Decentralized Fractional Order Control Scheme for LFC of Deregulated Nonlinear Power Systems in Presence of EVs and RER Hassan Haes Alhelou a, b a): dept. Electrical and Computer Engineering Isfahan University of Technology Isfahan, Iran b): dept. of Electrical Power Engineering Faculty of Electrical & Mechanical Engineering Tishreen University Lattakia, Syria
[email protected] [email protected]
Mohamad Esmail Hamedani-Golshan dept. Electrical and computer Engineering Isfahan University of Technology Isfahan, Iran
[email protected]
Ehsan Heydarian-Forushani Esfahan Electricity Power Distribution Company Isfahan, Iran
[email protected]
Ameena Saad Al-Sumaiti Masdar Institute Khalifa University of Science and Technology Masdar, United Arab Emirates
[email protected]
Pierluigi Siano dept. Industrial Engineering University of Salerno Salerno, Italy
[email protected]
Abstract— Load frequency control scheme is one of the main control procedures in large electric grids incorporating electric vehicles. Load frequency control controllers play an important role in maintaining both the frequency in each area and the exchanged power between the different areas in permissible range. With moving conventional power systems toward the smart grid concept, the penetration level of electric vehicles and renewable energy resources has been rapidly increased. With such a growth in renewable energy sources integration into the grid, controlling the load frequency is a major operational challenge encountered in electric grids necessitating to be carefully investigated. To this end, a new fractional order control scheme is designed for the interconnected power systems considering the deregulation environment. The fractional order controller is characterized with a higher freedom degree compared to the conventional that make it possible to have a much better control performance. Also, the participation of electric vehicles in providing a secondary power reserve for a future smart grid is studied in this paper. The controllers’ parameters are tuned via several evolutionary algorithms such as imperialist competitive algorithm, differential algorithm and others. Several numerical analyses are performed to evaluate the effectiveness of the control scheme that is proposed in this paper. Likewise, the effectiveness of electric vehicles and renewable generation’s participation in load frequency control is examined. Keywords— electric vehicles; fractional frequency control; renewable energy resource.
systems;
load
I. INTRODUCTION Large regulated electric grids can be decomposed into control regions that are interconnected. Each region is to supply its load and maintain the power exchange schedule with neighboring regions. These responsibilities become more and more difficult with moving toward restructuring electric grids. Load frequency control is a mechanism used in the control center to keep the balance between active power generation
and electric demand and consequently to maintain the frequency in its normal range in each area. Also, load frequency control should keep the power exchanged through tie lines at the planned scheduling values [1]. To this end, the parameters of load frequency controllers in each area need an optimal tuning to reach an acceptable functionality. In the last decades, many control structures have been suggested and used to control frequency deviations caused by small disturbances such as load fluctuation, and the uncertainties of renewable sources [2]. Due to their simplicity, not only the proportional integral (PI) but also the proportional integral derivative (PID) are the dominant type of load frequency controllers used in industry [3]. In [4-5], different fuzzy PID controller structures have been used for frequency control. Also to provide more degrees of freedom, the two and three degree of freedom integral derivative controllers have been suggested in [6-7] for frequency control. The Fractional order PID (FOPID) controller is another class of controllers that would provide more degrees of freedom with its better performance in comparison to conventional PID controllers [89]. To diminish the noise of the differentiation path in PID and FOPID controllers, PID/ FOPID with derivation filter (PIDF/FOPIDF) controllers have been used in [10-11]. Trial-and-error approach can be applied for load frequency controllers' tuning in power systems [1-2]. However, it is not an easy task to tune the controllers’ parameters using trial-anderror approach. Also, it might not lead to the optimal parameters. Hence, due to the great importance of optimal tuning of load frequency controllers for electric grid operation, a number of methods including evolutionary computing based optimization, model predictive control, and optimal control have been proposed in literatures [12-15]. Due to their good performance and simplicity, evolutionary algorithms have received remarkable attention from the researchers who worked on the topic of load frequency control (LFC). Thus,
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many algorithms (genetic [16], particle swarm [17], differential [18], bacterial foraging [18], firefly [20], imperialist competitive [21], and hybrid gravitational search and pattern search [22]) have been applied to find a solution for tuning the parameters of the load frequency controllers. The literature survey shows a knowledge gape regarding LFC design for future power systems considering the high penetration level of renewable energy resources (RERs) and their uncertainties. Also, the effect of electric vehicles in future interconnected power systems regarding the frequency behavior needs more investigations. Likewise, the traditional LFC schemes used for conventional power systems cannot be achieve the requirements of the modern power systems under deregulation environments. Therefore, more reliable and robust frequency control schemes are needed for future power systems. In the current paper, a new fractional order control scheme is suggested for future power systems with significant amounts of renewable energy integration as well as electric vehicles' incorporation. The freedom degree of the optimization problem of LFC is increased by using the fractional order controllers which leads to much better performance of LFC. Also, the participation of EVs in providing secondary reserve for future smart grid is investigated in this work, and an alternative participation strategy is also suggested. Furthermore, the controllers’ parameters is tuned via several evolutionary algorithms such as imperialist competitive algorithm (ICA), differential algorithm (DE) and others. Moreover, several numerical analyses are conducted for an assessment of the recommended control scheme. Likewise, the effectiveness of EVs and RERs participation in LFC is examined. In addition, several objective functions are used in the optimization problem defining and their performance are compared. At the end, the robustness of the recommended load frequency controllers based on evolutionary algorithms is investigated under different power system’s conditions. The organization of the rest of the paper is as the following: An overview of the fractional calculus is presented in section II. The recommended control strategy based on the fractional calculus is introduced in section III. The optimization problem of LFC is introduced in section IV. The power system under investigation demonstrated in section V. The obtained results are demonstrated in section VI. The conclusion is provided in section VII. II. AN OVERVIEW OF THE FRACTIONAL CALCULUS Fractional calculus is a mathematic issue deals with computing the integrations/differentiations with non-integer orders. By using fractional calculus methods, a complexity of integrations/differentiations with non-integer orders can be solved. During the history, different definitions has been suggested to describe the problem of fractional calculus. The Grunwald-Lentikov, Caputo and Reimann-Liouville definitions are the well-established definitions for fractional calculus during the history [8-9]. In the field of engineering, Caputo definition is the mostly used for defining the problem of control based on fractional calculus. The operator of integral/ differential with order ( α ) and operation bounds ( a , t ) can be
α
represented by ( a D t ). According to Caputo definition, the fractional calculus operator is denoted by the sign of the order ( α ) as follows: dα dt α α a D t = 1 t dt − α ( ) a
α 0 α =0
(1)
α 0
Taking in the consideration that m takes the smallest integer value that is greater than α , the fractional derivative is calculated based on Caputo definition as follows: d m dt m α D f (t) = a t χ t D m f χ (t ) 1 Γ m −α ( ) a (t −τ )α −m +1
α =m m −1α m
(2)
where ∞
Γ ( m − α ) = t m −α −1.exp ( −t ) dt
(3)
0
To transform time domain based computation into a frequency domain based computation, the Laplace transformation is applied. In the fractional calculus, the Laplace transform is given by Eq. (4). m −1
{ a Dtα f χ (t )} = s α F ( s ) − s α −k −1f ( 0 )
(4)
k =0
To implement and simulate the fractional order calculus, the Laplace operator of the fractional order is approximated with integer order transfer functions. The most known method to approximate fractional order to integer order is Oustaloup’s method [8-9]. III. LOAD FREQUENCY CONTROL BASED OF FRACTIONAL CALCULUS
Frequency control is essentially divided into three groups: 1) primary frequency control is associated with intercepting the frequency decline, 2) the secondary frequency control is responsible for removing the frequency deviation through a suitable controller in which the secondary control is also recognized as an automatic generation control and/or load frequency control, 3) tertiary frequency control is related to the economic dispatch problem in which the generation of each generating units is re-dispatched to achieve the economic operation goals. An overview of the load frequency control in a deregulated electric grid modelling is presented subsection A.
Then, the load frequency controller is designed according to the fractional calculus that is presented in subsection B. A. LFC under the deregulation environment A vertically integration utility (VIU) structure has been used in conventional power systems for a long time. In this structure, all generating units are owned by a one company which is responsible for providing electrical energy with its ancillary services to consumers. Nowadays, with moving power systems to award restructured environment, providing ancillary services, e.g. secondary reserve and load following control, would be done based on the negotiations between different generations (GENCOs) and distribution (DISCOs) companies based on electricity markets. In deregulated environment, wherever a change in the demand is occurred, GENCOS had contracts with the DISCOs of the load change, would provide the load following service. In this way, DISCOs should forecast the demand of their consumers and buy a sufficient electric energy for their consumers based on electricity market competitive. Any DISCO can purchase energy from one GENCO or more at the same time to meet the requirements of their consumers. Likewise, any DISCO can buy the electrical energy whether from GENCOs within its area, or from other areas [1-2]. In LFC studies, various mixtures of contracts between different GENCOs and DISCOs can be modeled via DISCO Participation Matrix (DPM). In DPM, rows indicate GENCOs, while columns indicate DISCOs. Every matrix enter, cpf, of this matrix refers to a contracted energy between correspond GENCO and DISCO so-called contract participation factor. Adding all entries in a column would lead to value of one. This indicates that the provided electrical energy from all GENCOs for one DISCOs equal to the DISCO’s demand in each time interval. For a typical electric grid with a number of m DISCOs and a number of n GENCOs, the DPM is given by (5) [1].
cpf 11 .. cpf 1n . .. . DPM = . . cpf m 1 .. cpf mn
(5)
nd
ΔPg ,i = cpf ik Pk
(6)
k =1
Due to the contracts signed by ISO between the different GENCOs and DISCOs, the scheduled power flow through tielines between area i and area j, is formulated through (7) [1].
cpf
k =n g ,i l =nd , j
lk
ΔPLl −
cpf
k =n g ,j l =nd ,i
lines between area i and area j,
ΔPtieact,ij =
2πT ij s
( Δf
i
ΔPtieact,ij , is calculated by (8).
− Δf
j
)
lk
ΔPLl (7)
(8)
The error in power exchange between region i and region j is described by (9).
ΔPtieerr,ij = ΔPtieact,ij − ΔPtiesch,ij
(9)
The area control error of area i (ACEi) needed to construct the control signal are given by (10) [1].
ACE i = β i Δf i + ΔPtieerr,i
(10)
Where
ΔPtieerr,i =
n
ΔPtieerr,ij
(11)
j =1& j ≠i
B. Design of LFC controller based on the fractional calculus Load frequency controller is usually used to remove the region's control error associated with each region. For this purpose, the classical PID controller is widely used in order to have a control over the frequency in interconnected electric grids. Due to its superiority, fractional order PID is proposed for controlling both deviations in not only the frequency, but also the power exchange through tie lines. The fractional order controllers is characterized with additional integral order (λ), and derivative order (µ) constants over proportional, integral and derivative constants. Therefore, the addition of such two operators is an added value to the controller providing it with two degrees of freedom. Thus, such a condition provides an improvement to the performance of the traditional. In the contentious forum, the control signal, u c ,i , is applied for each control region according to the fractional order PID that can be described as follows:
K u c ,i = k p ,i + k D ,i s μ + Iλ,i s
In this way, the change in the generated power from ith GENCO in a specific time is determined by (6) [1].
ΔPtiesch,ij =
In power systems, the actual power flow through the tie-
ACE i
(12)
It has been proven that the controller based on the fractional calculus provides a generalization of the fractional calculus beside the point to plane expansion [8-9]. The further decision variables, i.e. λ and µ, provide much more accuracy and flexibility in designing the LFC controllers. The next step is to find the optimal parameters characterizing the controller using a well-known optimization technique. IV. OPTIMAL PARAMETER TUNING FOR THE CONTROLLER In this paper. A new objective function considering the damping of the frequency oscillations and the settling time (ST) of not only the frequency but also the tie-lines.
NA J = ω1. α i Δfi (t) + α ijΔPtiei-j (t) .t.dt i=1 0 j=1 j¹i 1 (13) +ω2 . min {(1- ζ i ) ,i = 1..n} NA t sim
(
)
NA NA +ω3 . ST(Δfi (t)) + ST(ΔPtiei-j (t)) j=1 i=1 j¹i The settling time ( ST ) is defined as the time instant at which a signal settlement value of less than 0.000001 is achieved. Each term in the objective function has a weight ( ω ) describing its importance in the aggregated objective function Based on the proposed FOPID controller introduced in the previous subsection, the decision variables constraints, and the objective functions are given in (13), the optimization problem is modelled as follows:
min {J } s .t .
λ
≤λ≤λ
To show the superiority of the suggested control scheme, the scheme is applied to IEEE 39 bus system which is a large scale power system used for dynamic studies. The participation of renewable energy is assumed to be 30% of the total generation capacity. Also, it is assumed that the EVs aggregator consumes 5% of the total demand [22-23]. The data of the system under investigation can be found in [24-25]. It worth to mention that the studied system is parted to three control areas. VI. SIMULATION RESULTS AND DISCUTIONS For an assessment of the recommended load frequency control model, controllers' parameters in the different control areas are obtained based on the proposed objective function (13-14). As demonstrated in the aforementioned sections, ICA is used to solve the optimization problem of LFC. Values of controllers' parameters at different control regions using ICA are given in Table I.
Cont. No.
(14)
K Dmin ≤ K D ≤ K Dmax min
V. THE STUDIED DEREGULATED POWER SYSTEM
TABLE I.
K min ≤ K p ≤ K pmax p K Imin ≤ K I ≤ K Imax
where the goal is to achieve a minimum objective function, a less number of imperialist, and a better solution. This algorithm enjoys several advantages like it works well with non-linear systems and the solution obtained is a global one.
Controller 1
max
μ min ≤ μ ≤ μ max A. LFC controller parameters tuning using ICA ICA is a meta-heuristic approach with social and political characteristics. The approach was an inspiration from imperialists' competition as well as their colonization. The solution of such a method describes the countries set achieving a partition from many empires. One empire as well as many non-powerful countries recognized as colonies [20]. Two competition mechanisms are used in the algorithm which are the Intra-Empire Competition (ICE) and the Inter-Empire Competition (IEC). These competitions take place among either the empire's members as the case of ICE or among empires as the case of ICE. The power of each colony or imperialist is determined from the cost of the optimization algorithm. When the cost function is least, countries with such cost become imperialists and the process involves assimilation where the imperialists gets stronger and gain full control for the colonies or revolution where some colonies become stronger than the imperialists. Among the imperialist as well competition to gain full control of other colonies exists [20]. The process stops when powerless empires have been completely eliminated. The ICA algorithm can be used in the implementation of the optimal LFC scheme. With an objective defined as in (13)
Controller 2
Controller 3
CONTROLLERS’ PARAMETERS BASED ON ICA AND OTHERS
Parameters Kp Ki Kd
λ μ
Kp Ki Kd
λ μ
Kp Ki Kd
λ μ
ICA 1.11756 -0.37987 -0.23455
hGSA-PS 1.3232 -1.43 -0.187
DE -2 -1.8 1.36
0.232
0.5
0.65
0.63 -1.87535 -0.85221 2 0.5
0.3838 1.3434 -0.888 -2 0.5
0.65 1.1189 -1.998 1.675 0.6767
0.133 -2 -1.84575 -1.46660
0.35 -0.786 -1.6 -0.9898
0.6767 -2 -2 -2
0.60
0.5
0.333
0.72
0.3535
0.333
To prove the robustness of the recommended control approach based on fractional calculus, a comparison among the performance of the various controllers is conducted with respect to the well-known LFC control strategies. For the comparison purpose, different types of load disturbance including signal disturbance in one area, signal disturbance in all areas, and multi disturbance in the different control areas. Also, several simulations are applied to the studied power system to verify the robustness of the recommended control approach against variations in the power system parameters. To evaluate the control strategy in case of disturbances in all control areas, the functionality of FOPID controllers when the demand is stepped up by 0.01 p.u in all regions is evaluated. The performance of ICA in tuning the parameters of load
0.01
[p.u] tie1-2
0
-0.005
-0.01
-0.015
0.04
hGSA-PS ICA (Proposed) DE algorithm
-0.02
15 Time [Sec]
20
25
30
hGSA-PS DE Algorithm ICA (Proposed)
0
5
10
15 Time [Sec]
20
25
30
-0.01
(a)
0
5
10
15 Time [Sec]
20
0.015
0.02 0.01
Δ Ptie2-3 [p.u]
hGSA-PS ICA (Proposed) DE algorithm
0
25
30
hGSA-PS ICA (Proposed) DE algorithm
0.01
0.03
2
10
-0.005
-0.06 0
0.005
0
-0.01
-0.005
-0.02 -0.03
-0.01
-0.04 -0.05
0
5
10
15 Time [Sec]
20
25
0
5
10
15 Time [Sec]
30 0.04
25
30
0
2
0.01
hGSA-PS w/o EV ICA with EV (Proposed) ICA w/o EV DE algorithm w/o EV
0.02
Δf [Hz]
hGSA-PS ICA (Proposed) DE algorthim
0.02
20
Fig. 2. The tie-line power deviation in the different areas
(b) 0.03
-0.02
0 -0.04
3
Δ f [Hz]
5
0.005
0
-0.04
Δf [Hz]
0
0.01
Δ Ptie1-3 [p.u]
Δ f 1 [Hz]
0.02
hGSA-PS ICA (Proposed) DE Algorithm
0.005
ΔP
frequency controllers is compared to [22] and DE algorithms. Fig. 1 shows that the maximum deviation in the frequency for all regions when using the ICA algorithm has significantly decreased compared to [22] and DE algorithms. Fig. 2 shows that the maximum deviation in the power exchange of the tielines has significantly decreased compared to the approach suggested in [22].
-0.01 -0.06 0
-0.02
5
10
15 Time [Sec]
0.01 0.005
15 Time [Sec]
20
25
30
(c) Fig. 1. The frequency deviation in the different areas: a) in the frist control area, b) in the second control area, and c) in the third control area
In order to evaluate the contribution of EVs in supporting the frequency control in power systems, it is assumed that EVs can provide some secondary reserve. It is assumed that the participation of EVs in LFC is 15%. To show the advantages of EV participation in LFC, the recommended controller is investigated when the demand of all regions is stepped up by 0.01 p.u considering the participation of EVs. Fig.3a shows that the maximum deviation of frequency at different regions in case of using EVs is highly decreased compared to case study without EVs. Fig.3b shows that the maximum deviation of the tie-lines power is highly decreased in compare to the conventional LFC without EVs participation.
[p.u]
10
tie1-2
5
ΔP
0
25
30
hGSA w/o EV ICA with EV (Proposed) ICA w/o EV DE Algorithm w/o EV
-0.03 -0.04
20
0
-0.005 -0.01
-0.015
0
5
10
15 Time [Sec]
20
25
30
Fig. 3. The frequency and tie-lne power deviation in the different areas
For proving the robustness of the recommended control model on the studied system, a simulation case study is considered with a 0.01 p.u step increase in the demand of all regions, in case of change in Tij, and both of Tt and Tg is investigated. Fig. 4 demonstrates the robustness of the recommended controllers in the case of -20% and 20% change in the power system parameters, i.e., both Tt and Tg. Also, when the time constant of the governor and turbines of area 1 changes by -20 and 20 percentages, the proposed controllers
still have a good performance. Furthermore, both the deviation in the frequency and the settling time of the frequency deviation are not influenced at changes of -0.5, -0.25, 0, 0.25 and 0.50 per units, in tie-line synchronizing coefficient as shown in Fig. 4. Generally, the presented results verify the good performance of the tuned controllers by ICA.
[6]
[7]
[8] [9] [10]
[11] [12] [13]
[14]
[15] Fig. 4. The frequency deviation in the different areas
VII. CONCLUSION This paper presented an approach to control the load frequency. The approach was based on the fractional calculus. The recommended control approach was implemented for electric grids incorporating a significant amount of renewable energy resources which implies in reducing the inertia constant. Likewise, this paper taken into account the participation of electric vehicles (EVs). Furthermore, the simulation result showed the superiority of tuning the fractional controllers using ICA algorithm in case of comparison with other algorithm. Moreover, there results showed that EVs participation could help with improving the frequency response of interconnected electric grids. Likewise, the robustness of the suggested control approach was verified through several simulation scenarios. REFERENCES [1] H. Bevrani. Robust power system frequency control. Vol. 85. New York: Springer, 2009. [2] H. A. Shayeghi, H. A. Shayanfar, and A. Jalili. "Load frequency control strategies: A state-of-theart survey for the researcher." Energy Conversion and management 50.2 (2009): 344-353. [3] C. K. Shiva, and V. Mukherjee. "Comparative performance assessment of a novel quasi-oppositional harmony search algorithm and internal model control method for automatic generation control of power systems." IET Generation, Transmission & Distribution 9.11 (2015): 1137-1150. [4]
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