Implementation of Sliding Mode Control in DC Microgrids Leonardy Setyawan, Wang Peng, Xiao Jianfang School of Electrical and Electronic Engineering Nanyang Technology University, Singapore
[email protected],
[email protected],
[email protected]
Abstract—Upon the increasing implementation of direct current (DC) power sources, energy storages and loads in power systems, DC microgrids have drawn more attention from global stakeholders. Reliable operation of DC microgrids mainly depends on proper control method to cope with bus voltage variations due to renewable sources intermittency and load changes. The main objectives of the control method are to maintain the operating bus voltage and the power balance. This control method is applied in battery energy storage (BES) component. By charging and discharging power to and from BES the control objectives can be achieved. Sliding mode control (SMC) method is implemented because of its robustness for sudden variations of power sources and loads. SMC is also of fast response in dynamics. Washout filter is applied to minimize the transient response. DC microgrid model is developed in Matlab/Simulink simulation to verify the performance of SMC. The comparison between SMC and the conventional proportional-plus-integral (PI) control is also carried out in the analysis. Keywords—sliding mode control; DC microgrid; washout filter; battery energy storage
I.
INTRODUCTION
Semiconductors which are natively DC are about to dominate electrical devices since the invention of semiconductor material in 1960s. Hence, the majority of the load base will be DC-compatible [1]. Most carbon-free energy sources i.e. photovoltaic (PV) and fuel cell, and energy storages which are vastly increasing in number are also DC inherent. The continuous growth penetration of DC-compatible components in both loads and sources are inevitable. Nowadays, nearly 30% of all power generated will pass through a power electronic converter before it is utilized, and it is predicted to increase to 80% within the next 10-15 years [2]. The conversion process causes the power loss in the power system. It will be more efficient and sustainable if the number of conversions are reduced. Because of those factors, it is the time to reconsider the merits of DC over AC throughout the system. Nevertheless, the implementation of the DC microgrid alone for wider use has The authors are with School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, SINGAPORE 639798. This research is supported by Energy Research Institute @ NTU (ERI@N), Nanyang Technological University, Singapore.
c 978-1-4799-4315-9/14/$31.00 2014 IEEE
some barriers which include the aspect of standards, protection, safety, and equipment [1]. Therefore, the DC microgrid is implemented to enhance the performance of the overall power system rather than to substitute the existing AC power system. The main motivation of this research is to cope with stability issue existing in the DC microgrid which is mainly caused by the intermittent nature of renewable sources and load changes. BES is the main component to regulate the bus voltage through charge and discharge to maintain power balance of DC microgrid [3]. PI control is a common control technique used for converters [4-7]. It is a linear control that minimizes the error by adjusting the control input of the system with the control action. Since the converter is nonlinear, to simplify the control process, nonlinear control is implemented. The nonlinear control chosen in this research report is SMC. SMC is recognized as an efficient tool to do design robust controllers for complex high-order nonlinear dynamic plant operating under uncertain conditions [8]. SMC has major advantages including the guaranteed stability and the robustness against parameter, line, and load uncertainties [9, 10]. The simulation results are presented to validate this research work. In this research the performance comparison between SMC and PI control will be carried out. The organization of this paper is as follow: Section 2 exposes a typical DC microgrid from the overall system to its components including the mathematic modeling; Section 3 explains the implementation of the sliding mode control method in the DC microgrid; the results and analysis of the simulations of several case studies are presented in Section 4; and in the last Section 5, conclusions are provided. II.
DC MICROGRID CONFIGURATION AND MODELLING
A. DC Microgrid Configuration DC microgrid interconnects a localized grouping of electricity sources, storages and loads that predominantly generates, distributes, stores, and uses electricity in its native DC. It is able to operates either in grid-tied mode or isolated mode. The DC microgrids have advantages over the AC microgrid [11], including: a) simple to control, b) higher efficiency, c) higher power quality, d) higher reliability, and e) reduces the greenhouse effect.
578
Ipv
Rs
+
Iph
D
Rsh
Vpv
Load
DC Sources
Ͳ Fig. 2. PV Cell Equivalent Circuit
B. Modeling of DC Microgrid Components The detail of the model of each component in DC microgrid for the simulation is presented in the followings: 1) Modeling of Solar PV Panel A solar PV cell can be modelled as a current source driven by the sunlight in paralleled with a diode. A shunt resistor and a series resistor are connected at the output. The equivalent circuit of a solar PV cell is presented in Fig. 2.
AC link
DC Storages
The model of solar PV panel is represented in the equations below [12, 13]: ܫ௩ ൌ ݊ ܫ െ ݊ ܫ௦௧ ቈ݁ ݔቆቀ
்
ቁቀ
ೡ ೞ
DC loads
ܫ ൌ ቀܫ௦௦ ݇ ሺܶ െ ܶ ሻ ൈ ் ଷ
ܫ௦௧ ൌ ܫ ቀ ቁ ݁ ݔቆቀ ்ೝ
where: Voc
Fig. 1. The Schematic Layout of a DC microgrid
A generic schematic layout of the DC microgrid is displayed in Fig. 1 which consists of: a. DC sources These components include solar PV panels, wind turbine, and fuel cell (FC) with their respective converter. b. DC storages These components include BESs and super capacitor installed with converters. c. Loads These components include DC-compatible loads BES is the main voltage regulation component in DC microgrid which maintain system power balance through charge and discharge [4]. Excess power in DC microgrid induces bus voltage swell and, vice versa [3]. Therefore, the controller maintains the power balance of DC microgrid by charging to BES when power is excess and discharging from BES when power is deficit. Power balance on DC microgrid can be expressed with the following equation: ܲாௌ ൌ ܲ௦ െ ܲ
(1)
where PBES, PS and PL are the power of battery energy storages, DC sources, and loads respectively.
Iph Isat q A k Rs Rsh Isso ki Tr Irr Egap np ns S T
ாೌ
ܫ௩ ܴ௦ ቁቇ െ ͳ (2) ௌ ଵ
(3)
ቁ
ଵ
ଵ
்ೝ
்
ቁ ൈ ቀ െ ቁቇ
(4)
= Rated open circuit voltage = Photocurrent = Module reverse saturation current = Electron charge (1.602 x 10-19 C) = Ideality factor = Boltzman constant (1.38 x 10-23 J/K) = Series resistance of a PV cell = Parallel resistance of a PV cell = Short-circuit current = SC current temperature coefficient = Reference temperature (300 K) = Reverse saturation current at Tr = Energy of the band gap for silicon (1.12 eV) = Number of cells in parallel = Number of cells in series = Solar irradiation level = Surface temperature of the PV
2) Modeling of Battery The battery voltage terminal Vb and state of charge (SOC) are two important parameters for the indication of the battery status which are determined by the equations below [14]. ܸ ൌ ܸ െ ܭ
ொ ொି ್ ௗ௧
ܣȉ ݁ݔሺെ݅ ܤ ݀ݐሻ െ ܴ ȉ ݅ (5)
ܱܵ ܥൌ ͳͲͲ ቀͳ െ
್ ௗ௧ ொ
ቁ
(6)
where Rb, Vo, ib, Q, K, A and B are the internal resistance, open circuit voltage, battery current, rated capacity, polarization voltage, exponential voltage and exponential capacity respectively. This battery model is provided in MATLAB/Simulink tool. The battery equivalent circuit is
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shown in Fig. 3 and the parameters of the lead acid type battery model are provided as in Table I. TABLE I. Symbol V Q SOC
PARAMETERS OF THE BES MODEL Description Nominal Voltage Rated Capacity Initial State-of-Charge
Value 196 150 50
Units V Ah %
Fig. 4. The Simplified Model of DC microgrid
where: vc
= = = = = =
iL Vb R rL P
Instantaneous capacitor voltage Instantaneous inductor current Battery voltage Resistive load Equivalent series resistor of the inductor Difference power generated and consumed
by substituting ݐൌ ߬ξ ܥܮand ሼ݅ ǡ ݒ ሽ ൌ ቊට ܸ ݔǡ ܸ ݕቋ to
(8), the dynamics can be normalized to
Fig. 3. Battery Equivalent Circuit
ௗ௫
3) Modeling of Wind Turbine Generator Output power Pm from a wind turbine generator (WTG) can be expressed as [6, 7, 15]: ܲ ൌ ͲǤͷߩܥܣ ሺߣǡ ߚሻܸ௪ଷ
(7)
where: ȡ
= Air density A = Rotor swept area Cp(Ȝ,ȕ) = Power coefficient which is the function of tip speed ratio Ȝ and pitch angle ȕ Vw = Wind speed
WTG output is connected to AC-DC-DC converter. With a proper control, the maximum power from the WTG can be harnessed to DC microgrid [15]. Modeling of other components like super capacitor and loads are not presented due to the simplicity of the model. III.
ௗఛ
where: a
=
ଵ ோ
ଵ
ൌ ሺܸ െ ݎ ݅ െ ݒݑ ሻ
ௗ௧ ௗ௩ ௗ௧
ଵ
௩
ோ
ൌ ቀ݅ݑ െ
െ ቁ ௩
ൌ ݔݑെ ܽ ݕെ
=
ට ݎ ;
(9)
ௗ ௬
d
=
ට
್మ
Washout filter is equipped to the sliding mode control. Purposes of adding this washout filter are [16, 17]: a. To regulate the desired output voltage of DC microgrid b. To ensure robustness under variations c. To minimize the transient response The inclusion of the filter adds an additional differential equation to (8), given by ௗ௭ ௗఛ
DC microgrid model is simplified for the simulation. The simplified model of DC microgrid is as shown in Fig. 4. The dynamics of the simplified DC microgrid model can be represented as ௗಽ
ൌ ͳ െ ܾ ݔെ ݕݑ
ට ; b
IMPELEMENTATION OF SLIDING MODE CONTROL
Battery converter is scheduled to operate in voltage regulation (VR) mode to maintain system power balance. Sliding mode control method is implemented for control of BES DC-DC bi-directional boost converter. The sliding mode control used in this system is equipped with washout filter. The washout filter is responsible for controlling the power balance [16].
580
ௗఛ ௗ௬
ൌ ߱ ሺ ݔെ ݖሻ
(10)
where ߱ = ʹߨ݂ and ݂ is the cut-off frequency. The sliding surface that is used, represented as: ݄ ሺݔሻ ൌ ݕെ ݕ ݇ ሺ ݔെ ݖሻ
(11)
where: yr = The desired normalized DC bus voltage kn = Positive scalar control parameter to be adequately adjusted z = The low frequency part of signal x
The power switches have a frequency limitation to operate safely. A hysteresis band between the denormalized switching surface h and the commutation signal u represented in (12) is the most common solution to limit the switching frequency.
(8) ݑൌ ቐ
ͳǡ݂݄݅ ߜ Ͳǡ݂݄݅ ൏ െߜ ݑ ǡ݂݅ െ ߜ ݄ ߜ
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(12)
where į is a constant which defines the hysteresis band and upre is the last value of u. ߜൌ
್ ሺ௩ ି್ ሻ
(13)
ଶೞ ௩
where fs is the switching frequency in steady state. The stability limitation of each parameter is stated as [16]: m > 0, ܽ ܾ
ఠ ଶ
and kn is in the range as stated below: ఠ ିሺଶାఠ ሻξ ଵିξ
ܭൌ ቊ݇ ݉ܽ ݔቄ
ସ௬ೝ
ǡ
ଶ௬ೝ
ቅቋ
(14)
TABLE II. PARAMETERS FOR THE SIMULATION CASE STUDIES Symbol C L rL fs 2į Vb Vc(0) Ȧ k Q Ppv
Description Capacitance Inductance Inductor resistance Switching frequency Hysteresis band Battery voltage Initial vapacitor voltage Cut-off frequency Scalar control parameter Battery capacity Solar PV power
Value 50 2.5 5 100 0.3796 196 196 283 10 150 1.2
Units F mH m kHz A V V rad/s Ah kW
Since the analysis is done on the normalized system, it is necessary to denormalize the variables of the system so that the control can be implemented: a. ߱ ൌ
ఠ ξ
b. ݇ ൌ ݇ ට
In this research work, SMC is implemented in a DC microgrid with battery voltage of 196 V and DC bus voltage of 380 V. The switching frequency of the controller is determined so that the hysteresis band can be calculated using (13). This hysteresis band value will then be applied in the relay block of the simulation model. Other parameters that should be considered are the cut off frequency (fn) and the positive scalar (k). After both parameters have been determined, the values of those parameters are then applied in the control block. This control block is then implemented to conduct the simulation. IV.
SIMULATION SETUPS AND RESULTS
MATLAB/Simulink simulation is conducted to validate the sliding mode control method in the DC microgrid. A. Test System and Parameters The simulation is conducted in the DC microgrid model which includes a solar PV, lead acid battery energy storage, and a DC resistance load. The parameters used in battery energy storage converter circuit and the solar PV panel for this simulation are presented in the Table II. The general test system schematic layout for case studies is presented in Fig 5 with the control block diagram shown in Fig. 6.
Fig. 5. The General Test System Schematic Layout
Fig. 6. The Structure of SMC Based on Washout Filter
B. Case Studies Three case studies have been conducted in this paper. At the same time, results based on classical PI control are obtained for the comparison: 1) Bus Voltage Regulation The DC load set in this case study is 160 and the total simulation time is 0.05 s. The simulation result of this case study is presented in Figs. 7 – 8. The simulation result for this case study by using SMC has a rise time of 1.7 ms, settling time of 4.4 ms and no overshoot. The simulation result of this case study is compared with PI control method. The simulation result with SMC is drawn with blue solid line whereas PI control is drawn with red dash line. The simulation result of capacitor/output voltage with SMC has no overshoot compared with PI control which has 2.46% overshoot. PI control has slower settling time (6.9 ms) compared to SMC.
Fig. 7. Simulation Result of the Capacitor/Output Voltage
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Fig. 8. Simulation Result of the Inductor Current
Fig. 11. Power Balance in DC Microgrid
2) Solar Power Variation Event The power produced by the solar PV panel is different in time depending on the solar irradiation. Different levels of input solar PV power are applied to simulate this variation. The purpose of this case study setup is to verify the capability of the SMC to track changes caused by the fluctuated solar power. The DC load is 220 and the total simulation time is 0.35 s. The simulation result of this case study is presented in Figs. 9 – 10.
The power balance in DC microgrid is presented in Fig. 11. The power that consumed by DC load is 656.36 W. When the solar PV panel cannot meet the needed power for DC load, BES will discharge the power to the DC microgrid so that the power balance is realized. In the other side when solar PV panel power meet the DC load power and has an excess power, the controller will use the excess to charge the BES. By doing these the power balance in the DC microgrid is satisfied at all time.
Along with the variations in the solar PV panel output power the BES can track the bus voltage. The PI control also produces the similar result with the SMC, the only different is the PI control induces more oscillation compared to the SMC during the transient when the changes happen.
3) DC Load Variation Event The effect of load variation is investigated in this case study. The resistance changing caused the changing of DC load power consumption. The DC load will change from the initial value of 300 to 200 to 150 to 200 and then back to 300 sequentially in the duration of 0.1 s. The total simulation time is 0.5 s. The simulation result of this case study is presented in Figs. 12 – 13. A voltage dip happened when the load is increased and a little voltage swell happened when the load is decreased. The performance of SMC and PI control for this case study is similar. For the voltage overshoot or voltage undershoot which happened in the simulation, SMC has a bit better performance rather than PI control. The SMC has performance 0.053% better than PI control.
Fig. 9. Simulation Result of the Capacitor/Output Voltage
Fig. 12. Simulation Result of the Capacitor/Output Voltage
Fig. 10. Simulation Result of the Inductor Current
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[5]
[6] [7]
[8]
[9] Fig. 13. Simulation Result of the Inductor Current
PV converter operates in MPPT mode with constant power output of 940 W throughout the case study. V.
CONCLUSION
The sliding mode control method has been implemented in battery charging-discharging converter to maintain the stable operation of a DC microgrid. MATLAB simulation has been conducted to validate the performance of the sliding mode control. The sliding mode control can maintain voltage stability and power balance of a DC microgrid through controlling the charging and discharging of the BES in case of solar irradiation variations and load consumption changes. The sliding mode control gives a better response on the transient response compared to the PI control. In the transient response, the SMC has averagely 0.387% better performance on voltage overshoot/undershoot than the PI control.
[10] [11]
[12]
[13]
[14]
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