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    223. 

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    224. 

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    225. 

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    226. 

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  237. .prompt a.copybtn {
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    240. 

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    273. 

  273. }
    274. 

  274. </style>
    275. 

  275. <div class="section" id="Exploratory-Data-Analysis">
    276. 

  276. <h1>Exploratory Data Analysis<a class="headerlink" href="#Exploratory-Data-Analysis" title="Permalink to this headline">¶</a></h1>
    277. 

  277. <p>The purpose of this notebook is to explore potential relationships and build an intuition about the distribution of curtailment events. Naively, we are looking to find dimensions on which we might cluster or categorize different curtailment events, and to understand any seasonality or time dependence in the data.</p>
    278. 

  278. <div class="nbinput nblast docutils container">
    279. 

  279. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]:
    280. 

  280. </pre></div>
    281. 

  281. </div>
    282. 

  282. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    283. 

  283. <span></span>import pandas as pd
    284. 

  284. import numpy as np
    285. 

  285. import altair as alt
    286. 

  286. 

  287. from src.conf import settings
    288. 

  288. </pre></div>
    289. 

  289. </div>
    290. 

  290. </div>
    291. 

  291. <div class="nbinput docutils container">
    292. 

  292. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[2]:
    293. 

  293. </pre></div>
    294. 

  294. </div>
    295. 

  295. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    296. 

  296. <span></span># Enable Altair to Serve data from disk since we expect to have at least 8760 rows or more
    297. 

  297. alt.data_transformers.enable(&#39;json&#39;)
    298. 

  298. 

  299. # Uncomment if using JupyterLab (see: https://github.com/altair-viz/altair/issues/1867)
    300. 

  300. # alt.data_transformers.enable(&quot;data_server&quot;)
    301. 

  301. </pre></div>
    302. 

  302. </div>
    303. 

  303. </div>
    304. 

  304. <div class="nboutput nblast docutils container">
    305. 

  305. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[2]:
    306. 

  306. </pre></div>
    307. 

  307. </div>
    308. 

  308. <div class="output_area docutils container">
    309. 

  309. <div class="highlight"><pre>
    310. 

  310. DataTransformerRegistry.enable(&#39;json&#39;)
    311. 

  311. </pre></div></div>
    312. 

  312. </div>
    313. 

  313. <div class="nbinput nblast docutils container">
    314. 

  314. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[3]:
    315. 

  315. </pre></div>
    316. 

  316. </div>
    317. 

  317. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    318. 

  318. <span></span>df = pd.concat(
    319. 

  319.     [
    320. 

  320.         pd.read_parquet(fp_) for fp_ in settings.DATA_DIR.glob(&quot;processed/caiso/*.parquet&quot;)
    321. 

  321.     ]
    322. 

  322. ).tz_convert(tz=&quot;US/Pacific&quot;)
    323. 

  323. 

  324. # Single Year for debugging
    325. 

  325. 

  326. # year = 2019
    327. 

  327. # df = pd.read_parquet(settings.DATA_DIR / f&quot;processed/caiso/{year}.parquet&quot;).tz_convert(tz=&quot;US/Pacific&quot;)
    328. 

  328. </pre></div>
    329. 

  329. </div>
    330. 

  330. </div>
    331. 

  331. <div class="nbinput nblast docutils container">
    332. 

  332. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[4]:
    333. 

  333. </pre></div>
    334. 

  334. </div>
    335. 

  335. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    336. 

  336. <span></span>column_map = zip(
    337. 

  337.     df.columns.tolist(),
    338. 

  338.     df.columns.str.replace(&quot;\W+&quot;, &quot;_&quot;).str.lower().tolist()
    339. 

  339. )
    340. 

  340. 

  341. df = df.rename(columns=dict(column_map))
    342. 

  342. </pre></div>
    343. 

  343. </div>
    344. 

  344. </div>
    345. 

  345. <p><strong>Data Dictionary</strong></p>
    346. 

  346. <ul class="simple">
    347. 

  347. <li><p>load (MW): Total demand across the CAISO for a given interval.</p></li>
    348. 

  348. <li><p>solar (MW): Average interval Solar production</p></li>
    349. 

  349. <li><p>wind (MW): Average interval Wind production</p></li>
    350. 

  350. <li><p>net_load (MW): Load - solar - wind</p></li>
    351. 

  351. <li><p>renewables (MW): Average interval production from solar, wind, biomass, biogas, geothermal and small hydropower</p></li>
    352. 

  352. <li><p>nuclear (MW): Average nuclear production</p></li>
    353. 

  353. <li><p>large_hydro (MW): Average large hydro production</p></li>
    354. 

  354. <li><p>imports (MW): Imports coming into the ISO; note that exports are NOT deducted from imports.</p></li>
    355. 

  355. <li><p>generation (MW): Total generation across all generator types</p></li>
    356. 

  356. <li><p>thermal (MW): non-nuclear and non-geothermal thermal production</p></li>
    357. 

  357. <li><p>load_less_generation_imports_ (MW): data validation column to ensure supply ~ demand</p></li>
    358. 

  358. <li><p>wind_curtailment (MW): Curtailed wind in a given interval</p></li>
    359. 

  359. <li><p>solar_curtailment (MW): Curtailed solar in a given interval</p></li>
    360. 

  360. </ul>
    361. 

  361. <div class="nbinput docutils container">
    362. 

  362. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[5]:
    363. 

  363. </pre></div>
    364. 

  364. </div>
    365. 

  365. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    366. 

  366. <span></span>df.head()
    367. 

  367. </pre></div>
    368. 

  368. </div>
    369. 

  369. </div>
    370. 

  370. <div class="nboutput nblast docutils container">
    371. 

  371. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[5]:
    372. 

  372. </pre></div>
    373. 

  373. </div>
    374. 

  374. <div class="output_area rendered_html docutils container">
    375. 

  375. <div>
    376. 

  376. <style scoped>
    377. 

  377.     .dataframe tbody tr th:only-of-type {
    378. 

  378.         vertical-align: middle;
    379. 

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    380. 

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    387. 

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    388. 

  388. </style>
    389. 

  389. <table border="1" class="dataframe">
    390. 

  390.   <thead>
    391. 

  391.     <tr style="text-align: right;">
    392. 

  392.       <th></th>
    393. 

  393.       <th>load</th>
    394. 

  394.       <th>solar</th>
    395. 

  395.       <th>wind</th>
    396. 

  396.       <th>net_load</th>
    397. 

  397.       <th>renewables</th>
    398. 

  398.       <th>nuclear</th>
    399. 

  399.       <th>large_hydro</th>
    400. 

  400.       <th>imports</th>
    401. 

  401.       <th>generation</th>
    402. 

  402.       <th>thermal</th>
    403. 

  403.       <th>load_less_generation_imports_</th>
    404. 

  404.       <th>wind_curtailment</th>
    405. 

  405.       <th>solar_curtailment</th>
    406. 

  406.     </tr>
    407. 

  407.     <tr>
    408. 

  408.       <th>timestamp</th>
    409. 

  409.       <th></th>
    410. 

  410.       <th></th>
    411. 

  411.       <th></th>
    412. 

  412.       <th></th>
    413. 

  413.       <th></th>
    414. 

  414.       <th></th>
    415. 

  415.       <th></th>
    416. 

  416.       <th></th>
    417. 

  417.       <th></th>
    418. 

  418.       <th></th>
    419. 

  419.       <th></th>
    420. 

  420.       <th></th>
    421. 

  421.       <th></th>
    422. 

  422.     </tr>
    423. 

  423.   </thead>
    424. 

  424.   <tbody>
    425. 

  425.     <tr>
    426. 

  426.       <th>2018-01-01 00:00:00-08:00</th>
    427. 

  427.       <td>21552.671558</td>
    428. 

  428.       <td>0.0</td>
    429. 

  429.       <td>243.496014</td>
    430. 

  430.       <td>21309.175544</td>
    431. 

  431.       <td>2032.994475</td>
    432. 

  432.       <td>2259.991374</td>
    433. 

  433.       <td>2098.405092</td>
    434. 

  434.       <td>7586.553984</td>
    435. 

  435.       <td>13964.462727</td>
    436. 

  436.       <td>7573.071786</td>
    437. 

  437.       <td>1.654847</td>
    438. 

  438.       <td>NaN</td>
    439. 

  439.       <td>NaN</td>
    440. 

  440.     </tr>
    441. 

  441.     <tr>
    442. 

  442.       <th>2018-01-01 00:05:00-08:00</th>
    443. 

  443.       <td>21486.779943</td>
    444. 

  444.       <td>0.0</td>
    445. 

  445.       <td>238.499132</td>
    446. 

  446.       <td>21248.280811</td>
    447. 

  447.       <td>2026.481236</td>
    448. 

  448.       <td>2259.952873</td>
    449. 

  449.       <td>2143.557374</td>
    450. 

  450.       <td>7543.249094</td>
    451. 

  451.       <td>13944.799274</td>
    452. 

  452.       <td>7514.807791</td>
    453. 

  453.       <td>-1.268424</td>
    454. 

  454.       <td>NaN</td>
    455. 

  455.       <td>NaN</td>
    456. 

  456.     </tr>
    457. 

  457.     <tr>
    458. 

  458.       <th>2018-01-01 00:10:00-08:00</th>
    459. 

  459.       <td>21391.303108</td>
    460. 

  460.       <td>0.0</td>
    461. 

  461.       <td>227.229805</td>
    462. 

  462.       <td>21164.073304</td>
    463. 

  463.       <td>2014.528291</td>
    464. 

  464.       <td>2259.809808</td>
    465. 

  465.       <td>2130.224136</td>
    466. 

  466.       <td>7666.711084</td>
    467. 

  467.       <td>13727.433629</td>
    468. 

  468.       <td>7322.871394</td>
    469. 

  469.       <td>-2.841604</td>
    470. 

  470.       <td>NaN</td>
    471. 

  471.       <td>NaN</td>
    472. 

  472.     </tr>
    473. 

  473.     <tr>
    474. 

  474.       <th>2018-01-01 00:15:00-08:00</th>
    475. 

  475.       <td>21301.872170</td>
    476. 

  476.       <td>0.0</td>
    477. 

  477.       <td>228.026545</td>
    478. 

  478.       <td>21073.845624</td>
    479. 

  479.       <td>2016.257246</td>
    480. 

  480.       <td>2259.802584</td>
    481. 

  481.       <td>2093.382906</td>
    482. 

  482.       <td>7701.705829</td>
    483. 

  483.       <td>13598.816375</td>
    484. 

  484.       <td>7229.373638</td>
    485. 

  485.       <td>1.349966</td>
    486. 

  486.       <td>NaN</td>
    487. 

  487.       <td>NaN</td>
    488. 

  488.     </tr>
    489. 

  489.     <tr>
    490. 

  490.       <th>2018-01-01 00:20:00-08:00</th>
    491. 

  491.       <td>21242.270230</td>
    492. 

  492.       <td>0.0</td>
    493. 

  493.       <td>232.213448</td>
    494. 

  494.       <td>21010.056782</td>
    495. 

  495.       <td>2024.277588</td>
    496. 

  496.       <td>2260.008342</td>
    497. 

  497.       <td>2160.635742</td>
    498. 

  498.       <td>7677.751619</td>
    499. 

  499.       <td>13560.236628</td>
    500. 

  500.       <td>7115.314955</td>
    501. 

  501.       <td>4.281984</td>
    502. 

  502.       <td>NaN</td>
    503. 

  503.       <td>NaN</td>
    504. 

  504.     </tr>
    505. 

  505.   </tbody>
    506. 

  506. </table>
    507. 

  507. </div></div>
    508. 

  508. </div>
    509. 

  509. <p>Since our interval timeseries are not continuous and complete (i.e. significant irregular gaps exist across years), we must convert this to MWh to get additivity. All columns are in MW at 5 minute intervals.</p>
    510. 

  510. <p>MWh are calculated by taking</p>
    511. 

  511. <p><span class="math notranslate nohighlight">\(MWh = MW 5[min]\frac{1[hour]}{60[min]}\)</span></p>
    512. 

  512. <div class="nbinput docutils container">
    513. 

  513. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[6]:
    514. 

  514. </pre></div>
    515. 

  515. </div>
    516. 

  516. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    517. 

  517. <span></span>df_mwh = df * (5/60.)
    518. 

  518. df_mwh.head()
    519. 

  519. </pre></div>
    520. 

  520. </div>
    521. 

  521. </div>
    522. 

  522. <div class="nboutput nblast docutils container">
    523. 

  523. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[6]:
    524. 

  524. </pre></div>
    525. 

  525. </div>
    526. 

  526. <div class="output_area rendered_html docutils container">
    527. 

  527. <div>
    528. 

  528. <style scoped>
    529. 

  529.     .dataframe tbody tr th:only-of-type {
    530. 

  530.         vertical-align: middle;
    531. 

  531.     }
    532. 

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    534. 

  534.         vertical-align: top;
    535. 

  535.     }
    536. 

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    538. 

  538.         text-align: right;
    539. 

  539.     }
    540. 

  540. </style>
    541. 

  541. <table border="1" class="dataframe">
    542. 

  542.   <thead>
    543. 

  543.     <tr style="text-align: right;">
    544. 

  544.       <th></th>
    545. 

  545.       <th>load</th>
    546. 

  546.       <th>solar</th>
    547. 

  547.       <th>wind</th>
    548. 

  548.       <th>net_load</th>
    549. 

  549.       <th>renewables</th>
    550. 

  550.       <th>nuclear</th>
    551. 

  551.       <th>large_hydro</th>
    552. 

  552.       <th>imports</th>
    553. 

  553.       <th>generation</th>
    554. 

  554.       <th>thermal</th>
    555. 

  555.       <th>load_less_generation_imports_</th>
    556. 

  556.       <th>wind_curtailment</th>
    557. 

  557.       <th>solar_curtailment</th>
    558. 

  558.     </tr>
    559. 

  559.     <tr>
    560. 

  560.       <th>timestamp</th>
    561. 

  561.       <th></th>
    562. 

  562.       <th></th>
    563. 

  563.       <th></th>
    564. 

  564.       <th></th>
    565. 

  565.       <th></th>
    566. 

  566.       <th></th>
    567. 

  567.       <th></th>
    568. 

  568.       <th></th>
    569. 

  569.       <th></th>
    570. 

  570.       <th></th>
    571. 

  571.       <th></th>
    572. 

  572.       <th></th>
    573. 

  573.       <th></th>
    574. 

  574.     </tr>
    575. 

  575.   </thead>
    576. 

  576.   <tbody>
    577. 

  577.     <tr>
    578. 

  578.       <th>2018-01-01 00:00:00-08:00</th>
    579. 

  579.       <td>1796.055963</td>
    580. 

  580.       <td>0.0</td>
    581. 

  581.       <td>20.291334</td>
    582. 

  582.       <td>1775.764629</td>
    583. 

  583.       <td>169.416206</td>
    584. 

  584.       <td>188.332615</td>
    585. 

  585.       <td>174.867091</td>
    586. 

  586.       <td>632.212832</td>
    587. 

  587.       <td>1163.705227</td>
    588. 

  588.       <td>631.089315</td>
    589. 

  589.       <td>0.137904</td>
    590. 

  590.       <td>NaN</td>
    591. 

  591.       <td>NaN</td>
    592. 

  592.     </tr>
    593. 

  593.     <tr>
    594. 

  594.       <th>2018-01-01 00:05:00-08:00</th>
    595. 

  595.       <td>1790.564995</td>
    596. 

  596.       <td>0.0</td>
    597. 

  597.       <td>19.874928</td>
    598. 

  598.       <td>1770.690068</td>
    599. 

  599.       <td>168.873436</td>
    600. 

  600.       <td>188.329406</td>
    601. 

  601.       <td>178.629781</td>
    602. 

  602.       <td>628.604091</td>
    603. 

  603.       <td>1162.066606</td>
    604. 

  604.       <td>626.233983</td>
    605. 

  605.       <td>-0.105702</td>
    606. 

  606.       <td>NaN</td>
    607. 

  607.       <td>NaN</td>
    608. 

  608.     </tr>
    609. 

  609.     <tr>
    610. 

  610.       <th>2018-01-01 00:10:00-08:00</th>
    611. 

  611.       <td>1782.608592</td>
    612. 

  612.       <td>0.0</td>
    613. 

  613.       <td>18.935817</td>
    614. 

  614.       <td>1763.672775</td>
    615. 

  615.       <td>167.877358</td>
    616. 

  616.       <td>188.317484</td>
    617. 

  617.       <td>177.518678</td>
    618. 

  618.       <td>638.892590</td>
    619. 

  619.       <td>1143.952802</td>
    620. 

  620.       <td>610.239283</td>
    621. 

  621.       <td>-0.236800</td>
    622. 

  622.       <td>NaN</td>
    623. 

  623.       <td>NaN</td>
    624. 

  624.     </tr>
    625. 

  625.     <tr>
    626. 

  626.       <th>2018-01-01 00:15:00-08:00</th>
    627. 

  627.       <td>1775.156014</td>
    628. 

  628.       <td>0.0</td>
    629. 

  629.       <td>19.002212</td>
    630. 

  630.       <td>1756.153802</td>
    631. 

  631.       <td>168.021437</td>
    632. 

  632.       <td>188.316882</td>
    633. 

  633.       <td>174.448576</td>
    634. 

  634.       <td>641.808819</td>
    635. 

  635.       <td>1133.234698</td>
    636. 

  636.       <td>602.447803</td>
    637. 

  637.       <td>0.112497</td>
    638. 

  638.       <td>NaN</td>
    639. 

  639.       <td>NaN</td>
    640. 

  640.     </tr>
    641. 

  641.     <tr>
    642. 

  642.       <th>2018-01-01 00:20:00-08:00</th>
    643. 

  643.       <td>1770.189186</td>
    644. 

  644.       <td>0.0</td>
    645. 

  645.       <td>19.351121</td>
    646. 

  646.       <td>1750.838065</td>
    647. 

  647.       <td>168.689799</td>
    648. 

  648.       <td>188.334029</td>
    649. 

  649.       <td>180.052978</td>
    650. 

  650.       <td>639.812635</td>
    651. 

  651.       <td>1130.019719</td>
    652. 

  652.       <td>592.942913</td>
    653. 

  653.       <td>0.356832</td>
    654. 

  654.       <td>NaN</td>
    655. 

  655.       <td>NaN</td>
    656. 

  656.     </tr>
    657. 

  657.   </tbody>
    658. 

  658. </table>
    659. 

  659. </div></div>
    660. 

  660. </div>
    661. 

  661. <p>We roll up our data to an hourly basis to remove effects from sub-hourly markets and highly localized or temporal weather events.</p>
    662. 

  662. <div class="nbinput nblast docutils container">
    663. 

  663. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[7]:
    664. 

  664. </pre></div>
    665. 

  665. </div>
    666. 

  666. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    667. 

  667. <span></span># Roll up to hourly 8760 by year
    668. 

  668. hourly_mwh = df_mwh.groupby(
    669. 

  669.     by=pd.Grouper(freq=&quot;H&quot;)
    670. 

  670. )[[&quot;solar_curtailment&quot;, &quot;solar&quot;, &quot;net_load&quot;, &quot;load&quot;, &quot;generation&quot;, &quot;renewables&quot;, &quot;wind_curtailment&quot;]].sum()
    671. 

  671. 

  672. # Calculate some other potentially interesting metrics
    673. 

  673. 

  674. # How much of our load in a given hour was fulfilled by solar generation?
    675. 

  675. hourly_mwh[&quot;pct_solar&quot;] = hourly_mwh[&quot;solar&quot;]/hourly_mwh[&quot;generation&quot;]
    676. 

  676. 

  677. # How much curtailment is occurring for each unit of raw solar generation?
    678. 

  678. hourly_mwh[&quot;curtailment_intensity&quot;] = (hourly_mwh[&quot;solar_curtailment&quot;].fillna(0)/hourly_mwh[&quot;solar&quot;]).fillna(0)
    679. 

  679. 

  680. # Calculate Pct of Total Solar Potential
    681. 

  681. hourly_mwh[&quot;pct_solar_potential&quot;] = (hourly_mwh[&quot;solar_curtailment&quot;]/(hourly_mwh[&quot;solar&quot;] + hourly_mwh[&quot;solar_curtailment&quot;])).fillna(0)
    682. 

  682. 

  683. # Calculate Pct of Total Renewable Potential
    684. 

  684. hourly_mwh[&quot;pct_renewable_potential&quot;] = (hourly_mwh[&quot;solar_curtailment&quot;]/(
    685. 

  685.     hourly_mwh[&quot;renewables&quot;] + hourly_mwh[&quot;solar_curtailment&quot;] + hourly_mwh[&quot;wind_curtailment&quot;])
    686. 

  686. ).fillna(0)
    687. 

  687. </pre></div>
    688. 

  688. </div>
    689. 

  689. </div>
    690. 

  690. <p>For convenience, we define a subset of data with some non-zero amount of curtailment.</p>
    691. 

  691. <div class="nbinput nblast docutils container">
    692. 

  692. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[8]:
    693. 

  693. </pre></div>
    694. 

  694. </div>
    695. 

  695. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    696. 

  696. <span></span>curtailment_days = hourly_mwh.query(&quot;solar_curtailment &gt; 0&quot;).reset_index()
    697. 

  697. curtailment_days = pd.concat(
    698. 

  698.     [_dat.sort_values(&quot;solar_curtailment&quot;, ascending=False).reset_index(drop=True).reset_index() for (grp, _dat) in curtailment_days.groupby(by=curtailment_days[&quot;timestamp&quot;].dt.year)],
    699. 

  699.     ignore_index=True
    700. 

  700. )
    701. 

  701. </pre></div>
    702. 

  702. </div>
    703. 

  703. </div>
    704. 

  704. <p>Due to correlation between nearby hours, we are also interested in a daily totals.</p>
    705. 

  705. <div class="nbinput nblast docutils container">
    706. 

  706. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[9]:
    707. 

  707. </pre></div>
    708. 

  708. </div>
    709. 

  709. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    710. 

  710. <span></span>daily_curtailment = curtailment_days.groupby(
    711. 

  711.     by=pd.Grouper(key=&quot;timestamp&quot;, freq=&quot;D&quot;)
    712. 

  712. )[[&quot;solar&quot;, &quot;solar_curtailment&quot;, &quot;net_load&quot;, &quot;load&quot;, &quot;generation&quot;, &quot;renewables&quot;, &quot;wind_curtailment&quot;]].sum()
    713. 

  713. daily_curtailment[&quot;curtailment_intensity&quot;] = daily_curtailment.eval(&quot;solar_curtailment/solar&quot;)
    714. 

  714. daily_curtailment.reset_index(inplace=True)
    715. 

  715. </pre></div>
    716. 

  716. </div>
    717. 

  717. </div>
    718. 

  718. </div>
    719. 

  719. <div class="section" id="Exploration:-How-much-annual-Curtailment-is-there?">
    720. 

  720. <h1>Exploration: How much annual Curtailment is there?<a class="headerlink" href="#Exploration:-How-much-annual-Curtailment-is-there?" title="Permalink to this headline">¶</a></h1>
    721. 

  721. <p>We are primarily interested in finding explanatory variables for curtailment. We are interested specifically in time dependence at the hour-scale. The goal of this study is to identify exogenous data sets which could explain a given curtailment day.</p>
    722. 

  722. <p><strong>Chart Definitions</strong></p>
    723. 

  723. <div class="nbinput nblast docutils container">
    724. 

  724. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[10]:
    725. 

  725. </pre></div>
    726. 

  726. </div>
    727. 

  727. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    728. 

  728. <span></span># Interactive version to Drill Down Over Fixed Time periods
    729. 

  729. brush = alt.selection(type=&#39;interval&#39;, encodings=[&#39;x&#39;])
    730. 

  730. 

  731. base = alt.Chart(
    732. 

  732.     hourly_mwh.reset_index()
    733. 

  733. ).mark_rect().encode(
    734. 

  734.     alt.Y(&quot;hours(timestamp):T&quot;, title=&quot;Hour of Day&quot;, sort=&quot;descending&quot;),
    735. 

  735.     alt.X(&quot;yearmonthdate(timestamp):T&quot;, title=&quot;Date&quot;, sort=&quot;ascending&quot;),
    736. 

  736.     alt.Color(
    737. 

  737.         alt.repeat(&quot;row&quot;),
    738. 

  738.         type=&quot;quantitative&quot;,
    739. 

  739.         sort=&quot;descending&quot;,
    740. 

  740.         scale=alt.Scale(scheme=&quot;redgrey&quot;),
    741. 

  741.         legend=alt.Legend(orient=&quot;top&quot;)
    742. 

  742.     )
    743. 

  743. ).properties(
    744. 

  744.     width=1500,
    745. 

  745.     height=250
    746. 

  746. )
    747. 

  747. 

  748. background = base.encode(
    749. 

  749.     color=alt.value(&#39;#ddd&#39;)
    750. 

  750. ).add_selection(brush)
    751. 

  751. 

  752. highlight = base.transform_filter(brush)
    753. 

  753. 

  754. brush_chart = alt.layer(
    755. 

  755.     background,
    756. 

  756.     highlight
    757. 

  757. ).repeat(
    758. 

  758.     row=[&quot;solar_curtailment&quot;, &quot;solar&quot;, &quot;curtailment_intensity&quot;]
    759. 

  759. ).resolve_scale(color=&quot;independent&quot;)
    760. 

  760. </pre></div>
    761. 

  761. </div>
    762. 

  762. </div>
    763. 

  763. <div class="nbinput nblast docutils container">
    764. 

  764. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[11]:
    765. 

  765. </pre></div>
    766. 

  766. </div>
    767. 

  767. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    768. 

  768. <span></span># A better version of the chart above with units and things but not interactive
    769. 

  769. 

  770. basechart = alt.Chart(
    771. 

  771.     hourly_mwh.reset_index()
    772. 

  772. ).mark_rect().encode(
    773. 

  773.     alt.Y(&quot;hours(timestamp):T&quot;, title=&quot;Hour of Day&quot;, sort=&quot;descending&quot;),
    774. 

  774.     alt.X(&quot;yearmonthdate(timestamp):T&quot;, title=&quot;Date&quot;, sort=&quot;ascending&quot;),
    775. 

  775. ).properties(
    776. 

  776.     width=1500,
    777. 

  777.     height=250
    778. 

  778. )
    779. 

  779. 

  780. fixed_chart = alt.vconcat(
    781. 

  781.     basechart.encode(
    782. 

  782.         alt.Color(
    783. 

  783.             &quot;solar_curtailment:Q&quot;,
    784. 

  784.               scale=alt.Scale(type=&quot;pow&quot;, exponent=1/4, scheme=&quot;redgrey&quot;),
    785. 

  785.               sort=&quot;descending&quot;,
    786. 

  786.               title=&quot;Solar Curtailment (MWh)&quot;,
    787. 

  787.               legend=alt.Legend(orient=&quot;top&quot;),
    788. 

  788.          )
    789. 

  789.     ),
    790. 

  790.     basechart.encode(
    791. 

  791.         alt.Color(
    792. 

  792.             &quot;solar:Q&quot;,
    793. 

  793.               scale=alt.Scale(type=&quot;pow&quot;, exponent=2, scheme=&quot;redgrey&quot;),
    794. 

  794.               sort=&quot;descending&quot;,
    795. 

  795.               title=&quot;Solar Output (MW)&quot;,
    796. 

  796.               legend=alt.Legend(orient=&quot;top&quot;),
    797. 

  797.         )
    798. 

  798.     ),
    799. 

  799.     basechart.encode(
    800. 

  800.         alt.Color(
    801. 

  801.             &quot;curtailment_intensity:Q&quot;,
    802. 

  802.             scale=alt.Scale(scheme=&quot;redgrey&quot;, type=&quot;pow&quot;, exponent=1/4, domain=[0,1]),
    803. 

  803.             sort=&quot;descending&quot;,
    804. 

  804.             title=&quot;MWh Cur. per MWh Load&quot;,
    805. 

  805.             legend=alt.Legend(orient=&quot;top&quot;),
    806. 

  806.         )
    807. 

  807.     )
    808. 

  808. ).resolve_scale(color=&quot;independent&quot;)
    809. 

  809. </pre></div>
    810. 

  810. </div>
    811. 

  811. </div>
    812. 

  812. <div class="nbinput nblast docutils container">
    813. 

  813. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[12]:
    814. 

  814. </pre></div>
    815. 

  815. </div>
    816. 

  816. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    817. 

  817. <span></span># Let&#39;s inspect our curtailed hours a bit more closely
    818. 

  818. load_chart = alt.Chart(curtailment_days).mark_line().encode(
    819. 

  819.     alt.X(&quot;index&quot;, title=&quot;rank&quot;),
    820. 

  820.     alt.Y(&quot;solar_curtailment&quot;, title=&quot;Solar Curtailment (MW)&quot;),
    821. 

  821. ).facet(&quot;year(timestamp):N&quot;)
    822. 

  822. </pre></div>
    823. 

  823. </div>
    824. 

  824. </div>
    825. 

  825. <div class="nbinput nblast docutils container">
    826. 

  826. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[13]:
    827. 

  827. </pre></div>
    828. 

  828. </div>
    829. 

  829. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    830. 

  830. <span></span>curtail_v_solar_production = alt.Chart(curtailment_days).mark_point().encode(
    831. 

  831.     alt.X(&quot;solar&quot;, title=&quot;Solar Production&quot;),
    832. 

  832.     alt.Y(&quot;solar_curtailment&quot;, title=&quot;Solar Curtailment (MW)&quot;),
    833. 

  833.     alt.Color(&quot;month(timestamp):N&quot;, scale=alt.Scale(scheme=&quot;tableau20&quot;)),
    834. 

  834.     alt.Facet(&quot;year(timestamp):O&quot;, columns=3)
    835. 

  835. )
    836. 

  836. </pre></div>
    837. 

  837. </div>
    838. 

  838. </div>
    839. 

  839. <div class="nbinput nblast docutils container">
    840. 

  840. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[14]:
    841. 

  841. </pre></div>
    842. 

  842. </div>
    843. 

  843. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    844. 

  844. <span></span>base = alt.Chart().mark_point().encode(
    845. 

  845.     alt.X(&quot;monthdate(timestamp):T&quot;, title=&quot;Date (hour)&quot;),
    846. 

  846.     alt.Y(&quot;curtailment_intensity&quot;, title=&quot;Curtailment Intensity (MW/MW)&quot;),
    847. 

  847.     alt.Color(&quot;load:Q&quot;, scale=alt.Scale(scheme=&quot;redyellowblue&quot;), sort=&quot;descending&quot;, title=&quot;Load (MW)&quot;),
    848. 

  848.     # alt.Facet(&quot;year(timestamp):O&quot;, columns=3)
    849. 

  849. )
    850. 

  850. 

  851. curtailment_intensity = alt.layer(base, data=curtailment_days.query(&quot;curtailment_intensity &lt; 1&quot;)).facet(&quot;year(timestamp):O&quot;)
    852. 

  852. daily_curtailment_intensity = alt.layer(base, data=daily_curtailment).facet(&quot;year(timestamp):O&quot;)
    853. 

  853. </pre></div>
    854. 

  854. </div>
    855. 

  855. </div>
    856. 

  856. <div class="nbinput nblast docutils container">
    857. 

  857. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[15]:
    858. 

  858. </pre></div>
    859. 

  859. </div>
    860. 

  860. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    861. 

  861. <span></span>daily_curtailment_vs_load = alt.Chart(daily_curtailment).mark_point().encode(
    862. 

  862.     alt.X(&quot;load&quot;, title=&quot;Load (MWh)&quot;),
    863. 

  863.     alt.Y(&quot;solar_curtailment&quot;, title=&quot;Daily Solar Curtailment (MWh)&quot;),
    864. 

  864.     alt.Color(&quot;month(timestamp):N&quot;, scale=alt.Scale(scheme=&quot;tableau20&quot;)),
    865. 

  865.     alt.Facet(&quot;year(timestamp):O&quot;),
    866. 

  866. )
    867. 

  867. </pre></div>
    868. 

  868. </div>
    869. 

  869. </div>
    870. 

  870. </div>
    871. 

  871. <div class="section" id="Curtailment-Characteristics">
    872. 

  872. <h1>Curtailment Characteristics<a class="headerlink" href="#Curtailment-Characteristics" title="Permalink to this headline">¶</a></h1>
    873. 

  873. <div class="nbinput docutils container">
    874. 

  874. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[16]:
    875. 

  875. </pre></div>
    876. 

  876. </div>
    877. 

  877. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    878. 

  878. <span></span>alt.Chart(daily_curtailment).mark_bar().encode(
    879. 

  879.     alt.X(&quot;yearmonth(timestamp):T&quot;, title=&quot;Month&quot;),
    880. 

  880.     alt.Y(&quot;mean(solar_curtailment)&quot;, title=&quot;Mean Curtailment (MWh)&quot;)
    881. 

  881. ).interactive()
    882. 

  882. </pre></div>
    883. 

  883. </div>
    884. 

  884. </div>
    885. 

  885. <div class="nboutput nblast docutils container">
    886. 

  886. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[16]:
    887. 

  887. </pre></div>
    888. 

  888. </div>
    889. 

  889. <div class="output_area rendered_html docutils container">
    890. 

  890. <div id="altair-viz-cdf2828d2bbc45c596fd5bb5071b6a17"></div>
    891. 

  891. <script type="text/javascript">
    892. 

  892.   (function(spec, embedOpt){
    893. 

  893.     let outputDiv = document.currentScript.previousElementSibling;
    894. 

  894.     if (outputDiv.id !== "altair-viz-cdf2828d2bbc45c596fd5bb5071b6a17") {
    895. 

  895.       outputDiv = document.getElementById("altair-viz-cdf2828d2bbc45c596fd5bb5071b6a17");
    896. 

  896.     }
    897. 

  897.     const paths = {
    898. 

  898.       "vega": "https://cdn.jsdelivr.net/npm//vega@5?noext",
    899. 

  899.       "vega-lib": "https://cdn.jsdelivr.net/npm//vega-lib?noext",
    900. 

  900.       "vega-lite": "https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext",
    901. 

  901.       "vega-embed": "https://cdn.jsdelivr.net/npm//vega-embed@6?noext",
    902. 

  902.     };
    903. 

  903. 

  904.     function loadScript(lib) {
    905. 

  905.       return new Promise(function(resolve, reject) {
    906. 

  906.         var s = document.createElement('script');
    907. 

  907.         s.src = paths[lib];
    908. 

  908.         s.async = true;
    909. 

  909.         s.onload = () => resolve(paths[lib]);
    910. 

  910.         s.onerror = () => reject(`Error loading script: ${paths[lib]}`);
    911. 

  911.         document.getElementsByTagName("head")[0].appendChild(s);
    912. 

  912.       });
    913. 

  913.     }
    914. 

  914. 

  915.     function showError(err) {
    916. 

  916.       outputDiv.innerHTML = `<div class="error" style="color:red;">${err}</div>`;
    917. 

  917.       throw err;
    918. 

  918.     }
    919. 

  919. 

  920.     function displayChart(vegaEmbed) {
    921. 

  921.       vegaEmbed(outputDiv, spec, embedOpt)
    922. 

  922.         .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));
    923. 

  923.     }
    924. 

  924. 

  925.     if(typeof define === "function" && define.amd) {
    926. 

  926.       requirejs.config({paths});
    927. 

  927.       require(["vega-embed"], displayChart, err => showError(`Error loading script: ${err.message}`));
    928. 

  928.     } else if (typeof vegaEmbed === "function") {
    929. 

  929.       displayChart(vegaEmbed);
    930. 

  930.     } else {
    931. 

  931.       loadScript("vega")
    932. 

  932.         .then(() => loadScript("vega-lite"))
    933. 

  933.         .then(() => loadScript("vega-embed"))
    934. 

  934.         .catch(showError)
    935. 

  935.         .then(() => displayChart(vegaEmbed));
    936. 

  936.     }
    937. 

  937.   })({"config": {"view": {"continuousWidth": 400, "continuousHeight": 300}}, "data": {"url": "altair-data-a237a3ab57361c6fa90d72b13331653a.json", "format": {"type": "json"}}, "mark": "bar", "encoding": {"x": {"type": "temporal", "field": "timestamp", "timeUnit": "yearmonth", "title": "Month"}, "y": {"type": "quantitative", "aggregate": "mean", "field": "solar_curtailment", "title": "Mean Curtailment (MWh)"}}, "selection": {"selector002": {"type": "interval", "bind": "scales", "encodings": ["x", "y"]}}, "$schema": "https://vega.github.io/schema/vega-lite/v4.8.1.json"}, {"mode": "vega-lite"});
    938. 

  938. </script></div>
    939. 

  939. </div>
    940. 

  940. <div class="nbinput docutils container">
    941. 

  941. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[17]:
    942. 

  942. </pre></div>
    943. 

  943. </div>
    944. 

  944. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    945. 

  945. <span></span>fixed_chart
    946. 

  946. </pre></div>
    947. 

  947. </div>
    948. 

  948. </div>
    949. 

  949. <div class="nboutput nblast docutils container">
    950. 

  950. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[17]:
    951. 

  951. </pre></div>
    952. 

  952. </div>
    953. 

  953. <div class="output_area rendered_html docutils container">
    954. 

  954. <div id="altair-viz-c3bd11e42f8d4ce2902ea52c277c7ca7"></div>
    955. 

  955. <script type="text/javascript">
    956. 

  956.   (function(spec, embedOpt){
    957. 

  957.     let outputDiv = document.currentScript.previousElementSibling;
    958. 

  958.     if (outputDiv.id !== "altair-viz-c3bd11e42f8d4ce2902ea52c277c7ca7") {
    959. 

  959.       outputDiv = document.getElementById("altair-viz-c3bd11e42f8d4ce2902ea52c277c7ca7");
    960. 

  960.     }
    961. 

  961.     const paths = {
    962. 

  962.       "vega": "https://cdn.jsdelivr.net/npm//vega@5?noext",
    963. 

  963.       "vega-lib": "https://cdn.jsdelivr.net/npm//vega-lib?noext",
    964. 

  964.       "vega-lite": "https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext",
    965. 

  965.       "vega-embed": "https://cdn.jsdelivr.net/npm//vega-embed@6?noext",
    966. 

  966.     };
    967. 

  967. 

  968.     function loadScript(lib) {
    969. 

  969.       return new Promise(function(resolve, reject) {
    970. 

  970.         var s = document.createElement('script');
    971. 

  971.         s.src = paths[lib];
    972. 

  972.         s.async = true;
    973. 

  973.         s.onload = () => resolve(paths[lib]);
    974. 

  974.         s.onerror = () => reject(`Error loading script: ${paths[lib]}`);
    975. 

  975.         document.getElementsByTagName("head")[0].appendChild(s);
    976. 

  976.       });
    977. 

  977.     }
    978. 

  978. 

  979.     function showError(err) {
    980. 

  980.       outputDiv.innerHTML = `<div class="error" style="color:red;">${err}</div>`;
    981. 

  981.       throw err;
    982. 

  982.     }
    983. 

  983. 

  984.     function displayChart(vegaEmbed) {
    985. 

  985.       vegaEmbed(outputDiv, spec, embedOpt)
    986. 

  986.         .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));
    987. 

  987.     }
    988. 

  988. 

  989.     if(typeof define === "function" && define.amd) {
    990. 

  990.       requirejs.config({paths});
    991. 

  991.       require(["vega-embed"], displayChart, err => showError(`Error loading script: ${err.message}`));
    992. 

  992.     } else if (typeof vegaEmbed === "function") {
    993. 

  993.       displayChart(vegaEmbed);
    994. 

  994.     } else {
    995. 

  995.       loadScript("vega")
    996. 

  996.         .then(() => loadScript("vega-lite"))
    997. 

  997.         .then(() => loadScript("vega-embed"))
    998. 

  998.         .catch(showError)
    999. 

  999.         .then(() => displayChart(vegaEmbed));
    1000. 

  1000.     }
    1001. 

  1001.   })({"config": {"view": {"continuousWidth": 400, "continuousHeight": 300}}, "vconcat": [{"mark": "rect", "encoding": {"color": {"type": "quantitative", "field": "solar_curtailment", "legend": {"orient": "top"}, "scale": {"exponent": 0.25, "scheme": "redgrey", "type": "pow"}, "sort": "descending", "title": "Solar Curtailment (MWh)"}, "x": {"type": "temporal", "field": "timestamp", "sort": "ascending", "timeUnit": "yearmonthdate", "title": "Date"}, "y": {"type": "temporal", "field": "timestamp", "sort": "descending", "timeUnit": "hours", "title": "Hour of Day"}}, "height": 250, "width": 1500}, {"mark": "rect", "encoding": {"color": {"type": "quantitative", "field": "solar", "legend": {"orient": "top"}, "scale": {"exponent": 2, "scheme": "redgrey", "type": "pow"}, "sort": "descending", "title": "Solar Output (MW)"}, "x": {"type": "temporal", "field": "timestamp", "sort": "ascending", "timeUnit": "yearmonthdate", "title": "Date"}, "y": {"type": "temporal", "field": "timestamp", "sort": "descending", "timeUnit": "hours", "title": "Hour of Day"}}, "height": 250, "width": 1500}, {"mark": "rect", "encoding": {"color": {"type": "quantitative", "field": "curtailment_intensity", "legend": {"orient": "top"}, "scale": {"domain": [0, 1], "exponent": 0.25, "scheme": "redgrey", "type": "pow"}, "sort": "descending", "title": "MWh Cur. per MWh Load"}, "x": {"type": "temporal", "field": "timestamp", "sort": "ascending", "timeUnit": "yearmonthdate", "title": "Date"}, "y": {"type": "temporal", "field": "timestamp", "sort": "descending", "timeUnit": "hours", "title": "Hour of Day"}}, "height": 250, "width": 1500}], "data": {"url": "altair-data-6a1d0501b74f1f7cd0afd96313b5d741.json", "format": {"type": "json"}}, "resolve": {"scale": {"color": "independent"}}, "$schema": "https://vega.github.io/schema/vega-lite/v4.8.1.json"}, {"mode": "vega-lite"});
    1002. 

  1002. </script></div>
    1003. 

  1003. </div>
    1004. 

  1004. <p>Shown above are</p>
    1005. 

  1005. <ul class="simple">
    1006. 

  1006. <li><p>Hourly Solar curtailment in <span class="math notranslate nohighlight">\(x^{.25}\)</span> scale to exaggerate visual differences in curtailment scale.</p></li>
    1007. 

  1007. <li><p>Hourly Solar Output (MW) in <span class="math notranslate nohighlight">\(x^{2}\)</span> scale.</p></li>
    1008. 

  1008. <li><p>Hourly Curtailment “Intensity” w.r.t. Load (MW) in <span class="math notranslate nohighlight">\(x^{.25}\)</span> scale.</p></li>
    1009. 

  1009. </ul>
    1010. 

  1010. <p>By visual inspection, two large curtailment “zones” or “clusters” appear to exist – one centered around mid-March, and the other around mid-October. Another prominent feature is the fast adoption of solar over time.</p>
    1011. 

  1011. <div class="nbinput docutils container">
    1012. 

  1012. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[18]:
    1013. 

  1013. </pre></div>
    1014. 

  1014. </div>
    1015. 

  1015. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    1016. 

  1016. <span></span>daily_curtailment_vs_load
    1017. 

  1017. </pre></div>
    1018. 

  1018. </div>
    1019. 

  1019. </div>
    1020. 

  1020. <div class="nboutput nblast docutils container">
    1021. 

  1021. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[18]:
    1022. 

  1022. </pre></div>
    1023. 

  1023. </div>
    1024. 

  1024. <div class="output_area rendered_html docutils container">
    1025. 

  1025. <div id="altair-viz-2bb8409f5cd4477cb0ccee766e8f7da6"></div>
    1026. 

  1026. <script type="text/javascript">
    1027. 

  1027.   (function(spec, embedOpt){
    1028. 

  1028.     let outputDiv = document.currentScript.previousElementSibling;
    1029. 

  1029.     if (outputDiv.id !== "altair-viz-2bb8409f5cd4477cb0ccee766e8f7da6") {
    1030. 

  1030.       outputDiv = document.getElementById("altair-viz-2bb8409f5cd4477cb0ccee766e8f7da6");
    1031. 

  1031.     }
    1032. 

  1032.     const paths = {
    1033. 

  1033.       "vega": "https://cdn.jsdelivr.net/npm//vega@5?noext",
    1034. 

  1034.       "vega-lib": "https://cdn.jsdelivr.net/npm//vega-lib?noext",
    1035. 

  1035.       "vega-lite": "https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext",
    1036. 

  1036.       "vega-embed": "https://cdn.jsdelivr.net/npm//vega-embed@6?noext",
    1037. 

  1037.     };
    1038. 

  1038. 

  1039.     function loadScript(lib) {
    1040. 

  1040.       return new Promise(function(resolve, reject) {
    1041. 

  1041.         var s = document.createElement('script');
    1042. 

  1042.         s.src = paths[lib];
    1043. 

  1043.         s.async = true;
    1044. 

  1044.         s.onload = () => resolve(paths[lib]);
    1045. 

  1045.         s.onerror = () => reject(`Error loading script: ${paths[lib]}`);
    1046. 

  1046.         document.getElementsByTagName("head")[0].appendChild(s);
    1047. 

  1047.       });
    1048. 

  1048.     }
    1049. 

  1049. 

  1050.     function showError(err) {
    1051. 

  1051.       outputDiv.innerHTML = `<div class="error" style="color:red;">${err}</div>`;
    1052. 

  1052.       throw err;
    1053. 

  1053.     }
    1054. 

  1054. 

  1055.     function displayChart(vegaEmbed) {
    1056. 

  1056.       vegaEmbed(outputDiv, spec, embedOpt)
    1057. 

  1057.         .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));
    1058. 

  1058.     }
    1059. 

  1059. 

  1060.     if(typeof define === "function" && define.amd) {
    1061. 

  1061.       requirejs.config({paths});
    1062. 

  1062.       require(["vega-embed"], displayChart, err => showError(`Error loading script: ${err.message}`));
    1063. 

  1063.     } else if (typeof vegaEmbed === "function") {
    1064. 

  1064.       displayChart(vegaEmbed);
    1065. 

  1065.     } else {
    1066. 

  1066.       loadScript("vega")
    1067. 

  1067.         .then(() => loadScript("vega-lite"))
    1068. 

  1068.         .then(() => loadScript("vega-embed"))
    1069. 

  1069.         .catch(showError)
    1070. 

  1070.         .then(() => displayChart(vegaEmbed));
    1071. 

  1071.     }
    1072. 

  1072.   })({"config": {"view": {"continuousWidth": 400, "continuousHeight": 300}}, "data": {"url": "altair-data-a237a3ab57361c6fa90d72b13331653a.json", "format": {"type": "json"}}, "mark": "point", "encoding": {"color": {"type": "nominal", "field": "timestamp", "scale": {"scheme": "tableau20"}, "timeUnit": "month"}, "facet": {"type": "ordinal", "field": "timestamp", "timeUnit": "year"}, "x": {"type": "quantitative", "field": "load", "title": "Load (MWh)"}, "y": {"type": "quantitative", "field": "solar_curtailment", "title": "Daily Solar Curtailment (MWh)"}}, "$schema": "https://vega.github.io/schema/vega-lite/v4.8.1.json"}, {"mode": "vega-lite"});
    1073. 

  1073. </script></div>
    1074. 

  1074. </div>
    1075. 

  1075. <p>By inspection, we can see a very rough pattern of high curtailment events during periods of “medium” load. Intuitively, we might imagine these correspond to days with very high solar production, and very low demand (e.g. sunny in the desert, and temperate in populated centers.)</p>
    1076. 

  1076. <div class="nbinput docutils container">
    1077. 

  1077. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[19]:
    1078. 

  1078. </pre></div>
    1079. 

  1079. </div>
    1080. 

  1080. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    1081. 

  1081. <span></span>load_chart
    1082. 

  1082. </pre></div>
    1083. 

  1083. </div>
    1084. 

  1084. </div>
    1085. 

  1085. <div class="nboutput nblast docutils container">
    1086. 

  1086. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[19]:
    1087. 

  1087. </pre></div>
    1088. 

  1088. </div>
    1089. 

  1089. <div class="output_area rendered_html docutils container">
    1090. 

  1090. <div id="altair-viz-a78c165ac1b544d1a2b4fef95a5c8182"></div>
    1091. 

  1091. <script type="text/javascript">
    1092. 

  1092.   (function(spec, embedOpt){
    1093. 

  1093.     let outputDiv = document.currentScript.previousElementSibling;
    1094. 

  1094.     if (outputDiv.id !== "altair-viz-a78c165ac1b544d1a2b4fef95a5c8182") {
    1095. 

  1095.       outputDiv = document.getElementById("altair-viz-a78c165ac1b544d1a2b4fef95a5c8182");
    1096. 

  1096.     }
    1097. 

  1097.     const paths = {
    1098. 

  1098.       "vega": "https://cdn.jsdelivr.net/npm//vega@5?noext",
    1099. 

  1099.       "vega-lib": "https://cdn.jsdelivr.net/npm//vega-lib?noext",
    1100. 

  1100.       "vega-lite": "https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext",
    1101. 

  1101.       "vega-embed": "https://cdn.jsdelivr.net/npm//vega-embed@6?noext",
    1102. 

  1102.     };
    1103. 

  1103. 

  1104.     function loadScript(lib) {
    1105. 

  1105.       return new Promise(function(resolve, reject) {
    1106. 

  1106.         var s = document.createElement('script');
    1107. 

  1107.         s.src = paths[lib];
    1108. 

  1108.         s.async = true;
    1109. 

  1109.         s.onload = () => resolve(paths[lib]);
    1110. 

  1110.         s.onerror = () => reject(`Error loading script: ${paths[lib]}`);
    1111. 

  1111.         document.getElementsByTagName("head")[0].appendChild(s);
    1112. 

  1112.       });
    1113. 

  1113.     }
    1114. 

  1114. 

  1115.     function showError(err) {
    1116. 

  1116.       outputDiv.innerHTML = `<div class="error" style="color:red;">${err}</div>`;
    1117. 

  1117.       throw err;
    1118. 

  1118.     }
    1119. 

  1119. 

  1120.     function displayChart(vegaEmbed) {
    1121. 

  1121.       vegaEmbed(outputDiv, spec, embedOpt)
    1122. 

  1122.         .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));
    1123. 

  1123.     }
    1124. 

  1124. 

  1125.     if(typeof define === "function" && define.amd) {
    1126. 

  1126.       requirejs.config({paths});
    1127. 

  1127.       require(["vega-embed"], displayChart, err => showError(`Error loading script: ${err.message}`));
    1128. 

  1128.     } else if (typeof vegaEmbed === "function") {
    1129. 

  1129.       displayChart(vegaEmbed);
    1130. 

  1130.     } else {
    1131. 

  1131.       loadScript("vega")
    1132. 

  1132.         .then(() => loadScript("vega-lite"))
    1133. 

  1133.         .then(() => loadScript("vega-embed"))
    1134. 

  1134.         .catch(showError)
    1135. 

  1135.         .then(() => displayChart(vegaEmbed));
    1136. 

  1136.     }
    1137. 

  1137.   })({"config": {"view": {"continuousWidth": 400, "continuousHeight": 300}}, "data": {"url": "altair-data-2d3d4499b8a76c97427749523143b571.json", "format": {"type": "json"}}, "facet": {"type": "nominal", "field": "timestamp", "timeUnit": "year"}, "spec": {"mark": "line", "encoding": {"x": {"type": "quantitative", "field": "index", "title": "rank"}, "y": {"type": "quantitative", "field": "solar_curtailment", "title": "Solar Curtailment (MW)"}}}, "$schema": "https://vega.github.io/schema/vega-lite/v4.8.1.json"}, {"mode": "vega-lite"});
    1138. 

  1138. </script></div>
    1139. 

  1139. </div>
    1140. 

  1140. <p>Hourly curtailment by year in MW - Over time, the available curtailed capacity has increased drastically (by a factor of 3 from 2016 to 2019).</p>
    1141. 

  1141. <div class="nbinput docutils container">
    1142. 

  1142. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[20]:
    1143. 

  1143. </pre></div>
    1144. 

  1144. </div>
    1145. 

  1145. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    1146. 

  1146. <span></span>curtail_v_solar_production
    1147. 

  1147. </pre></div>
    1148. 

  1148. </div>
    1149. 

  1149. </div>
    1150. 

  1150. <div class="nboutput nblast docutils container">
    1151. 

  1151. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[20]:
    1152. 

  1152. </pre></div>
    1153. 

  1153. </div>
    1154. 

  1154. <div class="output_area rendered_html docutils container">
    1155. 

  1155. <div id="altair-viz-5eba22d01cb4476cb5a9401bc66e9b8a"></div>
    1156. 

  1156. <script type="text/javascript">
    1157. 

  1157.   (function(spec, embedOpt){
    1158. 

  1158.     let outputDiv = document.currentScript.previousElementSibling;
    1159. 

  1159.     if (outputDiv.id !== "altair-viz-5eba22d01cb4476cb5a9401bc66e9b8a") {
    1160. 

  1160.       outputDiv = document.getElementById("altair-viz-5eba22d01cb4476cb5a9401bc66e9b8a");
    1161. 

  1161.     }
    1162. 

  1162.     const paths = {
    1163. 

  1163.       "vega": "https://cdn.jsdelivr.net/npm//vega@5?noext",
    1164. 

  1164.       "vega-lib": "https://cdn.jsdelivr.net/npm//vega-lib?noext",
    1165. 

  1165.       "vega-lite": "https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext",
    1166. 

  1166.       "vega-embed": "https://cdn.jsdelivr.net/npm//vega-embed@6?noext",
    1167. 

  1167.     };
    1168. 

  1168. 

  1169.     function loadScript(lib) {
    1170. 

  1170.       return new Promise(function(resolve, reject) {
    1171. 

  1171.         var s = document.createElement('script');
    1172. 

  1172.         s.src = paths[lib];
    1173. 

  1173.         s.async = true;
    1174. 

  1174.         s.onload = () => resolve(paths[lib]);
    1175. 

  1175.         s.onerror = () => reject(`Error loading script: ${paths[lib]}`);
    1176. 

  1176.         document.getElementsByTagName("head")[0].appendChild(s);
    1177. 

  1177.       });
    1178. 

  1178.     }
    1179. 

  1179. 

  1180.     function showError(err) {
    1181. 

  1181.       outputDiv.innerHTML = `<div class="error" style="color:red;">${err}</div>`;
    1182. 

  1182.       throw err;
    1183. 

  1183.     }
    1184. 

  1184. 

  1185.     function displayChart(vegaEmbed) {
    1186. 

  1186.       vegaEmbed(outputDiv, spec, embedOpt)
    1187. 

  1187.         .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));
    1188. 

  1188.     }
    1189. 

  1189. 

  1190.     if(typeof define === "function" && define.amd) {
    1191. 

  1191.       requirejs.config({paths});
    1192. 

  1192.       require(["vega-embed"], displayChart, err => showError(`Error loading script: ${err.message}`));
    1193. 

  1193.     } else if (typeof vegaEmbed === "function") {
    1194. 

  1194.       displayChart(vegaEmbed);
    1195. 

  1195.     } else {
    1196. 

  1196.       loadScript("vega")
    1197. 

  1197.         .then(() => loadScript("vega-lite"))
    1198. 

  1198.         .then(() => loadScript("vega-embed"))
    1199. 

  1199.         .catch(showError)
    1200. 

  1200.         .then(() => displayChart(vegaEmbed));
    1201. 

  1201.     }
    1202. 

  1202.   })({"config": {"view": {"continuousWidth": 400, "continuousHeight": 300}}, "data": {"url": "altair-data-2d3d4499b8a76c97427749523143b571.json", "format": {"type": "json"}}, "mark": "point", "encoding": {"color": {"type": "nominal", "field": "timestamp", "scale": {"scheme": "tableau20"}, "timeUnit": "month"}, "facet": {"type": "ordinal", "columns": 3, "field": "timestamp", "timeUnit": "year"}, "x": {"type": "quantitative", "field": "solar", "title": "Solar Production"}, "y": {"type": "quantitative", "field": "solar_curtailment", "title": "Solar Curtailment (MW)"}}, "$schema": "https://vega.github.io/schema/vega-lite/v4.8.1.json"}, {"mode": "vega-lite"});
    1203. 

  1203. </script></div>
    1204. 

  1204. </div>
    1205. 

  1205. <p>One metric of interest may be the amount of solar curtailment per unit of solar production. Each mark represents a single hour in a year. By visual inspection, a vague envelope is visible on the right hand side. The sum of curtailment and production might represent the total solar capacity in a given hour. By inspection, we can also observe a larger portion of curtailment is occurring year on year.</p>
    1206. 

  1206. <div class="nbinput docutils container">
    1207. 

  1207. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[21]:
    1208. 

  1208. </pre></div>
    1209. 

  1209. </div>
    1210. 

  1210. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    1211. 

  1211. <span></span>curtailment_intensity
    1212. 

  1212. </pre></div>
    1213. 

  1213. </div>
    1214. 

  1214. </div>
    1215. 

  1215. <div class="nboutput nblast docutils container">
    1216. 

  1216. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[21]:
    1217. 

  1217. </pre></div>
    1218. 

  1218. </div>
    1219. 

  1219. <div class="output_area rendered_html docutils container">
    1220. 

  1220. <div id="altair-viz-cf2e895f8dc44ea9b01666aa44905c56"></div>
    1221. 

  1221. <script type="text/javascript">
    1222. 

  1222.   (function(spec, embedOpt){
    1223. 

  1223.     let outputDiv = document.currentScript.previousElementSibling;
    1224. 

  1224.     if (outputDiv.id !== "altair-viz-cf2e895f8dc44ea9b01666aa44905c56") {
    1225. 

  1225.       outputDiv = document.getElementById("altair-viz-cf2e895f8dc44ea9b01666aa44905c56");
    1226. 

  1226.     }
    1227. 

  1227.     const paths = {
    1228. 

  1228.       "vega": "https://cdn.jsdelivr.net/npm//vega@5?noext",
    1229. 

  1229.       "vega-lib": "https://cdn.jsdelivr.net/npm//vega-lib?noext",
    1230. 

  1230.       "vega-lite": "https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext",
    1231. 

  1231.       "vega-embed": "https://cdn.jsdelivr.net/npm//vega-embed@6?noext",
    1232. 

  1232.     };
    1233. 

  1233. 

  1234.     function loadScript(lib) {
    1235. 

  1235.       return new Promise(function(resolve, reject) {
    1236. 

  1236.         var s = document.createElement('script');
    1237. 

  1237.         s.src = paths[lib];
    1238. 

  1238.         s.async = true;
    1239. 

  1239.         s.onload = () => resolve(paths[lib]);
    1240. 

  1240.         s.onerror = () => reject(`Error loading script: ${paths[lib]}`);
    1241. 

  1241.         document.getElementsByTagName("head")[0].appendChild(s);
    1242. 

  1242.       });
    1243. 

  1243.     }
    1244. 

  1244. 

  1245.     function showError(err) {
    1246. 

  1246.       outputDiv.innerHTML = `<div class="error" style="color:red;">${err}</div>`;
    1247. 

  1247.       throw err;
    1248. 

  1248.     }
    1249. 

  1249. 

  1250.     function displayChart(vegaEmbed) {
    1251. 

  1251.       vegaEmbed(outputDiv, spec, embedOpt)
    1252. 

  1252.         .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));
    1253. 

  1253.     }
    1254. 

  1254. 

  1255.     if(typeof define === "function" && define.amd) {
    1256. 

  1256.       requirejs.config({paths});
    1257. 

  1257.       require(["vega-embed"], displayChart, err => showError(`Error loading script: ${err.message}`));
    1258. 

  1258.     } else if (typeof vegaEmbed === "function") {
    1259. 

  1259.       displayChart(vegaEmbed);
    1260. 

  1260.     } else {
    1261. 

  1261.       loadScript("vega")
    1262. 

  1262.         .then(() => loadScript("vega-lite"))
    1263. 

  1263.         .then(() => loadScript("vega-embed"))
    1264. 

  1264.         .catch(showError)
    1265. 

  1265.         .then(() => displayChart(vegaEmbed));
    1266. 

  1266.     }
    1267. 

  1267.   })({"config": {"view": {"continuousWidth": 400, "continuousHeight": 300}}, "data": {"url": "altair-data-ebaec80065fe0e5bc27d2a0116ef6d4b.json", "format": {"type": "json"}}, "facet": {"type": "ordinal", "field": "timestamp", "timeUnit": "year"}, "spec": {"layer": [{"mark": "point", "encoding": {"color": {"type": "quantitative", "field": "load", "scale": {"scheme": "redyellowblue"}, "sort": "descending", "title": "Load (MW)"}, "x": {"type": "temporal", "field": "timestamp", "timeUnit": "monthdate", "title": "Date (hour)"}, "y": {"type": "quantitative", "field": "curtailment_intensity", "title": "Curtailment Intensity (MW/MW)"}}}]}, "$schema": "https://vega.github.io/schema/vega-lite/v4.8.1.json"}, {"mode": "vega-lite"});
    1268. 

  1268. </script></div>
    1269. 

  1269. </div>
    1270. 

  1270. <p>Hourly curtailment per unit of solar production. A value of 1 represents an hour where 50% of solar capacity is curtailed.</p>
    1271. 

  1271. <div class="nbinput docutils container">
    1272. 

  1272. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[22]:
    1273. 

  1273. </pre></div>
    1274. 

  1274. </div>
    1275. 

  1275. <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
    1276. 

  1276. <span></span>daily_curtailment_intensity
    1277. 

  1277. </pre></div>
    1278. 

  1278. </div>
    1279. 

  1279. </div>
    1280. 

  1280. <div class="nboutput nblast docutils container">
    1281. 

  1281. <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[22]:
    1282. 

  1282. </pre></div>
    1283. 

  1283. </div>
    1284. 

  1284. <div class="output_area rendered_html docutils container">
    1285. 

  1285. <div id="altair-viz-5b6082b826c641d38c731e2cfa90fd59"></div>
    1286. 

  1286. <script type="text/javascript">
    1287. 

  1287.   (function(spec, embedOpt){
    1288. 

  1288.     let outputDiv = document.currentScript.previousElementSibling;
    1289. 

  1289.     if (outputDiv.id !== "altair-viz-5b6082b826c641d38c731e2cfa90fd59") {
    1290. 

  1290.       outputDiv = document.getElementById("altair-viz-5b6082b826c641d38c731e2cfa90fd59");
    1291. 

  1291.     }
    1292. 

  1292.     const paths = {
    1293. 

  1293.       "vega": "https://cdn.jsdelivr.net/npm//vega@5?noext",
    1294. 

  1294.       "vega-lib": "https://cdn.jsdelivr.net/npm//vega-lib?noext",
    1295. 

  1295.       "vega-lite": "https://cdn.jsdelivr.net/npm//vega-lite@4.8.1?noext",
    1296. 

  1296.       "vega-embed": "https://cdn.jsdelivr.net/npm//vega-embed@6?noext",
    1297. 

  1297.     };
    1298. 

  1298. 

  1299.     function loadScript(lib) {
    1300. 

  1300.       return new Promise(function(resolve, reject) {
    1301. 

  1301.         var s = document.createElement('script');
    1302. 

  1302.         s.src = paths[lib];
    1303. 

  1303.         s.async = true;
    1304. 

  1304.         s.onload = () => resolve(paths[lib]);
    1305. 

  1305.         s.onerror = () => reject(`Error loading script: ${paths[lib]}`);
    1306. 

  1306.         document.getElementsByTagName("head")[0].appendChild(s);
    1307. 

  1307.       });
    1308. 

  1308.     }
    1309. 

  1309. 

  1310.     function showError(err) {
    1311. 

  1311.       outputDiv.innerHTML = `<div class="error" style="color:red;">${err}</div>`;
    1312. 

  1312.       throw err;
    1313. 

  1313.     }
    1314. 

  1314. 

  1315.     function displayChart(vegaEmbed) {
    1316. 

  1316.       vegaEmbed(outputDiv, spec, embedOpt)
    1317. 

  1317.         .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));
    1318. 

  1318.     }
    1319. 

  1319. 

  1320.     if(typeof define === "function" && define.amd) {
    1321. 

  1321.       requirejs.config({paths});
    1322. 

  1322.       require(["vega-embed"], displayChart, err => showError(`Error loading script: ${err.message}`));
    1323. 

  1323.     } else if (typeof vegaEmbed === "function") {
    1324. 

  1324.       displayChart(vegaEmbed);
    1325. 

  1325.     } else {
    1326. 

  1326.       loadScript("vega")
    1327. 

  1327.         .then(() => loadScript("vega-lite"))
    1328. 

  1328.         .then(() => loadScript("vega-embed"))
    1329. 

  1329.         .catch(showError)
    1330. 

  1330.         .then(() => displayChart(vegaEmbed));
    1331. 

  1331.     }
    1332. 

  1332.   })({"config": {"view": {"continuousWidth": 400, "continuousHeight": 300}}, "data": {"url": "altair-data-a237a3ab57361c6fa90d72b13331653a.json", "format": {"type": "json"}}, "facet": {"type": "ordinal", "field": "timestamp", "timeUnit": "year"}, "spec": {"layer": [{"mark": "point", "encoding": {"color": {"type": "quantitative", "field": "load", "scale": {"scheme": "redyellowblue"}, "sort": "descending", "title": "Load (MW)"}, "x": {"type": "temporal", "field": "timestamp", "timeUnit": "monthdate", "title": "Date (hour)"}, "y": {"type": "quantitative", "field": "curtailment_intensity", "title": "Curtailment Intensity (MW/MW)"}}}]}, "$schema": "https://vega.github.io/schema/vega-lite/v4.8.1.json"}, {"mode": "vega-lite"});
    1333. 

  1333. </script></div>
    1334. 

  1334. </div>
    1335. 

  1335. <p>Total daily curtailment per unit of solar production. A value of 1 represents a day where 50% of solar capacity is curtailed.</p>
    1336. 

  1336. </div>
    1337. 

  1337. 

  1338. 

  1339.       </div>
    1340. 

  1340.       <div class="bottomnav" role="navigation" aria-label="bottom navigation">
    1341. 

  1341.       
    1342. 

  1342.         <p>
    1343. 

  1343.         «&#160;&#160;<a href="../data_sources.html">Data Sources</a>
    1344. 

  1344.         &#160;&#160;::&#160;&#160;
    1345. 

  1345.         <a class="uplink" href="../index.html">Contents</a>
    1346. 

  1346.         &#160;&#160;::&#160;&#160;
    1347. 

  1347.         <a href="../methods.html">Methods</a>&#160;&#160;»
    1348. 

  1348.         </p>
    1349. 

  1349. 

  1350.       </div>
    1351. 

  1351. 

  1352.     <div class="footer" role="contentinfo">
    1353. 

  1353.         &#169; Copyright Thomas Tu, 2020.
    1354. 

  1354.       Created using <a href="http://sphinx-doc.org/">Sphinx</a> 2.4.4.
    1355. 

  1355.     </div>
    1356. 

  1356.   </body>
    1357. 

  1357. </html>
    1358.
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