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Energy (2017) 000–000 464–469 EnergyProcedia Procedia138 00 (2017) www.elsevier.com/locate/procedia
2017 International Conference on Alternative Energy in Developing Countries and Emerging Economies 2017 International Conference on Alternative Energy in Developing 2017 AEDCEE, 25-26 May 2017, Bangkok,Countries Thailand and Emerging Economies 2017 AEDCEE, 25-26 May 2017, Bangkok, Thailand
The 15th Symposium on District Heating with and Cooling Novel approach toInternational Automatic Generation Control various NonNovel approach to Automatic Generation Control with various Nonlinearities using 2-degree-of-freedom PID controller Assessing theusing feasibility of using the heatPID demand-outdoor linearities 2-degree-of-freedom controller a a, Tapas Kumar Panigrahi Aurobindo Behera *, Arun Sahoo aa forecast temperature function for aa,long-term district heat Ku demand a,
Tapas Kumar Panigrahi , Aurobindo Behera *, Arun Ku Sahoo I. Andrić *, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
a Department of Electrical Engineering, International Institute of Information Technology Bhubaneswar (IIIT, BBSR), Bhubaneswar, India a,b,c a a b c c a Department of Electrical Engineering, International Institute of Information Technology Bhubaneswar (IIIT, BBSR), Bhubaneswar, India a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
b Abstract Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Abstract Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France In the proposal for modern power systems with automatic generation control (AGC) the controller suggested is, a TwoDegree-of-Freedom PIDmodern (2-DOF-PID) controller. The proposedgeneration controller,control for the(AGC) first time, is tested suggested on two unequal area In the proposal for power systems with automatic the controller is, a Twothermal systems considering boiler dynamics as well governor dead band concurrent optimization of Degree-of-Freedom PID (2-DOF-PID) controller. The as proposed controller, for non-linearity. the first time,The is tested on two unequal area numerous parameters of the controllers is achieved by Differential (DE) The and the Integral optimization Time Absolute Abstract thermal systems considering boiler dynamics as well as governor Evolution dead bandAlgorithm non-linearity. concurrent of Error (ITAE) is the implemented objective function.byExperimental evidently conceals dominance of the 2-DOF-PID numerous parameters of the controllers is achieved Differential result Evolution Algorithm (DE)theand the Integral Time Absolute controller considering transient time required stabilizing the system. Current research analyseoffor the usefulness of Error (ITAE) is the implemented objectiveand function. Experimental result evidently the dominance thedecreasing 2-DOF-PID District heating networks are behaviour commonly addressed in the for literature as one of the conceals most effective solutions the the Differential algorithm a technique forThese deriving the optimum controller parameter values. Sensitivity analysis for controller considering transient and sector. time required for stabilizing system. Current research the usefulness of greenhouse gasEvolution emissions frombehaviour the as building systems requirethe high investments which are analyse returned through the heat diverse load to settings justifies sturdiness of 2-DOF-PID controller. Furthermore, theheat simple PID values. controller usedcould abundantly in the Differential Evolution algorithm asconditions a technique for building deriving the optimum controller parameter analysis for sales. Due the changed climate and renovation policies, demand in the Sensitivity future decrease, industries is compared with return thesturdiness of the performance of proposed controller. diverse load settings justifies of 2-DOF-PID controller. Furthermore, the simple PID controller used abundantly in prolonging the investment period. industries isscope compared with theisof performance of proposed © 2017 The Authors. Published by Elsevier Ltd. main of this paper tothe assess the feasibility of usingcontroller. the heat demand – outdoor temperature function for heat demand ©The 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Ltd. Peer-review under responsibility of Elsevier thelocated Organizing Committee of 2017 AEDCEE. forecast. The district of Alvalade, in Lisbon (Portugal), was used as a case study. The district is Energy consisted Peer-review under responsibility of the scientific committee of the 2017 International Conference on Alternative in of 665 Peer-review under responsibility of the Organizing Committee of Three 2017 AEDCEE. vary inand both construction period and typology. weather scenarios (low, medium, high) and three district Dbuildings evelopingthat Countries Emerging Economies. Keywords: Automatic Generation Control (AGC); Differential Evolution Algorithm (DE); Integral Time Absolute Error (ITAE); Two-Degree-ofrenovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Freedom PID (2-DOF-PID) controller. Keywords: Automatic Generation Control (AGC); Differential Evolution Algorithm (DE); Integral Time Absolute Error (ITAE); Two-Degree-ofcompared with results from a dynamic heat demand model, previously developed and validated by the authors. Freedom PID (2-DOF-PID) controller. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.scenarios, Introduction the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1.The Introduction value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the In modern thehours system is being designed withseason greater numbersonoftheinterconnection for better decrease in the power number system of heating of 22-139h during the heating (depending combination of weather and In modern powerconsidered). system the ishand, being designed with greater numbers of better economics, stability and reliability of system. But the merits of the interconnection areinterconnection accompanied byfor a chance renovation scenarios Onsystem thethe other function intercept increased for 7.8-12.7% per decade (depending on the economics, stability andvalues of system. thecould system. But merits the of the interconnection arethe accompanied by a chance of fault being cascaded toreliability connected Thus thethe of analysis of the response of the interconnected coupled scenarios). The suggested be used torequirement modify function parameters for scenarios considered, and ofimprove fault being cascaded to connected system. Thus the requirement of analysis of the response of the interconnected the accuracy of heat demand estimations.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding author. Tel.: +91-7873250200 Cooling.
E-mail address:author.
[email protected] * Corresponding Tel.: +91-7873250200 E-mail address:
[email protected] Keywords: Heat demand; Forecast; Climate change 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review the Organizing Committee 1876-6102 ©under 2017responsibility The Authors. of Published by Elsevier Ltd. of 2017 AEDCEE. Peer-review under responsibility of the Organizing Committee of 2017 AEDCEE.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 2017 International Conference on Alternative Energy in Developing Countries and Emerging Economies. 10.1016/j.egypro.2017.10.182
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system to disturbance in the other areas is essential. Also the system is effected largely due the nonlinearities of the neighboring system makes it a major factor and the need to consider them for the analysis is essential [1]. To design a successful operating system the frequency along with interconnection exchange power has to be maintained within limits. Considering all the aspects of the system such as power demand, supplied power and the loss incurred in the system any small change in the system dynamics must not make the system unstable [2]. Thus the system requires an efficient controller for the dynamic regulation in the input and excitation system. In the paper a two degree of freedom PID controller (2-DOF-PID) proposed for 2 area thermal system using nonlinearities for instance Governor Dead Band (GDB) and Boiler Dynamics (BD). It can be observed that the 2DOFPID controller is very efficient under different loading condition and provide better response as compared to that of a simple PID controller. Differential Evolution (DE) Algorithm is implemented for the purpose of tuning control constraints for both the type of control scheme. The model is proposed for the analysis of the effect of nonlinearities on the 2-DOF-PID controller, which is not examined prior to this. The range of variation of the control parameter being too small as observed by the study the operation of the control scheme can be considered much effective for various operating condition. The prime concern for the present work can be stated as: a) To design and analyse a control scheme (i.e. 2-DOF-PID) for a 2 area AGC with numerous uncertainties. b) To make a comparative analysis of operation of simple PID to proposed scheme under the given operating conditions. c) To study the operation of the proposed scheme under random loading condition for different areas. d) To patterned the sturdiness of the optimal parameter values of 2-DOF-PID for varying loading condition. 2. Modeling of the system The system considered for the simulation based analysis in the paper is a thermal system with two unequal areas (area-1, 2 ) and rating being 2000 MW and 4000MW respectively [3]. The system is further introduced with uncertainties such as the GDB and BD in both the areas. The system block model for the analysis has been displayed in Fig. 1. The system constraints for nominal operation are Minimal constraints for system operation is: Hi = 5 s, Di = 0.00833 p.u, f = 50 Hz, Tgi = 0.08 s, Tti = 0.3 s, Kr = 0.5, Tri = 10 s, Tpi = 20 s, Kpi = 120 Hz/p.u MW, Tij = 0.545. The Differential Evolution (DE) Algorithm is realised for regulating several control parameters of two-DOF-PID controller. KP, TI, TD are the basic PID controller parameters. Al, Be are taken as the feed forward loop parameter essential for the modification of the simple PID into a 2-DOFPID controller [4]. Operation of DE algorithm is bounded by the integral of time multiplied by absolute error (ITAE) given by (1).
B1
1 R1
∆PD1 0.8 - 0.06366s 1 + sτ g1
ACE1
K3
1 1 + sτ t1
a12
a12 0.8 - 0.06366s 1 + sτ g2
ACE 2 B2
K P1 1 + sτ P 1
1 R2
K3
∆PD2
Fig.1.
T12 s K P2 1 + sτ P 2
1 1 + sτ t2
Block representation for System considered for analysis.
∆f1
∆f 2
Tapas Kumar Panigrahi et al. / Energy Procedia 138 (2017) 464–469 Author name / Energy Procedia 00 (2017) 000–000
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ITAE =
t
∫ t .( ∆ f
1
+ ∆ f 2 + ∆ Ptie )dt
3
(1)
0
The 2-DOF controller scheme is modified by taking certain assumption so as to implement it to the AGC system such as the feedback noise dm=0 and the feedback gain H(s) =1 thus giving the feedback sufficient precision and speed for better control purpose. The disturbance is directly applied to the plant system (i.e. Pd(s) = P(s)) [5]. So as per the assumptions the disturbance which was previously passing through the system Pd(s) and then summed to the output of the plant system is now directly provided to the plant power system. Also the loop is modified into a unity feedback loop [6]. The control scheme is implemented with the PID controller to make the scheme a 2-DOF-PID control scheme. The parameters of this scheme which are to be tuned for the efficient control actions are KP, TI, TD, Al, Be. These parameters are tuned using the DE algorithm [7].
C ( s ) = K P {1 +
1 + T D D ( s )} TI s
(2)
C f (s) = − K P { A l + B eT D D ( s )}
(3)
Cf (s) R(s)
D(s)
+ Σ E(s) C ( s) -
3. Differential Evolution Algorithm
Fig.2.
+ +
Σ
+ U(s) Σ +
P(s)
Y(s)
Control scheme with 2 DOF control
Differential Evolution (DE) algorithm is a stochastic optimization algorithm operating on the population evolution concept [8]. DE drives using 2 populations; present and next generation of the same population. Population extent is denoted by the parameter NP and D being the dimension consisting of tangible valued vectors. A random initialization is done within the predefined bounds and 3 foremost actions: Mutation, Crossover and Selection govern the optimization process.
Fig.3.
Flow map of the DE algorithm
The target vectors evolve from the elements of the recent population. The biased variance between 2 arbitrarily
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selected vectors is added to third vector, thereby generating mutant vector. A fresh population, called trial vector is spawned, by the crossover operation. If generated population attains an improved fitness result as compared to the target vector, at that juncture it is substituted by present trial vector in the succeeding generation. For every constraint k having lower limit X kL and upper limit X kU , first constraint values are arbitrarily designated L
U
homogenously within [ X k , X k ] . For some certain constraint vector X i,D 3 randomly selected vectors
(X r1,D , X r2,D , X r3,D ) have distinct keys i, r1, r2 and r3. A donor vector Vi,D+1 is generated by totalling the scaled
variance amid 2 vectors to third vector , = , + . (, − , ).
Crossover performed by 3 selected parents and child being a disconcertion from among them. Trial vector U i,D+1
established by recombination of essentials of target vector X i,D and that of donor vector. Essentials of donor vector pass in to trial vector per likelihood CR and F being fixed in (0, 2).
U k , i , D+1
V k , i , D+1 if = X k , i , D+1 if
rand k,i £ CR or
k = I rand
(4)
rand k,i > CR or
k ¹ I rand
With rand k,i � U(0,1) ,I rand an arbitrary figure from (1, 2, .., D). D the problem dimension (i.e. nos. of regulator parameters). I rand is to ensure Vi,D+1 ≠ X i,D . The target vector X i,D is paralleled with trial vector Vi,D+1 and one producing an improved objective fitness value is transferred to preceding generation [9]. Selection procedure in DE is characterized by the following equation:
Ui,D+1 if f(Ui,D+1 ) < f(X i,D ) X i,D+1 = otherwise. X i,D
(5)
Where i ε [1,N P ] The crossover operation in DE provides it the advantage of not being trapped by local minima and thereby converging to a global minimum point. 4. Result and Analysis The system studied in the paper is placed with a 2-degree of freedom PID controller. Appling DE algorithm with ITAE as the objective function shows the ability of the controller to mitigate the effect of the disturbance in any of areas successfully. A detailed analysis is done on the effect of the disturbance, initially by introducing disturbance to one area at a time and then the robustness is checked with varying loading applied to both areas simultaneously. Table. I present the controller parameter values. -3
1
0.01
-0.01 2DOF-PID PID
0
5
10
Time (Sec)
(a) Fig.4.
-1 -2
-0.015 15
20
2DOF-PID
-3
x 10
0 ∆ Ptie (p.u)
-0.005
-0.02
0.5
0
0
∆ F2 (Hz)
∆ F1 (Hz)
0.005
-3
x 10
PID
0
5
10
Time (Sec)
(b)
15
20
-0.5 -1 -1.5 -2 -2.5
2DOF-PID PID
0
2
4
6
8
Time (Sec)
10
12
14 15
(c)
Variation of (a) frequency for area-1 (b) frequency for area-2 (c) power exchange in tie line with step load surge of 10% in area-1.
Tapas Kumar Panigrahi et al. / Energy Procedia 138 (2017) 464–469 Author name / Energy Procedia 00 (2017) 000–000
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5
Fig.4-6 show the retort of change in the frequency for 1st area (∆f1), 2nd area (∆f2) and power exchange (∆Ptie) in the Tie line respectively due to the application of disturbance to area-1, area-2 and both the areas concurrently respectively. The mathematical analysis for the same is shown in Table. II - IV. Fig. 7 presents the stable AGC operation verified for robustness as the parameters generated must be applicable for dynamic load variation [10]. Table I. Sl. No.
Table II.
Controller parameter for the unequal area with simple PID controller Parameter value
Optimization technique/Controller
KP
TI
TD
1.
DE/PID
1.113
0.287
1.109
-
-
2.
DE/2-DOF-PID
1.167
0.367
1.197
0.205
0.190
Al
Be
System response parameters with different controller scheme for the unequal area with step load surge of 10% in area 1. Overshoot/ Undershoot
Settling Time (2%)
Steady State Error
Parameters
∆f1 (10-3)
∆f2 (10-3)
∆Ptie(10-3)
∆f1
∆f2
∆Ptie
∆f1 (10-5)
∆f2 (10-6)
∆Ptie(10-6)
DE/PID
-16.710
-2.767
-2.023
9.557
27.750
28.337
32.990
-55.690
-58.17
DE/2-DOF-PID
-16.640
-1.337
-0.779
7.967
14.770
14.550
1.277
-5.913
-5.312
-3
0.01
∆ F2 (Hz)
∆ F1 (Hz)
0 -2 -4 2DOF-PID
-6
2.5
0.005
PID
0
5
10
Time (Sec)
15
20
0 -0.005 -0.01
2DOF-PID PID
1.5 1 0.5
-0.015 -0.02
x 10
2 ∆ Ptie (p.u)
2
-3
x 10
PID 2DOF-PID
0
5
10
15
Time (Sec)
(a)
20
0 0
5
(b)
10
Time (Sec)
15
20
(c)
Fig.5. Variation of (a) frequency for area-1 (b) frequency for area 2 (c) tie line exchange power for step load surge of 10% in area-2 Table III. System response parameters with different controller scheme for the unequal area with step load surge of 10% in area-2. Overshoot/ Undershoot Parameters
-3
∆f1 (10 )
-3
Settling Time (2%) -3
∆f2 (10 )
∆Ptie(10 )
∆f1
∆f2
Steady State Error ∆Ptie
-5
∆f1 (10 )
∆f2 (10-6)
∆Ptie(10-6)
DE/PID
-5.574
-18.69
2.113
25.627
21.410
28.372
-10.990
-21.780
54.780
DE/2-DOF-PID
-2.848
-18.61
0.863
12.950
7.511
14.440
-1.147
5.693
5.152
Table IV. System response parameters with different controller scheme for the unequal area with step load surge of 10% to both area-1,2. Overshoot/ Undershoot Parameters
∆f1 (10-3)
∆f2 (10-3)
∆Ptie(10-3)
Settling Time (2%) ∆f1
∆f2
Steady State Error ∆Ptie
∆f1 (10-5)
∆f2 (10-5)
∆Ptie(10-5)
DE/PID
-17.000
-18.96
0.126
21.330
20.860
18.78
-77.450
-77.42
-3.363
DE/2-DOF-PID
-16.97
-18.85
0.109
7.681
7.437
9.439
0.081
-0.021
-0.015
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Tapas Kumar Panigrahi et al. / Energy Procedia 138 (2017) 464–469 Author name / Energy Procedia 00 (2017) 000–000 -4
-3
x 10
∆ F2 (Hz)
∆ F1 (Hz)
0 -5 -10 -15 -20
2DOF-PID
5
10
15
Time (Sec)
2
0.005
1.5
0 -0.005 -0.01 -0.015
PID
0
0.01
-0.02
20
5
10
15
Time (Sec)
(a)
PID 2DOF-PID
0.5 0 -0.5
2DOF-PID PID
0
x 10
1
∆ Ptie (p.u)
5
469
-1
20
0
5
(b)
10
Time (Sec)
15
20
(c)
Fig.6. Frequency variation for (a) area-1 (b) area-2 & (c) power exchange in tie line with step load surge of 10% in area-1 as well as area-2. -4
0.01
0.01
0
100% Loading
-0.02
+50% Loading -50% Loading -75% Loading +75% Loading
0
2
4
6
8
Time (Sec)
(a)
10
12
14 15
100% Loading
-0.02
+ 50% Loading
+ 75% Loading
0
2
4
(b)
6
Time (Sec)
8
10
0
100% Loading + 50% Loading
-1
- 50% Loading - 75% Loading
-0.03 -0.04
x 10
1
-0.01
∆ Ptie (p.u)
-0.01
∆ F2 (Hz)
∆ F1 (Hz)
0
-0.03
2
12
-2
- 50% Loading - 75% Loading + 75% Loading
0
(c)
5
Time (Sec)
10
15
Fig.7. Effect of load variation on the (a) frequency change of area-1 (b) frequency change of area-2 (c) response of tie-line exchange power.
5. Conclusion In the proposed approach a 2-Degree of freedom PID controller is applied to the Automatic Generation Controller system with Governor Dead Band (GDB) and Boiler dynamics (BD) for the first time. The performance of the proposed controller over the simple PID controller is presented in the present work. The DE algorithm tuned, control parameters are presented in the Table I. The mathematical analysis shown in Table II and III depicts the influence of the control scheme on the operation parameters such as settling time, transient response and steady state error. Further a random load variation is done to justify the robustness of the tuned parameters and the proposed controller. References [1]. O.I. Elgerd, Electric energy systems theory an introduction, 2nd ed. New Delhi: Tata McGraw-Hill; 1983. [2]. Bevrani H. Robust power system frequency control. Springer; 2009. [3]. L.C. Saikia, J.Nanda, S.Mishra, “Performance comparison of several classical controllers in AGC for multi-area interconnected thermal system.” Int J Electr Power Energy Syst 2011; 33:394–401. [4]. J.Sánchez, A.Visioli, S.Dormido, “A two-degree-of- freedom PI controller based on events.” J Process Control 2011; 21:639–51. [5]. S. Debbarma, L. C. Saikia, N. Sinha, “Automatic generation control using two degree of freedom fractional order PID controller”, Electrical Power and Energy Systems 58 (2014) 120–129. [6]. M. Araki, H. Taguchi, “Two-Degree-of-Freedom PID Controllers”, International Journal of Control, Automation, and Systems Vol. 1, No. 4, December 2003. [7]. R.K. Sahu, S. Panda, U.K.Rout, “DE optimized parallel 2-DOF PID controller for load frequency control of power system with governor dead-band nonlinearity.” Int J Electr Power Energy Syst 2013; 49:19–33. [8]. U.K. Rout, R.K. Sahu, S.Panda, “Design and analysis of differential evolution algorithm based automatic generation control for interconnected power system.” Ain Shams Eng J 2013; 4(3):409–21. [9]. B. Mohanty, S. Panda, P.K. Hota, “Controller parameters tuning of differential evolution algorithm and its application to load frequency control of multi-source power system”, International Journal of Electrical Power & Energy Systems Volume 54, January 2014, Pages 77– 85. [10]. S. Debbarma, L. C. Saikia, N. Sinha, “Robust two-degree-of-freedom controller for automatic generation control of multi-area system”, Electrical Power and Energy Systems 63 (2014) 878–886.
