## What does the Power Smoothing function do?

The **Power Smoothing** function in the SYSTM app will give a rolling **3-second average** power on the screen, rather than reporting instant power from your power source. The numbers you see on the screen will have less fluctuation. The app will record the actual data, not the smoothed data, so the graphs will still show the natural power fluctuations.

You can turn Power Smoothing ON or OFF with the toggle found on the SETTINGS screen in the workout player settings panel. Click on the gear in the top right corner of the workout player screen to access this panel.

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## Load peak shaving and power smoothing of a distribution grid with high renewable energy penetration

High penetration of renewable energy poses a significant challenge in operation of power system. A potential solution for this problem is utilizing Battery Energy Storage System (BESS). The purpose of this paper is to analyze the effectiveness of BESS ability to peak shave and smooth the load curve of an actual circuit on the island of Maui in Hawaii. The distribution circuit has about 850 kW of installed rooftop Photo-Voltaic (PV) generation. Higher penetration of PV increases the concern about the potential impacts on the transmission system. At first, we will present two different methods for load forecasting. Reliable forecasting of daily load is required to effectively utilize the BESS system. We have employed two different methods for load forecasting in order to achieve two main purposes including peak shaving and smoothing. For reaching these goals, two approaches are analyzed. The first approach is utilizing a nonlinear programming method in terms of load shifting and smoothing. The second approach includes a real time control strategy to have smoothing and peak shaving at the same time. As a real case study, these proposed methods have been applied within 108-day data collection period and pros and cons of these methods will be discussed.

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## Title: Solar Power Smoothing in a Nanogrid Testbed

Abstract: High penetration of solar power introduces new challenges in the operation of distribution systems. Considering the highly volatile nature of solar power output due to changes in cloud coverage, maintaining the power balance and operating within ramp rate limits can be an issue. Great benefits can be brought to the grid by smoothing solar power output at individual sites equipped with flexible resources such as electrical vehicles and battery storage systems. This paper proposes several approaches to a solar smoothing application by utilizing battery storage and EV charging control in a «Nanogrid» testbed located at a utility in Florida. The control algorithms focus on both real-time application and predictive control depending on forecasts. The solar smoothing models are then compared using real data from the Nanogrid site to present the effectiveness of the proposed models and compare their results. Furthermore, the control methods are applied to the Orlando Utilities Commission (OUC) Nanogrid to confirm the simulation results.

Subjects: | Systems and Control (eess.SY) |

Cite as: | arXiv:2206.15323 [eess.SY] |

(or arXiv:2206.15323v1 [eess.SY] for this version) | |

https://doi.org/10.48550/arXiv.2206.15323 |

## Design and implementation of a power smoothing system for cross-flow current turbines

This study presents an efficient system that smooths fluctuations in electrical power from a cross-flow (i.e., “vertical-axis”) turbine. The proposed solution is a two-stage approach consisting of a low-pass filter and a bi-directional buck-boost converter. The design and stability characteristics of the system are presented, followed by time-domain simulation and validation against small-scale experiments. When this validated simulation is applied to a full-scale system, we demonstrate a 99% root mean square reduction in fluctuating power output with only a 3% drop in electrical system efficiency. This could allow intracycle control strategies to increase mechanical power output without causing electrical power fluctuations that are incompatible with direct use.

Avoid common mistakes on your manuscript.

### 1 Introduction

One of the largest challenges for the electrical integration of distributed renewable resources is power fluctuation over both relatively short and long time scales [1]. Intermittent and unpredictable power from renewable resources, used to offset climate change associated with dispatchable fossil-fuel resources, may disrupt the stability of the power grid and the balance of supply and demand. Long-term power intermittency is a well-established concern in the renewable energy industry, and the feasibility of grid-scale energy storage systems (e.g., pumped hydropower, compressed-air storage) to mitigate this is an active area of research [2, 3]. Short-term power fluctuation is also problematic. For example, in wind energy generation, incident resource power is proportional to the cube of wind speed, such that turbulent gusts can disrupt grid frequency or cause voltage flicker [4].

Like generation from other renewable resources, current turbines operating in rivers, tidal channels, and strong ocean currents will be required to adhere to distribution and transmission grid standards [5]. Early market adoption is most likely in remote locations where conventional energy costs are higher and current turbines may be cost-effective [6]. However, for these remote microgrids, power quality of electrical generation is a particular concern [7].

Cross-flow turbines (“vertical-axis”) have distinct, potentially advantageous properties compared to axial-flow turbines (“horizontal-axis”), including lower maximum blade speed, bi-directional functionality in reversing tidal flows, and potential to increase system efficiency in tightly-packed, high-blockage arrays [8, 9]. Typical control strategies involve maintaining an optimal tip-speed ratio for a given inflow velocity through regulation of rotor speed or torque [10]. Turbines with a high mechanical conversion efficiency (i.e., power in flow to power on shaft) typically have a small number of straight blades [11]. Because of the variation in apparent angle of attack for the rotating blades, hydrodynamic torque varies periodically with blade position, leading to oscillations in mechanical power over a single rotation. The primary frequency of oscillation is the product of rotation rate and number of turbine blades. Depending on the control scheme, this instantaneous power can cycle between production (generating) and consumption (motoring) when net power is produced over a rotation [10]. Further, it has been demonstrated that optimizing the amplitude and frequency of turbine speed within a rotation, termed “intracycle control”, can increase mechanical conversion efficiency by up to 59% [12]. However, this increases the peak-to-average ratio of mechanical power, such that the associated electrical power may not be compatible with direct use [13].

Fig. 1 compares the active power delivered to the grid, normalized by average power, for a two-bladed turbine rotating at \(\approx\)

1 Hz utilizing constant speed or intracycle control [13]. Intracycle control increases the average power, but instantaneous power is characterized by large peak-to-peak power ratio (>25) and periodic power consumption. The design and implementation of a power smoothing system (PSS) and control scheme to mitigate these fluctuations, while introducing minimal power loss, is presented in this work. Such a system allows the turbine to be optimized for average power output, thus potentially reducing cost of energy, while delivering stable, high-quality power to an end use. The system comprises of two parts: an LC filter and a bi-directional DC-DC converter coupled with a capacitor for short-term (i.e., intracycle) energy storage.

Power smoothing is necessary for other renewable energy generators, including axial-flow wind turbines [14,15,16] and wave energy converters [17]. In solar photovoltaic (PV) systems, single phase grid-tie inverters are known to introduce power ripple at double the grid frequency onto the DC bus, which can degrade PV system performance. Ripple port circuits, typically a power decoupling circuit integrated on to the DC bus, can absorb these power fluctuations [18,19,20]. In general, ripple port and other power smoothing systems are designed for the characteristics of specific applications, utilizing topologies such as DC-DC converters, DC-AC H-bridge inverters, flyback converters, or active filters, and deploy energy storage devices such as supercapacitors, batteries, or flywheels.

In this work, we show how a PSS can be designed for the specific electrical power characteristics of cross-flow current turbines operating under intracycle control which results in power fluctuations that are an order of magnitude higher than in other renewable energy systems and requires intermittent power draw. This necessitates an additional LC filter on the DC bus to smooth power over a complete rotation, which is unnecessary for lower-amplitude power fluctuations. The main contributions of this work are to 1) demonstrate the effectiveness of PSS on a cross-flow turbine utilizing intracycle control and 2) validate a simulation of the proposed PSS using a benchtop experiment. This work is based on the corresponding author’s masters thesis [21], which contains supplementary detail and results.

The remainder of the paper is laid out as follows. Section 2 describes the design and optimization of the PSS and controller, as well as its implementation in a bench-top system and equivalent simulation. Section 3 shows experimental results from the bench-top system which validate the corresponding simulation. The performance and feasibility of a larger-scale system for a cross-flow turbine operating under intracycle control is then demonstrated through simulation.

### 2 Methodology

The power smoothing system, integrated on the DC bus of a generator-to-grid power collection scheme, is shown schematically in Fig. 2. The instantaneous active power shown in Fig. 1 is measured at the three-phase intersection with the grid, shown in green, without the use of the PSS system on the DC bus. The inputs to the system are a time series of the expected turbine rotational rate and control torque, derived from experimental measurements [13].

The proposed PSS is the combination of an LC filter and a bi-directional DC-DC converter utilizing Proportional-Integral (PI) current control. The LC filter (PSS Part I) is sized to smooth rapidly switching current on the DC bus arising from the motor drive control system which regulates turbine rotation. The LC filter attenuates high-frequency fluctuations (>20 kHz) in DC bus current and yields low-frequency, low-amplitude current (

#### 2.1 System design

The cut-off frequency of the low pass filter in PSS Part I is given by,

$$\begin

where \(L_1\) is inductance and \(C_1\) is capacitance. This attenuates frequencies above \(f_\) at 20 dB/decade. The capacitor size is a function of the cycle-average energy *E* produced from the turbine and voltage *V* across \(C_1\) , given by

$$\begin

To achieve a desired cut-off frequency, maximizing \(C_1\) and minimizing \(L_1\) reduces equivalent series resistance (ESR) in the circuit. A large capacitor has the added benefit of stabilizing the voltage input to the motor drive, but this must be balanced against relatively high component cost [22].

Part II of the power smoothing system takes the low-frequency filtered current from Part I and removes residual fluctuations such that power output to the grid is constant in time. This is achieved by a bi-directional DC-DC converter, where the inductor and capacitor ( \(L_\) and \(C_\) ) serve as short-term energy storage components. The synchronous switches ( \(Q_1\) and \(Q_2\) ) of the power converter are controlled at the switching frequency by the duty cycle *D*, the active input to this part of the PSS. The duty cycle determines the percentage of time over the switching period the top switch is on and storing energy in \(L_1\) and \(C_1\) . For the remainder of the switching period (1-*D*), the bottom switch is on and energy is released from \(L_1\) and \(C_1\) . A closed-loop PI controller is used to calculate *D* in real time.

The approach to regulating duty cycle is shown in Fig. 3, which was adapted from a system for smoothing power draw by a machine tool [23]. First, measurements of \(I_\) and \(V_\) (Fig. 3, bottom center) are used to calculate the instantaneous power \(P_\) on the DC bus. A digital low pass filter (LPF) estimates the running-average power, \(<\overline

>_\) — the desired constant power output from the DC-DC converter. The difference between average and instantaneous power \(P_\) must be handled by the PSS. The quotient of \(P_\) and the capacitor voltage \(V_\) gives the current to be demanded through the inductor, \(I_\) . Mathematically, this is given as

\(I_\) is compared to the measured inductor current \(I_\) , and the difference between the two is the PI controller’s error metric *e*.

The duty cycle, *D*, is given as

where \(k_p\) and \(k_i\) are the proportional and integral gains, respectively. *D* is used to synchronously control the two switches in the buck-boost converter, thus controlling the dynamics of the “plant” (i.e., physical system), simplified as a transfer function *G*(*s*) in Fig. 3.

#### 2.2 Controller performance

Controller gains must be selected to achieve the desired combination of system bandwidth and stability. Controller gains \(k_p\) and \(k_i\) are calculated using the complementary sensitivity function, *T*(*s*), defined in terms of an open loop transfer function *l*(*s*) [24] as

$$\begin

*l*(*s*) is defined using \(G_(s)\) , a transfer function relating current to voltage across \(L_2\) (including its equivalent series resistance \(R_\) ), and \(G_c(s)\) , the PI controller transfer function. This can be expressed as

$$\begin

*T*(*s*) is equated to a canonical second-order system,

$$\begin

characterized by controller damping ratio \(\xi\) and controller bandwidth \(\omega _o\) . By equating Eqns. (5) and (7), \(k_p\) and \(k_i\) are calculated as

$$\begin

$$\begin

For this system, controller bandwidth is chosen as 500 rad/s (10x the cycle-averaged blade pass frequency of the turbine) and damping ratio as 0.4, resulting in a \(k_p\) of 2.3 \(\Omega\) and \(k_i\) of 2500 \(H/s^2\) . This damping ratio is a typical value chosen to limit percent overshoot ( \(\%OS\) ) of the closed-loop step response to 25%, based on the relationship

$$\begin

To analyze controller stability, performance, and robustness before implementing in hardware, a linearized model of the closed-loop buck-boost converter and controller is created. This model is a useful tool for quickly iterating on controller design and component parameters and for quantifying controller performance by observing its time-domain and frequency-domain response. It requires less computational power (and therefore has a faster run time) than a simulation of the full circuit (Section 2.4), capturing dominant low-frequency dynamics while neglecting high-frequency switching pres-ent in a real system or higher-order simulation.

The linearized model uses a state space representation of the buck-boost converter comprising PSS Part II (highlighted in blue in Fig. 2) based on the two possible converter states (i.e., \(Q_1\) off and \(Q_2\) on, and vice versa), which is dependent on the system input, duty cycle *D*. The state space system is defined as

$$\begin

with the state variable *x*

$$\begin

A transfer function, utilized to simplify representation of the plant dynamics, is obtained as

$$\begin

The block diagram of the closed-loop control system, consisting of the buck-boost converter and PI controller, is highlighted in yellow in Fig. 3. A transfer function modeling this closed-loop system is given by the complementary sensitivity function, with the open loop transfer function *l*(*s*) defined as the product of the plant *G*(*s*) and the controller \(G_c(s)\) transfer functions. The step response for the linearized model is compared to a full system simulation (Section 2.4) of the same circuit in Fig. 4. Both the linearized model and full system model use component parameters \(L_2\) (and its ESR), \(C_2\) , and \(V_\) as listed in Table 1. The step response of the two models are in close agreement, suggesting that the linearized model is a good representation of the full, non-linear simulation on a switch cycle-averaged basis.

The linearized model can be used to assess system stability, robustness, and bandwidth by observing its frequency domain response [25]. A bode plot of the open loop system transfer function *l*(*s*), sensitivity function *S*(*s*), and the complementary sensitivity function *T*(*s*) is given in Fig. 5. *S*(*s*) is defined as

$$\begin

*S*(*s*) shows a small magnitude response at low frequencies ( \(\omega < 10^2~\mathrm \) ), meaning the controller will drive error close to zero in this region, forcing the output inductor current to closely track the desired reference. Meanwhile, *T*(*s*) shows a magnitude response drop-off at high frequencies ( \(\omega > 10^4~\mathrm \) ), resulting in desirable measurement noise attenuation in this region. The gain crossover frequency, or the point where *T*(*s*) and *S*(*s*) cross, is equivalent to the bandwidth of the controller. This bandwidth is \(20×10^3~\mathrm \) , indicating that the system should have no difficulty smoothing power from a turbine operating with a blade-pass frequency on the order of 10 rad/s.

Robustness relates to how much model uncertainty the system can sustain before going unstable. The true system will have parameters that are slightly different than the model; for example, inductor and capacitor values typically have ±20% tolerance. If the system is not robust, these differences could push the real system to instability even though it is theoretically stable. Robustness can be evaluated on the basis of the maximum value of the frequency response of the sensitivity function. A relatively large peak at approximately the gain crossover frequency is an indicator of a non-robust system. As shown in Fig. 5, there is no peak and the maximum value of the sensitivity function is \(\approx\) 1 which indicates that the closed-loop system should tolerate significant changes in parameters without instability. Additionally, the phase margin of the open loop system *l*(*s*) is 87 \(^\circ\) , suggesting that there is a high tolerance to time delay in the real system before instability.

This analysis suggests that the controller and DC-DC converter components can achieve the desired combination of stability, robustness, and performance when implemented in hardware.

#### 2.3 Bench-top set-up

The topology used to validate a small-scale version of the PSS (e.g., 10 W average power output) is shown in Fig. 6. The system is an abstraction of the DC bus in Fig. 2, where the turbine, generator, and motor drive are replaced with an equivalent controllable current sou-rce input mimicking turbine electrical power output. The inverter, transformer, and utility grid are emulated by a DC voltage source and a resistive load in parallel. This system is not meant to perfectly emulate a grid-connected turbine; rather it is intended to demonstrate the capability of the PSS.

Time series data for the current source input, \(I_\) , is synthesized from experiment and simulation. First, phase-averaged experimental measurements of rotation rate \(\omega\) and control torque \(\tau\) (equivalent to the electrical torque imposed by a generator [10]) were taken from a laboratory-scale two-bladed turbine operating in a recirculating flume with a mean current velocity of 1 m/s and a turbulence intensity of 1.6%. The turbine has radius of 0.086 m, which is 1:5 scale of the full-scale system described in Section 2.4. A servomotor was used to hold rotational speed constant at a tip-speed ratio of 2.2, which maximized time-average mechanical power. This gives a rotor rotational frequency of 4 Hz and primary oscillation in shaft power at 8 Hz. As the turbulence in the inflow had a dominant frequency \(

Second, the phase-average experimental \(\omega\) and \(\tau\) are used as inputs to the PMSM generator in a simulation of a baseline system (i.e., layout shown in Fig. 2, but without the PSS). Specifically, \(\tau\) is prescribed and \(\omega\) is taken as the reference speed (i.e., commanded speed). In post-processing, the reference speed is compared to the generator speed to verify that the PSS is not affecting turbine hydrodynamic performance. The characteristics of the simulated generator are modeled after a motor sized for laboratory-scale experiments (Parker SM233AL-KPSM). The simulation, implemented in Matlab Simulink, is discussed in further detail in Section 2.4. For the generator, mechanical power input and simulated electrical power output are given by

$$\begin

$$\begin

where \(I_\) is the current produced by the turbine (and observed on the DC bus) and \(V_\) is the constant DC bus voltage. Under constant speed control, \(\omega\) remains steady while phase-varying torque produces a time varying DC bus current to be smoothed by the PSS. Fig. 7 shows the mechanical power input to the simulation \(P_\) and the resulting electrical power \(P_\) observed on the DC bus for one turbine rotation. As the turbine is two-bladed, oscillations in mechanical and electrical power occur twice per rotation.

Detail of the DC bus current, \(I_\) , is shown in Fig. 8. The polarity of current fluctuates rapidly at the rate of the emulated motor drive switching frequency (20 kHz) enacting constant speed control, resulting in a discontinuous waveform with a higher peak-to-average ratio than the turbine mechanical power.

For the benchtop PSS validation, this rapidly fluctuating current is emulated with an arbitrary function generator (Agilent 33220A). An effective current source is realized from the voltage signal output of the function generator \(V_\) using Thẽvenin and Norton circuit equivalents [26]. The voltage source \(V_\) required to produce the desired current input \(I_\) is provided by a high-power operational amplifier, with \(V_\) on the inverting input and a constant voltage source \(V_\) on the non-inverting input. The current input to the system, \(I_\) , is given by

$$\begin

$$\begin

with the resistances, *R*, described in Fig. 9.

The bench-top PSS is shown schematically in Fig. 10 and in implementation in Fig. 11. A summary of all system components and controller parameters is provided in Table 1. Inductor ESRs are measured using a digital multimeter and capacitor values are taken from component data sheets. The DC bus voltage is set at 80 V, consistent with the motor drive selection for this scale of turbine. The cut-off frequency of the PSS Part I LC filter (150 Hz) is 130-times lower than the switching frequency of the input current.

The PSS Part II controller is implemented on a TI TMS320F280049C microcontroller (MPU) and TI C2000 LaunchXL breakout board that has a system clock of 10 ns. A symmetrical triangle carrier at 10 kHz is used for PWM generation, with current ( \(I_\) , \(I_\) ) and voltage ( \(V_\) , \(V_\) ) sampled at the analog-to-digial converter (ADC) pins twice per switch cycle, when the carrier signal is high or low and these measurements are closest to their cycle-averaged value. Measurements of current (LEM LAH 25-NP) and voltage (LEM LV 25-P) on the input and output of the system are acquired by a data acquisition device (NI DAQ 6353) at a sample rate of 250 kHz. Prior to real-time control, the measurements of \(V_\) , \(I_\) , and \(V_\) are digitally low-pass filtered to mitigate effects of sensor noise. Similarly, an LC filter ( \(L_\) and \(C_\) ) is added to the output of the bench-top system to filter high-frequency switching noise introduced by the DC-DC converter. This allows for easier observation of the low-frequency smoothing capabilities of the system and does not affect the performance metrics used for evaluation. This LC filter would not be needed for a grid-integrated system, since power would be fed through an inverter and converter switching noise on the DC bus would not be observed on the grid side.

Table 3 compares experimental and simulated system efficiency and reduction in low-frequency (\) ) while maintaining greater than 99% efficiency. Experimental results show a slightly reduced performance, with a 94.7% reduction in \(P_\) at 89.5% efficiency. The efficiency decrease is primarily attributable to DC-DC converter losses from non-zero switching times. Efficiency across the ten experimental trials is consistent, with a standard deviation of 0.023%. Table 3 shows that PSS Part I does not significantly affect low-frequency oscillations, as expected given the LC filter cut-off frequency of 130 Hz.

A comparison between the reference current, \(I_\) , and measured current, \(I_\) , for the simulation and experiment, is shown in Fig. 13. In simulation, there is almost perfect tracking between the measured and reference current, with an RMS error of 7.1 mA, which is small compared to the current range of 230 mA. In experiment, switch node ringing and noise leads to a larger RMS error of 32.5 mA and contributes to the poorer performance. A higher switching frequency would increase controller response bandwidth and simplify filtering of switching noise, but would also increase switching losses and, therefore, reduce system efficiency.

#### 3.2 Large-scale system

Results of the large-scale PSS simulation for a turbine utilizing intracycle control are shown in Fig. 14. For a baseline simulation without PSS, low-frequency power \(P_\) is initially 7.1 kW per cycle, 7-times larger than the average power generated by the turbine. With the PSS, low-frequency power is reduced by 99.8% with 97.0% efficiency. This means that the inverter, transformer, and transmission line used to connect the DC bus to the utility grid could be rated to significantly lower currents than for a system without the PSS.

The implementation of the PSS on the DC bus does not affect turbine hydrodynamics or its mechanical efficiency. As long as the PSS components are sized appropriately, the DC bus voltage input to the generator will remain steady and the generator will produce or consume electrical current as needed to maintain the commanded turbine speed. In other words, a well-designed PSS should not affect the hydrodynamic performance of turbine. For example, in the full-scale simulation, no deviation between command speed and generator speed is observed with the specified components. However, if components are not sized correctly, generator speed diverges from command speed.

#### 3.3 Extensions to other systems

In laboratory experiments to characterize turbine performance, intracycle fluctuations in \(\tau\) dominate over turbulence. This will not necessarily be the case for a larger turbine operating in a natural environment. Consequently, turbulence may cause larger fluctuations in output power than considered here. However, the overall design of a capacitor-based PSS is well suited to smooth variation in electrical power resulting from turbulence [22], which will be substantially smaller than the intracycle variation (i.e., order of magnitude oscillation within a single rotation).

All our simulations and experiments focus on a two-bladed cross-flow turbine with straight blades. This represents a relatively extreme case for variations in power output. Torque oscillation frequency is proportional to the number of blades and, as the blade count increases, the amplitude of the torque oscillation is also reduced. For turbines with a higher blade count, PSS components could be downsized, as the components from Part II would absorb less energy with each turbine rotation.

Further simplification to the PSS may be possible. For example, an alternative system design could forego the LC filter in Part I and estimate DC bus power, \(P_\) , using measurements on the generator side. In this arrangement, \(P_\) can be estimated using the dot product of back-EMF voltage, \(V_\) , and three phase AC current, \(I_\) , measured on the generator stator windings, given by

where *p* is the number of generator pole pairs, \(\lambda\) is flux linkage, \(\varTheta\) is rotor position, and \(>\) is rotor speed. The power delivered to the grid when simulating the large-scale PSS with this method, which still includes a large input capacitor \(C_\) but does not include \(L_\) , is shown in Fig. 15.

While this approach performs relatively well, the control errors at phases of turbine rotation when instantaneous power changed most rapidly (at \(0^\circ\) and \(180^\circ\) ) contribute to intermittent power draw from the grid. However, this suggests that, as peak-to-average power ratio decreases, an approach that forgoes PSS Part I could be effective. This approach also utilizes existing generator side current and voltage measurements, whereas the full system is entirely self contained on the DC bus.

### 4 Conclusion

Cross-flow turbine design and control schemes used to maximize average power output may produce instantaneous power that, in its raw form, is unsuitable for end-use, particularly in remote communities with weak grids or directly-coupled electric loads. A simple power smoothing system is proposed to transform power on the DC bus with order of magnitude oscillations on time scales of

The proposed two-part system has been shown, in simulation, to reduce low-frequency power oscillations by 98% with negligible efficiency penalty. These results have been validated using a bench-top system, with slightly reduced performance and efficiency arising from switch-node ringing from parasitic inductance, losses from non-zero switching times, and sensor noise — all of which could be mitigated in a commercial design. A larger-scale version is demonstrated in simulation for a turbine utilizing intracycle control, where low-frequency power oscillations are reduced by 99% with 3% power loss.

A limitation to this work is that the experimental validation is for the power input from a small-scale turbine utilizing constant speed control. Future work could include validating the larger-scale version of the system and deploying it in the field on a turbine operating with a more complex intracycle control scheme. Such a system could employ improved circuit design practices to mitigate the implementation issues identified at small-scale and achieve efficiencies closer to those predicted by simulation.

### Data availability

The supporting data are available from the corresponding author upon reasonable request.

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### Funding

This work is supported by the U.S. Department of Defense Naval Facilities Engineering Command.

### Author information

- Hannah Aaronson Present address: Tesla, Inc., Palo Alto, CA, USA

#### Authors and Affiliations

- Department of Mechanical Engineering, University of Washington, Seattle, WA, USA Hannah Aaronson & Brian Polagye
- Department of Electrical and Computer Engineering, University of Washington, Seattle, WA, USA Brian Johnson
- Pacific Northwest National Laboratory, Sequim, WA, USA Robert J. Cavagnaro
- Applied Physics Lab, University of Washington, Seattle, WA, USA Robert J. Cavagnaro

- Hannah Aaronson