Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver...
Transcript of Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver...
![Page 1: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/1.jpg)
Optimization Based Microgrid and DER Modelling: Introduction to XENDEE MAE/CER Energy Seminars University of California at San Diego, 30 Oct 2019 Xendee.com Michael Stadler, PhD; Zack Pecenak, PhD [email protected]; [email protected]
![Page 2: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/2.jpg)
San Diego based software and research focused company
Slide 2
Team of 14 with 1/3 in research and engineering Adib Nasle, Scott Mitchell, Michael Stadler, Alan Zhang, Zachary K. Pecenak, Patrick Mathiesen, Jisun Lee, Kelsey Taylor Fahy, Rich Goldman, Jaime Rios, Margit Temper, Andrea Ruotolo, Tristan Jackson, Nathan Johnson
Some of our partners and clients
![Page 3: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/3.jpg)
A bit about myself
Chief Technology Officer of XENDEE Corporation since August 2017 Area head of the Microgrid and Smartgrid department at Bioenergy2020+ in Austria,
currently Senior Scientific Advisor - March 2017 to December 2018 Lawrence Berkeley National Laboratory at the University of California Berkeley 2005 –
2016 • Staff Scientist and lead of Grid Integration Group with 40 scientists and students • Presidential Award from the White House for the economic optimization engine
within XENDEE (DER-CAM) 2013/2016 240 publications, 9 copyrights, H-index 30 leading the design, implementation, and operation of the first Austrian Microgrid
testbed https://www.linkedin.com/in/StadlerMichael
https://scholar.google.com/citations?user=MHJVYuIAAAAJ&hl=en
Michael Stadler, PhD, MS
Slide 3
![Page 4: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/4.jpg)
1) Microgrid and DER commercial state
2) Introduction to DER-CAM
3) Research and improvements on DER-CAM 1) Impact of down sampling input data 2) Multiyear optimization approaches 3) Ancillary service modeling (backup slides)
4) Conclusion
Talk overview
Slide 4
![Page 5: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/5.jpg)
Microgrid and DER Background A.K.A. Why are we here today?
Slide 5
![Page 6: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/6.jpg)
What is a Microgrid? Smartgrid ≠ Microgrid
Slide 6
![Page 7: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/7.jpg)
Growing market
Slide 7
![Page 8: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/8.jpg)
• Utility bills in excess of $45M/year just for electricity
• On average 8 power outages every year • Each outage costs $2.7M
• 170 MT of CO2 emissions
• Internal distribution services over 20 nodes
• Want to improve : • cost • reliability • carbon footprint • system operations
Nutrien Potash plant
Slide 8
![Page 9: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/9.jpg)
To model such cases: Need to consider 1. customer operation 2. physical and financial constraints 3. physical circuit 4. DER costs and characteristics 5. local climate
Most use a combination of complex spreadsheets with bulk approximations of the real system and multiple power design tools
Typically takes 12-18 months and several engineers
Nutrien Potash plant
Slide 9
![Page 10: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/10.jpg)
How to compare alternatives quickly (in weeks and not months)?
Net Present Value? Internal Rate
Return? Emissions?
Grid health? Etc.
Need for a standardized approach
Slide 10
![Page 11: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/11.jpg)
XENDEE to the rescue
XENDEE aims to be an end-to-end, standardized solution to microgrid design and implementation
Research to develop a state of the art Microgrid investment and decision making platform
Four core technologies - All in one platform Security constrained economic optimization based on the Distributed Energy Resources Customer Adoption Model (DER-CAM) from Berkeley Lab Power systems analysis engine based on EPRI‘s OpenDSS Transient stability framework based on XENDEE‘s own transient solver Implementation management based on XENDEE‘s own Project Management Tool
Slide 11
![Page 12: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/12.jpg)
https://xendee.s3-us-west-2.amazonaws.com/videos/WikiMovies/Website+Intro+Vid+_+Final+_+BW+Text.mp4
Microgrid and DER deployment in one platform
Slide 12
![Page 13: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/13.jpg)
Introduction to DER-CAM How XENDEE optimizes the DER selection in a Microgrid
Slide 13
![Page 14: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/14.jpg)
• Continuous development since 2000
• 300+ publications about or using model
• Millions in cumulative funding • XENDEE only professional
entity developing DER-CAM further
• More than 80 revisions and features of XENDEE version
The Distributed Energy Resources Customer Adoption Model
Slide 14
![Page 15: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/15.jpg)
Complexity of energy flows
Slide 15
![Page 16: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/16.jpg)
Simplified objective function min 𝑐 = 𝑐tariff + 𝑐fuel + 𝑐carbon + 𝑐invest + 𝑐O&M − 𝑟sales
Subject to
Energy balance 𝐷𝑚,𝑑,ℎ + 𝐿𝑚,𝑑,ℎ = Σ𝑡𝐺𝑡,𝑚,𝑑,ℎ + 𝑃𝑚,𝑑,ℎ
Payback constraint 𝐴𝑛𝑛𝑢𝑎𝑙𝑆𝑎𝑣𝑖𝑛𝑔𝑠
𝑇𝑜𝑡𝑎𝑙𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡≤ 𝑀𝑎𝑥𝑃𝑎𝑦𝑏𝑎𝑐𝑘𝑌𝑒𝑎𝑟𝑠 *Does not show all constraints
In total there are over 230,000 equations solved in the model
DER-CAM minimizes the objective considering a typical operational year, where amortized investment costs are balanced with operational
costs
Where: 𝑐 = Total Annual Cost 𝑟 = Revenue 𝑚 = Month (typically 12) 𝑑 = Day (typically 30) ℎ = Hour (typically 24) 𝑡 = Technology
𝐷 = Demand 𝐿 = Losses 𝐺 = Generation 𝑃 = Purchases
Mixed Integer Linearized formulation ≠ simulations
Slide 16
![Page 17: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/17.jpg)
Indices can be manipulated for different scenarios: Example: 𝐷𝑒𝑚𝑎𝑛𝑑𝑚,𝑑,ℎ
• m,d,h represent months, days, and hours • Can add indices for minutes, seconds, or
years
More indices increase search space of solutions
Increases computational time non-linearly
Can down-sample indices to reduce complexity
• DER-CAM down-samples days into 3 representative day types
• Impact discussed in later slides
We solve d=3 “representative” days each month 1. Peak demand day 2. Week day 3. Weekend day
Impact of optimization indices on runtime
Slide 17
![Page 18: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/18.jpg)
Dispatch is solved using operational planning constraints, mimics microgrid controller
DER are selected to minimize total cost considering each timestep and optimized dispatch
Coupled unit commitment and investment decision
Slide 18
![Page 19: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/19.jpg)
Such modeling provides detailed financials
Slide 19
![Page 20: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/20.jpg)
The impact of down-sampling data How does using three daytypes impact accuracy of optimization?
Slide 20
![Page 21: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/21.jpg)
COMPUTATIONALLY INTRACTABLE
Prohibitive computational time
REPRESENTATIVE DEMAND PROFILES
One minute One hour One day
Need for “daytype” down-sampling
Slide 21
![Page 22: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/22.jpg)
Slide 22
Contributions
Quantify impact of down-sampling
Introduce demand data reduction method which captures demand peaks
Validation and comparison against existing data reduction approach
Demonstration of the importance of capturing demand peaks
Two classes of down-sampling tested
XENDEE Peak Preservation (M0, M1, M2, M3, M4, M5)
K-Means Clustering (K1, K2, K3)
Approach
Use full 8760 timestep model as benchmark and compare down sampling approaches
Testing impact of down-sampling
![Page 23: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/23.jpg)
Slide 23
• Peak demand values subtracted from total weekday demand data
• Remaining data averaged
Example: Peak, Weekday, Weekend representative profiles constructed for March
• Peak demand values subtracted from total weekend demand data
• Remaining data averaged
• Total weekend demand data summed • Total weekday demand data summed
XENDEE peak perseveration approach
![Page 24: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/24.jpg)
Slide 24
3 k-means approaches were considered (1-3 centroids)
Allows for comparison of common literature approach
K-means clustering
![Page 25: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/25.jpg)
XENDEE
XENDEE
Methods do not preserve peak
Impact on optimization results
Slide 25
More research ongoing for also islanded Microgrids
Fahy Kelsey, Michael Stadler, Zachary K. Pecenak, and Jan Kleissl, “The Impact of Representative Days on the Precision of Microgrid and DER Modeling,“ Journal of Renewable and Sustainable Energy, ISSN: 1941-7012.
![Page 26: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/26.jpg)
Novel multiyear modeling A new approach to make multiyear modeling feasible and open up business cases
for continued investment
Slide 26
![Page 27: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/27.jpg)
Common use cases
This work is patent pending and published The energy landscape is constantly changing, projects
should be adaptive
When project financials aren’t attractive today Can model when a project should start
Prevention of unnecessary oversizing Most companies significantly oversize for
degradation and factor of safety
Investors need more accuracy over project lifetime to secure capital
Projecting current financials is not sufficient
Slide 27
Multiyear optimization
Pecenak Zachary K., Michael Stadler, Kelsey Fahy, “Efficient Multi-Year Economic Energy Planning in Microgrids,“ Applied Energy Journal by Elsevier, Volume 255, 1 December 2019, ISSN: 0306-2619, https://doi.org/10.1016/j.apenergy.2019.113771
![Page 28: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/28.jpg)
Forward looking approach XENDEE adaptive approach
• Does not change problem formulation
• Solves consecutive single year optimization • Representing different years
• Investments in previous optimizations are considered fixed assets
• Applies a new index ‘𝑦’ to the optimization problem, which represents the year in considerations
• Solves entire horizon in one optimization
Standard DER-CAM formulation
min 𝑐 = Σ𝑦 𝑐tariff𝑦+ 𝑐fuel𝑦 + 𝑐carbon𝑦
+ 𝑐investy + 𝑐O&My
− 𝑟sales𝑦
Subject to
Energy Balance 𝐷𝑦,𝑚,𝑑,ℎ + 𝐿𝑦,𝑚,𝑑,ℎ = Σ𝑡𝐺𝑡,𝑦,𝑚,𝑑,ℎ + 𝑃𝑦,𝑚,𝑑,ℎ
Slide 28
Different approaches to multiyear modeling
![Page 29: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/29.jpg)
• Forward looking approach is unpredictable and can increase runtime by 12000%
• Adaptive approach is linear and predictable
• Both approaches improve over the single year projection
Slide 29
Comparison of approaches
![Page 30: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/30.jpg)
• When considering forecasting error, forward looking approach is dangerous since it assumes foresight for e.g. 25 years
• Making sequential investment decisions with information only is a safer play
Slide 30
Forecast error is impetus for adaptive approach
![Page 31: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/31.jpg)
Slide 31
New business cases for continuous investments
![Page 32: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/32.jpg)
Conclusions What did we discuss?
Slide 32
![Page 33: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/33.jpg)
Summary • There is a market need for
smart decision making tool
• DER-CAM is a flexible optimization framework
• XENDEE has researched a number of improvements
• Impact of data down-sampling
• Multiyear method
• Ancillary services
• Stochastic behavior • Outages • Solar/wind potential
• Sub hourly optimization time-scales
• Variable equipment lifetimes
• Fast 8760 optimization
• Much more…
Ongoing work
Slide 33
![Page 34: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/34.jpg)
Slide 34
![Page 35: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/35.jpg)
Ancillary Service Modeling An example of modeling a value stream in XENDEE’s DER-CAM
Slide 35
![Page 36: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/36.jpg)
• Four AS products considered:
– Spinning reserves
– Non-Spinning Reserves
– Up-Regulation
– Down-Regulation
• Key assumptions:
– Building/microgrid is a price taker
– Historic market clearing prices are used
– Bids are won according to user defined ratio (WinRatio)
– Currently only generators and storage systems can provide AS
– Bid is called for delivery according to utilization factor (𝛼)
Ancillary Services (AS) modelling
Slide 36
![Page 37: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/37.jpg)
Generation capacity limits 𝑃𝑔 ≤ 𝐺𝑒𝑛𝑈𝑠𝑒g,m,d,h,e + 𝐺𝑒𝑛𝑆𝑒𝑙𝑙g,m,d,h,e + 𝐺𝑒𝑛𝑅𝑠𝑟𝑣g,m,d,h ≤ 𝑃𝑔
Continuous bid requirements (applies a binary to ensure bid length requirements) Σ𝑔𝐺𝑒𝑛𝑅𝑠𝑟𝑣𝑔,𝑚,𝑑,ℎ ≤ 𝑏𝑖𝑛𝑅𝑠𝑟𝑣𝑚,𝑑,ℎ × MaxBid Σ𝑔𝐺𝑒𝑛𝑅𝑠𝑟𝑣𝑔,𝑚,𝑑,ℎ ≥ 𝑏𝑖𝑛𝑅𝑠𝑟𝑣𝑚,𝑑,ℎ × MinBid
Σℎ 𝑏𝑖𝑛𝑅𝑠𝑟𝑣𝑚,𝑑,ℎ ≥ 𝑏𝑖𝑛𝑅𝑠𝑟𝑣𝑚,𝑑,ℎ − 𝑏𝑖𝑛𝑅𝑠𝑟𝑣𝑚,𝑑,ℎ−1 ∗ MinBidTime ℎ ≡ {ℎ, ℎ + 1,… , ℎ + MinBidTime}
𝑏𝑖𝑛𝑅𝑠𝑟𝑣𝑚,𝑑,ℎ ∈ 0, 1
Revenue from market participation 𝑅𝑒𝑣𝑒𝑛𝑢𝑒𝑅𝑠𝑟𝑣 = Σ𝑚,𝑑,ℎ,𝑔 𝐺𝑒𝑛𝑅𝑠𝑟𝑣𝑔,𝑚,𝑑,ℎ ∗ 𝑀𝑟𝑘𝑡𝑃𝑟𝑖𝑐𝑒𝑚,𝑑,ℎ ∗ WinRatio
0 ≤ winRatio ≤ 1
Cost to participate
𝐹𝑢𝑒𝑙𝐶𝑜𝑠𝑡𝑚,𝑑,ℎ =𝐺𝑒𝑛𝑅𝑠𝑟𝑣𝑔,𝑚,𝑑,ℎ × α
𝜂𝑔∗ FuelCost
𝑂&𝑀𝐶𝑜𝑠𝑡𝑚,𝑑,ℎ = 𝐺𝑒𝑛𝑅𝑠𝑟𝑣𝑔,𝑚,𝑑,ℎ × α ∗ O&MVarCost
Similar equations applied for other markets, as well as storage devices
Modeling spinning reserve with generators
Slide 37
![Page 38: Introduction to XENDEE · Transient stability framework based on XENDEE‘s own transient solver ... method which captures demand peaks Validation and comparison against existing](https://reader034.fdocuments.in/reader034/viewer/2022042513/5fa4b71bcc54e208e97b2814/html5/thumbnails/38.jpg)
Benefits • Value stacking for storage and generator during times where they would traditionally sit idle • Lower O&M costs and longer life, since traditional use periods can be offset with reserve
(stationary) activity and compensated
Can impact investment decisions, making those DER more attractive
Impacts of ancillary reserve participation
Slide 38