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Retrofitting centralized air compressor stations with end-use-aware predictive set-pressure control using a physics-constrained pressure-drop model

Taito Watanabe, Yohei Kono, Akira Iyozumi, Takashi Nakajima

arXiv:2610.36678v1eess.SYcs.SY

TL;DR

The paper addresses lowering compressor set pressure without letting end-use pressure fall below its requirement. It uses a constrained pressure-drop model in a lightweight NMPC; under real demand, it met the required pressure and reduced estimated annual energy consumption by 2.8% relative to current constant operation.

  • Problem

    The control problem is to keep set pressure as low as possible without letting end-use pressure fall below its requirement.

    Source: §2.3 · p. 3

  • Method

    A constrained least-squares pressure-drop model lets the NMPC hold the measured pressure drop over its horizon with unit gain.

    Source: §5.3 · p. 10, §8 · p. 18

  • Results

    2.8% lower estimated annual energy consumption than K0′, with no required-pressure violations under real demand.

    Source: §6.2 · pp. 12–13

  • Takeaways & Limitations

    The required-pressure margin is a design parameter sized from plant data and the update period.

    Source: §7.2 · p. 17

    The method serves a centralized station through one representative critical end-use point; drops that outrun receiver pressurization are beyond set-pressure control.

    Source: §7.2 · p. 17

Abstract

from arXiv · show

Compressed air systems usually run at a constant set pressure well above the end-use requirement; the excess margin is wasted energy. A lightweight hierarchical nonlinear model predictive control (NMPC) scheme, retrofitted to the sequencing controller of a centralized compressor station typical of small and medium-sized plants, lowers the set pressure as far as the end-use requirement allows. It uses only two pressure gauges (receiver and one critical end-use point) and compressor data, without flow meters or piping surveys. The end-use pressure is predicted by a low-order pressure-drop model identified by least squares under stability, damping and steady-state equilibrium constraints, which serve use rather than accuracy: they let the measured pressure drop be held over the horizon with unit gain. Validated in three stages (plant data, a pipe-network simulator checked against measurements, and the actual controller, at most 1.41 s per update), the NMPC meets the required pressure under real demand and reduces the estimated annual energy consumption by 2.8 % relative to the current constant operation (9.3 % relative to 0.70 MPa). A PID cascade with the same gauge saves about as much only when tuned by a standard rule at its recommended setting from a constant-load step test, difficult in an operating plant; the NMPC needs no such test and keeps its performance with its initial model and default weights after plant expansion and network split. The margin becomes a design parameter instead of a fixed excess, and the controller's signals show where the supply system lacks headroom.

1. Introduction

Compressed-air plants often waste energy by maintaining set pressure above end-use needs, while practical constraints limit instrumentation, modeling, and controller retuning. This paper proposes a staged-validated hierarchical NMPC that lowers set pressure using limited measurements and existing controller hardware.

1.1. Background and practical constraints

  • Excess set pressure is wasted energy, but hidden piping, costly flow meters, limited controller resources, and changing networks constrain pressure reduction.The study targets centralized compressor stations typical of small and medium-sized factories.Source: §1.1 · p. 1

1.2. Existing approaches and their limitations

  • Existing approaches often omit network pressure drops, require surveys or distributed instruments, lack facility-change procedures, or permit unstable multi-step predictions.Prior work includes physical-model optimization, local end-use measures, and data-driven prediction and optimization.Source: §1.2 · pp. 1–2

1.3. Contributions

  • The hierarchical NMPC lowers set pressure using one added end-use gauge and compressor data, while constrained pressure-drop modeling and fixed-weight control address prediction and facility changes.The method also runs on existing sequencing-controller hardware. The new work extends the authors’ conference paper with real-demand closed-loop evaluation, PID comparison, facility-change scenarios, and simulator validation.Source: §1.3 · pp. 2–3

1.4. Staged validation

  • The method is assessed through plant-data identification, closed-loop simulation checked against plant measurements, and execution-time measurement on the actual sequencing controller.Closed-loop plant trials follow these validation stages because an unvalidated controller could let end-use pressure fall below production requirements.Source: §1.4 · p. 3

2.1. System configuration and conventional operation

  • The system lowers the sequencing controller’s set pressure dynamically while leaving compressor control loops and sequencing logic unchanged.Conventional operation instead keeps set pressure fixed above the required end-use pressure.Source: §2.1 · p. 3

2.2. Target plant and available measurements

  • The validation plant uses receiver and end-use pressure gauges, compressor current data to estimate discharge flow, and one added gauge at the critical end-use point.P5 is the selected end-use pressure; its measured dips were deepest among the end-use points over the eight-day period, although P3 was often slightly lower.Source: §2.2 · p. 3

2.3. Problem statement

  • The objective is to minimize set pressure while keeping end-use pressure above its requirement, without piping data or flow meters, on the existing controller, and without manual retuning after facility changes.The controller updates the set pressure at a period well below the compressor response time.Source: §2.3 · pp. 3–4

3. Physics-constrained data-driven modeling

The controller predicts end-use pressure by chaining low-order compressor, receiver, and end-use models rather than building a physical pipe-network model. Physics constraints shape the end-use model’s transients and steady-state behavior, while identification uses a constrained, repeatable procedure.

3.1. Modeling approach

  • The prediction chain links compressor flow, receiver pressure, and end-use pressure models, using estimated total demand as an input without a physical pipe-network model.The three models have six states in total.Source: §3.1 · p. 4

3.2. Receiver pressure model

  • The receiver model represents pressure changes from the difference between compressor inflow and total plant demand, assuming mass conservation and isothermal conditions.Receiver volume is a known rating, and compressor discharge flow comes from internal compressor data.Source: §3.2 · p. 5

3.3. Compressor discharge flow model

  • A nonlinear first-order compressor model represents feedback on set-pressure error, rated-flow saturation, and steady-state delivery; its identified block includes the receiver-pressure PI response.The lower bound β ≥ 29.44 encodes at least 90% saturation when set pressure exceeds receiver pressure by 0.1 MPa; modeling the PI explicitly changed mean end-use pressure by 0.001 MPa.Source: §3.3 · p. 5

3.4. End-use pressure model: second-order ARX with a pressure-drop variable

  • The second-order end-use model makes pressure drop explicit; its steady-state equalities carry changes in drop level through measured p_diff while parameters describe transient delay and overshoot.Adding p_diff is a reparameterization of the standard ARX(2,2) regressor space, not additional information.Source: §3.4 · p. 5

3.5. Physical constraints and their meaning

  • Constrained least squares enforces stable multi-step predictions and a transient that settles to constant pressure drop, matching the model’s use with measured p_diff held fixed.The stability condition is designed for that prediction use; computing p_diff from model output instead would place poles at 1 and 1.047.Source: §3.5 · pp. 5–6

3.6. Identification procedure

  • The identification procedure uses constrained optimization with specified data windows and checks constraint satisfaction and one-step error; apart from stated bounds and window choices, it has no tuning parameters.For the same data and initial guess, it returns the same model; the end-use model identification takes about 0.03 s.Source: §3.6 · p. 6

4. Lightweight hierarchical nonlinear MPC

A supervisory NMPC layer adjusts the set pressure above the existing sequencing logic and receiver-pressure PI, using measured signals to predict end-use pressure. Its single-variable optimization is designed for limited controller resources, and its pressure-drop model structure supports operation through facility changes.

4.1. Control architecture

  • The supervisory NMPC runs on the existing sequencing controller above unchanged compressor control and plant layers, using three measured signal types and a single online decision variable.The architecture takes 1-s measurements of receiver pressure, end-use pressure, and compressor flow; identification can be rerun on logged data when triggered and replaces parameters only after a passed check.Source: §4.1 · p. 6, Figure 3 · p. 7

4.2. Demand estimation

  • Total plant demand is estimated by inverting the receiver model from compressor flow and receiver pressure, then assumed constant over the 30-s prediction horizon.The estimate uses a 1-s backward difference without filtering and updates in the next control cycle after a demand change.Source: §4.2 · pp. 6–7

4.3. NMPC formulation

  • Each cycle optimizes one set-pressure value to track the required-pressure target with a margin, predicting end-use pressure through the model chain and holding measured pressure drop over the horizon.A terminal weight makes end-of-horizon deviation dominate stage deviations; the end-use lower bound is not an explicit state constraint, and power is absent from the objective.Source: §4.3 · pp. 7–8

4.4. Computation and implementation

  • Online SQP is kept lightweight through analytic Jacobians, a warm start from the previous cycle, and a three-iteration cap; each iteration simulates the model chain across the horizon.The implementation uses one decision variable and has computational load O(T_pN_iter).Source: §4.4 · p. 8

4.5. Coping with facility changes: structure and re-identification

  • The pressure-drop model absorbs changes in drop level through its online estimate, while altered delay or overshoot can prompt re-identification on post-change data and replacement only after checks pass.The initial model is also evaluated under plant expansion and network split; re-identification may be triggered by a facility change, schedule, or excessive one-step prediction error.Source: §4.5 · p. 8

5. Validation on plant data

Plant data, constrained-model comparisons, and simulator measurements validate the pressure predictions across transient and multi-step conditions. The constrained end-use model remains stable and accurate when the measured pressure drop is held over the prediction horizon.

5.1. Dataset

  • The end-use model was identified on 34,113 samples and validated on 19,623 daytime samples, while compressor identification used 258 samples around a set-pressure change.The operating data came from a plant system other than the one modeled by the simulator; the compressor test included set-pressure excitation and required no constant load.Source: §5.1 · pp. 8–9

5.2. Identified parameters and prediction accuracy

  • Plant-data predictions achieve MAPE of 1.10 % for discharge flow and 0.03 % for receiver pressure; recursive end-use prediction has MAPE of 0.24 % and maximum error of 25.8 kPa.During a rapid pressure-drop-change interval, end-use prediction has MAPE of 0.30 % and maximum error of 17.3 kPa.Source: §5.2 · p. 9

5.3. Multi-step prediction: constrained versus unconstrained identification

  • Held, M-con is stable and as accurate (1.43–1.49 kPa) as M-std without hold (1.45 kPa), while M-unc diverges and held M-std error grows to 4.5 kPa.Without hold, M-std is accurate but after about 20 s no longer contains measured end-use pressure, leaving the NMPC without feedback.Source: §5.3 · p. 10
  • The equality constraints make M-con’s held prediction a unit-gain filter of receiver pressure minus the held pressure drop, settling within 2–3 s.The equalities and stability matter more than exact pole values, which the data determine only weakly.Source: §5.3 · p. 10

5.4. Comparison of the pipe-network simulator with measurements

  • The simulator follows measured end-use pressure through transients and oscillations, with mean pressure error of 5 kPa at steady receiver pressure and 8 kPa during oscillation.The comparison was made before closed-loop evaluation, with no separate held-out validation data.Source: §5.4 · p. 10

6. Closed-loop evaluation

Across real and synthetic demand, K2 reduced supply pressure while meeting the end-use requirement. The evaluation also examines facility changes, field tuning, controller runtime, and estimated energy savings.

6.1. Evaluation setup

  • The simulator links receiver, compressor, and pipe-network models across 20 end-use points; compared controllers share targets, bounds, and scenarios.The real-demand input reconstructed controlled-point flow from measured pressure drop; simulator replay reproduced measured end-use pressure with 3.9 kPa MAE.Source: §6.1 · pp. 11–12, §6.2 · p. 12

6.2. Evaluation with real demand at the controlled end-use point (main result)

  • 9.3% lower estimated annual energy use than K0 and 2.8% lower than K0′; K2 met required pressure under real demand.K2 averaged 0.589 MPa set pressure and 0.571 MPa end-use pressure, with a 0.565 MPa minimum. K0′ represents idealized operation at the actual operation’s mean pressure; simulated compressors omit load/unload losses.Source: §6.2 · pp. 12–13, Table 7 · p. 13, Figure 8 · p. 13

6.3. Evaluation with synthetic load

  • 0.617 MPa mean set pressure with K2 versus 0.699 MPa with K0; minimum end-use pressure was 0.5002 MPa, meeting the 0.50 MPa requirement.K2 raises set pressure in anticipation of increasing demand and lowers it when load returns; K1-SIMC had larger post-load overshoot and undershoot.Source: §6.3 · pp. 13–14, Table 8 · p. 14, Figure 9 · p. 14

6.4. Robustness to facility changes (plant expansion and network split)

  • Without retuning, K2 and K1-SIMC avoided violations after expansion and network split; K2 settled earlier in both cases and saved as much or more energy.K2’s initial end-use model absorbed pressure-drop shifts; even with receiver volume off by a factor of two, its metrics changed little.Source: §6.4 · pp. 14–15, Table 9 · p. 15, Figure 10 · p. 16

6.5. PID tuning sensitivity and the difficulty of tuning in the field

  • Reducing the PI closed-loop time constant degraded energy reduction by 0.2–0.8 points at τc=θ/2 and 2.3–3.6 points at τc=0.Higher gain adds overshoot rather than speed in this dead-time-dominant loop; tuning in a running plant is difficult because the required constant-load test takes about 80 seconds and must be repeated after facility changes.Source: §6.5 · p. 15

6.6. Execution time on the industrial controller

  • 0.7109–1.4125 s per computation on the industrial controller; a 2-s update applied 1.4 s late produced a 0.498 MPa minimum, about 2 kPa below requirement.The measured runtime was bounded by the iteration limit; the 1-s update used in the evaluation met the stated requirement.Source: §6.6 · pp. 15–16

6.7. Estimated energy saving

  • Under synthetic load, estimated annual energy use was 376,087 kWh with K2 versus 400,904 kWh with K0, a 6.2% reduction.The annual estimate uses a power model, not a measurement; its assumptions include 8.4% less power per 0.1 MPa lower discharge pressure and 6,000 operating hours per year.Source: §6.7 · p. 16

7. Discussion

Staged validation supports the constrained model and shows that the controller lowers set pressure while meeting required pressure under simulated real demand. Its demonstrated scope is bounded by the evaluation setup and by the headroom available in the supply system.

7.1. What the staged validation shows and does not show

  • Constrained identification produced usable NMPC models from plant data, and simulation showed pressure compliance under real demand, robustness to facility changes, and performance comparable to a SIMC-tuned PI cascade.The simulator agreed with measurements within 5–8 kPa; actual-controller updates completed within the compressor response time.Source: §7.1 · p. 16
  • Only closed-loop trials in the plant can confirm what the staged validation establishes before operational-risk exposure.The evaluation describes plant trials as stage (iv).Source: §7.1 · p. 17

7.2. Scope and limitations

  • The method controls one representative critical end-use point, and a pressure drop faster than receiver pressurization lies beyond set-pressure control.The required-pressure margin is sized from plant data and the update period; robustness was tested with facility changes and a twofold receiver-volume error, not a stability-margin analysis.Source: §7.2 · p. 17
  • The closed-loop evaluation uses an idealized simulator and estimated energy, leaving plant cycling, long-term operation, actual consumption, and real-change re-identification for plant trials.The energy estimate excludes load/unload losses and assumes pressure-independent demand.Source: §7.2 · p. 17

7.3. Deployment and implications for supply-system operation

  • Deployment adds a critical-point gauge and uses operating data without piping surveys or flow meters; multiple critical points can share one set-pressure decision.Supervised introduction widens the set-pressure lower bound gradually, with fallback to conventional operation on sensor, prediction, or solver faults.Source: §7.3 · p. 17
  • The pressure margin trades energy savings against headroom and can be sized from expected pressure-drop increases and the relative rates of end-use pressure fall and receiver pressurization.During the 1200 L/min design event, the drop rose about 0.08 MPa in 35 s; minimum end-use pressure was 0.500 MPa with K2 and 0.502 MPa with K1-SIMC.Source: §7.3 · p. 17
  • At 1500 and 2800 L/min steps, both K1-SIMC and K2 fell below required pressure, while constant 0.70 MPa operation avoided it.The compressors were saturated at 1500 L/min; minimum pressure was 0.45–0.47 MPa over 77–84 s.Source: §7.3 · p. 17
  • Controller signals can identify excessive pressure losses and indicate where branch-pipe enlargement, a local receiver, or feedforward could permit further set-pressure reduction.The controlled-point drop reached 128 kPa at 1200 L/min, versus 35 kPa at the largest real demand.Source: §7.3 · p. 18

8. Conclusions

The paper presents end-use-aware NMPC as a retrofit for centralized compressor stations and explains how physics-constrained identification makes its pressure-drop model usable for prediction. The controller reduces estimated energy use while meeting the required pressure, and its explicit margin also informs supply-system design.

8. Conclusions

  • Estimated annual energy consumption fell by 2.8 % relative to current operation while the NMPC met required end-use pressure.The method used one added pressure gauge, retained performance after plant expansion and network split with its initial model and default weights, and updated within 1.41 s.Source: §8 · p. 18
  • Stability, damping, and constant-drop equilibrium constraints make the identified model usable with a held measured pressure drop, rather than improving its accuracy.The constrained model passes the held drop through with unit gain; unconstrained regressors diverged, and a standard ARX model amplified held error eightfold.Source: §8 · p. 18
  • One added pressure gauge and sequencing-controller software turn set-pressure reduction into a retrofit based on a fixed procedure and operating data.No piping survey, flow meters, or constant-load site step test are needed for the NMPC deployment.Source: §8 · p. 18
  • The margin p_ref − p_need becomes an explicit design parameter, while controller signals indicate where branch capacity may need improvement.The signals can inform decisions about branch enlargement and adding local receivers.Source: §8 · p. 18

A. Power model

The appendix specifies how compressor power and annual energy are estimated from load, discharge flow, pressure, and operating time.

A. Power model

  • Rated-load power is approximately 45.1 kW, calculated from 42.55 kW rated power and 0.943 overall efficiency; unload power is 10 % of load power.The fixed-speed compressor runs at 4000 L/min, while the variable-speed compressor supplies the remaining demand.Source: A. Power model · p. 18
  • Annual energy is estimated as mean total power over the evaluation interval multiplied by 6000 operating hours per year.For the variable-speed compressor, set-pressure peaks coinciding with high discharge flow increase power beyond what mean set pressure alone implies.Source: A. Power model · p. 18

B. Details of the PID cascade

The PID cascade uses a PI outer loop with bounded output and anti-windup; its SIMC tuning is derived from a constant-load pressure step response.

B. Details of the PID cascade

  • The outer PID cascade is implemented as a PI loop with output saturation from 0.50 to 0.95 MPa, clamping anti-windup, and a 0.70 MPa initial output.All parameter sets use zero derivative time.Source: B. Details of the PID cascade · pp. 18–19
  • A 0.60-to-0.65 MPa constant-load step yielded a FOPDT model with K = 1.03, τ = 15.7 s, and θ = 19.7 s; SIMC tuning at τ_c = θ gave K_c = 0.388.The estimated dead time differed by 27 % between FOPDT and second-order-plus-dead-time fits to the same response.Source: B. Details of the PID cascade · p. 19

Declaration of competing interest

The authors report relevant corporate relationships, no specific grant funding, proprietary data and simulator access, and their use of generative AI in preparing the manuscript.

Declaration of competing interest

  • The authors are employees of Hitachi companies that make compressors and sequencing controllers; the target plant, simulator, cited 8.4% coefficient, and related patent application also involve those companies.They declare no other competing interests.Source: Declaration of competing interest · p. 19

Funding

  • The authors report that the research received no specific grant funding.Source: Funding · p. 19

Data availability

  • The plant data and simulator are proprietary to the authors’ companies and cannot be shared; paper parameters, settings, algorithm, and supplementary scenario and pipe-network parameters are provided.Source: Data availability · p. 19

Declaration of generative AI and AI-assisted technologies in the manuscript preparation process

  • The authors used Claude Opus 5.5 to organize, draft, revise, and translate the manuscript, write code, and draw explanatory figures, then reviewed and edited the content.Source: Declaration of generative AI and… · p. 19

CRediT authorship contribution statement

Supplementary material for “Retrofitting centralized air compressor stations with

The supplementary-material heading names the paper’s topic and lists its four authors and two institutional affiliations.

Supplementary material

  • The supplementary material accompanies a paper on retrofitting centralized air compressor stations with end-use-aware predictive set-pressure control.Source: Supplementary material for… · p. 21

Authors

Affiliations

  • Watanabe and Kono are affiliated with Hitachi, Ltd., while Iyozumi and Nakajima are affiliated with Hitachi Industrial Equipment Systems Co., Ltd.Source: Supplementary material for… · p. 21

Numbering convention

S1 Conventional and target operation (Section 2.1)

The supplementary sections explain the target pressure-control concept, model connections, identification constraints, and control-cycle implementation, then report receiver-pressure prediction accuracy. In particular, the constrained model supports stable multi-step prediction, while the receiver model tracks pressure changes closely.

S1 Conventional and target operation (Section 2.1)

S2 Signal connections of the three models (Section 3.1)

  • The NMPC predicts end-use pressure through linked compressor, receiver-tank, and end-use models, using estimated demand held constant over the prediction horizon.The set pressure is the only decision variable, and model parameters are obtained without a piping model.Source: S2 Signal connections of the three… · p. 22, Figure S2 · p. 22

S4 Constraints on the end-use pressure model (Section 3.5)

S5 One control cycle of the NMPC (Section 4.4)

  • Each control cycle reads receiver and end-use pressures and compressor flow, estimates demand and pressure drop, then uses a warm-started SQP routine to update set pressure.It sends the resulting set pressure, including an intermediate iterate; after an infeasible solver stop, it retains the prior cycle’s set pressure.Source: S5 One control cycle of the NMPC… · pp. 23–24

S6 Receiver-pressure prediction (Section 5.2)

  • 0.03% mean absolute percentage error: the receiver model closely predicts pressure over a 258-s interval that includes a set-pressure increase from 0.60 to 0.65 MPa.Discharge flow saturates at rated flow as receiver pressure rises toward the new set pressure.Source: S6 Receiver-pressure prediction… · p. 24, Figure S4 · p. 24

S7 Multi-step prediction (Section 5.3)

The supplementary results assess multi-step prediction, real-demand evaluation conditions, PID tuning sensitivity, controller execution time, and model robustness. They also qualify a transient comparison by showing that its advantage depends on the simulator’s slower compressor.

S7 Multi-step prediction (Section 5.3)

  • From 30 to 120 s, M-con held-pressure prediction has 1.43–1.49 kPa MAE, comparable to uncorrected M-std at 1.45 kPa; M-unc diverges and held-error M-std is about three times worse.Uncorrected M-std loses dependence on measured end-use pressure after about 20 s, while held-pressure M-con retains it.Source: S7 Multi-step prediction (Section 5.3) · p. 24, Figure S5 · p. 25

S8 Real demand input (Section 6.2)

  • The real-demand evaluation covers weekday daytime demand changes on timescales of at least one minute, with reconstructed E20 flow averaging 367 L/min and ranging from 196–814 L/min.The simulator’s open-loop replay matches measured end-use pressure with 3.9 kPa MAE.Source: S8 Real demand input (Section 6.2) · p. 25, Figure S6 · p. 26

S9 PID tuning sensitivity (Section 6.5)

  • Shortening the PID cascade’s closed-loop time constant increases set-pressure variation and reduces energy saving, so it matches K2 only near the recommended setting.The compared tuning settings use the same step test and vary only the closed-loop time constant.Source: S9 PID tuning sensitivity (Section 6.5) · p. 26, Table S1 · p. 27

S10 Execution time on the industrial controller (Section 6.6)

S11 Compressor parameters of the simulator (Section 7.2)

  • The transient tracking advantage of K2 over retuned K1-SIMC occurs with the simulator’s slower compressor, but the controllers perform alike with the target-plant compressor.With the plant compressor, tracking MAE is 6.9 and 6.8 kPa and energy is −6.3 and −6.5% for K1-SIMC and K2, respectively.Source: S11 Compressor parameters of the… · p. 28, Table S2 · p. 28

S12 Robustness of the end-use identification (Section 7.2)

  • Across 13 files, the sign-constrained fit’s one-step error changes little, but removing the sign condition halves that error while making held-pressure prediction about 16 times worse.The one-step residuals are autocorrelated, so multi-step prediction is evaluated directly.Source: S12 Robustness of the end-use… · p. 28, Table S3 · p. 29

S13 Sources of data, models and settings (Data availability)

The supplement identifies the data sources, systems, settings, and simulator network used in the study. Plant data and the simulator are not shareable, so the tables document their sources and configurations.

S13 Sources of data, models and settings (Data availability)

  • Plant data and the simulator cannot be shared; Tables S4–S6 document their sources, models, and settings.System R is the compressed-air system with receiver b0 and end-use point b4; System Y is the simulator modeled from Fig. 2.Source: S13 Sources of data, models and… · p. 29, Table S4 · p. 30
  • The closed-loop scenarios use a 1-s sampling and control period, pneed = 0.50 MPa, pref = 0.572 MPa, and set-pressure bounds of 0.50–0.95 MPa.The table also records controller weights and horizons, simulator parameters, compressor capacities, and receiver volume.Source: Table S5 · p. 30
  • Real-demand scenarios use a 200–300 L/min base load, a reconstructed E20 load averaging 367 L/min, and a 7200-s duration; synthetic scenarios include 18 base-load points and E1/E20 steps.Expansion changes pipe diameters and receiver volume; the split scenario raises E20 demand to 1.6 times its nominal value.Source: S13 Sources of data, models and… · p. 30
  • Validation data for system R comprise 1,951 origins spaced 10 s apart, and the held term is set at each origin to reproduce measured end-use pressure.The supplementary material also lists synthetic-load parameters and simulator and controller settings for a multi-step prediction.Source: S13 Sources of data, models and… · p. 30
  • The simulator network has 63 nodes, including 20 end-use points, one pressure boundary, and one reservoir, in addition to the compressor-model receiver.End uses are flow boundaries, while the compressor side is a pressure boundary; the separate 2.26 m3 air reservoir remains unchanged in the expansion and split cases.Source: Table S6 · p. 31
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