A Rigorous Two-Scale Predictive Optimization Framework for RE100 Grid Integration: Upcycling Urban Stormwater Detention Basins into Low-Head Variable-Speed Pumped Hydropower Plants with Hybrid Storage

Abstract

The global mandate for RE100 compliance has accelerated the deployment of distributed photovoltaic (PV) generation, posing significant challenges to grid inertia and voltage stability in land-scarce urban networks. To address these challenges, this study proposes an infrastructure upcycling paradigm that transforms subterranean urban stormwater detention basins into decentralized, low-head variable-speed pumped hydro energy storage (VS-PHES) systems coupled with flywheel (FESS) and lithium-ion battery (BESS) hybrid energy storage systems (HESS). The facility is governed by a two-stage hierarchical energy management system (EMS): Stage 1 utilizes mixed-integer linear programming (MILP) for day-ahead macroeconomic scheduling with battery degradation penalties, while Stage 2 executes a dual-rate non-linear model predictive control (NMPC) framework (100 ms supervisory/10 ms local loop) for sub-second micro-transient voltage and frequency regulation. Incorporating a 1D-CNN predictive feature extraction model refined with Symlet-4 wavelet pre-filtering, the system achieves 97.85% transient state classification accuracy. A fail-safe, flood control-priority state-switching logic ensures municipal flood safety during severe precipitation events. Validated on a modified IEEE 33-bus radial grid and a practical 22.9 kV 134-bus Korean urban distribution network under a localized 5 MW PV dropout contingency (within a 20 MW total installed capacity), the coordinated 3.5 MW hybrid facility mitigates transient voltage sags from 0.931 p.u. to 0.952 p.u. and arrests frequency nadirs at 59.35 Hz. A 20-year life-cycle cost (LCC) analysis demonstrates that FESS shielding saves up to USD 1.91 million in BESS replacement overheads, supported by a dynamic nodal tariff mechanism for private RE100 investment.

1. Introduction

The rapid transition toward carbon-neutral energy architectures, driven by international sustainability frameworks like the RE100 initiative, has fundamentally altered the topology of modern urban distribution networks [1]. The massive expansion of distributed energy resources (DERs), particularly distributed photovoltaic (PV) arrays, provides zero-emission active power but introduces critical operational vulnerabilities [2,3]. Because distributed PV systems are interfaced with the grid through static power electronic inverters, they lack the physical rotational mass inherent in conventional synchronous thermal generation units [4]. Consequently, high-penetration PV environments experience a dramatic reduction in total system rotational inertia. Under these low-inertia conditions, localized radial distribution feeders become highly susceptible to extreme rates of change of frequency (RoCoF), deep frequency nadirs, and transient voltage sags triggered by sudden cloud-shading events or localized feeder tripping [5]. Figure 1 illustrates the critical grid vulnerabilities and wide-area variability disturbances caused by spatial-temporal correlations when multiple distributed photovoltaic (PV) arrays experience sudden simultaneous drops due to cloud-shading events. It demonstrates that traditional average-value-based and historical deterministic control methods fail to accurately predict and defend against these multi-MW sudden generation dropouts. Consequently, the diagram highlights the imperative need for advanced probabilistic and distributed control frameworks to ensure stable urban distribution network operation.

Figure 1. Grid vulnerability, low-inertia degradation, and severe transient voltage violations under conditions of high distributed PV penetration.

A primary bottleneck preventing the installation of dedicated grid-stabilizing utility assets in metropolitan centers is the acute scarcity and prohibitive cost of urban land [6]. To address both physical spatial constraints and electrical stability challenges, this paper proposes an infrastructure upcycling framework. Densely populated metropolitan areas maintain extensive underground networks of stormwater detention basins and drainage tunnels engineered to mitigate flash flooding during severe precipitation events [7]. These massive civil engineering assets remain completely dry, idle, and unutilized for over 90% of the year. By partitioning these subterranean reservoirs into upper and lower hydraulic chambers, or by coupling them with adjacent low-elevation urban waterways, they can be re-engineered into decentralized low-head variable-speed pumped hydro energy storage (VS-PHES) facilities [8].

Figure 2 illustrates the inelastic water hammer pressure transients and hydro-mechanical response delays associated with governor valve opening and closing. Specifically, the top subplot demonstrates the transient response of the penstock flow rate (Q) and the water-hammer peak (2.25 p.u.) triggered by a rapid step closure event of the guide vane opening (G) at t = 2.0 s. Concurrently, the bottom subplot depicts the non-linear elastic water-hammer dynamics, highlighting the severe pressure surges and fluctuations in the effective hydraulic head (H) at the turbine inlet before eventually stabilizing.

Figure 2. Inelastic water hammer pressure transients and hydro-mechanical response delays associated with governor valve opening and closing.

However, integrating hydro-mechanical machinery into real-time microgrid regulation introduces severe fluid-dynamic constraints. Due to the inertia of the water column within the penstock, wicket gate adjustment delay, and the necessity of mitigating destructive water hammer phenomena, conventional and variable-speed pumped-storage units possess an intrinsic hydro-mechanical response lag ranging from hundreds of milliseconds to several seconds [9,10]. This hydrodynamic latency creates a critical control vacuum during the highly vulnerable sub-cycle transient window immediately following a massive renewable energy dropout. To bridge this dynamic operational gap, this study develops a multi-carrier hybrid energy storage system (HESS) co-located directly within the upcycled VS-PHES facility [11]. By coupling flywheel energy storage systems (FESSs)—which excel at instantaneous, sub-cycle kinetic power injection—with high-energy-density lithium-ion battery energy storage systems (BESSs), an organically balanced, multi-time-scale defense framework is established [12]. This structural co-location effectively eliminates response lag mismatch between heavy fluid infrastructure and ultra-fast electrical grid dynamics. While recent studies have explored Volt-VAR and Volt-Watt control optimization strategies to manage voltage stability in high-penetration PV radial feeders [12], these conventional methods lack active kinetic inertia; therefore, this study overcomes such limitations by proposing a robust infrastructure upcycling paradigm utilizing a VS-PHES and HESS multi-carrier framework

Figure 3 illustrates the multi-time-scale organic role-sharing mechanism for frequency defense and battery lifetime preservation within the hybrid energy storage system (HESS). Specifically, the top subplot demonstrates the power allocation strategy, where the high-frequency transient components of the total grid demand are absorbed by the flywheel energy storage system (FESS), while the smooth, bulk energy requirements are handled by the lithium-ion battery energy storage system (BESS). The middle subplot shows the FESS kinetic dynamics and its rotational angular velocity variations corresponding to high-frequency power fluctuations. Finally, the bottom subplot verifies that FESS shielding successfully maintains the BESS state-of-charge (SOC) within safe operational bounds and significantly mitigates cumulative cell degradation over time.

Figure 3. Multi-time-scale organic role-sharing mechanism for frequency defense and battery lifetime preservation.

Grounded in the multi-frequency admittance and harmonic decoupling principles articulated by Meng et al. [13], a high-speed frequency-decoupling filter topology is developed to allocate power components across storage assets seamlessly.

The recent literature on power system stability has increasingly emphasized the challenges of integrating inverter-based resources (IBRs) into weak distribution grids. As demonstrated by recent landmark studies, evaluating and forecasting data-driven system strength levels in IBR-integrated weak grids using multi-objective machine learning algorithms is paramount for anticipating voltage collapse and designing active inertia compensation strategies [14]. Furthermore, recent advancements in hybrid system architectures have demonstrated the critical importance of computationally efficient linear approximations for complex power flow dynamics. For instance, Zhang et al. [15] successfully proposed a robust linearization of the power flow model for asymmetrically coupled electrified railway-grid hybrid systems, achieving significant computational enhancements while preserving physical accuracy. Building upon these conceptual foundations of hybrid power flow linearization, our study extends this paradigm by introducing a two-stage hierarchical EMS architecture that leverages MILP for the macroeconomic integration of decentralized variable-speed pumped hydropower. When IBR penetration rises, traditional short-circuit ratio (SCR) metrics fail to capture localized dynamic impedance shifts, necessitating real-time predictive optimization frameworks capable of multi-scale dynamic response [14].

Specific Methodological Contributions

To address the limitations of conventional fixed-speed hydro units, uncoordinated storage assets, and weak grid voltage instability, this paper provides five key scientific and engineering contributions:

• Civil Infrastructure Upcycling Model: A realistic structural framework that transforms unutilized subterranean urban stormwater detention basins into decentralized 2.0 MVA low-head VS-PHES facilities without additional land acquisition costs.
• Dual-Rate Hierarchical EMS Architecture: A multi-time-scale predictive optimization system comprising Stage 1 day-ahead MILP macroeconomic scheduling and Stage 2 dual-rate NMPC (100 ms supervisory/10 ms local inverter control) with 1D-CNN real-time feature prediction.
• Hydro-Mechanical Physical Formulation: Comprehensive mathematical modeling incorporating non-linear inelastic water hammer pressure transients, variable-speed turbine kinetics, and electro-hydraulic governor latency.
• BMS Hardware Integration and Aged Cell Degradation Modeling: Complete Master-Slave BMS hardware specification with CAN 2.0B communication and B0005 431st cycle knee-point degradation modeling for conservative LCC evaluation.
• Validation on Practical Urban Feeder and HIL Architecture: Extensive validation on both standard IEEE 33-bus and a practical 22.9 kV 134-bus Korean distribution grid, complemented by control hardware-in-the-loop (CHIL) latency benchmarking.

To highlight the scientific and engineering contributions of this study, Table 1 presents a comprehensive methodological comparison between the proposed framework and the existing literature. Unlike conventional hybrid energy management systems and traditional urban pumped hydro configurations, the proposed architecture leverages unutilized subterranean stormwater detention basins, achieving a zero land cost footprint. Furthermore, it introduces a tri-hybrid storage coupling (VS-PHES, BESS, and FESS) governed by a dual-rate non-linear model predictive control (NMPC) architecture. The table also emphasizes the integration of non-linear water hammer dynamics, advanced weak grid validation methodologies on a practical 134-bus network, and a robust economic model featuring life-cycle cost (LCC) degradation shielding alongside a dynamic nodal tariff.

Table 1. Methodological comparison with the existing literature.

Comparative Dimension	Conventional Hybrid EMS	Urban Pumped Hydro	Proposed Framework
Civil Asset Footprint	Dedicated land acquisition	Surface reservoirs	Subterranean stormwater upcycling (zero land cost)
Control Architecture	Single-rate linear MPC/PI	Fixed-speed PI control	Dual-rate NMPC (100 ms supervisory/10 ms local loop)
Hydro Dynamics	Linearized constant head	Inelastic fluid model	Non-linear water hammer (Tw = 2.15 s) & variable speed
Storage Coupling	BESS only	Hydro standalone	Tri-hybrid (VS-PHES + BESS + FESS)
Grid Assessment and Validation	Static SCR/IEEE 33-bus	Uncoupled offline study	Weak grid strength ML (Ref [14]) + practical 134-bus grid + CHIL
Economic Model	Fixed tariff pricing	Peak-shaving arbitrage	LCC degradation shielding and dynamic nodal tariff

2. Dynamic Modeling of Upcycled Multi-Carrier Infrastructure

2.1. Non-Linear Water Hammer Dynamics & VS-PHES Response

As illustrated in Figure 2 illustrates the hydraulic transient response and water hammer pressure variations within the penstock during a rapid governor valve opening/closing sequence for the proposed low-head variable-speed pumped-storage hydropower plant (VS-PHES). Due to the massive volumetric flow rate required by the low-head municipal stormwater basin infrastructure, the fluid column inertia is substantially prolonged, resulting in an extended water starting time constant (T_w). The non-linear inelastic water hammer pressure dynamics inside the penstock are governed by the differential equation:

T_w·[^dq(t)/_dt] = h(t) − h₀ − h_f(t)

(1)

where q(t) is the normalized penstock flow rate (p.u.), h(t) is the normalized effective hydraulic head at the turbine inlet (p.u.), h₀ is the static head (12.5 m nominal), h_f(t) = f_r·q(t)|q(t)| represents hydraulic friction head loss, and T_w is the water starting time constant. T_w is defined as follows:

T_w = (L_p·Q_base)/(g_acc · A_p · H_base) = 2.15 s

(2)

The governor wicket gate actuator dynamics and mechanical power output P_hydro(t) are modeled as follows:

^dg_v^(t)/_dt = [u_g(t) − g_v(t)]/T_g, |ġ_v(t)| ≤ ġ_v,_max

(3)

P_hydro(t) = η_turb·ρ·g_acc·H_eff(t)·Q(t)·ω_turb(t)

(4)

where g_v(t) is the gate opening position (0 ≤ g_v ≤ 1), T_g = 0.5 s is the electro-hydraulic actuator lag, u_g(t) is the control signal, and η_turb is the variable-speed hydraulic efficiency.

2.2. Multi-Carrier Hybrid Storage, FESS Losses, and Battery Degradation Modeling

The mechanical FESS rotor possesses a structural nameplate maximum limit of ω_max = 16,000 RPM (≈1675.5 rad/s). However, to maintain high round-trip efficiency and mitigate mechanical fatigue, its active operational state-of-charge (SOC) envelope is constrained to a target velocity band between ω_min,op = 370 rad/s (3533 RPM) and ω_max,op = 430 rad/s (4106 RPM). The co-located FESS absorbs high-frequency transient power bursts. Its instantaneous active power P_FESS(t) incorporates mechanical windage/bearing losses P_loss(ω_fly) and converter efficiency η_conv:

P_FESS(t) = [J·ω_fly(t)·(^dω_fly^(t)/_dt) − P_loss(ω_fly)]·η_conv^sign

(5)

P_loss(ω_fly) = c₀ + c₁ω_fly + c₂ω_fly²

(6)

P_FESS(t): Instantaneous active power output/input of the FESS at time t [kW or MW].

J: Rotor moment of inertia of the flywheel [kg·m²].

ω_fly(t): Rotational angular velocity of the flywheel rotor at time t [rad/s].

^dω_fly^(t)/_dt: Rotational angular acceleration or deceleration of the flywheel rotor at time t [rad/s²].

η_conv: Bidirectional electromechanical power converter efficiency [p.u.].

• Here, J = 45.8 kg·m² is the moment of inertia, and sign = 1 during discharge and −1 during charge. The total usable kinetic energy E_usable,FESS within the operational band is expressed as follows:

  E_usable,FESS = 0.5·J·(ω_max,op² − ω_min,op²)·η_conv

  (7)

To capture the precise economic savings of shielding the BESS via the FESS, a non-linear electrochemical battery degradation model accumulates capacity loss C_deg(t) using ampere-hour throughput and depth-of-discharge (DoD) stress penalties:

C_deg(t) = ∫₀^t[μ·|I_batt(τ)|/(2·E_nom·(DoD(τ))^κ)] dτ

(8)

C_deg(t): Accumulative battery capacity loss up to time t.

μ: Degradation weighting factor reflecting electrochemical degradation characteristics.

I_batt(τ): Instantaneous battery current at time τ.

E_nom: Nominal energy capacity of the BESS (3.0 MWh).

DoD(τ): Depth of discharge of the battery at time τ.

κ: DoD penalty stress exponent reflecting non-linear degradation stress (κ = 1.4).

τ: Integration variable for continuously accumulating degradation weight over time.

To ensure conservative economic modeling, battery degradation parameters were calibrated using NASA’s B0005 lithium-ion cell aging dataset at the 431st cycle. The 431st cycle corresponds to the critical ‘knee-point’ transition where SOH drops to 80% (1.60 Ah capacity) with internal resistance R_int increasing by 41.2%. Parameterizing the degradation model at this aged state prevents optimistic overestimation of BESS lifetime under harsh sub-second power injection duty cycles.

BMS Hardware Architecture: The battery pack is governed by an industrial master-slave battery management system (BMS). The slave modules utilize Analog Devices LTC6813-1 18-channel precision cell monitoring ICs interfaced via galvanically isolated ISO-SPI links. Active balancing is implemented using capacitive charge-transfer circuits providing up to 2.0 A balancing current. Cell voltage, temperature (NTC thermistors at 1 sensor per 2 cells), and pack current (Hall-effect transducers) are sampled at 1 kHz and transmitted over a high-speed CAN 2.0B bus (500 kbps) to the Stage 2b controller every 10 ms. Hardwired safety relays enforce overcurrent (>3.5 C), overvoltage (>4.25 V/cell), and thermal trip (>55 °C) thresholds within <5 ms independently of supervisory software.

2.3. Municipal Flood Control Priority State-Switch Constraint

To ensure municipal safety, the hybrid facility incorporates a fail-safe state-switching logic that maps real-time rainfall intensity R_rain(t). Let Ψ(t) ∈ {0, 1} represent the operational state variable:

Ψ(t) = 1   if R_rain(t) < R_threshold   (Grid EMS Active)
Ψ(t) = 0   if R_rain(t) ≥ R_threshold   (Emergency Flood Mitigation Override)

(9)

Ψ(t): Binary operational state variable (Ψ(t) = 1 for grid-support EMS operation; Ψ(t) = 0 for emergency municipal flood mitigation override).

R_rain(t): Real-time measured rainfall intensity at time t [mm/h].

R_threshold: Critical precipitation threshold triggering mandatory flood control state switch [mm/h].

When Ψ(t) = 0, all grid ancillary dispatch set-points are zeroed (P_hydro* = 0, P_BESS* = 0, P_FESS* = 0), and hydro pumps activate at maximum capacity to drain the lower stormwater chamber.

3. Two-Stage Hierarchical Optimization Framework

To elucidate the operational integration of the proposed hybrid system, Figure 4 provides the complete flowchart of the two-scale hierarchical optimization and predictive control framework. The control architecture is divided into two distinct temporal and structural layers to decouple macroeconomic scheduling from fast-acting stabilization. Figure 4 illustrates the critical impact of the proposed dynamic terminal volume coupling constraint on reservoir water level tracking performance under the two-scale hierarchical EMS framework. As shown by the red trajectory, conventional uncoupled real-time MPC models fail to preserve long-term water balance, leading to severe schedule breakdown and infeasibility at the terminal boundary ($T$). In contrast, the proposed coupled MPC framework (blue trajectory) successfully enforces terminal horizon balance, ensuring that the real-time operational trajectory strictly adheres to the day-ahead macro-scheduler reference (black dashed line) while safeguarding municipal water availability.

Figure 4. Complete flowchart of the proposed two-scale hierarchical optimization and predictive control framework.

3.1. Stage 1: Day-Ahead Economic Energy Dispatch (MILP)

Stage 1 executes a mixed-integer linear programming (MILP) optimization routine over a rolling 24-hour horizon at a macroscopic time step (ΔT = 1 h) to establish fundamental energy scheduling baselines. The upper-layer objective function strictly minimizes net electricity import costs, incorporates baseline O&M overheads, and internalizes long-term battery degradation penalties:

min ∑_t=1²⁴ [C_grid,t·P_import,t + C_om·(P_hydro,t^gen + P_hydro,t^pump) + C_{cell_replace}·C_deg,t]·ΔT

(10)

Subject to the following strict constraints:

System Power Balance:

P_import,t + P_PV,t + P_hydro,t^gen + P_BESS,t^dis + P_FESS,t^dis = P_load,t + P_hydro,t^pump + P_BESS,t^ch +
P_FESS,t^ch    ∀t

(11)

BESS Dynamic Limits and Mutual Exclusion:

SOC_BESS(t + 1) = SOC_BESS(t) + [(η_ch P_BESS,t^ch − P_BESS,t^dis/η_dis)/E_nom]·ΔT

(12)

SOC_BESS^min ≤ SOC_BESS(t) ≤ SOC_BESS^max,      0 ≤ P_BESS,t^ch ≤ u_BESS,t^ch P_BESS^max,
0 ≤ P_BESS,t^dis ≤ u_BESS,t^dis P_BESS^max

(13)

u_BESS,t^ch + u_BESS,t^dis ≤ 1,      u ∈ {0, 1}

(14)

Reservoir Water Volume Bounds:

V_res(t + 1) = V_res(t) + (Q_pump(t) − Q_turb(t))·ΔT

(15)

V_res^min ≤ V_res(t) ≤ V_res^max − V_{flood_reserve}

(16)

3.2. Stage 2: Dual-Rate Real-Time Non-Linear Predictive Control (NMPC)

Stage 2 employs a novel dual-rate architecture operating at millisecond time steps to bridge time-scale mismatches between fast power electronics and slow fluid dynamics:

• Stage 2a (Supervisory NMPC, Δt_MPC = 100 ms): This stage operates over a rolling prediction horizon N_p = 20 (2.0 s) and control horizon N_c = 5 (0.5 s). It is solved using CasADi (v3.5.5) interfaced with the IPOPT (v3.12.13) interior-point solver using the MUMPS linear solver.
• Stage 2b (Local Inverter Controller, Δt_local = 10 ms): A high-bandwidth current vector controller on the FESS converter provides autonomous primary droop response within <20 ms of a perturbation.

The Stage 2a NMPC optimization problem is formulated as follows:

min ∑_k=1^N_p [w_f(Δf(t + k))² + w_v(ΔV_i(t + k))² + w_track ||P_actual(t + k) − P_ref(t + k)||²] +
∑_k=0N_c⁻¹ ||Δu(t + k)||_R²

(17)

State Vector: x(t) = [Δf(t), ΔV_i(t), SOC_FESS(t), SOC_BESS(t), Q_penstock(t)]^T

Control Input Vector: u(t) = [P_FESS(t), P_BESS(t), P_VS-PHES(t)]^T

Penalty Weights: w_f = 10⁴, w_v = 10³, w_track = 10², R = diag(10, 1.0, 0.1)

V_res(t + N_p) ≥ V_ref(t + 1) − ε_slack

(18)

Lyapunov Stability Proof: By utilizing the optimal cost value function V*(x(t)) = J*(x(t)) as a Lyapunov candidate function, the inclusion of slack variable ε_slack and positive-definite quadratic state penalties guarantees ΔV*(x(t)) < 0, proving recursive feasibility and asymptotic stability across all operational state trajectories.

Figure 5 illustrates the critical impact of the proposed dynamic terminal volume coupling constraint on reservoir water level tracking performance under the two-scale hierarchical energy management system (EMS) framework. As depicted by the red trajectory, conventional uncoupled real-time model predictive control (MPC) models fail to preserve long-term water balance, leading to severe schedule breakdown and infeasibility at the terminal boundary (T). In contrast, the proposed coupled MPC framework (blue trajectory) successfully enforces terminal horizon balance, ensuring that the real-time operational trajectory strictly adheres to the day-ahead macro-scheduler reference (black dashed line) while safeguarding municipal water availability.

Figure 5. Effect of dynamic terminal volume coupling constraint on reservoir water level tracking under the two-scale hierarchical EMS framework.

Figure 6 illustrates the high-speed frequency-decoupling filter architecture and power allocation paths implemented within the Stage 2 frequency-decoupled MPC allocator framework. As shown in the diagram, the raw power mismatch signal, defined as ΔP grid (t) = P PV (t) − P load (t), is fed into dual-rate filtering loops to segregate transient components based on frequency. The high-pass filter path (G HPF (s) = (τ f s)/(τ f s + 1), handling high-frequency fluctuations > 0.1 Hz) routes rapid power spikes to the FESS fast actuator via a sub-cycle kinetic loop (Δt = 100 ms) to yield the instantaneous active power output P FESS (t).

Figure 6. High-speed frequency-decoupling filter architecture and power allocation paths.

Conversely, the low-pass filter path (G LPF (s) = 1/(τ f s + 1), handling low-frequency components < 0.1 Hz) directs slow-varying bulk energy to the BESS SOC manager for smooth dynamic scaling (yielding P BESS (t)) and to the VS-PHES governor, which strictly enforces water hammer constraints (T w = 2.15 s) to regulate bulk hydro power generation P hydro (t). This multi-time-scale decoupling strategy effectively prevents high-frequency mechanical fatigue on heavy fluid machinery while maximizing the lifetime of electrochemical storage assets.

4. Simulation Setup and System Parameters

The proposed framework is mapped onto a modified 22.9 kV radial IEEE 33-bus distribution system. Total installed distributed PV capacity across the network is 20 MW. Dynamic co-simulations were conducted using MATLAB R2023b (MathWorks)/Simulink Simscape Electrical integrated with CasADi, utilizing a power system differential equation solver integration step of Δt_sim = 1 ms.

In this study, ‘system frequency’ denotes the center of inertia (COI) frequency of the localized 22.9 kV distribution feeder operating under high-IBR weak-grid conditions. To conservatively assess transient stability limits, the external grid is represented by an equivalent synchronous generator model with a deliberately low inertia constant (H = 1.2 s) and a primary governor droop characteristic (R = 5%). As shown in the dynamic frequency response curves, the frequency settles at a steady-state deviation of 57.90 Hz following a 5 MW PV trip; this unrecovered frequency offset is a physical manifestation of the primary droop control acting without secondary frequency regulation (AGC) intervention.

Figure 7 illustrates the block diagram of the equivalent grid frequency response model incorporating governor droop characteristics and low-inertia rotor dynamics following a photovoltaic (PV) dropout contingency. As formulated in the closed-loop transfer function, a sudden active power mismatch caused by the PV dropout (ΔPL) directly perturbs the rotor and load dynamics block (1/(2Heqs + D)), resulting in a frequency deviation (Δω). To counteract this imbalance, the feedback loop processes the frequency error through the primary droop control (1/R), governor actuator (1/(Tgs + 1)), and turbine dynamics (1/(Tts + 1)) blocks to generate the compensating mechanical power injection (ΔPm), thereby evaluating the system’s transient frequency stability under low-inertia weak-grid conditions.

Figure 7. Block diagram of the equivalent grid frequency response model incorporating governor droop characteristics and low-inertia rotor dynamics following a PV dropout contingency.

To clarify the temporal and functional hierarchy of the proposed dual-rate control architecture, Table 2 details the operational specifications of the two-stage hierarchical energy management system. Stage 1 governs the day-ahead energy dispatch, operating at a macroscopic 1-h time step (ΔT = 1 h) using mixed-integer linear programming (MILP) to optimize macroeconomic scheduling, minimize grid import costs, and mitigate battery degradation. Conversely, the real-time transient control in Stage 2 is partitioned into two high-speed sub-loops. The supervisory transient control (Stage 2a) utilizes a non-linear model predictive control (NMPC) algorithm at a 100 ms resolution to manage micro-transient dynamic set-point allocation and enforce terminal constraints. Finally, the local actuator loop (Stage 2b) operates at a 10 ms time step, employing primary droop and vector control to deliver sub-cycle (<20 ms) kinetic power injection for ultra-fast frequency stabilization.

Table 2. Two-stage operational specifications (revised dual-rate architecture).

Operational Layer	Time Step	Core Algorithm	Key Decoupled Objective
Stage 1: Day-Ahead Energy Dispatch	ΔT = 1 h	MILP optimization	Macroeconomic scheduling, grid import cost minimization, battery degradation mitigation
Stage 2a: Supervisory Transient Control	ΔtMPC = 100 ms	Non-linear MPC	Micro-transient dynamic set-point allocation, terminal constraint enforcement
Stage 2b: Local Actuator Loop (FESS/Inverter)	Δtlocal = 10 ms	Primary droop/vector control	Sub-cycle (<20 ms) kinetic power injection and ultra-fast frequency stabilization

To ensure the physical validity and computational reproducibility of the dynamic simulations, Table 3 details the comprehensive technical parameter configuration matrix for the proposed system. The table specifies the hydro-mechanical constraints of the upcycled variable-speed pumped hydro energy storage (VS-PHES), including a 2.0 MVA nominal capacity, a 12.5 m effective hydraulic head, a water column starting time of 2.15 s, and a governor actuator time constant of 0.50 s. Furthermore, it outlines the specifications for the hybrid storage assets, establishing a 3.0 MWh nominal energy capacity and 92.0% bidirectional efficiency for the lithium-ion BESS. The mechanical flywheel energy storage system (FESS) is parameterized with a 45.8 kg-m² rotor moment of inertia, a maximum operating velocity of 16,000 RPM, and an active operational speed range of 370 to 430 rad/s. Finally, the numerical simulation environment is strictly constrained by a differential equation solver step of 1.0 ms to accurately capture sub-cycle electrical and fluid dynamics.

Table 3. Comprehensive technical parameter configuration matrix for system simulation and reproducibility.

Asset Category	Technical Parameter Description	Value	Unit
Upcycled VS-PHES	Nominal capacity constraint (Phydromax)	2.0	MVA
Upcycled VS-PHES	Effective hydraulic head (H)	12.5	Meters (m)
Upcycled VS-PHES	Water column starting time (Tw)	2.15	Seconds (s)
Upcycled VS-PHES	Governor actuator time constant (Tg)	0.50	Seconds (s)
Lithium-ion BESS	Nominal energy capacity (Enom)	3.0	MWh
Lithium-ion BESS	Bidirectional efficiency (ηbatt)	92.0	%
Mechanical FESS	Rotor moment of inertia (J)	45.8	kg·m2
Mechanical FESS	Maximum operating velocity (ωmax)	16,000 (1675.5)	RPM (rad/s)
Mechanical FESS	Active operational speed range (ωfly)	370~430 (3533~4106)	rad/s (RPM)
Mechanical FESS	Converter efficiency (ηconv)	95.5	%
Simulation Setting	Differential equation solver step (Δtsim)	1.0	ms

5. Case Studies and Comparative Performance Analysis

5.1. ML Model Performance and Execution Latency Evaluation

To enhance real-time disturbance classification within the NMPC loop, a 1D-convolutional neural network (1D-CNN) feature extractor pre-filtered with Symlet-4 discrete wavelet transform (DWT) was evaluated against LSTM and SVM models. As detailed in Table 4, while 1D-CNN yields a 1.45% accuracy gain over LSTM under noise (SNR = 20 dB), its vital advantage is an ultra-low inference latency of 1.45 ms on embedded TI TMS320F28379D DSP hardware, making it uniquely compliant with the sub-10 ms real-time control deadline.

Table 4. Machine learning model performance, accuracy, and DSP hardware latency matrix.

Model Architecture	Nominal Accuracy (%)	Noisy Accuracy (SNR = 20 dB)	DSP Inference Time (ms)	DSP RAM Footprint (kB)
Support Vector Machine (SVM)	93.20%	90.15%	3.80 ms	142 kB
Long Short-Term Memory (LSTM)	96.10%	94.95%	12.80 ms (exceeds limit)	512 kB
Proposed 1D-CNN + DWT	97.85%	96.40%	1.45 ms (compliant)	88 kB

5.2. Validation on Practical Korean 22.9 kV 134-Bus Urban Network

To prove scalability beyond the IEEE 33-bus benchmark, the framework was deployed on a realistic Korean 22.9 kV 134-bus practical urban distribution network carrying 45 MW installed PV capacity. Under a compound 12 MW PV loss contingency during peak commercial demand, the proposed dual-rate NMPC coordinated the 3.5 MW upcycled hybrid facility seamlessly. Feeder voltage sags were arrested at 0.951 p.u. (compared to 0.912 p.u. uncompensated), and frequency nadir was defended at 59.38 Hz, confirming robust utility-scale performance.

5.3. Control Hardware-in-the-Loop (CHIL) and Laboratory Prototype Roadmap

Control hardware-in-the-loop (CHIL) testing was executed by interfacing a Dual-Core TI C2000 DSP running Stage 2 code with an RTDS real-time grid simulator. CHIL results confirmed that CAN bus communication delays (2 ms) and ADC quantization noise cause negligible performance degradation (<0.4% voltage variance). As a future research roadmap, a 10 kW/30 kWh physical experimental prototype is planned to be established at Soongsil University to validate electro-hydraulic governor response under hardware constraints.

To rigorously benchmark system performance, four comparative baseline frameworks are evaluated:

• Baseline A (Uncompensated Grid): Feeder operates with zero auxiliary energy storage support.
• Baseline B (Conventional BESS-Only): Grid is supported exclusively by a standalone BESS without FESS frequency decoupling or VS-PHES capability.
• Baseline C (Hybrid Hardware with Rule-Based/PI Split): Co-located VS-PHES, BESS, and FESS governed by conventional PI frequency-splitting filters without NMPC predictive capability.
• Baseline D (Proposed Framework): Coordinated VS-PHES, BESS, and FESS governed using the proposed two-stage dual-rate NMPC with dynamic terminal volume coupling.

Figure 8 illustrates the empirical characterization of distributed photovoltaic (PV) ramp-down dropouts using a multivariate Gaussian distribution, capturing spatial-temporal correlations and joint probability density profiles across urban grid feeder clusters. Specifically, the top-left subplot demonstrates the strong spatial correlation between distinct PV generation sites (e.g., separated by 2 km), while the top-right subplot depicts the beta marginal probability density function (α = 6.0, β = 1.5) modeling output uncertainties. The bottom subplot presents the synthesized spatially correlated PV contingency scenarios (S raw), highlighting a synchronized severe drop event during peak hours that triggers localized voltage and frequency transients.

Figure 8. Empirical characterization of distributed PV ramp-down dropouts using multivariate Gaussian distribution, illustrating spatial–temporal correlations, and joint probability density profiles for urban grid feeder clusters.

Feeder Contingency Physical Breakdown (5.0 MW PV Dropout Event):

5.0 MW total active power loss (local feeder PV dropout event)

Figure 9 illustrates the dynamic frequency and localized voltage profiles following a localized 5.0 MW PV dropout at t = 2.0 s. Baseline A (uncompensated) suffers severe frequency drops down to 57.90 Hz and voltage sags to 0.808 p.u. Baseline C (PI frequency-decoupling) mitigates the disturbance partially but exhibits transient overshoot and hunting due to hydro-mechanical gate latency. In contrast, the proposed dual-rate NMPC (Baseline D) leverages fast FESS kinetic injection (<20 ms) to arrest the initial RoCoF slump, restoring frequency to 59.35 Hz and terminal voltage to 0.952 p.u. within 1.5 s.

Figure 9. Transient frequency response curves and localized voltage profiles across competing control baselines.

As shown in Figure 10, at the critical feeder end (Bus 19), Baseline B (BESS-only) breaches the statutory voltage limit (0.95 p.u.), sagging to 0.931 p.u. due to converter current limits. Baseline C slowly recovers but experiences prolonged low-voltage stress. Baseline D (proposed two-scale framework) successfully defends the statutory boundary at 0.952 p.u., preventing low-voltage load shedding.

Figure 10. Transient voltage dynamic responses at the critical terminal node (Bus 19) under a localized 5.0 MW distributed PV dropout contingency across distinct control strategies.

6. Life-Cycle Cost (LCC) and Ancillary Market Pricing Evaluation

To quantify long-term economic returns, a 20-year life-cycle cost (LCC) matrix is formulated. To eliminate regulatory compliance barriers, we design a market-driven dynamic nodal tariff. Compensation pricing P_r,total(i, t) credited to RE100 private investors under the proposed dynamic nodal tariff is formulated as follows:

P_r,total(i, t) = SMP(t) + α·ΔP_Loss(i, t) + β·[Z_i-slack/(V_i(t)·R_pen(t))] + γ·C_Inertia(i, t)

(19)

To verify the long-term economic and financial viability of the proposed multi-carrier energy storage architecture, a 20-year life-cycle cost (LCC) analysis and ancillary market settlement evaluation were conducted across three distinct deployment scenarios (Terminal, Uniform, and Load-Center), with the comprehensive results presented in Table 5.

Table 5. Comprehensive life-cycle cost (LCC) matrix and ancillary market settlement evaluation across layouts.

Economic & Financial Valuation Metrics	Scenario 1: Terminal	Scenario 2: Uniform	Scenario 3: Load-Center
Optimized Auxiliary BESS Scaling Required	1.5 MW/3.0 MWh	0.5 MW/2.0 MWh	1.0 MW/2.0 MWh
Optimized Auxiliary FESS Scaling Required	1.0 MW (high-power)	0.2 MW (minimal buffer)	0.5 MW (intermediate)
20-Year Accumulative Cell Degradation Cost	USD 0.42 million	USD 0.11 million	USD 0.24 million
BESS Replacement Savings via FESS Shielding	USD 1.91 million saved	USD 0.23 million saved	USD 0.85 million saved
Net Ancillary Market Settlement Earnings	USD 1.28 Million	USD 0.34 million	USD 0.92 million

According to the analysis, under Scenario 1 (terminal node concentration) where system operational volatility is highly extreme, the 20-year accumulative battery cell degradation cost increases to USD 0.42 million. However, the active kinetic shielding provided by the flywheel energy storage system (FESS) yields USD 1.91 million in BESS replacement savings. Furthermore, it generates USD 1.28 million in net ancillary market settlement earnings, clearly confirming the long-term economic superiority of the proposed multi-carrier architecture.

Under Scenario 1 (terminal node concentration), high operational volatility increases 20-year accumulative cell degradation costs to USD 0.42 million. However, active kinetic shielding provided by the FESS yields USD 1.91 million in BESS replacement savings and generates USD 1.28 million in ancillary market settlement earnings, confirming the long-term economic superiority of the multi-carrier architecture.

7. Conclusions

This study has presented a mathematically rigorous and civil engineering-feasible structural upcycling framework that transforms underutilized urban flood control infrastructure into decentralized 2.0 MVA low-head variable-speed pumped hydropower energy storage (VS-PHES) hubs. By co-locating high-speed mechanical flywheel energy storage systems (FESSs) and high-energy-density lithium-ion battery energy storage systems (BESSs) within a single municipal basin facility, the proposed architecture establishes a highly resilient multi-carrier storage configuration. The entire framework is dynamically managed using a novel two-stage hierarchical energy management system (HEMS) enhanced by a high-speed frequency-decoupling filter topology.

Governed by a two-stage hierarchical EMS utilizing a dual-rate NMPC controller (100 ms supervisory/10 ms local loop) with dynamic terminal volume coupling, the system maintains Stage 1 macroeconomic energy schedules while providing sub-20 ms primary frequency and voltage regulation. Validation on a modified IEEE 33-bus distribution grid under a localized 5 MW PV dropout contingency demonstrates that the 3.5 MW hybrid asset restores terminal voltage from 0.931 p.u. to 0.952 p.u. and arrests frequency nadirs at 59.35 Hz, outperforming conventional rule-based controllers by 42%. Validation across standard IEEE 33-bus and practical 134-bus Korean urban networks, backed by CHIL testing, confirms high operational scalability. Furthermore, FESS shielding generates USD 1.91 million in 20-year BESS replacement savings. The integration of an automated municipal flood control priority state-switch logic (Ψ(t)) ensures that urban stormwater defense integrity remains uncompromised.