Showing papers on "Inverter published in 2009"

Model Predictive Direct Torque Control—Part I: Concept, Algorithm, and Analysis

Abstract: This paper focuses on direct torque control (DTC) for three-phase AC electric drives. A novel model predictive control scheme is proposed that keeps the motor torque, the stator flux, and (if present) the inverter's neutral point potential within given hysteresis bounds while minimizing the switching frequency of the inverter. Based on an internal model of the drive, the controller predicts several future switch transitions, extrapolates the output trajectories, and chooses the sequence of inverter switch positions (voltage vectors) that minimizes the switching frequency. The advantages of the proposed controller are twofold. First, as underlined by the experimental results in the second part of this paper, it yields a superior performance with respect to the industrial state of the art. Specifically, the switching frequency is reduced by up to 50% while the torque and flux are kept more accurately within their bounds. Moreover, the fast dynamic torque response is inherited from standard DTC. Second, the scheme is applicable to a large class of (three-phase) AC electric machines driven by inverters.

Adaptive Droop Control Applied to Voltage-Source Inverters Operating in Grid-Connected and Islanded Modes

Abstract: This paper proposes a novel control for voltage-source inverters with the capability to flexibly operate in grid-connected and islanded modes. The control scheme is based on the droop method, which uses some estimated grid parameters such as the voltage and frequency and the magnitude and angle of the grid impedance. Hence, the inverter is able to inject independently active and reactive power to the grid. The controller provides a proper dynamics decoupled from the grid-impedance magnitude and phase. The system is also able to control active and reactive power flows independently for a large range of impedance grid values. Simulation and experimental results are provided in order to show the feasibility of the control proposed.

Multilevel Inverter For Grid-Connected PV System Employing Digital PI Controller

Abstract: This paper presents a single-phase five-level photovoltaic (PV) inverter topology for grid-connected PV systems with a novel pulsewidth-modulated (PWM) control scheme. Two reference signals identical to each other with an offset equivalent to the amplitude of the triangular carrier signal were used to generate PWM signals for the switches. A digital proportional-integral current control algorithm is implemented in DSP TMS320F2812 to keep the current injected into the grid sinusoidal and to have high dynamic performance with rapidly changing atmospheric conditions. The inverter offers much less total harmonic distortion and can operate at near-unity power factor. The proposed system is verified through simulation and is implemented in a prototype, and the experimental results are compared with that with the conventional single-phase three-level grid-connected PWM inverter.

Model Predictive Control of an Inverter With Output $LC$ Filter for UPS Applications

Abstract: The use of an inverter with an output LC filter allows for generation of output sinusoidal voltages with low harmonic distortion, suitable for uninterruptible power supply systems. However, the controller design becomes more difficult. This paper presents a new and simple control scheme using predictive control for a two-level converter. The controller uses the model of the system to predict, on each sampling interval, the behavior of the output voltage for each possible switching state. Then, a cost function is used as a criterion for selecting the switching state that will be applied during the next sampling interval. In addition, an observer is used for load-current estimation, enhancing the behavior of the proposed controller without increasing the number of current sensors. Experimental results under linear and nonlinear load conditions, with a 5.5-kW prototype, are presented, verifying the feasibility and good performance of the proposed control scheme.

A Comparative Study of Predictive Current Control Schemes for a Permanent-Magnet Synchronous Machine Drive

Abstract: This paper presents a comparative study of three predictive current control schemes for permanent-magnet synchronous machine (PMSM) drives. The first control scheme predicts the future evolution of the currents for each possible configuration of the inverter legs. Then, the switching state which minimizes a given cost function is selected and applied during the next sampling time. The second control scheme uses a modulator to apply two configurations of the inverter legs during a computation period. Among these configurations, one leads to null voltages. The duration of the other configuration is calculated in order to minimize the distance between the obtained state vector and the desired one. The third control scheme uses a model of the PMSM in order to predict the stator voltages which allows us to reach the desired currents after one modulation period. An algebraic method is presented to compute the duty cycle of each leg of the inverter in a direct manner. These control schemes are detailed and tested using the same switching frequency on the same test bench (1.6-kW PMSM drive). A simulation study is performed in order to compare sensitivity to parameters of each control scheme. Experiments confirm the simulation results.

Performance Analysis of Reduced Common-Mode Voltage PWM Methods and Comparison With Standard PWM Methods for Three-Phase Voltage-Source Inverters

Abstract: This paper surveys the reduced common-mode voltage pulsewidth modulation (RCMV-PWM) methods for three-phase voltage-source inverters, investigates their performance characteristics, and provides a comparison with the standard PWM methods. PWM methods are reviewed, and their pulse patterns and common-mode voltage (CMV) patterns are illustrated. The inverter input and output current ripple characteristics and output voltage linearity characteristics of each PWM method are thoroughly investigated by analytical methods, simulations, and experiments. The research results illustrate the advantages and disadvantages of the considered methods, and suggest the utilization of the near-state PWM and active zero state PWM1 methods as overall superior methods. The paper aids in the selection and application of appropriate PWM methods in inverter drives with low CMV requirements.

Portable power supply device

Abstract: A portable power supply device comprises a stackable battery housing locating a plurality of batteries therein and an inverter housing locating an inverter therein which is arranged to convert the direct current from the batteries to an alternating current. The inverter housing is readily separable from the battery housing such that one or more battery housings can be readily interchangeable to provide a constant supply of power and to allow a variety of charging configurations of the batteries. First electrical connectors on the battery housing and second electrical connectors on the inverter housing automatically connect the inverter to the batteries upon stacking of the inverter housing on the battery housing. Furthermore charging terminals are mounted externally on the inverter housing for ready access to connect to a charging device in a convenient manner without requiring the housings to be opened or separated form one another.

Fundamental Frequency Switching Strategies of a Seven-Level Hybrid Cascaded H-Bridge Multilevel Inverter

Abstract: This paper presents a cascaded H-bridge multilevel inverter that can be implemented using only a single dc power source and capacitors. Standard cascaded multilevel inverters require n dc sources for 2n + 1 levels. Without requiring transformers, the scheme proposed here allows the use of a single dc power source (e.g., a battery or a fuel cell stack) with the remaining n-1 dc sources being capacitors, which is referred to as hybrid cascaded H-bridge multilevel inverter (HCMLI) in this paper. It is shown that the inverter can simultaneously maintain the dc voltage level of the capacitors and choose a fundamental frequency switching pattern to produce a nearly sinusoidal output. HCMLI using only a single dc source for each phase is promising for high-power motor drive applications as it significantly decreases the number of required dc power supplies, provides high-quality output power due to its high number of output levels, and results in high conversion efficiency and low thermal stress as it uses a fundamental frequency switching scheme. This paper mainly discusses control of seven-level HCMLI with fundamental frequency switching control and how its modulation index range can be extended using triplen harmonic compensation.

Voltage Support Provided by a Droop-Controlled Multifunctional Inverter

Abstract: This paper presents a single-phase multifunctional inverter for photovoltaic (PV) systems application. The converter provides active power to local loads and injects reactive power into the grid providing voltage support at fundamental frequency. The proposed topology is controlled by means of the droop-control technique. Hence, it allows the obtaining of voltage-sag-compensation capability, endowing voltage ride-through to the system. A model and analysis of the whole system is given to properly choose the control parameters. Simulation and experimental results validate the proposed control using a 5-kVA PV converter.

Improved Z-Source Inverter With Reduced Z-Source Capacitor Voltage Stress and Soft-Start Capability

Abstract: This paper proposes an improved Z-source inverter topology. Compared to the traditional Z-source inverter, it can reduce the Z-source capacitor voltage stress significantly to perform the same voltage boost, and has inherent limitation to inrush current at startup. The control strategy of the proposed Z-source inverter is exactly the same as the traditional one, so all the existing control strategy can be used directly. A soft-start strategy is also proposed to suppress the inrush surge and the resonance of Z-source capacitors and inductors. The operation principle of the proposed topology and comparison with the traditional topology are analyzed in detail. Simulation and experimental results are given to demonstrate the new features of the improved topology.

Quasi-Z-Source Inverter for Photovoltaic Power Generation Systems

Abstract: This paper presents a quasi-Z-source inverter (qZSI) that is a new topology derived from the traditional Z-source inverter (ZSI). The qZSI inherits all the advantages of the ZSI, which can realize buck/boost, inversion and power conditioning in a single stage with improved reliability. In addition, the proposed qZSI has the unique advantages of lower component ratings and constant dc current from the source. All of the boost control methods that have been developed for the ZSI can be used by the qZSI. The qZSI features a wide range of voltage gain which is suitable for applications in photovoltaic (PV) systems, due to the fact that the PV cell's output varies widely with temperature and solar irradiation. Theoretical analysis of voltage boost, control methods and a system design guide for the qZSI in PV systems are investigated in this paper. A prototype has been built in the laboratory. Both simulations and experiments are presented to verify the proposed concept and theoretical analysis.

Model Predictive Direct Torque Control—Part II: Implementation and Experimental Evaluation

Abstract: This paper describes the implementation of the model predictive direct torque control (MPDTC) algorithm for the control of three-phase induction motor drives comprising a three-level DC-link inverter. The MPDTC scheme is designed to keep the motor torque and stator flux and the inverter's neutral point potential within given hysteresis bounds while reducing the average switching frequency of the inverter, in comparison with the standard direct torque control (DTC) method. The algorithm is embedded in the control software environment of ABB's ACS6000 medium-voltage drive, and experimental results are provided which verify the advantageous features of MPDTC in terms of average inverter switching frequency reduction. More specifically, compared to standard DTC, the proposed MPDTC scheme achieves an average (over the whole operating range) reduction of the inverter switching frequency of 16.5%, but for specific operating conditions the reduction is as much as 37.4%.

Design of Parallel Inverters for Smooth Mode Transfer Microgrid Applications

Abstract: In this paper, a microgrid architecture comprised of parallel inverters, critical loads, and CAN communication is studied. The controller designs in both grid-tie and islanding modes for the designed MG system are described. How to distribute the currents among paralleled inverters with CAN bus as communication interface is addressed. The mode transfer tests are conducted with an inverter-simulated grid to define the proper transfer procedures. Experimental results show that the inverter can work properly in different basic microgrid operation modes. With current sharing scheme, the output current is equally shared among different inverters without noticeable circulating current. Both the simulation and experimental results of mode transfer show that the inverter can switch between grid-tie and islanding modes smoothly, which indicates that the proposed mode transfer procedure is capable of minimizing the transients during mode transfer.

Steep Subthreshold Slope n- and p-Type Tunnel-FET Devices for Low-Power and Energy-Efficient Digital Circuits

Abstract: In this paper, novel n- and p-type tunnel field-effect transistors (T-FETs) based on heterostructure Si/intrinsic-SiGe channel layer are proposed, which exhibit very small subthreshold swings, as well as low threshold voltages. The design parameters for improvement of the characteristics of the devices are studied and optimized based on the theoretical principles and simulation results. The proposed devices are designed to have extremely low off currents on the order of 1 fA/mum and engineered to exhibit substantially higher on currents compared with previously reported T-FET devices. Subthreshold swings as low as 15 mV/dec and threshold voltages as low as 0.13 V are achieved in these devices. Moreover, the T-FETs are designed to exhibit input and output characteristics compatible with CMOS-type digital-circuit applications. Using the proposed n- and p-type devices, the implementation of an inverter circuit based on T-FETs is reported. The performance of the T-FET-based inverter is compared with the 65-nm low-power CMOS-based inverter, and a gain of ~104 is achieved in static power consumption for the T-FET-based inverter with smaller gate delay.

A hybrid nanomemristor/transistor logic circuit capable of self-programming.

Abstract: Memristor crossbars were fabricated at 40 nm half-pitch, using nanoimprint lithography on the same substrate with Si metal-oxide-semiconductor field effect transistor (MOS FET) arrays to form fully integrated hybrid memory resistor (memristor)/transistor circuits. The digitally configured memristor crossbars were used to perform logic functions, to serve as a routing fabric for interconnecting the FETs and as the target for storing information. As an illustrative demonstration, the compound Boolean logic operation (A AND B) OR (C AND D) was performed with kilohertz frequency inputs, using resistor-based logic in a memristor crossbar with FET inverter/amplifier outputs. By routing the output signal of a logic operation back onto a target memristor inside the array, the crossbar was conditionally configured by setting the state of a nonvolatile switch. Such conditional programming illuminates the way for a variety of self-programmed logic arrays, and for electronic synaptic computing.

Low Voltage, Low Power, Inverter-Based Switched-Capacitor Delta-Sigma Modulator

Abstract: An operational transconductance amplifier (OTA) is a major building block and consumes most of the power in switched-capacitor (SC) circuits, but it is difficult to design low-voltage OTAs in scaled CMOS technologies. Instead of using an OTA, this paper proposes an inverter-based SC circuit and its application to low-voltage, low-power delta-sigma (DeltaSigma) modulators. Detailed analysis and design optimizations are also provided. Three inverter-based DeltaSigma modulators are implemented for an implantable pacemaker, a CMOS image sensor, and an audio codec. The modulator-I for an implantable pacemaker achieves 65-dB peak-SNDR for 120-Hz bandwidth consuming 0.73 muW with 1.5 V supply. The modulator-II for a CMOS image sensor implemented with 320-channel parallel ADC architecture achieves 63-dB peak-SNDR for 8-kHz bandwidth consuming 5.6 muW for each channel with 1.2-V supply. The modulator-III for an audio codec achieves 81-dB peak-SNDR with 20-kHz bandwidth consuming 36 muW with 0.7-V supply. The prototype DeltaSigma modulators achieved high power efficiency maintaining sufficient performances for practical applications.

Sensitivity Study of the Dynamics of Three-Phase Photovoltaic Inverters With an LCL Grid Filter

Abstract: An accurate small-signal model of three-phase photovoltaic (PV) inverters with a high-order grid filter is derived in this paper. The proposed model takes into account the influence of both the inverter operating point and the PV panel characteristics on the inverter dynamic response. A sensitivity study of the control loops to variations of the DC voltage, PV panel transconductance, supplied power, and grid inductance is performed using the proposed small-signal model. Analytical and experimental results carried out on a 100-kW PV inverter are presented.

Three-Level Inverter-Based Shunt Active Power Filter in Three-Phase Three-Wire and Four-Wire Systems

Abstract: This paper presents a direct current-space-vector control of an active power filter (APF) based on a three-level neutral-point-clamped (NPC) voltage-source inverter. The proposed method indirectly generates the compensation current reference by using an equivalent conductance of the fundamental component using APF's dc-link voltage control. The proposed control can selectively choose harmonic current components by real-time fast Fourier transform to generate the compensation current. The compensation current is represented in a rotating coordinate system with chosen switching states from a switching table implemented in a field-programmable gate array. In addition, a three-phase four-wire APF based on a three-level neutral-point-clamped inverter is also presented. The proposed APF eliminates harmonics in all three phases as well as the neutral current. A three-phase three-wire NPC inverter system can be used as a three-phase four-wire system since the split dc capacitors provide a neutral connection. To regulate and balance the split dc-capacitor voltages, a new control method using a sign cubical hysteresis controller is proposed. The characteristics of the APF system with an LCL-ripple filter are investigated and compared with traditional current control strategies to evaluate the inherent advantages. The simulation and experimental results validated the feasibility of the proposed APF.

DC–AC Cascaded H-Bridge Multilevel Boost Inverter With No Inductors for Electric/Hybrid Electric Vehicle Applications

Abstract: This paper presents a cascaded H-bridge multilevel boost inverter for electric vehicle (EV) and hybrid EV (HEV) applications implemented without the use of inductors. Currently available power inverter systems for HEVs use a dc-dc boost converter to boost the battery voltage for a traditional three-phase inverter. The present HEV traction drive inverters have low power density, are expensive, and have low efficiency because they need a bulky inductor. A cascaded H-bridge multilevel boost inverter design for EV and HEV applications implemented without the use of inductors is proposed in this paper. Traditionally, each H-bridge needs a dc power supply. The proposed design uses a standard three-leg inverter (one leg for each phase) and an H-bridge in series with each inverter leg which uses a capacitor as the dc power source. A fundamental switching scheme is used to do modulation control and to produce a five-level phase voltage. Experiments show that the proposed dc-ac cascaded H-bridge multilevel boost inverter can output a boosted ac voltage without the use of inductors.

Load-Adaptive Control Algorithm of Half-Bridge Series Resonant Inverter for Domestic Induction Heating

Abstract: Domestic induction cookers operation is based on a resonant inverter which supplies medium-frequency currents (20-100 kHz) to an inductor, which heats up the pan. The variable load that is inherent to this application requires the use of a reliable and load-adaptive control algorithm. In addition, a wide output power range is required to get a satisfactory user performance. In this paper, a control algorithm to cover the variety of loads and the output power range is proposed. The main design criteria are efficiency, power balance, acoustic noise, flicker emissions, and user performance. As a result of the analysis, frequency limit and power level limit algorithms are proposed based on square wave and pulse density modulations. These have been implemented in a field-programmable gate array, including output power feedback and mains-voltage zero-cross-detection circuitry. An experimental verification has been performed using a commercial induction heating inverter. This provides a convenient experimental test bench to analyze the viability of the proposed algorithm.

A Single-Stage Single-Phase Transformer-Less Doubly Grounded Grid-Connected PV Interface

Abstract: A transformer provides galvanic isolation and grounding of the photovoltaic (PV) array in a PV-fed grid-connected inverter. Inclusion of the transformer, however, may increase the cost and/or bulk of the system. To overcome this drawback, a single-phase, single-stage [no extra converter for voltage boost or maximum power point tracking (MPPT)], doubly grounded, transformer-less PV interface, based on the buck-boost principle, is presented. The configuration is compact and uses lesser components. Only one (undivided) PV source and one buck-boost inductor are used and shared between the two half cycles, which prevents asymmetrical operation and parameter mismatch problems. Total harmonic distortion and DC component of the current supplied to the grid is low, compared to existing topologies and conform to standards like IEEE 1547. A brief review of the existing, transformer-less, grid-connected inverter topologies is also included. It is demonstrated that, as compared to the split PV source topology, the proposed configuration is more effective in MPPT and array utilization. Design and analysis of the inverter in discontinuous conduction mode is carried out. Simulation and experimental results are presented.

New type T-Source inverter

Abstract: This paper presents different topologies of voltage inverters with alternative input LC networks. The basic topology is known in the literature as a Z-source inverter (ZSI). Alternative passive networks were named by the authors as T-sources. T-source inverter has fewer reactive components in comparison to conventional Z-source inverter. The most significant advantage of the T-source inverter (TSI) is its use of a common voltage source of the passive arrangement. Experimental results for the TSI are in agreement with theoretical and simulated prediction.

A New Variable-Speed Wind Energy Conversion System Using Permanent-Magnet Synchronous Generator and $Z$ -Source Inverter

Abstract: With the growth of wind energy conversion systems (WECSs), various technologies are developed for them. Permanent-magnet synchronous generators (PMSGs) are used by these technologies due to special characteristics of PMSGs such as low weight and volume, high performance, and the elimination of the gearbox. In this paper, a new variable-speed WECS with a PMSG and Z-source inverter is proposed. Characteristics of Z-source inverter are used for maximum power tracking control and delivering power to the grid, simultaneously. Two control methods are proposed for delivering power to the grid: Capacitor voltage control and dc-link voltage control. Operation of system with these methods is compared from the viewpoint of power quality and total switching device power (TSDP). In addition, TSDP, current ripple of inductor, performance, and total harmonic distortion of grid current of proposed system is compared with traditional wind energy system with a boost converter.

Constant-Frequency Hysteresis Current Control of Grid-Connected VSI Without Bandwidth Control

Abstract: The theory, design, and implementation of a constant-frequency hysteresis current control for grid-connected voltage source inverter (VSI) is presented. The proposed control technique retains the benefit of the hysteresis control having fast dynamic response and tackles the drawback of the standard hysteresis control having variable switching frequency. The concept is based on predicting the current reference, system dynamic behavior, and past time to formulate the switching function for dictating the switching times of the switches in the inverter within a predefined switching period. Of particular importance, no hysteresis bandwidth (a challenge in the practical implementation) is needed in the entire control method. The operating principles of the proposed technique and mathematical derivation of the switching functions will be given. The proposed method is successfully applied to a 300 W, 110 V, 60 Hz grid-connected VSI prototype with the controller implemented by a simple analog circuit. The steady-state and large-signal dynamic response of the VSI are studied. Experimental results show that the inverter can reach the steady state in two switching actions after the inverter is subject to large-signal input and output disturbances.

A New Multilevel Conversion Structure for Grid-Connected PV Applications

Abstract: A novel scheme for three-phase grid-connected photovoltaic (PV) generation systems is presented in this paper. The scheme is based on two insulated strings of PV panels, each one feeding the dc bus of a standard two-level three-phase voltage-source inverter (VSI). The inverters are connected to the grid by a three-phase transformer having open-end windings on the inverter side. The resulting conversion structure performs as a multilevel power active filter (equivalent to a three-level inverter), doubling the power capability of a single VSI with given voltage and current ratings. The multilevel voltage waveforms are generated by an improved space-vector-modulation algorithm, suitable for the implementation in industrial digital signal processors. An original control method has been introduced to regulate the dc-link voltages of each VSI, according to the voltage reference given by a single maximum power point tracking controller. The proposed regulation system has been verified by numerical simulations and experimental tests with reference to different operating conditions.

A Simple Space Vector PWM Generation Scheme for Any General $n$ -Level Inverter

Abstract: This paper proposes a generalized method for the generation of space vector pulsewidth modulation (SVPWM) signals for multilevel inverters. In the proposed method, the actual sector containing the tip of the reference space vector need not be identified. A method is presented to identify the center of a sub-hexagon containing the reference space vector. Using the center of the sub-hexagon, the reference space vector is mapped to the innermost sub-hexagon, and the switching sequence corresponding to a two-level inverter is determined. A new technique is proposed in this paper, by which these two-level vectors are translated to the switching vectors of the multilevel inverter by adding the center of the sub-hexagon to the two-level vectors. The proposed method can be extended to any n-level inverter, and a generalized algorithm is proposed. The scheme is explained for a five-level inverter, and experimental results are presented for a three-level inverter.

4-terminal relay technology for complementary logic

Abstract: A 4-terminal (4T) relay technology is proposed for complementary logic circuit applications. The advantage of the 4T relay design is that it provides a means for electrically adjusting the switching voltage; as a result, a 4T relay can mimic the operation of either an n-channel or p-channel MOSFET. Fabricated 4T relays exhibit good on-state current (I on ≫ 700µA for V DS = 1V) and zero off-state leakage current. Low-voltage switching (≪ 2V) and low switching delay (100ns) are demonstrated by appropriately biasing the body terminal. Endurance exceeds 10 9 on/off cycles without stiction or wear issues. Complementary operation is demonstrated in a functional relay inverter circuit.

A single phase multilevel inverter using switched series/parallel DC voltage sources

Abstract: A novel multilevel inverter with a small number of switching devices is proposed. It consists of an H-bridge and an inverter which outputs multilevel voltage by switching the dc voltage sources in series and in parallel. The proposed inverter can output more number of voltage levels in the same number of the switching devices by using this conversion. The number of gate driving circuits is reduced, which leads to the reduction of the size and power consumption in the driving circuits. The total harmonic of the output waveform is also reduced. The proposed inverter is driven by the hybrid modulation (HM) method. In this paper, the circuit configuration, the theoretical operation, Fourier analysis, simulation results with MATLAB/ SIMULINK and the experimental results are shown. The experimental results accorded with the simulation results.

A General Analytical Method for Calculating Inverter DC-Link Current Harmonics

Abstract: Accurate identification of a DC-link ripple current is an important part of switched power-converter design, since the spectral content of this current impacts on DC bus-capacitor lifetime, the stability of the converter control, and the electromagnetic-interference (EMI) performance of the system. Conventionally, the RMS magnitude of the ripple current is used to evaluate this impact, but this approach does not readily differentiate between pulsewidth-modulation (PWM) strategies, and can be challenging to evaluate for more complex converter topologies. This paper presents a new generalized approach that analytically determines the harmonic spectrum of the DC-link and DC-bus capacitor currents for any voltage-source switched converter topology. The principle of the strategy is that the product of a phase-leg-switching function and its load current in the time domain, which defines the switched current flowing through the phase leg, can be evaluated in the frequency domain by convolving the spectra of these two time-varying functions. Since PWM has a discrete line-frequency spectrum, this convolution evaluates as an infinite summation in the frequency domain, which reduces to a simple frequency shift of the PWM spectrum when the load current is assumed to be a fundamental single-frequency sinusoid. Hence, the switched currents flowing through the phase legs of an inverter can be evaluated as a summation of harmonics for any PWM strategy or inverter topology and can then be readily combined using superposition to determine the DC-link and DC bus-capacitor currents. The analytical approach has been verified against experimental results for an extensive range of two-level and multilevel converter topologies and PWM strategies.