OPTIMIZATION OF SOLAR PV SMOOTHING ALGORITHMS FOR REDUCEDSTRESS ON A UTILITY-SCALE BATTERY ENERGY STORAGE SYSTEM

W. Greenwood1, O. Lavrova2, A. Mammoli1, F. Cheng2, S. Willard31Department of Mechanical Engineering, 2Department of Electrical and Computer Engineering

University of New Mexico, Albuquerque, New Mexico 871313Public Service Company of New Mexico (PNM)

With the increase in grid-tied utility-scale solar PV energy production, there is a growing concern for dis-tributed power variability due to high-frequency intermittency caused by clouds and other atmospheric ob-structions. Using battery energy storage, power can be “smoothed” before being dispatched to the grid bycalculating the smoothed profile of the raw power, then charging or discharging storage to achieve all or partof this difference in profile. There are many algorithms for calculating the smoothed profile, each providingvarying smoothing quality in terms of ramp rate reduction and battery stress which shortens the lifespancausing increased system O&M costs. In this analysis, modeled system behaviors using three smoothing al-gorithms, including one which simulates a short-term power forecast, are compared for battery stress underequivalent ramp rate reduction performance. Results show that battery stress is most significantly reducedwhen using a centered moving average algorithm which utilizes the short-term prediction.

Keywords: optimization, PV, smoothing, battery storage

INTRODUCTION

Grid-tied utility-scale solar photovoltaic (PV)distributed energy production is becoming moreprevalent thanks to increasing affordability andimproved performance of equipment. While thisprovides many benefits regarding sustainabilityand future grid structure, it creates new chal-lenges for power quality regulation. PV powercan change nearly instantaneously due to passingscattered clouds and other atmospheric obstruc-tions. Large fluctuations in grid power can disruptdistribution by causing flicker and overall incon-sistent power which can lead to penalties againstutility companies. Currently, changes in powerare typically mitigated with the use of load tapchanger (LTC) operations which keep an accept-able range of voltage. However, the increase indistributed PV power generation introduces moreinstances where an LTC operation is required, thusinflicting more wear on the equipment and possi-bly increasing O&M and equipment replacementcosts.

High-frequency intermittency can also be ad-dressed on-site with generation through smoothingwhich involves using fast-response energy storageto dampen severe power ramps before electricityis dispatched onto the grid [1]. This is done bycalculating the smoothed profile of the raw PV

power, then charging or discharging storage ap-propriately to achieve all or part of this differencein profile. There are many algorithms for cal-culating this smoothed profile and they providevarying quality of smoothing in terms of ramprate (change in power) reduction, stress on en-ergy storage, and system requirements for makingthe calculation. In the case of a battery energystorage system (BESS), increased stress shortensthe lifespan leading to increased system O&Mand replacement costs. The goal of this analysisis to determine which of three different smooth-ing algorithms inflicts minimal BESS stress whileproviding equivalent smoothing performance, thusoptimizing the batteries’ longevity. Knowing this,one can tailor algorithm operation parameters toprovide the desired reduction of ramp rates.

This analysis was performed using, in part, his-torical power data (before and after smoothing)from the Prosperity Energy Storage Project nearMesa del Sol in Albuquerque, New Mexico shownin figure 1 [2]. This DOE/ARRA funded SMARTGrid Storage Project is investigating large-scalegrid-tied PV energy production with utility-scalebattery storage capable of simultaneous load shift-ing and smoothing [3]. The pre-smoothing (raw)power data were used to numerically model thetheoretical power output which was then calibratedto the Prosperity’s historical post-smoothing pri-

1

mary meter (PM) power data.

Figure 1: Prosperity Energy Storage Project near Mesadel Sol in Albuquerque, New Mexico whichhas 500kW PV capacity with BESS capableof simultaneous shifting and smoothing.

The numerical model used for this analy-sis was produced by modifying a model usedby Sandia National Laboratories for an unrelatedstudy [4]. The modifications included introducinga third algorithm which simulates a perfect short-term solar power forecast. Running each algorithmfor the project’s one-second temporal resolutionPV power data, theoretical ramp rate distributionsand BESS usage characteristics are compared sideby side for algorithms using a low pass filter, lag-ging moving average, or centered moving average(simulating a short-term solar forecast). Prior toalgorithm comparison, parameters such as dead-band and system response delays are calibrated toadequately reproduce historical output data fromthe Prosperity Site for days using either laggingmoving average or low pass filter real-time.

THEORY

Algorithms

The first step to apply PV power smooth-ing is to determine a goal output power valuewhich closely follows solar resource while remov-ing high-frequency intermittency. The differencebetween the smooth profile and raw power arethen mitigated by the BESS to achieve the desiredoutput. The smooth profile is calculated basedon a span of real-time raw PV power data. Twocommon algorithms for calculating this smooth-ing profile are a moving average (MA) and lowpass filter (LPF). A moving average is the mean

of all data within a user-determined time window(tw) either immediately before (lagging) or around(centered) the current time stamp. A LPF is ameans of removing variability at frequencies be-low the cut-off frequency represented by the timeconstant (tc). Example smoothed profiles resultingfrom the lagging MA, centered MA and LPF basedon real data are shown in figure 2.

Figure 2: Model smoothed power profiles by whichbattery operation is determined; note charac-teristics in different algorithms.

The lagging MA has the advantage of utilizingonly known past data but exhibits a delay in pro-file causing larger differences in raw and desiredpower. The LPF offers a seemingly flatter pro-file but also creates some considerable differenceswhich the battery storage would need to mitigate.A centered MA yields a profile which best followsthe real-time power, however this method requiresknowledge of future power obtained from a short-term forecast. In this study actual data is usedto simulate a forecast even though a real forecastwould have a degree of error. Regardless, this pro-vides a means to evaluate the potential for short-term forecasting to reduce battery stress.

Applied Smoothing

In real world application smoothing is imper-fect causing the net output to maintain some vari-ability greater than that of the smooth profile. Thiscan be due to unintentional factors such as controlsystem or battery response delays which can mag-nify power ramps if there is a sudden ramp in theopposite direction from the previous time stamp.

2

Net output can also deviate unintentionally due toload at the power station as required by heating orcooling causing ramps outside of the algorithm’svisibility. Lastly, unforeseen ramps can be intro-duced after applied smoothing when the power,which is smoothed at residential/commercial volt-age (e.g. 480 V), is passed through the step-uptransformer to transmission voltage levels (e.g.12.47 kV). This effect was experienced during thisanalysis and addressed by utilizing data only frommeters on the low side of the transformer.

Deviation can also be user controlled in anattempt to prevent unnecessary battery use whilemaintaining desired smoothing quality. A dead-band is a ramp rate value below which smoothingwill not be applied because the ramp is deemed notsignificant enough to justify mitigation. For theProsperity Site a 20 kW deadband is utilized andthus used for the algorithms tested here. Likewise,though algorithms tested in this study attempt tosmooth 100% of power ramps, smoothing can beapplied to mitigate a percentage of ramps as longas output is satisfactory. Perhaps the simplest wayto control smoothing quality is to adjust the MA’stime window or LPF’s time constant. Increasingthese values produce a flatter goal power profilebut also increases BESS use. These factors in ap-plied smoothing yield a smoothed output power asshown in figure 3 for the profiles shown previouslyin figure 2.

Figure 3: Model smoothed power with applied smooth-ing characteristics caused by system delaysand smoothing deadband.

Though there are many factors affecting

smoothing quality, the goal in this study was toestablish equality among the algorithms which isshown by ramp rate distribution, mean ramp rates,and 99th percentile ramp rates. All ramp rateswere calculated using an absolute value two-pointbackwards difference. This allows comparison tobe made with regards to battery stress which is rep-resented by the running total of displaced energyand frequency response figures. The end-of-daytotal displaced energy values for each algorithmare then compared to quantify usage.

RESULTS

Ramp Rate Reduction

Matching the model’s user-defined parametersto those used at the Prosperity Site, sufficientlyequivalent smoothing quality was exhibited amongthe three algorithms. The ramp rate distributionin figure 4 shows the three algorithms to be visu-ally identical and this behavior was found to beconsistent for all data sets evaluated. The distribu-tion shown is zoomed to a window which removeslower ramps in order to increase high-magnituderamp visibility though distributions overlapped atlower ramps as well.

Figure 4: Distribution of ramp rates for historical andalgorithm power signals; looking for equiva-lent performance among algorithms.

Note that historical smoothed power data ex-perienced worse ramps after smoothing. This isattributed to noise introduced by the step-up trans-former as mentioned in the theory section. Themean ramp rate for each data set shown in this fig-ure is shown in table 1.

3

Table 1: Mean ramp rates for net outputs modeled using1/3/12 data set; note roughly equivalent valuesamong algorithms.

Algorithm Mean Ramp Rate (W/s)Lagging MA 508.62Cenetered MA 513.29LPF 508.20

Among the algorithms, the mean ramp ratesare sufficiently close to each other to establishequality. However, the centered MA would sug-gest a slightly higher quantity of maximum ramprates. To quantify this higher-magnitude ramprate probability, the 99th percentile ramp rates areshown in table 2. Again the algorithms’ valuesshow roughly equivalent smoothing quality.

Table 2: 99th percentile ramp rates for net outputs mod-eled using 1/3/12 data set; note roughly equiv-alent values among algorithms; equality con-sistent for all data sets.

Algorithm Ramp Rate (kW/s)Lagging MA 4.00Cenetered MA 4.04LPF 4.00

BESS Stress: Energy Displacement

With equivalent smoothing quality established,the algorithms can be compared based on batterystress. This is first presented by a running sumof energy displaced (charged or discharged) by theBESS to smooth the historic raw PV power sig-nal from three different data sets. These days hadvarying degrees of intermittency as shown by themaximum and mean raw PV ramp rates listed intable 3.

Table 3: Maximum and mean raw PV power ramp ratesfor time periods used for analysis.

Date (M/D/Y)Max RampRate (kW/s)

Mean RampRate (kW/s)

1/3/12 10.19 0.502/11/13 47.28 2.7512/18/12 87.10 1.22

The first of these data sets (1/3/12) experiencedthe lowest magnitude maximum ramp and leastsustained variability as seen from the mean ramprate. It also showed the greatest contrast in perfor-mance among the algorithms with respect to en-ergy displaced as shown in figure 5.

Figure 5: Running sum energy dispatched by BESS asresult of smoothing for a moderately intermit-tent time period (1/3/12).

The next data set (2/11/13) experienced a mid-range maximum ramp rate but significantly moresustained variability. In figure 6 note the reducedadvantage of any algorithm over another. Thecentered MA still exhibits better performance butit’s margin is greatly reduced due to the sustainedhigher-magnitude variability. Despite the reduc-tion, the advantage is still significant and couldtranslate into long-term reduced BESS wear andO&M costs.

Figure 6: Running sum energy dispatched by BESS asresult of smoothing for a highly intermittenttime period; note reduced advantage of anyalgorithm over another (2/11/13).

The final data set (12/18/12) experienced the

4

highest magnitude maximum ramp rate but lackedthe sustained variability experienced during the2/11/13 data set. However, it’s energy displace-ment curves reinforce the results shown in figure 5showing a slight advantage of lagging MA overLPF. This behavior is repeated in figure 7 and,again, the centered MA performs best overall.

Figure 7: Running sum energy dispatched by BESS asresult of smoothing for a highly intermittenttime period (12/18/12).

Visually, these three data sets provide impres-sions for each algorithms behavior. To aid in draw-ing conclusions, the end total displaced energy bythe BESS using each algorithm and the percentagewith respect to the worst performing algorithm arealso displayed. First consider table 4 which showsthe totals for the 1/3/12 data set.

Table 4: BESS energy displaced and percent of worstcase for each algorithm during 1/3/12 data set;worst case shows 100%.

AlgorithmDisp. Energy(kWh)

Percent ofWorst Case

Lagging MA 89.75 83.51Cenetered MA 43.14 40.13LPF 107.48 100

As with figure 5, the numerical results for1/3/12 show the potential for the centered MAwhich displaced 40% of the energy that the worstcase did. Even though the centered MA’s percent-age increases with increased intermittency, thisoutcome is still noteworthy. This sort of intermit-tency may be the most common in particular cli-mates. Low to moderate intermittency would also

be more common for either higher-capacity PVarrays which have a larger footprint or dispersedsmaller arrays because they would experience ge-ographic smoothing [5, 6]. Either case would leadto larger BESS stress savings which would betterjustify increased investment costs for forecastingequipment and technology.

The numerical results for the 2/11/13 data setreveal an outcome not apparent in figure 6. Thetotal displaced energy was largest for the laggingMA closely followed by the LPF. This 0.8% dif-ference may be interpreted as negligible, thus re-sulting in equivalent performance, but testing ofnew data sets may reveal this outcome to be sig-nificant. The centered MA, though not as advanta-geous as before, provides a 14% energy displace-ment reduction.

Table 5: BESS energy displaced and percent of worstcase for each algorithm during 2/11/13 dataset; worst case shows 100%.

AlgorithmDisp. Energy(kWh)

Percent ofWorst Case

Lagging MA 142.2 100Cenetered MA 122.4 86.1LPF 141.0 99.2

The final data set (12/18/12) further demon-strates dependency on mean ramp rate as shownin table 6. The LPF inflicted the most stress onthe battery while the lagging and centered MAsfollowed at percentages slightly higher than in ta-ble 4. Based on these three data sets’ totals, thereis a definite dependancy on mean ramp rate as op-posed to maximum ramp rate.

Table 6: BESS energy displaced and percent of worstcase for each algorithm during 12/18/12 dataset; worst case shows 100%.

AlgorithmDisp. Energy(kWh)

Percent ofWorst Case

Lagging MA 312.5 88.2Cenetered MA 245.6 69.4LPF 354.3 100

BESS Stress: Frequency Response

Total energy displacement provides insightinto charge/discharge cycles experienced by theBESS, but stress is also caused by rate of change

5

and frequency of power flow in and out of the bat-teries. The frequency response plots of ramp ratesare useful to visualize smoothing quality, but itcan also used here to show BESS activity. Fig-ure 8 shows the frequency response of the historicbattery activity data and battery activity resultingfrom the three algorithms for the 1/3/12 data set.

Figure 8: Frequency response of historic and modelbattery activity as a result of smoothing.

The figures exhibit similar magnitude to histor-ical data. The lagging MA, particularly, correlateswell which is to be expected because the histori-cal data set from 1/3/12 utilized the lagging MAsmoothing algorithm. Deviation exists at higherfrequencies which can be attributed to the noiseintroduced by system delays and the step-up trans-former.

Comparing the three algorithms, the frequencyresponse suggests reduced high-frequency activityfor the centered MA. This is represented in the farright area of the frequency response curve whichlands at a magnitude of 10−6 kW for the centeredMA whereas the lagging MA and LPF land at oraround 10−5 kW.

CONCLUSIONS

Current results suggest that a centered mov-ing average algorithm utilizing a short-term solarforecast provides an advantage over a conven-tional lagging moving average or low-pass filterdue to significantly reduced stress on the batter-

ies for roughly equivalent reduction in ramp rates.Though the simulated forecast used actual datawhich would correlate to a perfect forecast, theresults still show the potential for PV power fore-casts to optimize the benefits of PV power pro-duction with battery energy storage. Modern solarforecasting methods, however, are still under de-velopment and require added system investmentssuch as ground imagery equipment and calibra-tion.

Between conventional methods, some resultsshow lagging moving average to be slightly lessbattery-intensive for, again, comparable smooth-ing quality. This apparently superior performancemay be dependent on the type of intermittency asis evident in figure 5 where the lagging moving av-erage and low pass filter curves cross over at onepoint. Moreover, the advantage of any algorithmover another is highly dependant on the degree ofvariability experienced. This is apparent by thecurves’ positions relative to each from figure 5 tofigure 6.

FUTURE WORK

Currently there are many ways in which thiswork could be improved to provide higher valueconclusions. For example, results show signifi-cantly better performance in terms of battery stresswhen using a short-term power forecast. However,these results were obtained using actual data whichcorrelate to a perfect forecast. For a more plausi-ble performance comparison, this analysis couldincorporate error into the forecasted power data tothen be used in the centered MA. Alternatively, anactual short-term forecast could be implementedif resources are available. Methods for short-termpower forecasting currently in development areshowing promise to provide useful results [7].

Another means of improvement could be rep-resenting smoothing quality in terms of numberof utility ramp rate violations. Presently, there isno formally stated ramp rate magnitude warrant-ing legal or financial repercussions in the conti-nental United States though increased distributionof PV power generation will likely prompt one inthe future. For the purposes of this study the re-quirements could be adopted as published by thePuerto Rico Electric Power Authority (PREPA)which limits ramps to 10% of plant capacity perminute [8]. This is lower frequency than the pri-

6

mary concern of this analysis but may provide areal-world metric by which the algorithm can bemeasured. Lastly, smoothing quality can be evalu-ated by number of LTC operations due to net out-put ramp rates. This is useful because it representsa real concern for increased wear on utility equip-ment leading to added O&M costs.

References

[1] Thomas D Hund, Sigifredo Gonzalez, andKeith Barrett. Grid-tied pv system en-ergy smoothing. In Photovoltaic SpecialistsConference (PVSC), 2010 35th IEEE, pages002762–002766. IEEE, 2010.

[2] Public service company of new mexico(pnm) prosperity energy storage project.http://www.pnm.com/systems/docs/prosperity_energy_storage_factsheet2013.pdf, 2013.

[3] Feng Cheng, Steve Willard, JonathanHawkins, Brian Arellano, Olga Lavrova,and Andrea Mammoli. Applying batteryenergy storage to enhance the benefits ofphotovoltaics. In Energytech, 2012 IEEE,pages 1–5. IEEE, 2012.

[4] Jay Johnson, Abraham Ellis, Atsushi Denda,Kimio Morino, Takao Shinji, Takao Ogata,and Masayuki Tadokoro. Pv output smoothingusing a battery and natural gas-engine genera-tor. Technical report, Sandia National Labora-tories (SNL-NM), Albuquerque, NM (UnitedStates), 2013.

[5] M Sengupta. Measurement and modeling ofsolar and pv output variability. In Proc. Solar,2011.

[6] Matthew Lave, Jan Kleissl, and Ery Arias-Castro. High-frequency irradiance fluctua-tions and geographic smoothing. Solar En-ergy, 86(8):2190–2199, 2012.

[7] Chi Wai Chow, Bryan Urquhart, MatthewLave, Anthony Dominguez, Jan Kleissl, JanetShields, and Byron Washom. Intra-hour fore-casting with a total sky imager at the uc sandiego solar energy testbed. Solar Energy,85(11):2881–2893, 2011.

[8] Matthew Lave and Jan Kleissl. Cloud speedimpact on solar variability scaling–applicationto the wavelet variability model. Solar Energy,91:11–21, 2013.

7