*1226 The weather conditions giving rise to this case may have been out of the ordinary, but the legal principles controlling its resolution are decidedly routine. In January 2014, a period of exceptionally cold temperatures, commonly referred to as a "Polar Vortex," descended on the Eastern United States. As temperatures plunged, the demand for electricity soared. In working to help meet that demand, Old Dominion Electric Cooperative, an electricity generator and provider, found that its operational costs outstripped the amounts it could charge for electricity under the governing tariff. Old Dominion then asked the Federal Energy Regulatory Commission to waive provisions of the governing tariff retroactively so that it could recover its costs. The Commission declined on the ground that such retroactive charges would violate the filed rate doctrine and the rule against retroactive ratemaking. The Commission was right to do so, and we accordingly deny Old Dominion's petition for review. We also deny the motion of the Independent Market Monitor to intervene, but will accord it amicus curiae status.

I

A

The Federal Power Act charges the Commission with ensuring that "[a]ll rates and charges made, demanded, or received by any public utility for or in connection with the transmission or sale of electric energy subject to the jurisdiction of the Commission * * * shall be just and reasonable." 16 U.S.C. § 824d(a). To effectuate those goals, regulated utilities must file with the Commission and keep open for public inspection a schedule of the rates they intend to charge ratepayers. Id. § 824d(c), (d). While the Act permits regulated utilities to set their filed rate unilaterally and record it in a tariff, see id . § 824d(c), the rates actually charged may not exceed those on file with the Commission, Towns of Concord, Norwood, and Wellesley Mass. v. FERC , 955 F.2d 67 , 68 (D.C. Cir. 1992).

The Act also empowers the Commission to fix or change rates and charges, but only prospectively. 16 U.S.C. § 824e(a). When a utility wishes to alter the rates it charges, it must provide sixty-days' notice to the Commission and file new rate schedules "stating plainly the change or changes to be made in the schedule or schedules then in force and the time when the change or changes will go into effect." Id . § 824d(d). The Commission may waive the sixty-day notice requirement for good cause, but the Commission has no authority under the Act to allow retroactive change in the rates charged to consumers. See id .; Columbia Gas Transmission Corp. v. FERC , 895 F.2d 791 , 795-796 (D.C. Cir. 1990) ( Columbia III ); see also Consolidated Edison Co. v. FERC , 958 F.2d 429 , 434 (D.C. Cir. 1992).

Those rules mandating the open and transparent filing of rates and broadly proscribing their retroactive adjustment *1227 are known collectively as the "filed rate doctrine." At bottom, that doctrine means that "a regulated seller of [power]" is prohibited "from collecting a rate other than the one filed with the Commission," and "the Commission itself" cannot retroactively "impos[e] a rate increase for [power] already sold." Arkansas Louisiana Gas Co. v. Hall , 453 U.S. 571 , 578, 101 S.Ct. 2925 , 69 L.Ed.2d 856 (1981).

In a similar vein, the rule against retroactive ratemaking "prohibits the Commission from adjusting current rates to make up for a utility's over- or under-collection in prior periods." Towns of Concord , 955 F.2d at 71 n.2. That otherwise categorical prohibition against retroactively charging rates that differ from those that were on file during the relevant time period yields in only two limited circumstances: (i) when a court invalidates the set rate as unlawful, and (ii) when the filed rate takes the form not of a number but of a formula that varies as the incorporated factors change over time. See West Deptford Energy, LLC v. FERC , 766 F.3d 10 , 22-23 (D.C. Cir. 2014) (compiling cases). Neither of those exceptions apply to this case. 1

B

PJM Interconnection, LLC ("PJM") is a Regional Transmission Organization and Independent System Operator that exercises operational control over, but not ownership of, the electrical transmission facilities belonging to its participating members. See Midwest ISO Transmission Owners v. FERC , 373 F.3d 1361 , 1364 (D.C. Cir. 2004). The Commission has tasked PJM, as a Regional Transmission Organization, with supervising and coordinating the movement of electricity throughout its market area, 18 C.F.R. § 35.34 , which comprises thirteen states and the District of Columbia, see Hughes v. Talen Energy Mktg., LLC , --- U.S. ----, 136 S.Ct. 1288 , 1292-1293, 194 L.Ed.2d 414 (2016).

One way that electricity is transferred throughout the PJM market is through competitive auctions. See Hughes , 136 S.Ct. at 1293 . In same-day auctions, generators bid to provide the immediate delivery of electricity needed to slake sudden spikes in demand. In next-day auctions, generators bid to satisfy anticipated near-term demand. And in a "capacity auction," generators make bids that, if accepted, bind them to providing needed electricity in the longer term. See id .

Old Dominion Electric Cooperative is a not-for-profit electrical generation and transmission utility that participates as both a generator and a load-serving entity (that is, a public utility) in the PJM market. This case involves three of Old Dominion's natural-gas-fired electrical power plants in Maryland and Virginia: Marsh Run, Louisa, and Rock Springs. Each of those facilities is a "generation capacity resource," which means that Old Dominion contractually committed itself to offer all of those units' available generation capacity into PJM's daily market and to generate electricity whenever called upon by PJM. Old Dominion Elec. Coop. , 151 FERC ¶ 61,207 at P 2 n.2 (2015).

*1228 PJM fulfills its oversight and market management responsibilities through rules prescribed in (1) the PJM Open Access Transmission Tariff and (2) the PJM Operating Agreement, to which participating generators like Old Dominion subscribe. Several provisions of those instruments bear on the dispute in this case.

First, the Operating Agreement empowers PJM to take "measures appropriate to alleviate an Emergency, in order to preserve reliability" in the electricity market and to meet consumer need. Agreement § 1.6.2(vii). That authority includes directing generators "to start, shutdown, or change [the] output levels of [their] generations units[.]" Agreement § 1.7.20(b). According to Old Dominion, generators "understand[ ] PJM dispatch instructions to be determinations with which [they are] expected to comply" under the PJM Tariff § 1.8.2(a). J.A. 56 n.2.

Second, generation capacity resources "must offer" capacity into the same-day and day-ahead auctions. Agreement § 1.10.1A(d). That "must offer" requirement commands generators to submit offers for all "available capacity" of any designated capacity generation facilities. Tariff § 1.10.1A(d).

Third, the Tariff caps the prices at which generators may offer their capacity into the day-ahead market at $1,000/megawatt-hour. Tariff § 1.10.1A(d)(viii).

Finally, Commission regulations require transmission organizations, like PJM, to self-monitor their markets and report any issues affecting their reliability, efficiency, and non-discriminatory operation. 18 C.F.R. § 35.34 (k)(6). PJM retained a private company, Monitoring Analytics, LLC ("Monitor") to act as its independent market monitor. Monitor has moved to intervene in this appeal.

C

In January 2014, a Polar Vortex brought extraordinarily cold temperatures for an unusually prolonged period of time to broad swaths of the continental United States, including the PJM market region. The plunging temperatures triggered a corresponding surge in the demand for electrical power to heat homes and businesses. Increased demand for power generation caused a regional spike in the price of natural gas, which is one of the primary fuels that generators like Old Dominion use to produce electricity.

Invoking market rules, PJM used its emergency authority to make sure that the electrical service needed to meet consumer demand was available and reliable. As part of those actions, beginning in early January, PJM repeatedly called on its generators to prepare for additional outputs of electricity. As relevant here, PJM tasked Old Dominion with ensuring that three of its generation capacity resources (Rock Springs, Louisa, and Marsh Run) would be able to fulfill their contractual commitments and run at full capacity during several anticipated acute spikes in energy demand: January 7-9, January 23, and January 28.

To meet that need, Old Dominion had to purchase natural gas at inflated prices. In turn, Old Dominion's marginal costs to generate electricity spiked to approximately $1,200/megawatt-hour. PJM Interconnection, LLC , 146 FERC ¶ 61,041 at P 2 (2014). But the Tariff prohibited it from submitting bids for its electricity in the day-ahead auction that exceeded $1,000/megawatt-hour. In other words, runaway generation costs driven by extreme weather and market conditions ran headlong into the PJM Tariff's pre-set rate cap. As a result, some generators, including Old Dominion, were forced temporarily to sell energy capacity at a loss. See also *1229 Duke Energy Corp. v. FERC , No. 16-1133, 892 F.3d 416 , 2018 WL 2993214 (D.C. Cir. June 15, 2018).

Old Dominion sought assurances from PJM that it would be able to recover those losses. On January 21, 2014, PJM posted a statement on its website that reiterated the generators' contractual obligation to offer full capacity into the day-ahead market at a price not to exceed $1,000/megawatt-hour, notwithstanding the unanticipated circumstances. PJM also expressed its intent to file with the Commission "as soon as practical" a "retroactive waiver" of the rate cap to compensate those generation capacity resources whose costs for electricity generation had exceeded the Tariff's rate cap. J.A. 137. PJM further stated that it would file a second waiver request seeking a temporary, prospective waiver of the rate cap provision.

Two days later, PJM filed two concurrent waiver requests with the Commission. In one waiver, PJM requested immediate "make whole" relief-to be effective the next day ( i.e. , January 24, 2014)-that would allow generators to recover the difference between the actual costs of generating capacity and the Tariff's rate cap for "must offer" bids submitted in the price auctions for forthcoming electricity generation.

The second waiver sought to stop the financial hemorrhaging by waiving the filed Tariff's rate cap "only prospectively." J.A. 140. With that waiver, generation capacity resources that were contractually obligated to continue providing electricity could submit bids into the same-day and next-day auctions that exceeded the $1,000/megawatt-hour rate cap. That waiver would apply going forward until March 31, 2014.

Notably, and contrary to PJM's January 21 website post, neither waiver requested retroactive relief. The Commission promptly granted both waivers. PJM Interconnection, LLC , 146 FERC ¶ 61,041 , on reh'g , 149 FERC ¶ 61,059 (2014) ; PJM Interconnection, LLC , 146 FERC ¶ 61,078 (2014), on reh'g , 149 FERC ¶ 61,060 (2014).

As it turned out, PJM had overestimated the amount of energy that would be required on several of the Polar Vortex's coldest days. To correct its mistake, PJM reduced or cancelled some of its orders for generation services.

But that was too late to help the many generators that had purchased the expensive natural gas needed to supply the forecasted output and that had sunk start-up costs responding to now-cancelled or curtailed orders. Old Dominion had to resell some of its excess natural gas at a loss after the surge in demand had subsided and the market price had dropped. And it absorbed losses on the excess quantities it could not, or did not, resell. More specifically, the Polar Vortex and PJM's call for generation capacity resources to meet the anticipated spike in demand caused Old Dominion to incur losses in the form of: (i) actual costs in excess of the $1,000/megawatt-hour rate that pre-dated the January 24, 2014 waiver; (ii) start-up costs arising from PJM's cancelled requests for service; and (iii) costs that arose when units dispatched to generate for a certain period were instructed to cease operations earlier than anticipated.

D

Old Dominion requested that the Commission provide dual-faceted relief for its losses. First, Old Dominion sought to have the effective date of PJM's "make whole" waiver extend back one additional day to cover losses it suffered on January 23, the date PJM filed its waiver request with the Commission. PJM Interconnection, LLC , 146 FERC ¶ 61,041 (2014). Second, Old *1230 Dominion requested a waiver of provisions in the Tariff and PJM Agreement proscribing retroactive rate charges so that it could recover the start-up costs of its unused energy production that it incurred when PJM cancelled or cut back on prior orders for service. Combined, Old Dominion claimed nearly $15 million in costs attributable to PJM's emergency measures during the Polar Vortex.

The Commission denied Old Dominion's request in all respects. The Commission agreed with Old Dominion's concession that the filed Tariff precluded its requested retroactive changes to the rates. The Commission also found that Old Dominion's ratepayers lacked sufficient notice that the approved rate was subject to change. For those reasons, the Commission concluded that Old Dominion's waiver was impermissible under the filed rate doctrine and the closely related rule against retroactive ratemaking.

Old Dominion sought rehearing based entirely on grounds of fairness and equity. Specifically, it argued that the Commission has discretionary authority to "retroactively waive a tariff in order to authorize 'actions other than those prescribed by the filed rate[ ]' " when "it concludes that the 'tariff should not be applied under a particular out-of-the-ordinary set of facts[.]' " Old Dominion Elec. Coop. , 154 FERC ¶ 61,155 at P 11 (2016).

The Commission disagreed, explaining that Old Dominion's requested waiver constituted "a classic example of a violation of the filed rate doctrine and the prohibition of retroactive ratemaking." Old Dominion Elec. Coop. , 154 FERC ¶ 61,155 at P 9. The Commission also found that this court's precedent stripped it of any power to disregard on equitable grounds either the filed rate doctrine or the rule against retroactive ratemaking, no matter how compelling the equities might be. Id. at P 17 (citing Columbia III , 895 F.2d at 797 ).

II

We review final orders of the Commission, 16 U.S.C. § 825 l (b), under the Administrative Procedure Act's familiar "arbitrary and capricious" standard, 5 U.S.C. § 706 (2)(A) ; see FERC v. Electric Power Supply Ass'n , --- U.S. ----, 136 S.Ct. 760 , 782, 193 L.Ed.2d 661 (2016). Under that standard, we defer to the Commission's reasonably explained decisions, Alcoa Inc. v. FERC , 564 F.3d 1342 , 1347 (D.C. Cir. 2009), and to its interpretations of its own precedent, NSTAR Elec. & Gas Corp. v. FERC , 481 F.3d 794 , 799 (D.C. Cir. 2007). Those same principles apply with equal force to our review of the Commission's application of the filed rate doctrine, which is " Chevron -like in nature." Old Dominion Elec. Coop. v. FERC , 518 F.3d 43 , 48 (D.C. Cir. 2008) (internal quotation marks omitted). Put simply, we afford the Commission's interpretation of the filed Tariff and the PJM Operating Agreement "substantial deference" unless "the tariff language is unambiguous." Id . (internal quotation marks omitted).

A

The governing law is not in question here. The filed rate doctrine and the rule against retroactive ratemaking leave the Commission no discretion to waive the operation of a filed rate or to retroactively change or adjust a rate for good cause or for any other equitable considerations. Columbia III , 895 F.2d at 794-797 . These corollary rules operate as a nearly impenetrable shield for consumers, ensuring rate predictability and preventing discriminatory or extortionate pricing. West Deptford , 766 F.3d at 12 ; see Arkansas La. , 453 U.S. at 578 , 101 S.Ct. 2925 (explaining that not even "the Commission *1231 itself" possesses the authority to contravene the prospective application of rates).

Given those emphatic rules against retroactively changing filed rates and the absence of any equitable waiver authority in the Commission, the only question in this case is whether granting Old Dominion the waiver it sought would have violated one of those prohibitions. We agree with the Commission that either waiver would have run afoul of both.

To begin with, there is no dispute that the PJM Tariff's filed rate did not allow the cost recovery that Old Dominion seeks. In fact, Old Dominion repeatedly conceded before the Commission and this court that the filed Tariff categorically precluded its compensation for losses caused by the rate cap.

That would seem to be the end of the matter. But Old Dominion argues that recouping its losses would be consistent with the filed rate doctrine because ratepayers were on notice that the Tariff set a market rate for electricity, and the Polar Vortex altered that market rate.

Close, but no cigar. Old Dominion is correct that no violation of the filed rate doctrine occurs when "buyers are on adequate [advance] notice that resolution of some specific issue may cause a later adjustment to the rate being collected at the time of service." Natural Gas Clearinghouse v. FERC , 965 F.2d 1066 , 1075 (D.C. Cir. 1992). When the very terms of the filed rate warn customers, at the time they contract for service, that the price charged will fluctuate based on an identified formula with specified cost drivers, then the rate is allowed to change when fluctuations in those cost drivers occur. That, after all, is how formulae work. And that comports with the filed rate doctrine because the rate changes are foreordained, not retroactive. See, e.g. , Public Utilities Comm'n , 254 F.3d at 254 (explaining the well-established acceptability of formula rates that specify the cost components that form the basis of the rates a utility charges its customers); Transwestern Pipeline Co. v. FERC , 897 F.2d 570 , 578 (D.C. Cir. 1990) ("The Commission need not confine rates to specific, absolute numbers but may approve a tariff containing a rate 'formula' or a rate 'rule' * * *; it may not, however, simply announce some formula and later reveal that the formula was to govern from the date of announcement[.]").

Old Dominion's notice theory does not work in this case. Old Dominion has failed to identify any Tariff provisions that openly specify the type of market-variable cost components required for formula rates. Cf. Public Utilities Comm'n , 254 F.3d at 255 (citing, as an example, rate increases caused by new wage agreements where the utility agreed to a formula rate with a labor cost component); West Deptford , 766 F.3d at 22 (ratepayers have notice that rates determined by filed formulas will be determined according to the formula); NSTAR , 481 F.3d at 801 (rates may constantly change as long the changes are consistent with the formula on file with the Commission).

Plus, if there were such variables, then they presumably would run in both directions. Yet tellingly, Old Dominion is unable to cite a single instance in which bull market conditions for utilities produced a refund to consumers of over-billed amounts.

The coup de grace for Old Dominion's theory is that the filed rate on its face assured customers that, however the market might change, charges would be capped at $1,000 per megawatt-hour. Tariff, Attachment K, Appendix § 1.10.1A(d)(viii). Customers, in other words, were on explicit notice that, although *1232 market forces might cause some variation within a range, the rates charged would never exceed the agreed-upon rate cap. Old Dominion points to nothing in the Tariff's terms that lifts that cap for the charges for which it seeks recoupment. To toss that cap aside after the fact just because it did exactly what a cap is supposed to do-serve as a firm ceiling on market prices-would retroactively rewrite the terms of the filed rate. The filed rate doctrine and rule against retroactive rulemaking flatly forbid such a result.

Old Dominion argues alternatively that PJM's January 21 statement on its website, noting that it was seeking FERC's approval for certain generators to exceed the rate-cap, gave customers the required prospective notice that emergency retroactive rate increases could ensue. That argument fails at every step.

First, the website statement was not filed with the Commission. That is required for all rate changes. 16 U.S.C. § 824d(d) ; see West Deptford , 766 F.3d at 23-24 ; see also City of Piqua v. FERC , 610 F.2d 950 , 954 (D.C. Cir. 1979). As a result, the statement did not provide the legally required notice to even first-line purchasers in the wholesale markets, such as load-serving entities, let alone to the downstream retail customers. See Columbia III , 895 F.2d at 797 (citing Columbia Gas Trans. Corp. v. FERC , 831 F.2d 1135 , 1140-1141 (D.C. Cir. 1987), abrogated on other grounds by Transwestern , 897 F.2d at 579 ); cf . City of Piqua, 610 F.2d at 954-955 (approving a seemingly retroactive rate because a pre-existing contractual agreement provided ratepayers prospective notice of the impending rate change from the date of the contract).

Second, the website post was limited to retroactive "make whole" payments (which the actual waiver did not request), and to prospective relief allowing generators to submit cost-based offers into the day-ahead market above $1,000/megawatt-hour. On top of that, the website post reiterated that, unless and until the Commission granted the prospective waiver of the Tariff's rate cap provision, the market rules remained in effect-including the $1,000 rate cap. To be sure, the Commission ultimately waived the sixty-day statutory notice period and granted PJM's requested prospective relief effective January 24, 2014. That just confirms that the Commission stuck to its prospective-only authority to adjust rates and that it left the past rates as it found them.

For all of those reasons, we uphold the Commission's decision denying retroactive rate adjustments and deny Old Dominion's petition for review.

B

Turning to Monitor's pending motion to intervene, we hold that Monitor has no legally cognizable interest in this case, and thus lacks standing. Accordingly, its motion to intervene is denied.

Intervenors become full-blown parties to litigation, and so all would-be intervenors must demonstrate Article III standing. 2 See *1233 Fund for Animals, Inc. v. Norton , 322 F.3d 728 , 732-733 (D.C. Cir. 2003). To do so, the prospective intervenor must establish injury-in-fact to a legally protected interest, causation, and redressability. See Crossroads Grassroots Policy Strategies v. FEC , 788 F.3d 312 , 316 (D.C. Cir. 2015). This court also looks to the timeliness of the motion to intervene and to whether the existing parties can be expected to vindicate the would-be intervenor's interests. See Deutsche Bank Nat'l Trust Co. v. FDIC , 717 F.3d 189 , 192 (D.C. Cir. 2013). The Monitor, however, has failed to establish that the litigation implicates any legally protected interest sufficient to confer Article III standing.

The role of the Monitor is, as explained in the PJM Agreement, to "objectively monitor, investigate, evaluate and report on the PJM Markets, including, but not limited to, structural, design or operational flaws" that the markets might display. Monitor Br. A10-A11. 3 PJM retained the Monitor as an outside consultant to undertake those market-monitoring tasks. The Monitor is charged with "mak[ing] such recommendations" to PJM "as [it] shall deem appropriate" to "address design flaws, structural problems, compliance" and other market anomalies that the Monitor detects. Monitor Br. A4.

The Monitor's role, however, is much in the nature of an auditor-it is largely confined to observing the market's operations and then offering recommendations to PJM. The Monitor has no authority to enforce or to interpret the PJM Agreement or Tariff, to direct changes in the market's operations, to alter market rules, or to police individual members' compliance. Other than making some regulatory filings, all the Monitor can do is inform the Commission, authorized government agencies, or PJM's participating members if it disagrees with PJM's implementation of the market rules or operation of the PJM market. Beyond its contractually assigned tasks, the Monitor has no independent legal interest of its own in the PJM markets.

That is not enough for Article III. The Monitor's professional assignment to monitor the markets so that PJM and its members can promote the market's efficient and successful operation does not invest the Monitor with any legally cognizable rights concerning either how PJM addresses Old Dominion's application for retroactive relief or how Old Dominion complies with the Tariff or Agreement. The Monitor is not a contractual party to either the Tariff or the Agreement, and it has no legal interests that are affected one way or the other by any parties' non-compliance. It is, instead, an outside observer hired to study and report objectively on the market's operations.

The Monitor nonetheless asserts that its "responsibility to monitor the markets" under the Agreement would be impaired if Old Dominion prevails in this action. Monitor Br. A4. The Monitor adds that it was a "core participant," not just a "mere observer," in the Commission proceeding that led to the order on review. Id. The Monitor further worries that, if the Commission's order were reversed, then the competitive market design that the Monitor is "charged to protect" will need "repair," requiring the Monitor to "redeploy its limited resources in an effort * * * to craft new rules that are harder to undermine." Monitor Br. A6.

We fail to see how this proceeding imperils any legally protected interest of the *1234 Monitor. Whether Old Dominion wins or loses, the Monitor's ability to observe the market's operations and to make recommendations or to inform potentially interested parties of its observations remains the same.

Nor did the Commission's order determine any legal rights belonging to the Monitor or benefit the Monitor in any discernable way. The Monitor thus has no "significant and direct interest" in defending the Commission's denial of Old Dominion's requested relief. Crossroads , 788 F.3d at 318 . The Monitor faces no "threatened loss" from this court's review, nor did it acquire any tangential benefit from the Commission's order. Cf . Fund for Animals , 322 F.3d at 733 (allowing Mongolian entity to intervene where Secretary of Fish and Wildlife's decision to not list argali sheep as endangered indirectly benefitted Mongolian tourism and conservation industries); Military Toxics Project v. EPA , 146 F.3d 948 , 954 (D.C. Cir. 1998) (allowing manufacturers' association to intervene on the side of the EPA because some of its members indirectly benefitted from an EPA rule regarding munitions).

The Monitor, for its part, identifies no law that vests it with independent legal rights. The Monitor is not a creature of statute and operates under no affirmative duty imposed by public law. Quite the contrary, even its existence is a matter entirely within PJM's discretion. And its function is limited to monitoring, advising, encouraging compliance, and informing others through regulatory filings and other informal communications, none of which are at stake in this case. Cf. Sea-Land Serv., Inc. v. Department of Transp. , 137 F.3d 640 , 648 (D.C. Cir. 1998) ("[M]ere precedential effect within an agency is not, alone, enough to create Article III standing, no matter how foreseeable the future litigation.").

Because it lacks any legally cognizable interest or right in this proceeding, the Monitor lacks standing, and intervention is denied. We will, however, grant the Monitor amicus curiae status.

* * * * *

For the foregoing reasons, we deny the petition for review and the motion to intervene, but we will allow the Monitor to participate as an amicus curiae .

So ordered.