Power Generation Modeling Framework

• Power generation modeling frameworks are comprehensive sets of methodologies that translate physical phenomena and empirical data into quantitative simulation and optimization tools.
• They integrate diverse paradigms including mechanistic device models, machine-learning surrogates, neural operator methods, and economic optimization for real-time and planning applications.
• These frameworks enable practical analysis of grid stability, renewable integration, and system-level co-optimization under realistic operational and environmental constraints.

A power generation modeling framework comprises the methodologies, mathematical abstractions, architectures, and computational tools that enable quantitative representation, simulation, optimization, or dispatch of electric power generation systems across multiple spatial and temporal scales. Such frameworks span mechanistic physical models, empirical or data-driven surrogates, integrated techno-economic solvers, and uncertainty quantification engines; they support both component-level dynamical analysis and system-level co-optimization of renewable, hybrid, and conventional resources under realistic operational or environmental constraints. This article surveys leading modeling paradigms in the contemporary literature, emphasizing their structural assumptions, mathematical formulations, scalable computational architectures, and representative applications in the context of real-world power system engineering.

1. Fundamental Physical and Semi-Empirical Device Models

Core to any power generation modeling framework is the translation of device-level physics—generator dynamics, network interactions, and aggregated behavior—into mathematically explicit forms suitable for both steady-state and transient simulation.

The split equivalent-circuit approach, exemplified by the GLASS framework, encodes complex generation and load devices using rectangular voltage and current phasors: $V = V_R + j\,V_I, \qquad I = I_R + j\,I_I$ and formulates all device laws as analytical I–V relationships cast into coupled real subcircuits. Nonlinear dependencies (e.g., PQ loads) are expressed as functions of $(V_R, V_I)$ and then Taylor-expanded to finite order, yielding semi-empirical models fit directly to data. Circuit embedding allows unified power flow, harmonic, and dynamic studies using SPICE-style solvers, with rapid real-time updates feasible by refit of polynomial coefficients on streaming phasor data. This structure supports both bottom-up (physics-derived) and top-down (aggregate response) parameterization (Pandey et al., 2017).

Modern symbolic-numeric frameworks, notably ANDES, encode devices at the DAE level by declaring all parameters, state variables, algebraic variables, and discrete elements symbolically, with automatic code-generation producing efficient vectorized numerical implementations. Extensive built-in libraries of governor, exciter, and renewable unit models are provided, supporting large-scale simulation, eigenvalue analysis, and validation against commercial time-domain tools (Cui et al., 2020).

2. Data-Driven and Machine-Learning-Based Surrogate Models

Data-driven power generation models leverage historical measurements, meteorological inputs, and empirical operational characteristics through statistical, machine-learning, or neural approaches. Contemporary frameworks span ensemble learning, deep recurrent networks, and stochastic scenario engines.

Ensemble learning schemes such as cluster-based AdaBoost regression pipelines (see "Cluster-based ensemble learning for wind power modeling with meteorological wind data") partition meteorological inputs into clusters (e.g., via K-means, EM, Farthest-First, or Canopy algorithms), fit local regressors to each cluster, and then fuse predictions via stacking meta-models. This architecture systematically reduces error (NMAE and NRMSE) by $15$–$30$% over non-clustered models, exploiting local regime homogeneity and ensemble error decorrelation. Gains are maximized by maximally separated clusters, and computational performance is order(s) faster for Farthest-First clustering on large datasets (Chen, 2022).

Advanced neural quantile function recurrent networks (NQF-RNN) conditionally learn the full probabilistic distribution of wind power output given exogenous weather and plant variables. The architecture (LSTM encoder + feedforward NQF) supports direct quantile prediction at arbitrary probability levels, CRPS-based training for calibration and sharpness, and temporal smoothing for physically realistic trajectories. Empirical results on multi-year data demonstrate 9.5% RMSE improvement and $\sim$19% higher power-curve similarity over industry baselines (Lawrence et al., 30 Nov 2025). These models generalize to other renewables by reparameterizing input covariates and distributional targets.

Probabilistic scenario generation at system-scale (hundreds of assets) is realized using block-hierarchical Gaussian copulas with asset-specific normalization and empirical calibration. Hierarchically clustered asset groups enable stable estimation of high-dimensional covariance matrices, and scenario sampling proceeds via conditional draws informed by observed forecast–actual distributions and meta-calibration routines. This construction yields calibrated marginal and joint uncertainty quantification, with energy/variogram scores and uniform PIT histograms across diverse assets (Ludkovski et al., 2022).

3. Dynamic System Simulation and Neural Operator Surrogates

Fast, accurate simulation of power generation system trajectories under transient or time-varying conditions is a central requirement for stability analysis and real-time control. Traditional approaches solve coupled ODE/DAE models using numerical integration, but recent advances employ data-driven neural operator surrogates that approximate entire solution operators.

Physics-Informed Deep Operator Networks (PI-DeepONet) learn the mapping $x(t) = \mathcal{G}(x_0, u)(t)$ from initial conditions $x_0$ and time-dependent inputs $u(t)$ to the full system state trajectory (Karampinis et al., 7 Nov 2025). This framework encodes the ODE residuals into the learning loss, enforcing physical consistency and improving generalization. Branch and trunk neural networks represent input trajectories and query coordinates, respectively, yielding batched operator inference. Empirical benchmark results show sub-0.5% trajectory errors and >$30\times$ speedup over RK45, with physics-informed regularization enhancing both stability and scalability relative to PINN surrogates. Such neural operators are directly integrable into digital twin and real-time control loops.

4. Economic, Techno-Economic, and Capacity–Dispatch Optimization Frameworks

The economic optimization of generation assets—including siting, sizing, dispatch, and investment decisions—brings together engineering models, regulatory inputs, and market mechanisms within integrated optimization frameworks.

REopt Lite is a mixed-integer-linear programming engine that jointly selects, sizes, and dispatches a portfolio of behind-the-meter DERs (PV, wind, storage, generators, CHP, etc.) to minimize life-cycle cost, subject to load, tariff, technical, and resilience constraints (Mishra et al., 2020). The model balances hour-by-hour power flow and storage dynamics over annual or multi-year time horizons; economic parameters (capital, O&M, tax credits, net-metering, and utility rates) are embedded directly; open-source implementation supports batch scenario runs and robust sensitivity analysis.

The ECOGEN-CCD framework formulates convex co-design of generator and multi-domain storage size/dispatch strategies (including thermal, battery, and hydrogen) for maximizing system net present value under operational and market constraints. The system is represented as coupled affine dynamic equations, discretized and solved as large-scale LP/QP using direct transcription in DTQP. Real case studies demonstrate integration of NGCC with thermal storage and CCS, wind with BESS, and nuclear with hydrogen, validating computational efficiency and extensibility (Azad et al., 22 Apr 2024).

For multi-regional capacity modeling under environmental stressors, analytical frameworks propagate plant-level derating laws (e.g., hydrological, thermal, meteorological constraints) through the regional generator fleet, computing aggregate capacity factors under baseline and perturbed climate scenarios. This modular approach enables quantitative resilience analysis for both conventional and renewable fleets (Shuai et al., 2023).

5. Scenario Generation and Uncertainty Quantification

Rigorous scenario and uncertainty modeling for power generation integrates multivariate probabilistic forecasts, scenario ensembles, and quantification of joint spatiotemporal uncertainty for robust operations and planning.

Copula-based constructions (Gaussian and R-vine) generate joint prediction intervals (MPIs) for solar and wind power, coupling univariate predictive marginals (quantile regression) with learned dependence structures fit by maximum likelihood or information criteria. Scenario ensembles are sampled via inverse-transform or conditional algorithms, and scenario quality is assessed by coverage (calibration), sharpness (volume), and skill scores (energy, variogram). R-vine copulas capture asymmetric and non-Gaussian dependencies, enabling sharper and more reliable MPIs (Golestaneh et al., 2018).

Dynamic temporal correlation neural frameworks (DCQN) decouple marginal and joint dependency modeling: implicit quantile networks approximate nonparametric marginal quantiles for each timestep, while dynamic correlation networks generate time-varying Gaussian copula parameters as functions of input covariates. This two-stage approach supports continuous, scenario-based probabilistic forecasting with adaptive temporal correlation structure, yielding state-of-the-art performance on both deterministic and probabilistic metrics (Dong et al., 24 Jan 2025).

6. Integrated System and Hybrid Generation–Storage Models

Contemporary grids require frameworks that capture the interplay of diverse generation assets (renewable, thermal, hybrid) and storage under multi-level operational coordination.

Control-affine hybrid plant frameworks cast each subsystem (wind, solar, storage) in the canonical $\dot{x}=f(x)+g(x)u$ form, enabling modular composability and certified stability/safety properties via nonlinear control laws and control barrier functions (CBFs). Supervisory control schemes implement rule-based power sharing, allocate setpoints to maximize demand tracking, and integrate component-level CBF-QP/PI modes to ensure closed-loop invariance of critical safety states (e.g. SoC bounds, tipspeed, etc.). Empirical studies validate second-scale dynamic response and robust operation under fluctuating wind/solar (Ampleman et al., 6 Nov 2025).

At the grid-optimization scale, integrated transmission–distribution OPF frameworks (PowerModelsITD.jl) support co-optimization of generation across unbalanced multi-phase distribution and single-phase transmission networks. Formulations admit AC-polar, AC-rectangular, current-voltage, and linear approximations, enabling direct modeling of boundary conditions, DER integration, and centralized or decomposed solver architectures leveraging JuMP/Julia and commercial or open-source NLP/QP solvers (Ospina et al., 2022).

7. Specialized Physical Modeling: Unsteady and Nonconventional Generation

Emergent frameworks model physical phenomena directly impacting generation efficiency and capacity in unconventional settings.

Unsteady inflow wind/tidal turbine modeling frameworks employ nonlinear dynamical equations for variable flow, linking actuator-disc swing equations, quasi-steady aerodynamics, and potential-flow induction theory to capture time-averaged power enhancement relative to steady flow. Such models, validated by wind tunnel experiments, demonstrate that unsteady inflows and judicious control can yield systematic increases in average output, contingent on steady-state $C_p(\lambda)$ curve concavity (Wei et al., 2022).

At the device physics frontier, submicron-gap thermionic energy conversion frameworks model quantum and near-field radiative effects coupling charge transport, image-charge barrier lowering, electron tunneling, and fluctuational electrodynamics. Parametric optimization under these models predicts $4\times$ gains in power density and $5$–$10$% efficiency increases over micron-scale TECs, with combined-cycle architectures leveraging collector waste heat for total $\sim 48\,\%$ system efficiency (Jensen et al., 2019).

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These modeling frameworks represent the current state-of-the-art in the quantitative representation, simulation, optimization, control, and scenario-based risk analysis of power generation systems. Researchers and practitioners implement or select among these according to problem context, data availability, computational constraints, and required fidelity across physical, operational, and economic domains.