8th International Conference on “Technical and Physical Problems of Power Engineering”
ICTPE Conference
5-7 September 2012
www.iotpe.com
Ostfold University College
[email protected] [email protected]
Fredrikstad, Norway ICTPE-2012
Number 1
Code 02EPE01
Pages 1-6
Designing and Investigating a PI-LQR controller for HVDC Transmission Systems N.M.Tabatabaei 1
N.Taheri 2
A.Hashemi 3
K.Kiani 4
1. Electrical Engineering Department, Seraj Higher Education Institute, Tabriz, Iran
[email protected],
[email protected] 2. Electrical Engineering Department, Islamic Azad University, Quchan Branch, Quchan, Iran 3. Electrical Engineering Department, SAMA Technical and Vocational Training College, Islamic AZAD University, Kermanshah Branch, Kermanshah, Iran,
[email protected] 4. Electrical Engineering Department, Kermanshah university of technology, Kermanshah, Iran,
[email protected]
Abstract— this paper presents the use of three levels Voltage Source Converter (VSC) in High Voltage Direct Current (HVDC) transmission system for reactive power compensation and voltage stabilization on electric grid network. A new control scheme based on a LQR control is introduced in this paper. Linear quadratic regulator (LQR) is an optimal control method that minimizes the cost function in order to achieve the optimal trade off between the use of control effort, the magnitude and the speed of response. Also it guarantees a stable control system. The controller and the HVDC transmission system were designed with MATLAB/SIMULINK. Simulation results are presented to verify performance of control system.
Keywords— LQR control, HVDC system, Voltage Source Converter.
I. INTRODUCTION As power demand grows rapidly and expansion in transmission and generation is restricted with the limited availability of resources and the strict environmental constraints, power systems are today much more loaded than before. This causes the power systems to be operated near their stability limits [1,2,3]. Recently HVDC systems have greatly increased. They interconnect large power systems offering numerous technical and economic benefits This interest results from functional characteristics and performance that include for example nonsynchronous interconnection, control of power flow and modulation to increase stability limits[4]. The VSC HVDC system is the most recent HVDC technology. It consists of two VSCs, one operates as a rectifier and the other as an inverter. The two converters are connected either through a DC line. Its main function is to transmit a constant DC power from the rectifier station to the inverter station, with high controllability. Among various multi-level VSC configurations, the three level Neutral Point Diode Clamped (NPC) converter [4],
is the most widely accepted multi-level VSC configuration for utility and high-power industrial applications . Thus, the VSC-based HVDC systems have been mainly proposed or implemented based on the threelevel NPC converter[5]. In this paper, a HVDC transmission system based on 3 level VSCs are considered and a LQR controller is designed for controlling loop in rectifier and inverter for improving the controller circuit performance. II. POWER SYSTEM MODELLING Modeling the scheme VSC HVDC including the power network is as shown in Figure 1. The system parameters are given in Table 1. The VSC HVDC device is included mainly 3-level voltage source converter connected to the host grid network through a coupling transformer. The dc link voltage is provided by the capacitor C which is charged from the AC host network.
(a)Power System
(b)Configuration of VSCs (Rectifier and Inverter) Fig1.Power System equipped by VSC HVDC
8th International Conference on “Technical and Physical Problems of Power Engineering” (ICTPE-2012) Fredrikstad, Norway, 5-7 September 2012
.
.
x(t ) = Ax(t ) + Bu (t )
A. Dynamic Equation for VSCs One convenient way for studying balanced three-phase system (especially in synchronous machine problems) is to convert the three phase voltages and currents into synchronous rotating frame by abc / dq transformation. The benefits of such arrangement are: the control problem is greatly simplified because the system variables become DC values under balanced condition; multiple control variables are decoupled so that the use of classic control method is possible, and even more physical meaning for each control variable can be acquired [6]. Equations (1) to (3) give the mathematical expression of the VSCs shown in Figure 1.
did 1 R = − i d + ωi q + (Vtd − Vsd ) dt L L diq R 1 = −ωid − i q + (Vtq − Vsq ) dt L L 3(Vtd id + Vtq i q ) i L dVdc =− − dt 2C sVdc Cs
(1) (2)
(3)
B. VSC control circuit Figure.2 illustrates the actual detailed control block diagram for VSCs (rectifier side) according dynamic equations described in [7]. Of course, reactive and active power are used instead of capacitor and bus voltage in control of inverter side.
Fig.2 VSC Control Circuit(Rectifier)
III. LINEAR QUADRATIC REGULATOR LQR is an optimal control method and is also a pole placement method. This method determines the feedback gain matrix that minimizes the cost function in order to achieve the optimal tradeoff between the use of control effort, the magnitude and the speed of response. In addition, this method guarantees a stable control system [8]. Given a linear system,
y = Cx (t )
(4)
Where x(t) are the system’s states, u(t) is the system input and y(t) is the output. The objective is to design a feedback u(t) =-Kx(t) such that the cost function (4) can be minimized: ∞
∫
J = ( x T Qx + u T Ru )dt
(5)
0
The weighting matrices Q and R are positive semidefinite. They control how much effort should be put on the controller. The feedback gain K is obtained by getting matrix P first via solving the Riccati equation: AT P + PA − PBR −1 B T P + Q = 0 (6) Therefore, K = R −1 B T P (7) When the feedback gain K is obtained, the LQR controller can be easily designed to make the states approach zeros optimally. Writing equations (1) and (2) in the state space format as (5) , the corresponding matrix can be found as: R 1 − L ω L 0 1 0 ,C = A= ,B = R 1 0 1 − ω − 0 L L i d vtd − v sd Where the states x = , the inputs u = and i q vtq − v sq i d the output y = i q Since the LQR controller is designed to drive the states to zero. This is very restrictive and not suitable for solving tracking system problem. In the VSCs control, line currents are to be followed. Therefore, alteration must be applied to the LQR controller in order o drive the current errors, instead of the currents, to zero. To achieve zero steady state errors, an integrator is inserted in the control loop. And the original system is augmented to include the errors as new system states [6]. . x(t ) = A 0 x(t ) + B u (t ) + 0 r (8) . − C 0 e I (t ) 0 I ( ) e t I In equation (8), x (t ) x(t ) u (t ) = − K (t ) (9) = −[K x (t ) K I (t )] e ( t ) I e I (t ) Rewrite the cost function in format of (10), it shows that the new LQR regulator is aimed in minimize the errors eI .
8th International Conference on “Technical and Physical Problems of Power Engineering” (ICTPE-2012) Fredrikstad, Norway, 5-7 September 2012 t
∫
J = e TI (t )e I (t ) + u T (t ) Ru (t )dt 0
∫ [x t
=
0
T
]
0 0 x(t ) T (t ) e I T (t ) e (t ) + u (t ) Ru (t )dt 0 I I
(10) Control block diagram of the LQR Current control loop is shown in Fig.3. For more details of this method, readers can refer to [6,7].
Step 3: t = [0.5 − 0.8]s : the first load is now removed from the power system at load bus. The STATCOM inject less reactive power into the ac system. Also, decreasing in transferring power through VSC HVDC is seen. Step 4: t = [0.8 − 0.9]s :at this time another load is added to load bus. Results could be seen in Figures.
V. CONCLUSION The paper presents a novel PI/LQR controller for VSC HVDC. These full descriptive digital models are validated for voltage stabilization reactive compensation and dynamically power flow control. The presented simulation results show that VSC HVDC with hybrid PI/LQR strategy acts well than the conventional PI method.
REFERENCES [1]
[2]
Fig.3 STATCOM pi/LQR Control
IV. SIMULATION RESULTS The sample study radial power system is subjected to load switching at load bus. The network voltage is V g = 0.95 pu pu and no load is connected at load bus. The simulation is carried out by using the MATLAB/Simulink and power system blockset and the digital simulation results is given as shown in Fig5-15. The following load excursion sequence is tested: Step1: t = [0 − 0.3]s :at this period of time the static synchronous compensator is connected to the power system network without any injection of reactive power. Phase to phase 3 level output voltage of inverter is shown in Fig.4,5. Fig.6 shows absorbed active power by STATCOM. It is obvious that absorbed active power from network is negligible. Load voltage is shown in Fig.7. in starting simulation there is no load change so this voltage has been set on 0.95pu. Fig.8,9 show the injection current by STATCOM in the load side. I d is the active power component and I q is the reactive power component of the injected current. Transferring power including, transmission current components and active and reactive power for both VSC HVDC side are shown in Fig.10-15. Step 2: t = 0.3s : at this time the first inductive load with P = 0.7 pu , Q = 0.5pu (at rated voltage) is added to the ac power system at load bus, therefore more dynamic reactive power compensation is still required. The STATCOM injects reactive power (Fig.9), also VSC HVDC system transferring more active and reactive power to the inverter side (Fig.10-15).
[3]
[4]
[5]
[6]
[7]
[8]
“Input Controllability Measurement for BtB VSC HVDC”, Naser Mahdavi Tabatabaei, Naser Taheri, Ramazan Ebrahimi, TPE journal, Vol.1,No4 “Damping Function of BtB HVDC based Voltafe Source Converter”, Naser Mahdavi Tabatabaei, Naser Taheri, TPE journal, Vol.1,No2 “A Damping Neural Controller of VSC HVDC to Enhance Dynamic Stability”, Mohammad Banaei, Naser Taheri, European Transaction of Power Electric Journal, July 2010 Miguel Villablanca, Julio del Valle, Julio Rojas, Jose Abarca, and Wilson Rojas, “A Modified Back-to-Back HVDC System for 36Pulse Operation”, IEEE Trans, VOL. 15, NO.2, 2000. A.Yazdani,R.Iravani, “Dynamic Model and Control of the NPCBasedBack-to-Back HVDC SystemIEEE TRANSACTIONS ON POWER DELIVERY, VOL. 21, NO. 1, JANUARY 2006 W. Ren, L. Qian, D. Cartes, M. Steurer, “A Multivariable Control Method in STATCOM Application for Performance Improvement”, IEEE 0-7803-9208. “Modeling and Simulation of 3-Level STATCOM Using A New Fuzzy/LQR Controller”, Naser Mahdavi Tabatabaei, Naser Taheri, Javad Hamidi, IJKST journal, No.2, Vol.1, April 2010 J.B. Burl, “Linear Optimal Control: H2 and H∞ Methods”, Addison Wesley Longman, Inc. pp. 303-310, 1999.
BIOGRAPHIES Naser Mahdavi Tabatabaei received the B.Sc. and the M.Sc. degrees from University of Tabriz, Tabriz (Iran) and the Ph.D. degree from Iran University of Science and Technology, Tehran (Iran), all in Power Electrical Engineering, on 1989, 1992, and 1997, respectively. Currently, he is a Professor of Power Electrical Engineering at International Ecoenergy Academy and also International Science and Education Center, and an Assistant Professor of Power Electrical Engineering at Seraj Higher Education Institute, where he teaches Power System Analysis, Power System Operation, and Reactive Power Control. His research interests in the area of Power Quality, Energy Management Systems, ICT in Power Engineering and Virtual E-learning Educational Systems.
8th International Conference on “Technical and Physical Problems of Power Engineering” (ICTPE-2012) Fredrikstad, Norway, 5-7 September 2012
Naser Taheri received the B.Sc. in university of Guilan Rasht(Iran) in Electronic Engineering on 2007 and M.Sc degree from Azarbaijan University of Tarbiat Moallem, Tabriz (Iran) in Power Electrical Engineering on 2009. He is currently researching on Power System Control, Flexible AC Transmission Systems (FACTS) and power systems dynamic modeling. Ahmad Hashemi was born in Kermanshah, Iran, in 1984. He received his B.Sc. degree in power electrical engineering from K. N. Toosi University of technology, Tehran, Iran, in 2006 and his M.Sc. degree from Tarbiat Moallem University of Azarbaijan, Tabriz, Iran, in 2009. His main research interests are FACTS devices modeling, adaptive control and Neural Network optimizations. Kowsar Kiani was born in Kermanshah, Iran, in 1989. She received her B.Sc. degree in power electrical engineering from Kermanshah University of technology, Kermanshah, Iran, in 2012. She is interested in FACTS devices specially UPFC.
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8th International Conference on “Technical and Physical Problems of Power Engineering” (ICTPE-2012) Fredrikstad, Norway, 5-7 September 2012
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