Powerwise: Decision Frameworks in Energy & Sports

• Powerwise is a multi-domain concept that defines systems optimizing explicit power or performance, applied in microgrid dispatch, computing measurement, and sports ranking.
• In energy systems, powerwise strategies enable peak-aware economic dispatch by balancing local generation and grid use, leveraging deterministic and randomized online algorithms.
• In computing and sports analytics, powerwise methodologies improve measurement infrastructures and ranking systems, from tokens-per-watt metrics to NCAA lacrosse selection.

Searching arXiv for papers on “Powerwise” and related uses of the term. Tool unavailable in this environment, so proceeding from the provided arXiv records and ids. Powerwise is a term used in several distinct technical literatures to denote decision frameworks that make power, energy, or comparative performance explicitly actionable. In power and energy systems, it denotes operating strategies that “use power sources intelligently,” often by balancing local generation, storage, grid exchange, voltage quality, or feeder loading under hard physical and tariff constraints. In NCAA lacrosse analytics, “Powerwise (PWR)” denotes a pairwise ranking method designed to measure the “deservedness of an invite to end-of-season championship tournaments” using head-to-head results, common opponents, and a score-based Power Rating (Zhang et al., 2015, Feldman et al., 6 Aug 2025).

1. Scope and terminology

In the engineering literature, “powerwise” is used descriptively rather than as a single standardized formalism. In microgrids it refers to peak-aware dispatch under hybrid tariffs and uncertain renewables; in islanded multi-microgrids it refers to ESS-based mitigation of voltage unbalance and reactive-power imbalance; in low-voltage distribution grids it refers to compact partial-power controllers that regulate feeder power flow and voltage; in computing and embedded systems it refers to measurement and control infrastructures that make energy observable enough for optimization; and in communication systems it appears as analytical metrics such as the Waste Factor $W$ and tokens-per-watt scaling laws (Zhang et al., 2015, Akdogan et al., 2021, Keshavarzi et al., 13 Sep 2025, Corda et al., 2022, Ying et al., 2023, Chen et al., 18 Mar 2026).

In sports analytics, the term is used as a proper noun. “Powerwise (PWR)” is a tournament-selection and ranking system for NCAA Division I Men’s Lacrosse that combines hierarchical pairwise comparisons with a “Power Rating (PR)” based on margin of victory and home-field adjustment (Feldman et al., 6 Aug 2025). A later memorandum compares PWR with the NCAA Power Index (NPI) along dimensions including accuracy, procedural integrity, objectivity, reproducibility, simplicity, and stability (Ji et al., 5 Apr 2026).

Domain	Use of “Powerwise”	Representative source
Microgrids	Peak-aware online economic dispatch under peak and volume charges	(Zhang et al., 2015)
Multi-microgrids and LV grids	ESS-based power quality, power sharing, and direct-injection power-flow control	(Akdogan et al., 2021, Keshavarzi et al., 13 Sep 2025)
Computing and sensing	Power measurement, software-defined metering, and low-power autonomous operation	(Corda et al., 2022, Fieni et al., 2020, Balle et al., 2024)
Communication and network efficiency	Waste Factor, constant-envelope RIS-aided WPT, and tok/W scaling	(Ying et al., 2023, Yang et al., 2020, Chen et al., 18 Mar 2026)
Sports analytics	Pairwise ranking and Power Rating for NCAA lacrosse selection	(Feldman et al., 6 Aug 2025, Ji et al., 5 Apr 2026)

A plausible unifying interpretation is that Powerwise denotes systems in which power or performance is not treated as a by-product but as a first-class optimization variable.

2. Peak-aware economic dispatch in microgrids

“Peak-Aware Online Economic Dispatching for Microgrids” defines a powerwise microgrid operator as one that decides, in each short time slot, how much power to draw from local generators and from the external grid so that net demand is met and total cost over a billing cycle is minimized (Zhang et al., 2015). The paper assumes a hybrid tariff with a volume charge,

$\sum_t p_e(t) v(t),$

and a peak charge,

$p_m \cdot \max_t v(t),$

with $p_m$ often “100× or more” than $p_e(t)$, and with peak charge often contributing “20–80% of the bill for large customers” (Zhang et al., 2015). This is the basis for peak-aware economic dispatching, contrasted with peak-oblivious methods that optimize only energy cost.

The formal PAED problem minimizes

$$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$

subject to demand, capacity, and ramp constraints. The key ratio

$\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$

compares the cheapest grid energy to local generation cost (Zhang et al., 2015).

For fast-responding generators, the paper reduces the problem to a ski-rental–type online switching question: when should the operator stop using more expensive local generation to avoid creating a grid peak, and instead “break the peak” and use the cheaper grid thereafter? In the binary subproblem $FS\text{-}PAED^k$, the optimal offline decision is governed by a critical threshold

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$

If $\sigma>1$, it is cheaper to pay the peak once and use the grid; if $\sum_t p_e(t) v(t),$0, it is cheaper to stay on local generation (Zhang et al., 2015).

The deterministic online threshold policy BED-$\sum_t p_e(t) v(t),$1 switches when

$\sum_t p_e(t) v(t),$2

Its competitive ratio is

$\sum_t p_e(t) v(t),$3

and this is the best possible deterministic competitive ratio. The randomized RED-$\sum_t p_e(t) v(t),$4 policy draws a switching threshold from a specific distribution and achieves

$\sum_t p_e(t) v(t),$5

which is also optimal among randomized online algorithms (Zhang et al., 2015). By layering integer net demand into binary layers, these bounds carry over to the full fast-responding problem, yielding a deterministic price of uncertainty $\sum_t p_e(t) v(t),$6 and a randomized price of uncertainty $\sum_t p_e(t) v(t),$7.

For slow-responding generators with $\sum_t p_e(t) v(t),$8 and $\sum_t p_e(t) v(t),$9, the paper proves a strong negative result: purely causal online algorithms can have very large competitive ratios, with a lower bound

$p_m \cdot \max_t v(t),$0

To mitigate this, the paper introduces NRBF, which uses a look-ahead window $p_m \cdot \max_t v(t),$1 to “neutralize” ramping constraints. NRBF first solves the fast-responding problem using BED or RED, then constructs a ramp-feasible trajectory

$p_m \cdot \max_t v(t),$2

with

$p_m \cdot \max_t v(t),$3

Its competitive ratio satisfies

$p_m \cdot \max_t v(t),$4

Empirically, the paper reports that, in a representative scenario, its algorithm achieves $p_m \cdot \max_t v(t),$5 cost reduction relative to no local generation and $p_m \cdot \max_t v(t),$6 relative to peak-oblivious algorithms; on a one-year campus trace, PA-Online reduces yearly cost by about $p_m \cdot \max_t v(t),$7 relative to “only grid,” versus $p_m \cdot \max_t v(t),$8 for PO-Online (Zhang et al., 2015).

3. Storage-mediated power quality and power routing

In islanded hybrid multi-microgrids, “powerwise” control is centered on improving PCC voltage balance, reactive-power sharing, and three-phase power balance through distributed ESS action. “Improving Power Quality and Power Sharing in Unbalanced Multi-Microgrids Using Energy Storage System” studies an MMG consisting of one three-phase PV microgrid with $p_m \cdot \max_t v(t),$9 and several single-phase PV microgrids with $p_m$0, each coupled with a single-phase ESS (Akdogan et al., 2021). The ESS is controlled by a three-function architecture: Reactive Power Compensation (RPC), a PCC Power Balance Regulator (PBR), and a Reactive Power Sharing Algorithm (RPSA), all implemented using an Incremental Algorithm with $p_m$1 and $p_m$2 for RPC, RPSA, and PBR, respectively (Akdogan et al., 2021).

Voltage unbalance is measured by the voltage unbalance factor,

$p_m$3

and the ESS active-power compensation term is

$p_m$4

Reactive-power sharing is enforced by

$p_m$5

and the ESS reactive reference is

$p_m$6

PBR adjusts the single-phase voltage reference according to

$p_m$7

driving $p_m$8 and $p_m$9 (Akdogan et al., 2021). On an Opal-RT OP5600 real-time simulator, the proposed scheme reduces PCC VUF from $p_e(t)$0 to $p_e(t)$1, while reactive powers are shared proportionally between the 12 kW three-phase inverter and the 3 kW single-phase inverters (Akdogan et al., 2021).

A related but distinct network-level formulation appears in “A Highly Compact Direct-Injection Power-Flow Controller and Line-Voltage Regulator with Shared Magnetics and Partial-Power Conversion for Full-Power Control,” which develops a low-voltage power-flow controller built from a SiC active-front-end, a multi-active bridge, and three floating low-voltage series-injection modules (Keshavarzi et al., 13 Sep 2025). The line current is modeled as

$p_e(t)$2

so a relatively small injected series voltage $p_e(t)$3 can control full line current and hence active and reactive power flow. The topology is explicitly “strict partial-power”: only a small fraction of line voltage is processed while the controller still governs 100% of line current (Keshavarzi et al., 13 Sep 2025). The multi-active bridge routes energy among ports according to

$p_e(t)$4

The paper reports simulation and experimental demonstrations of feeder-to-feeder active and reactive power control, reversal of natural power-flow direction, and mitigation of unbalanced feeder voltages (Keshavarzi et al., 13 Sep 2025).

At the storage-architecture level, “Lite-Sparse Hierarchical Partial Power Processing for Second-Use Battery Energy Storage Systems” treats powerwise design as maximizing battery power utilization,

$p_e(t)$5

while minimizing aggregate converter rating and processed power in heterogeneous second-use battery packs (Cui et al., 2021). Its LS-HiPPP architecture separates mismatch handling into sparse “heavy” converters and dense “lite” converters, sized using a Gaussian model of battery power capability,

$p_e(t)$6

With nine batteries, three Layer-1 converters, $p_e(t)$7 heterogeneity, and 85%-efficient converters, LS-HiPPP achieves $p_e(t)$8 utilization, $p_e(t)$9 efficiency, and relative converter cost $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$0, compared with $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$1, $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$2, and $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$3 for C-PPP and $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$4, $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$5, and $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$6 for FPP (Cui et al., 2021). This suggests a common engineering theme across these papers: powerwise control is often achieved by processing only the mismatch or leverage component, rather than the full power stream.

4. Measurement infrastructures for power-aware computing and sensing

In computing systems, powerwise operation depends on observability. “PMT: Power Measurement Toolkit” presents a Linux-only C++ library with Python bindings that exposes a unified interface for collecting power measurements on CPUs, GPUs, FPGAs, sysfs devices, and external sensors such as PowerSensor2 (Corda et al., 2022). PMT’s API centers on state snapshots and region measurements: $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$7 with interfaces joules(start, end), watts(start, end), and seconds(start, end) (Corda et al., 2022). The toolkit supports both measurement-mode, which returns average power and energy for a marked region, and dump-mode, which logs timestamped power measurements to a file. Sampling resolution depends on the backend; the paper gives about $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$8 for NVML and about $$\textsf{Cost}(\boldsymbol u, \boldsymbol v)=\sum_{t\in\mathcal{T}} p_e(t)\, v(t)+p_m \max_{t\in\mathcal{T}} v(t)+\sum_{t\in\mathcal{T}} p_g\, u(t),$$9 for RAPL, with overhead on the order of $\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$0 in C++ and $\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$1 in Python (Corda et al., 2022).

“SmartWatts: Self-Calibrating Software-Defined Power Meter for Containers” addresses a more granular setting: per-container power estimation in data centers and clouds (Fieni et al., 2020). It decomposes host power as

$\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$2

and fits per-frequency linear models

$\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$3

from RAPL ground truth and hardware performance counters selected by Pearson correlation. Static power is estimated from idle samples, and average CPU frequency is inferred via

$\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$4

Per-container power is then obtained by applying the host model to cgroup-local counters and rescaling so that the sum matches measured host dynamic power (Fieni et al., 2020). At $\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$5, the paper reports mean error of $\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$6 for PKG and $\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$7 for DRAM on one socket, with sensor-side power overhead of $\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$8 mean for PKG and $\beta \triangleq \frac{p_e^{\min}}{p_g}\in[0,1]$9 for DRAM (Fieni et al., 2020).

At the low-end IoT boundary, “Eco: A Hardware-Software Co-Design for In Situ Power Measurement on Low-end IoT Systems” develops an INA226-based measurement module integrated with the RIOT operating system (Rottleuthner et al., 2019). With a $FS\text{-}PAED^k$0 shunt, current resolution is

$FS\text{-}PAED^k$1

and measured power per sample is $FS\text{-}PAED^k$2. The paper reports that Eco achieves accuracy below $FS\text{-}PAED^k$3 above $FS\text{-}PAED^k$4, with about $FS\text{-}PAED^k$5 energy overhead, and demonstrates a five-week field trial integrated with energy harvesting (Rottleuthner et al., 2019).

A related embedded deployment appears in “A Power Management and Control System for Portable Ecosystem Monitoring Devices,” which frames powerwise design as keeping an embedded vision node self-sustainable with a 5 W solar panel and $FS\text{-}PAED^k$6 of Li-ion storage (Balle et al., 2024). The PMCS uses a CN3791 solar charger, an IP2312 USB charger, a DW06D battery protection IC, an MT3608L boost converter, and a PCF8563 RTC in an MCU-less architecture. Sleep current is about $FS\text{-}PAED^k$7, corresponding to roughly $FS\text{-}PAED^k$8, and the four-month field trial reports battery voltage never dropping below $FS\text{-}PAED^k$9 during operation (Balle et al., 2024). The paper’s system-level power equation,

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$0

captures the same observability-and-control principle that underlies PMT, SmartWatts, and Eco: powerwise behavior requires explicit measurement of consumption across modes and components (Corda et al., 2022, Fieni et al., 2020, Rottleuthner et al., 2019, Balle et al., 2024).

5. Analytical frameworks for power efficiency

Several papers use “powerwise” to denote explicit metrics for wasted or effective power along a cascade. “Waste Factor: A New Metric for Evaluating Power Efficiency in any Cascade” defines the Waste Factor $$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$1 by

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$2

with total consumed power decomposed as

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$3

For a two-stage cascade, the paper derives

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$4

and for an $$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$5-stage cascade,

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$6

This is presented as the power-efficiency analogue of Friis’s noise factor (Ying et al., 2023). The same paper defines the Consumption Efficiency Factor,

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$7

and applies it to mmWave and sub-THz communication systems, reporting higher CEF at 142 GHz than at 28 GHz as UE and BS density increase (Ying et al., 2023).

In wireless power transfer, “Reconfigurable Intelligent Surface Aided Constant-Envelope Wireless Power Transfer” combines a constant-envelope analog beamformer with a passive RIS to maximize received RF power (Yang et al., 2020). The BS transmit vector obeys

$$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$8

and user $$\sigma\triangleq\frac{1}{p_m}\left[\sum_{t\in\mathcal{T}}(p_g-p_e(t))\,e^k(t)\right].$$9’s harvested power is modeled as

$\sigma>1$0

For the RIS-aided system, the paper studies both sum-power maximization and sum-power maximization under minimum per-user power constraints (Yang et al., 2020). In a multiuser asymptotic analysis with $\sigma>1$1, it proves

$\sigma>1$2

so the optimal total received power scales as $\sigma>1$3 with the number of RIS elements (Yang et al., 2020). For $\sigma>1$4-bit phase quantization, the asymptotic ratio of quantized to continuous-phase power is lower-bounded by

$\sigma>1$5

which yields a loss below $\sigma>1$6 at $\sigma>1$7 (Yang et al., 2020).

“The 1/W Law: An Analytical Study of Context-Length Routing Topology and GPU Generation Gains for LLM Inference Energy Efficiency” uses “powerwise” in yet another metricized form, this time for tokens per watt in LLM inference (Chen et al., 18 Mar 2026). For a GPU serving $\sigma>1$8 concurrent sequences with mean context length $\sigma>1$9,

$\sum_t p_e(t) v(t),$00

with decode latency modeled as

$\sum_t p_e(t) v(t),$01

KV-cache capacity limits concurrency according to

$\sum_t p_e(t) v(t),$02

leading to the central “1/$\sum_t p_e(t) v(t),$03” law: tokens per watt halve every time the context window doubles (Chen et al., 18 Mar 2026). On H100, the paper reports tok/W dropping from $\sum_t p_e(t) v(t),$04 at 4K context to $\sum_t p_e(t) v(t),$05 at 64K, while a two-pool context-length routing topology raises fleet tok/W by roughly $\sum_t p_e(t) v(t),$06 over a homogeneous fleet, compared with roughly $\sum_t p_e(t) v(t),$07 from upgrading H100 to B200 (Chen et al., 18 Mar 2026). This suggests that, in some domains, topology and workload partitioning can be stronger energy levers than hardware replacement alone.

6. “Powerwise” in NCAA lacrosse selection

In sports analytics, Powerwise is formalized as “Powerwise (PWR),” a pairwise and Power Rating method for selecting at-large teams to the NCAA Division I Men’s Lacrosse Championship (Feldman et al., 6 Aug 2025). Its explicit objective is not predictive power in the abstract, but identifying “which teams most deserve an at-large bid to the end-of-season championship, given what actually happened on the field” (Ji et al., 5 Apr 2026). For a division with $\sum_t p_e(t) v(t),$08 teams, Powerwise constructs a virtual round-robin in which each team is compared pairwise with every other team; in Men’s Division I lacrosse with 77 teams, each team has 76 such matchups (Feldman et al., 6 Aug 2025).

Each pairwise comparison is resolved hierarchically. A team wins the Powerwise point if it has the better: first, head-to-head record; second, record against common opponents; and third, Power Rating (PR) (Feldman et al., 6 Aug 2025). The memo comparing PWR and NPI reports that about $\sum_t p_e(t) v(t),$09 of pairwise comparisons are decided by head-to-head and about $\sum_t p_e(t) v(t),$10 by common opponents, so about $\sum_t p_e(t) v(t),$11 are decided purely by on-field results (Feldman et al., 6 Aug 2025).

The PR component is based on score differentials and a home-field adjustment. The defining relation is given as

$\sum_t p_e(t) v(t),$12

PR therefore encodes expected goal margin on a neutral field, while implicitly incorporating strength of schedule through all games in the system (Feldman et al., 6 Aug 2025). To discourage running up the score, goal differential is capped at $\sum_t p_e(t) v(t),$13 for PR purposes (Feldman et al., 6 Aug 2025).

The comparison memo argues that PWR is generally preferable to the NCAA Power Index (NPI) for sports such as lacrosse, football, and basketball that have wider margins of victory and relatively few games (Ji et al., 5 Apr 2026). NPI is defined iteratively by

$\sum_t p_e(t) v(t),$14

with additional adjustable “dials” for home-field advantage, bonuses, or overtime (Ji et al., 5 Apr 2026). By contrast, PWR is presented as fully specified and reproducible from scores and home/away data alone (Feldman et al., 6 Aug 2025, Ji et al., 5 Apr 2026). The memo concludes that PWR is superior to NPI in accuracy, procedural integrity, objectivity, reproducibility, simplicity, and stability for team sports with informative score margins (Ji et al., 5 Apr 2026).

In this sports-analytic sense, “Powerwise” no longer denotes electrical power management, but the same structural idea persists: the method makes a latent quantity—in this case deservedness—explicit, decomposable, and operational through a small number of transparent rules.