
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4.2 NEURO-FUZZY CONTROLLER
The proposed online Neuro-fuzzy controller is made in embedded block in SIMULINK.The MATLAB program of a neuro fuzzy controller is written and is being called in the embedded block in SIMULINK in each iteration. Input to the controller is area control error (ACE) and change in area control error (ACĖ) as given in equation (4.4). Xi (k)=ACEi(k) + ACĖ i(k) ACEi (k)=Xi (k)=ΔFi (k)Bi+ ΔPtie (k)
(4.4)
ACĖ i(k)= ACEi(k)- ACEi(k-1) where:i is number of areas in power system under study, Xi is input to the controller of ith area, is change in frequency, B is frequency bias constant, is change in tie line power. The fuzzification of error and change in error is done and after firing of rules and manipulation of membership functions, defuzzification is done using neural network. Figure 4.3 shows the model of neuro fuzzy network. As clear from the figure three steps are involved in a neuro fuzzy network- Crisp value of input converted to fuzzified values. Then rule base is applied to get fuzzified output. Defuzzification is done using neural network[103]. The three steps are explained in brief as follows:
56
Fig 4.3. A neuro Fuzzy neuron.
4.2.1 Fuzzification of input: The input space is divided into fuzzy segments which are characterized by Gaussian type membership functions within the range X(min) and X(max) given in equation (4.5). The reason for selecting this gaussian membership function is that it can approximate triangular and trapezoidal membership functions. Strength of a rule is given in the following equation: n
n
p 1
p 1
lpi
(k , i) ip ( x p ) exp( a pi {x p (k ) c pi } )
(4.5)
(k,i) is the normalized membership function of the fuzzy set, api determines the width of membership function, cpi represents the center of membership function, lpi give the shape of membership function, p is the pth input.
4.2.2. Rule Base: The neuro fuzzy block can be described by a set of fuzzy rules in TakagiSugano (T-S) form. 57
Ri is the ith rule (1 ≤ i ≤ r); n is the total number of input variables.
4.2.3 Defuzzification: Changing the fuzzied output to crisp values is called defuzzification. is the defuzzified output represented by the following simple equation: (4.6) In the above equation, μ(k, i) is the strength of the rule, which must be weighted by w(k,i) in direct proportion to the output error because the error is caused by the weight. It is noted that the final output of neural network, is proportional to the system output. From this, we assert that defuzzification is taking place in the neural network. The computed output is given as input to the two area power system. The whole two area power system is reduced to transfer functions. 1% step load perturbation is given in area one as disturbance to the system and changes in frequency in each area and change in tie line power are computed. Under steady state condition, change in tie line power and change in frequency of each area should converge to zero. The objective function to be minimized by the controller is: (4.7) ΔF1 and ΔF2 are frequency deviation in area 1 and 2 respectively, ΔPtie is tie line power deviation The whole structure is shown in figure 4.4. As seen in the figure the input Xi is computed and fuzzified for each sampling time. Five gaussian membership functions are taken for both the inputs. Defuzification is done using three layer feed forward neural network. Sigmoidal and purelin non –linear functions are chosen with 10 neurons in each layer respectively. The output of neuro fuzzy network is fed in area system with 1% step load perturbation in area one at time t =1 second. Performance index (J) is computed; the weights and membership functions are updated by the new values. Values of objective function (J) and the new values of ΔF1, ΔF2, are computed. 58
Neuro Fuzzy Controller
∆F1
B1
-1
Z
-
W11
+ +
+
∆F2
µi1 ACĖ µi2
W12
B2 ∆Ptie
+ µi5
W15
∆F1
Control Area 1 (F2 & Ptie also get affected)
∆F2 ∆Ptie
Learning Algorithm
Calculate J
Fig. 4.4 The whole structure of power system control with on-line neuro-fuzzy control.
Fig. 4.5 Plots showing initial and final membership functions. 59
∆PD
The corresponding weight w(k,i) is increased in direct proportion to the output error because the error is caused by the weight. Online training of weights and updation of parameters of gaussian function is done using, back propagation and gradient descent algorithms respectively. Then output of neuro fuzzy network is computed using these new values of ΔF1 , ΔF2 ,
as inputs.
This completes one cycle. This is repeated till the objective function is reduced to a minimum value. Now again new value of input is computed feed to the neuro fuzzy controller with these new values. This is repeated till steady state error reduces to a minimum value. Membership functions being trained are shown in figure 4.5. The on line training of the neuro fuzzy controller makes it more robust to changes in system parameters and the disturbances.
4.3 SIMULATED RESULTS AND DISCUSSION
A comparative study of frequency deviation in area 1 (ΔF1) is plotted in figure 4.6, frequency deviation in area 2 (ΔF2) in figure 4.7 and tie line power deviation (ΔPtie) in figure 4.8 for 1% step load perturbation in area one of the system for different type of controllers(PI, NN, NF). This study uses ACE as error signal to control the frequency of the power system. From figures 4.6-4.8 it is observed that the proposed on line controller exhibits very good performance with smaller overshoot and steady state errors. Figure 4.9 shows the bar graph for comparison of different controllers when simulated for ΔF2. The bar graph clearly shows that on line neuro fuzzy controller gives the least values for peak overshoot, settling time and steady state error. 0.2 0.1 0
∆F1 in Hz
delf1
-0.1 -0.2 -0.3 neurofuzzy controller neural controller pi controller
-0.4 -0.5
Time in seconds
-0.6 -0.7
0
20
40
60
80
100
Fig.4.6 Frequency deviation in Area-1 time
120
140
160
180
200
60
0.2 neurofuzzy controller neural controller pi controller
0.1 0 -0.1
delf2
∆F2 in Hz
-0.2 -0.3 -0.4 -0.5 -0.6 -0.7
0
20
40
60
80
100 time
120
140
160
180
200
Time in seconds
Fig. 4.7. Frequency deviation in Area-2.
0.4 neurofuzzy controller neural controller pi controller
0.2
0
ptie
-0.2
-0.4
-0.6
-0.8
-1
0
20
40
60
80
100 time
120
140
160
180
200
Fig. 4.8 Tie-line power deviation.
61
Fig. 4.9. Comparative analysis of different controllers for ∆F2
Peak overshoot decreases to approximately 65% as compared to when PI is used and to about 7% as compared to when on line NN controller. Steady state error also reduces by 80% when NF controller is compared with PI and 8% when compared with NN. Settling time has also decreased with the use of neurofuzzy controller as compared to NN controller. There is slight increase in settling time as compared with PI, but other advantages over PI are much appreciable that this settling time point can be ignored. Detailed comparison of the dynamic responses of the various controllers is shown in table 4.1. The simulation results proved that Neuro Fuzzy controller is robust in its operation and gives a superb damping performance both for frequency and tie line power deviation compared to conventional PI as well as neural counterpart as clear in table 4.1. Besides the simple architecture of the controller it has the potentiality of implementation in a real time environment. Simulated results clearly show that neuro-fuzzy controller exhibits relatively good performance with smaller overshoot, lesser steady state error and settling time, in the response curves of frequency deviations of area one and two and tie line power deviations.
62
Table 4.1 Comparative Study of Dynamic Response Peak undershoot
Settling time
Steady state error
Frequency Deviation in Area 1 (ΔF1) PI Controller
0.68
120
0.1
Neural Controller
0.12
130
0.02
Neuro Fuzzy Controller
0.1
120
0.001
Frequency Deviation in Area 2 (ΔF2) PI Controller
0.68
120
0.1
Neural Controller
0.15
140
0.02
Neuro Fuzzy Controller
0.08
130
0.009
PI Controller
0.85
130
0.51
Neural Controller
0.9
130
0.512
Neuro Fuzzy Controller
0.85
125
0.58
Tie Line Power Deviation (Δptie),
PART II
4.4. ELECTRONIC LOAD CONTROLLER
One problem that is typically seen in most of the micro-hydro systems is the fluctuation on frequency generated by the generator which causes adverse effect on various electrical appliances connected as load. The micro hydro systems are based on run-off-river type. In micro hydel systems, storage system is not put into practice because of its high cost. This result in the generation of constant power by the generator but the consumer load may vary from time to time. In the case of peak load almost all the generated power is consumed but when the required load is less than the generated power the voltage and the speed of the generator increases which causes serious problems in the appliances used by the consumer and other system components such as transformer and motor loads. To overcome such problems, Electronic Load Controller 63
(ELC) is used such that the generator faces a constant load all the time. In micro hydro systems in which cost is the major factor, ELC is the best way of controlling the speed of the generator. The conventional mechanical and hydraulic governors to control the flow of the water in the penstock are uneconomical. The electronic load controller is an electronic device that maintains a constant electrical load on the generator in spite of changing user loads. This permits the use of turbine with no flow regulating their governor control system. The ELC maintains a constant generator output by supplying a secondary ballast load with the power not required by the main load.
4.4.1 ELC Structure ELC is a shunt connected dummy load, which is controlled according to the voltage variations. The basic diagram of ELC is shown in figure 4.10. ELC has been used to provide constant frequency operation. ELC consists of a three leg diode bridge rectifier (uncontrolled rectifier) which converts the ac terminal voltage to dc voltage. The dc voltage has ripples which are smoothened by a filtering capacitor. An IGBT is used as a chopper to provide variable dc voltage across the auxiliary dump load. The ELC uses the difference between the power generated and the power consumed by the load to control the duty cycle of the IGBT which decide the amount of power to be dumped, thus the active power generated remains constant even during varying consumer loads [98].
Fig.4.10. Electronic load controller .
64
4.4.2. Control Strategy of ELC
The control scheme for ELC as shown in figure 4.11 works on the principle that the generated power (Pgen) should be equal to the sum of power consumed by the consumer load (Pload) and power absorbed by the ELC (PELC) – (4.8) Thus to maintain the active power at the generator terminals to a constant value the error power which is the difference between rated power of the generator and the power measured at the generator terminals is fed to the controller [104]. Conventionally a simple PI controller is used.
Fig. 4.11. Control strategy of ELC.
The output of the controller is compared with a triangular carrier waveform thus producing gating pulses for the IGBT chopper of the ELC. After concluding that neuro fuzzy controller gives better system performance, an attempt has been made to use this neuro fuzzy technique in Electronic Load Controller (ELC), thereby making it intelligent. Figure 4.12 shows the subsystem of the proposed ELC. At every sampling time, first the actual active power consumed or the generated power (Pgen) is calculated, compared with the rated active power (Pr) of the generators. The error of two becomes the input to the controller and its output is compared with a saw tooth wave generating in PWM output of varying duty cycle of the IGBT to be triggered that finally adds/ removes the load required.
65
Replacement of conventional PI with on line NF controller makes the ELC more adaptable to the changes in system parameter and thereby making it more robust.
Repeating Sequence -CP rated
1 Vabc
Vabc PQ
In 1
Out1
Iabc
1 generating signal
neuro fuzzy controller
2 Iabc
Fig. 4.12 Schematic diagram of control scheme for load frequency.. controller
4.5. THE PROPOSED SYSTEM The schematic diagram of parallel-operated isolated feeding three wire three phase loads is shown in figure 4.13. For numerical values of constants refer appendix B. Intelligent Load Controller is used to regulate the active power at the generator terminals, thus controlling the system frequency. Simulink model of the proposed ELC is shown in figure 4.12. The ELC consists of an uncontrolled diode bridge rectifier, filtering capacitor, a chopper and a series auxiliary load (resistor). For maintaining the constant power at the generator terminals, the DC chopper of the ELC consumes/ supplies the difference in the active power (generated- consumer load power). Thus the system frequency is not affected and remains constant during the change in consumer loads.
66
Continuous powergui Repeating Sequence
Constant Neuro Fuzzy Controller Out1
-C-
In1
g
m
Iabc
Vabc
PQ
C
E Terminator
IGBT
3-phase Instantaneous Active & Reactive Power
Diode L
A
A
B
B
Vabc Iabc a b
C
10 ,000 MVA, 230 kV source
A
c
+
B C
-
R
C
Universal Bridge
Phase 1
B
Phase 2
C
Phase 3
10 ,000 MVA, 230 kV source1
Fig. 4.13.
C
Three -Phase V-I Measurement 1
A
LOAD 1
MATLAB based simulation model of a two area system with frequency
controller. 4.6
SIMULATION AND RESULTS
Transient waveforms of parallel-operated isolated feeding three wire three phase non linear loads are shown in figure 4.14. The line to ground fault with a delta load has been simulated using a three phase series RLC Branch. The variable star load is introduced from t = 0.01 sec to t = 0.03 sec. During this time period, each phase of the supply is open circuited, one after the another. As a result, the voltage transforms into a two phase voltage for some time, then to a single phase before transforming back into a three phase. The objective is to keep the load frequency constant irrespective of these changes in load. Voltage and current plots at point of common coupling are shown in figure 4.14(a) and 4.14(b). Before the load is applied it is observed that ELC absorbs all the power generated by the two generators. Harmonics are introduced due to ELC. This is the main disadvantage of ELC which can easily be rectified by using various types of available filters. In this problem since we are restricting to frequency control, the voltage control is not done, so there are large variations in 67
voltage. Power consumed by the load, ωt and load frequency plots are shown in figure 4.14(c), 4.14(d) and 4.14(e) respectively. There is delay in calculating ωt (angular frequency multiplied by instantaneous time) and frequency because for the first cycle of simulation the output is held to the rms value of the specified initial input. It is clear from the simulated results that the frequency remains fairly constant i.e. between 60Hz to 59.8 Hz irrespective of the variations in active power demand.
Fig. 4.14, Transient waveforms of a parallel operated system on a 3-phase, 3-wire system. 4.14(a) vabc 4.14(b) iabc 4.14(c) power consumed by load 4.14(d) ωt 4.14(e) load frequency.
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4.7 CONCLUSION
This chapter deals in enhancing the load frequency control by using on line intelligent controller. Modeling of a two area interconnected reheat thermal system incorporating governor dead band, generation rate constraint (GRC) non-linearity and boiler dynamics is done using transfer function approach. A comparative study of dynamic responses with different controllers like PI, NN and NF is done for 1% step load perturbation in area1. Parameters of NN and NF controllers are trained on line to incorporate the effects of change in system parameters and disturbances. In the proposed controller both the parameters of membership functions and weights of neural network are trained. This makes the neuro fuzzy controller superior over the other two controllers as clarified from the simulation results. The non-linearities incorporated make the system more realistic, but this transfer function approach is for small variations about the operating point. In the next part of the chapter the problem is tackled in a real time environment. After checking the superiority of on-line neuro fuzzy controller it is used to make a conventional Electronic Load Controller intelligent. The proposed ELC is modeled in simulink environment using neuro fuzzy controller. Its effectiveness for load frequency control is checked in parallel operated isolated asynchronous generators feeding three wire three phase loads for asymmetrical fault. Simulated results show fairly good frequency control.
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