Dynamic Horizon-Based Energy Management for PEVs Considering Battery Degradation in Grid-Connected Microgrid Applications

Abstract

The growing integration of plug-in electric vehicles (PEVs) into microgrids presents both challenges and opportunities, particularly through vehicle-to-grid (V2G) services. This paper proposes a dynamic horizon optimization (DHO) framework with adaptive pricing for real-time scheduling of PEVs in a renewable-powered microgrid. The system integrates solar and wind energy, V2G capabilities, and time-of-use (ToU) tariffs. The DHO strategy dynamically adjusts control horizons based on forecasted load, generation, and electricity prices, while considering battery health. A PEV-specific pricing scheme couples ToU tariffs with system marginal prices. Case studies on a microgrid with four heterogeneous EV charging stations show that the proposed method reduces peak load by 23.5%, lowers charging cost by 12.6%, and increases average final SoC by 12.5%. Additionally, it achieves a 6.2% reduction in carbon emissions and enables V2G revenue while considering battery longevity.

1. Introduction

The integration of plug-in electric vehicles (PEVs) into modern microgrids presents operational challenges and optimization opportunities. Stochastic PEV charging can stress grid infrastructure during peak hours [1], while their bidirectional power flow enables cost reduction and grid stabilization [2]. Numerous studies optimize PEV charging schedules using event-driven model predictive control (MPC) [3,4,5,6]. These strategies adapt to dynamic arrivals/departures and stochastic renewable generation but often rely on fixed prediction horizons.

Other studies examine broader microgrid operational challenges using MPC dispatch frameworks, stochastic unit commitment, and optimization algorithms [7,8]. While effective in simulations, they generally lack mechanisms to adjust control horizons dynamically, reducing effectiveness under frequent fluctuations.

Real-time coordination methods, including distributed control schemes [9,10], decentralized fuzzy controllers [11,12], and multi-agent frameworks [13,14], improve flexibility. However, most assume static configurations and fail to adapt to sudden EV arrivals, SoC variations, or intermittent renewable outputs.

Another critical dimension is PEV battery degradation from frequent charging or discharging, especially under V2G operation, accelerates aging, leading to capacity fade and reduced service life [15,16,17,18,19,20,21,22]. Existing models using fixed penalty costs [23,24] or linear approximations [25,26] may not fully capture nonlinear relationships between aging and operational parameters (DoD, charge/discharge rates, temperature). Without accurate degradation modeling, real-time scheduling risks undermining V2G sustainability and PEV owner economics.

To address these limitations, this work introduces a real-time V2G-enabled microgrid-optimization framework with three key innovations:

1.

Real-time coordination optimizing power flows based on current grid state and PEV availability.

2.

Dynamic horizon adjustment that scales prediction windows based on EV connection patterns and renewable generation.

3.

Bidirectional power flow optimization incorporating detailed battery-degradation constraints.

To clearly contextualize our contribution within the broader research landscape and differentiate our approach from existing methods,

Table 1. Comparative analysis of MPC strategies for microgrid energy management with V2G Integration.

Feature	Fixed-Horizon MPC (FH-MPC)	Adaptive Horizon MPC (AH-MPC)	Proposed DHO Framework
Prediction Horizon	Static, fixed window size	Dynamically adjusts based on EV arrival/departure events	Adapts based on EV connectivity + real-time economic and degradation state
Primary Trigger Mechanism	Time-based (periodic updates)	EV connection and disconnection events	Multi-faceted: EV events + grid price signals + battery health status
Core Optimization Objective	Reference tracking + operational cost minimization	Cost minimization with computational efficiency	Multi-objective: cost + degradation minimization with computational optimization
Battery Health Consideration	Typically simplified or neglected through fixed penalty terms	Often uses simplified degradation models as secondary constraint	Explicit, detailed degradation modeling integrated as primary optimization objective
Computational Characteristics	Constant computational load, potentially excessive for long horizons	Variable load, reduced through event-triggered horizon adjustment	Adaptive complexity, optimized for current system conditions and problem size
Key Innovation/Advantage	Implementation simplicity	Responsiveness to EV uncertainty	Holistic adaptation to EV, market, AND degradation uncertainty
Market Price Integration	Limited to pre-defined tariffs or fixed price signals	Basic price response through parameter adjustment	Real-time dynamic pricing integration with SMP/ToU coupling and conditional adjustments

and

Table 2. Comparative assessment of optimization methodologies for PEV charging in microgrid systems with renewable generation.

Paper	Objective	Methodology	Uncertainty	WT	PV	Storage Degradation
[27]	Minimize charging cost	Stochastic optimization	Scenario-based stochastic modeling	No	No	Yes
[28]	Reduce PEV operational cost	Adaptive rolling horizon	Scenario-based uncertainties	Yes	Yes	No
[29]	Energy and reserve market management	Mixed-integer linear programming	Mixed-integer programming with uncertainty	Yes	Yes	Yes
[30]	Optimal scheduling	Two-step scheduling model	Scenario-based modeling	Yes	Yes	No
[31]	PEV charging	Hierarchical MPC	Scenario-based uncertainties	Yes	No	No
[32]	Minimize costs	Multi-criteria optimization	Scenario-based uncertainties	Yes	Yes	Yes
[33]	Optimize charging and discharging costs	Genetic Algorithm	Stochastic modeling	Yes	Yes	No
[34]	Minimize operation cost	PSO with hierarchical MAS	Stochastic modeling	Yes	Yes	No
Pro. method	Minimize operation cost, EV charging/discharging cost, and Optimal Schedule	Dynamic horizon optimization, MILP	Monte Carlo simulation with scenario reduction	Yes	Yes	Yes

provide systematic comparisons across multiple dimensions. Table 2 positions our work within the field of PEV charging-optimization methodologies, while Table 1 offers a focused analysis of MPC-specific strategies, highlighting the novel integration of economic signals and degradation-aware triggering mechanisms that distinguish our DHO framework from both conventional and adaptive MPC approaches.

Simulation results demonstrate the practical efficacy of this integrated approach. The proposed DHO framework achieves a 12.6% reduction in operational costs compared to conventional strategies, while simultaneously lowering peak demand from 170 $\mathrm{k}$$\mathrm{W}$ to 130 $\mathrm{k}$$\mathrm{W}$ (23.5% reduction). The framework significantly improves user satisfaction by increasing average final State of Charge from 74% to 86.5% while suggesting a potential 18% reduction in battery degradation under the applied semi-empirical model. Furthermore, the system enables substantial V2G revenue generation and contributes to environmental sustainability through a 6.2% reduction in carbon emissions. These comprehensive improvements highlight the value of co-optimizing economic, operational, and battery health objectives within a unified adaptive framework.

2. System Characterization and Mathematical Formulation

The microgrid (MG) integrates loads, PV and wind generation, the utility grid, and multiple EVCSs with bidirectional power capabilities (Figure 1). PV and wind sources are considered distributed energy sources (DESs). The system aims to minimize grid electricity consumption by utilizing local renewable generation and storing surplus DES power in EV batteries through vehicle-to-grid (V2G) operation.

2.1. PV Array Modeling

PV output is stochastic due to weather variations. The generated PV power $P_{\mathrm{pv}}$ depends on solar irradiance G and cell temperature $T_{\mathrm{cell}}$:

$$P_{\mathrm{pv}}=P_{\mathrm{st}}{\displaystyle \frac{G}{G_{\mathrm{st}}}}\left[1+C_T(T_{\mathrm{cell}}-T_{\mathrm{st}})\right].$$

(1)

Here, $P_{\mathrm{st}}$ is the rated PV power at standard test conditions (STC), $G_{\mathrm{st}}=1 \mathrm{k}\mathrm{W}/{\mathrm{m}}^2$, $T_{\mathrm{st}}=25 °\mathrm{C}$, and $C_T$ is the temperature coefficient in $\%/°\mathrm{C}$. The cell temperature is estimated from ambient temperature $T_{\mathrm{amb}}$ and irradiance:

$$T_{\mathrm{cell}}=T_{\mathrm{amb}}+G\left({\displaystyle \frac{\mathrm{NOCT}-20}{800}}\right),$$

(2)

where NOCT is the nominal operating cell temperature.

Solar irradiance variability is modeled with a beta distribution due to its bounded nature. The PDF is:

$$f\left(x\right)=\left\{\begin{array}{cc}{\displaystyle \frac{x^{a_i-1}{(1-x)}^{b_i-1}}{\beta (a_i,b_i)}},\hfill & 0\le x\le 1,\hfill \\ 0,\hfill & \mathrm{otherwise},\hfill \end{array}\right.$$

(3)

where x is normalized irradiance, and $a_i$, $b_i$ are shape parameters computed from the mean ${\mu }_i$ and standard deviation ${\sigma }_i$ of measured irradiance:

$$\begin{array}{cc}\hfill a_i& ={\displaystyle \frac{{\mu }_i{b}_i}{1-{\mu }_i}},\hfill \end{array}$$

(4)

$$\begin{array}{cc} \hfill b_i& =(1-{\mu }_i)\left({\displaystyle \frac{{\mu }_i(1+{\mu }_i)}{{\sigma }_i^2}}-1\right).\hfill \end{array}$$

(5)

Ambient temperature is treated as a normal random variable with time-varying mean and standard deviation:

$$f\left(T_{\mathrm{amb}}\right)={\displaystyle \frac{1}{\sqrt{2\pi }{\sigma }_i}}exp\left(-{\displaystyle \frac{{(T_{\mathrm{amb}}-{\mu }_i)}^2}{2{\sigma }_i^2}}\right).$$

(6)

2.2. EV Load Modeling

EV charging and discharging behavior introduces stochastic loads into the microgrid. To capture this, we model vehicle arrival time at charging stations, daily driving distance, battery SoC dynamics, and charging/discharging constraints. Monte Carlo simulation is employed to account for randomness.

2.2.1. Arrival Time Modeling

EV arrival times at the charging station are bimodal due to typical commuting patterns, with peaks in the morning and evening. This is modeled as a bimodal normal distribution:

$$f_{\mathrm{arr}}\left(t\right)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{\sqrt{2\pi }{\sigma }_i}}exp\left(-{\displaystyle \frac{{(t+24-{\mu }_i)}^2}{2{\sigma }_i^2}}\right),\hfill & 0<t\le {\mu }_i-12,\hfill \\ {\displaystyle \frac{1}{\sqrt{2\pi }{\sigma }_i}}exp\left(-{\displaystyle \frac{{(t-{\mu }_i)}^2}{2{\sigma }_i^2}}\right),\hfill & {\mu }_i-12<t\le 24,\hfill \end{array}\right.$$

(7)

where ${\mu }_i=17.47$ h and ${\sigma }_i=3.41$ h.

2.2.2. Daily Driving Distance

Daily distance traveled by each EV, D, is modeled as a log-normal random variable:

$$f_D\left(d\right)={\displaystyle \frac{1}{d{\sigma }_D\sqrt{2\pi }}}exp\left(-{\displaystyle \frac{{(lnd-{\mu }_D)}^2}{2{\sigma }_D^2}}\right),$$

(8)

where ${\mu }_D$ and ${\sigma }_D$ are the mean and standard deviation of the natural logarithm of daily distance.

2.2.3. SoC Dynamics and Charging Requirements

Given the daily distance D, the required final SoC for the next day is:

$${\mathrm{SoC}}_{\mathrm{final}}={\mathrm{SoC}}_{\mathrm{init}}+{\displaystyle \frac{DE}{C_{\mathrm{EV}}^{\max }}},$$

(9)

where E is the energy consumption per km and $C_{\mathrm{EV}}^{\max }$ is the EV battery capacity. Charging time to reach this SoC is:

$$T_{\mathrm{ch}}={\displaystyle \frac{({\mathrm{SoC}}_{\mathrm{final}}-{\mathrm{SoC}}_{\mathrm{init}})·C_{\mathrm{EV}}^{\max }}{P^{\mathrm{ch}}·{\eta }^{\mathrm{ch}}}},$$

(10)

with charging power $P^{\mathrm{ch}}$ and efficiency ${\eta }^{\mathrm{ch}}$. SoC evolves dynamically:

$${\mathrm{SoC}}_{t+1}={\mathrm{SoC}}_t+P_t^{\mathrm{ch}}\mathrm{\Delta }T-P_t^{\mathrm{dis}}\mathrm{\Delta }T,{\mathrm{SoC}}_{min}\le {\mathrm{SoC}}_t\le {\mathrm{SoC}}_{max}.$$

(11)

2.2.4. Charging/Discharging Constraints

EV charging/discharging power is limited by station rating and battery characteristics:

$$\begin{array}{cc}\hfill 0\le P_t^{\mathrm{ch}}& \le P_{\mathrm{rated}}·{\eta }_{\mathrm{ch}},\hfill \end{array}$$

(12)

$$\begin{array}{cc}\hfill 0\le P_t^{\mathrm{dis}}& \le P_{\mathrm{rated}}·{\eta }_{\mathrm{dis}}.\hfill \end{array}$$

(13)

To prevent simultaneous charging and discharging, a binary control variable $z_t$ is introduced:

$$\begin{array}{cc}\hfill P_t^{\mathrm{ch}}& =P_t^{\mathrm{ch}}·z_t,\hfill \end{array}$$

(14)

$$\begin{array}{cc} \hfill P_t^{\mathrm{dis}}& =P_t^{\mathrm{dis}}·(1-z_t),\hfill \end{array}$$

(15)

with $z_t=1$ for charging and $z_t=0$ for discharging.

2.2.5. Scheduling Rules and Assumptions

The EV scheduling algorithm enforces:

1.

EVs can only be dispatched after returning home

2.

Charging/discharging power must remain within battery limits

3.

SoC at departure must meet next-day travel requirements

4.

EVs are not dispatched during working hours (08:00–17:00)

5.

Valley hours (22:00–07:00) are preferred for charging

2.2.6. Monte Carlo Simulation

Monte Carlo methods are applied to generate large-scale EV behavior scenarios based on the above distributions.

2.3. Battery Aging Cost Modeling

Limitations of Model: It is important to note that the presented semi-empirical degradation model is calibrated from parameters reported in secondary literature sources [15,16] for NMC chemistry cells. While this provides a reasonable estimate of aging costs for operational scheduling, the model has not been validated against experimental charge-discharge cycle data conducted specifically for this study. Consequently, the absolute predictions of capacity fade should be interpreted with caution. The primary value of the model in this work is its ability to provide a comparative basis for evaluating the impact of different scheduling strategies on relative battery degradation.

Lithium-ion degradation is captured using a semi-empirical model accounting for calendar and cycling effects [15,16].

$$\begin{array}{cc} \hfill F_1^{\mathrm{cap}}& =\left(K_1^{\mathrm{SoC}}·\overline{\mathrm{SoC}}+K_2^{\mathrm{SoC}}\right)exp\left({\displaystyle \frac{-E_a+K_I·\overline{I}}{R(273.15+\overline{T})}}\right)E_{\mathrm{thrpt}}^Z,\hfill \end{array}$$

(16)

$$\begin{array}{cc} \hfill E_{\mathrm{thrpt}}& =\sum _{t=\mathrm{HAT}+1}^{\mathrm{HDT}}\left(P_t^{\mathrm{G}2\mathrm{V}}+P_t^{\mathrm{V}2\mathrm{G}}\right)·\mathrm{\Delta }t,\hfill \end{array}$$

(17)

$$\begin{array}{cc} \hfill F_2^{\mathrm{cap}}& =\sum _{t=\mathrm{HAT}+1}^{\mathrm{HDT}}{K}^{\mathrm{DoD}}{\displaystyle \frac{P_t^{\mathrm{V}2\mathrm{G}}}{{\eta }^{\mathrm{V}2\mathrm{G}}}}\mathrm{\Delta }t,\hfill \end{array}$$

(18)

$$\begin{array}{cc} \hfill F^{\mathrm{cap}}& =F_1^{\mathrm{cap}}+F_2^{\mathrm{cap}},\hfill \end{array}$$

(19)

$$\begin{array}{cc} \hfill E_{\mathrm{total}}& =\sum _{t=\mathrm{HAT}+1}^{\mathrm{HDT}}\left(P_t^{\mathrm{G}2\mathrm{V}}·{\eta }^{\mathrm{G}2\mathrm{V}}+{\displaystyle \frac{P_t^{\mathrm{V}2\mathrm{G}}}{{\eta }^{\mathrm{V}2\mathrm{G}}}}\right)·\mathrm{\Delta }t,\hfill \end{array}$$

(20)

$$\begin{array}{cc}\hfill P^{\mathrm{age}}& ={\displaystyle \frac{C^{\mathrm{age\_daily}}}{E_{\mathrm{total}}}},\hfill \end{array}$$

(21)

$$\begin{array}{cc} \hfill C^{\mathrm{age\_daily}}& ={\displaystyle \frac{r\left(C^{\mathrm{bat}}{(1+r)}^N-C^{\mathrm{scr}}\right)}{{(1+r)}^N-1}},N={\displaystyle \frac{0.2C_{\mathrm{init}}}{F^{\mathrm{cap}}}}.\hfill \end{array}$$

(22)

The parameters used in the degradation model are listed in

Table 3. Key parameters for the semi-empirical battery-degradation model.

Parameter	Value	Description/Source
$K_1^{\mathrm{SoC}}$	$3.5\times {10}^{-3}$	SoC stress coefficient [15]
$K_2^{\mathrm{SoC}}$	$1.2\times {10}^{-2}$	Offset constant [15]
$E_a$	$3.5\times {10}^4$ J/mol	Activation energy for SEI growth [16]
$K_I$	$1.1\times {10}^{-5}$	Current stress factor [16]
R	$8.314$ J/(mol·K)	Universal gas constant
Z	$0.65$	Throughput degradation exponent
$K^{\mathrm{DoD}}$	$2.7\times {10}^{-3}$	Depth-of-Discharge degradation factor [16]
${\eta }^{\mathrm{G}2\mathrm{V}}$	$0.95$	Charging efficiency (grid-to-vehicle)
${\eta }^{\mathrm{V}2\mathrm{G}}$	$0.93$	Discharging efficiency (vehicle-to-grid)
r	$0.08$	Annual discount rate
$C^{\mathrm{bat}}$	1200 CNY/kWh	Battery replacement cost
$C^{\mathrm{scr}}$	200 CNY/kWh	Scrap value
$C_{\mathrm{init}}$	60 kWh	Initial rated capacity of battery pack

. These values are taken from [15,16] and calibrated to NMC battery cells. A sensitivity analysis evaluates the impact of parameter uncertainty on the estimated aging cost [35].

2.4. Wind Energy Conversion Modeling

A horizontal-axis wind turbine (HAWT) extracts power from wind, with total wind power:

$$P_{\mathrm{wind}}={\displaystyle \frac{1}{2}}\rho A{V}_{\mathrm{w}}^3,$$

(23)

and mechanical power captured:

$$P_{\mathrm{t}}=C_p(\lambda ,\beta )·P_{\mathrm{wind}},\lambda ={\displaystyle \frac{{\omega }_{\mathrm{t}}R}{V_{\mathrm{w}}}}.$$

(24)

The empirical power coefficient model:

$$C_p(\lambda ,\beta )=0.5\left({\displaystyle \frac{116}{{\lambda }_i}}-0.4\beta -5\right)exp\left(-{\displaystyle \frac{21}{{\lambda }_i}}\right),{\displaystyle \frac{1}{{\lambda }_i}}={\displaystyle \frac{1}{\lambda +0.08\beta }}-{\displaystyle \frac{0.035}{{\beta }^3+1}}.$$

(25)

These relations provide a foundation for variable-speed wind energy conversion system modeling.

3. Proposed Framework

The proposed framework addresses the challenges of real-time energy management in microgrids by dynamically optimizing power exchanges among the grid, distributed energy sources (DESs), and electric vehicles (EVs) with bidirectional capabilities. Unlike conventional day-ahead scheduling methods [10,11], which rely on static forecasts and assume perfect knowledge of DES generation and EV behavior, our approach implements a closed-loop optimization strategy that continuously adapts to evolving system conditions. Key uncertainties—including intermittent PV/wind output, stochastic EV arrivals and departures, and fluctuating electricity prices—are mitigated through a combination of short-term forecasting and a reactive dynamic horizon optimization (DHO) approach.

3.1. Framework Architecture

At the core of the framework is an LSTM-based forecasting module [12,13], which provides updated predictions of DES generation and load demand over a sliding time window. Forecasts are continuously refined using real-time measurements, ensuring robustness under rapidly changing conditions. The DHO strategy formulates a mixed-integer linear programming (MILP) problem over an adaptive prediction horizon, $W_{\mathrm{dho}}^i$, which adjusts dynamically based on system states:

$$W_{\mathrm{dho}}^i=\left\{\begin{array}{cc}min(T_{\mathrm{EV}\text{-}\mathrm{depart}},W_{\max }),\hfill & \mathrm{if}\mathrm{EVs}\mathrm{are}\mathrm{connected},\hfill \\ W_{\mathrm{base}},\hfill & \mathrm{otherwise},\hfill \end{array}\right.$$

(26)

where $T_{\mathrm{EV}\text{-}\mathrm{depart}}$ is the earliest expected EV departure time, $W_{\max }$ is the maximum allowable horizon, and $W_{\mathrm{base}}$ is the default horizon for grid/DES-only optimization. This flexibility enables cost-efficient operation without relying on long-term, potentially unreliable forecasts.

The optimization proceeds in a receding-horizon manner. At each time step $t_i$, the framework:

1.

Collects real-time measurements (DES output, EV connections, grid prices)

2.

Updates LSTM forecasts for load and generation

3.

Computes $W_{\mathrm{dho}}^i$ based on current EV/DES states

4.

Solves the MILP problem over the adaptive horizon

5.

Implements only the control action for $t_i$

This iterative approach mitigates two critical microgrid challenges: (1) Peak-demand penalties are reduced by opportunistic EV discharging during high-price intervals (2) Renewable energy curtailment is minimized by redirecting excess generation to flexible EV loads

The framework’s novelty lies in the synergistic combination of:

• Time-adaptive optimization: Horizon length is dynamically adjusted based on real-time EV/DES availability
• Closed-loop forecasting: LSTM models are continuously updated with real-time measurements
• MILP precision: Discrete EV charging decisions and grid constraints are accurately modeled

Simulation results in Section 8 demonstrate superior performance compared to conventional day-ahead and fixed-horizon MPC approaches, especially under high uncertainty scenarios.

3.2. Objective Function

The microgrid energy-management system aims to minimize the total operating cost, which comprises three components: net energy cost, peak-demand penalty, and battery-degradation cost. As shown in Figure 2, the optimization is performed over the adaptive DHO window $W_{\mathrm{dho}}^i$ at each time step i.

$$min{C}_i^{\mathrm{obj}}=C_i^{\mathrm{NEC}}+C_i^{\mathrm{PDC}}+C_i^{\mathrm{age}}$$

(27)

3.2.1. Net Energy Cost ($C_i^{\mathrm{NEC}}$)

This term accounts for energy exchanges with the grid, including EV charging costs, revenue from discharging to the grid, electricity import/export costs, and DES utilization. Dynamic pricing signals such as time-of-use ($C_j^{\mathrm{ToU}}$) and system marginal prices ($C_j^{\mathrm{SMP}}$) are considered:

$$\begin{array}{cc}\hfill C_i^{\mathrm{NEC}}& =\sum _{j=i}^{i+W_i^{\mathrm{dho}}}\sum _{m=1}^{N_i^{\mathrm{EV}}}\left(C_j^{\mathrm{ch}}{S}_{m,j}{r}_{m,j}^{\mathrm{ch}}{P}_m^{\mathrm{ch},max}+C_j^{\mathrm{dis}}{S}_{m,j}{r}_{m,j}^{\mathrm{dis}}{P}_m^{\mathrm{dis},max}\right)\hfill \\ \hfill & +\sum _{j=i}^{i+W_i^{\mathrm{dho}}}\left(C_j^{\mathrm{ToU}}{P}_j^{\mathrm{grid},\mathrm{imp}}-C_j^{\mathrm{SMP}}{P}_j^{\mathrm{grid},\exp }\right).\hfill \end{array}$$

(28)

3.2.2. Peak Demand Cost ($C_i^{\mathrm{PDC}}$)

Designed to penalize net load exceeding a critical threshold $P^{\mathrm{cri}}$, this term encourages peak shaving via controlled EV discharging:

$$C_i^{\mathrm{PDC}}=\sum _{j=i}^{i+W_i^{\mathrm{dho}}}{C}^{\mathrm{PC}}u(P_j^{\mathrm{NL}}-P^{\mathrm{cri}})\left(u(P_j^{\mathrm{NL}}-P^{\mathrm{cri}})+r_{m,j}^{\mathrm{ch}}{P}_m^{\mathrm{ch},max}-r_{m,j}^{\mathrm{dis}}{P}_m^{\mathrm{dis},max}\right),$$

(29)

with the unit step function defined as

$$u\left(x\right)=\left\{\begin{array}{cc}1,\hfill & x>0\hfill \\ 0,\hfill & x\le 0.\hfill \end{array}\right.$$

(30)

Here, $C^{\mathrm{PC}}$ is the penalty cost per unit power exceeding $P^{\mathrm{cri}}$, and $P_j^{\mathrm{NL}}$ is the net load at time j.

4. Constraints

To ensure reliable and feasible operation, the optimization is subject to several constraints. The fundamental constraint is the power balance at each time step j, ensuring that the total supply from the grid, EV discharging, and DES generation matches the demand from local loads, EV charging, and exported power. This is expressed as [36]:

$$\begin{array}{c}\hfill P_j^{\mathrm{grid},\exp }+\sum _{m=1}^{N_i^{\mathrm{EV}}}{r}_{m,j}^{\mathrm{dis}}{P}_m^{\mathrm{dis},max}+P_j^{\mathrm{DES}}=P_j^{\mathrm{grid},\mathrm{imp},}+P_j^L+\sum _{m=1}^{N_i^{\mathrm{EV}}}{r}_{m,j}^{\mathrm{ch}}{P}_m^{\mathrm{ch},max}.\end{array}$$

(31)

Grid import/export operations are mutually exclusive at any time step, enforced through a binary variable ${\mu }_j^{\mathrm{grid}}$ that toggles between import and export modes. Additionally, the imported power must remain within the grid’s maximum capacity limits to ensure safe operation and prevent overload conditions:

$$\begin{array}{cc}\hfill P_j^{\mathrm{grid},\exp }& \le {\mu }_j^{\mathrm{grid}}{P}_{max}^{\mathrm{grid},\exp }\hfill \end{array}$$

(32)

$$\begin{array}{cc} \hfill P_j^{\mathrm{grid},\mathrm{imp}}& \le (1-{\mu }_j^{\mathrm{grid}})P_{max}^{\mathrm{grid},\mathrm{imp}}\hfill \end{array}$$

(33)

$$\begin{array}{cc} \hfill {\mu }_j^{\mathrm{grid}}& =\left\{\begin{array}{cc}1,\hfill & \mathrm{import}\hfill \\ 0,\hfill & \mathrm{export}.\hfill \end{array}\right.\hfill \end{array}$$

(34)

For each connected EV, only one action—charging, discharging, or idling—is permitted at any time. This is governed by a binary control variable ${\kappa }^j$ and corresponding constraints:

$$\begin{array}{cc} \hfill 0\le r_{m,j}^{\mathrm{ch}}& \le {\kappa }_j\hfill \end{array}$$

(35)

$$\begin{array}{cc} \hfill 0\le r_{m,j}^{\mathrm{dis}}& \le 1-{\kappa }_j\hfill \end{array}$$

(36)

$$\begin{array}{cc} \hfill {\kappa }_j& =\left\{\begin{array}{cc}1,\hfill & \mathrm{charging}\hfill \\ 0,\hfill & \mathrm{discharging}.\hfill \end{array}\right.\hfill \end{array}$$

(37)

The state of charge (SoC) of each EV battery must remain within manufacturer-specified limits and meet user-defined minimum requirements by the time of departure:

$$\begin{array}{cc} \hfill {\mathrm{SoC}}_m^{min}& \le {\mathrm{SoC}}_{m,j}\le {\mathrm{SoC}}_m^{max}\hfill \end{array}$$

(38)

$$\begin{array}{cc}\hfill {\mathrm{SoC}}_{m,k}& \ge {\mathrm{SoC}}_m^{\mathrm{req}}.\hfill \end{array}$$

(39)

The SoC is dynamically updated over time based on the net energy exchanged, considering the efficiencies of the charging and discharging processes. The SoC of the m-th connected EV at time j is given by:

$${\mathrm{SoC}}_{m,j}={\mathrm{SoC}}_{m,j-1}+{\displaystyle \frac{{\eta }_m^{\mathrm{ch}}{P}_{m,j}^{\mathrm{ch}}\mathrm{\Delta }t}{E_m^{\mathrm{cap}}}}-{\displaystyle \frac{P_{m,j}^{\mathrm{dis}}\mathrm{\Delta }t}{{\eta }_m^{\mathrm{dis}}{E}_m^{\mathrm{cap}}}}.$$

(40)

This equation ensures that charging and discharging actions respect physical efficiency limits and keep the battery operating within safe thresholds, while also satisfying user mobility requirements by departure time.

By integrating these operational constraints with the cost-minimizing objective in Section 3, the proposed DHO-based optimization achieves both economic efficiency and operational reliability. The adaptive design enables the model to dynamically respond to variations in load forecasts, EV availability, and pricing signals.

5. Dynamic Horizon Optimization Framework for Microgrid Optimization Considering Dynamic EV Arrivals

Numerous studies have explored rolling horizon (RH) frameworks for online microgrid optimization [37]. Typically, these frameworks employ a fixed rolling horizon (FRH) with a predetermined window size, denoted as $W^{\mathrm{FRH}}$, but they do not fully consider the temporal flexibility provided by plug-in electric vehicles (EVs) acting as distributed energy resources (DERs).

While a fixed horizon enables periodic updates to system states, such as distributed energy source (DES) output forecasts, load predictions, and EV arrival/departure times, it has inherent limitations. For instance, if the connection duration of the m-th EV, denoted by $N_m^{\mathrm{conn}}$, exceeds the FRH window size $W_t^{\mathrm{FRH}}$, the optimization process cannot fully leverage the flexibility offered by the EV over its entire availability period.

Conversely, if $N_m^{\mathrm{conn}}<W_t^{\mathrm{FRH}}$, the problem dimension increases unnecessarily due to irrelevant time slots being considered, thereby leading to increased computational complexity.

To address these limitations, the proposed dynamic horizon optimization (DHO) framework dynamically adjusts the horizon size in response to the changing availability of EVs. In the DHO approach, the rolling window $W_t^{\mathrm{dho}}$ at each time step t is adapted based on the longest connection duration among all EVs currently connected to the EV charging station (EVCS).

5.1. Step 1: Connection Period Determination

At the current time step t, the system operator retrieves real-time information about the EVs connected to the EVCS, including their number, arrival times, and anticipated departure times. For the m-th EV, its connection period is defined as:

$$T_{m,t}^{\mathrm{conn}}=[t,t+N_m^{\mathrm{conn}}],m=1,\dots ,N_t^{\mathrm{EV}},$$

(41)

where $N_m^{\mathrm{conn}}$ is the number of time intervals that the m-th EV will remain connected at time t, and $N_t^{\mathrm{EV}}$ is the number of EVs currently connected.

Based on these connection periods, the DHO time window is defined as:

$$T_t^{\mathrm{dho}}=[t,t+W_t^{\mathrm{dho}}],$$

(42)

where the adaptive horizon size is:

$$W_t^{\mathrm{dho}}=\underset{1\le m\le N_t^{\mathrm{EV}}}{max}{N}_m^{\mathrm{conn}}.$$

(43)

If no EVs are connected at time t, the default DHO window is set to the minimum possible size:

$$T_t^{\mathrm{dho}}=[t,t+1],W_t^{\mathrm{dho}}=1.$$

(44)

5.2. Step 2: Dynamic Update of DHO

At the next time step $t+1$, the system updates all EV information to reflect new arrivals or departures. The same procedure as in Step 1 is used to determine the new DHO window $W_{t+1}^{\mathrm{dho}}$. This continuous update allows the scheduling algorithm to remain adaptive and responsive to changes in system state, thereby improving cost-effectiveness and utilization of flexible resources.

5.3. Illustrative Example

To illustrate the operation of the DHO mechanism, consider the following scenario:

• At time t, one EV is connected with:

  $$T_{1,t}^{\mathrm{conn}}=[t,t+6],N_1^{\mathrm{conn}}=6.$$
  Then:

  $$T_t^{\mathrm{dho}}=[t,t+6],W_t^{\mathrm{dho}}=6.$$
• At time $t+1$, a second EV arrives. The updated connection durations are:

  $$N_1^{\mathrm{conn}}=7,N_2^{\mathrm{conn}}=5.$$
  So:

  $$W_{t+1}^{\mathrm{dho}}=max\{7,5\}=7,T_{t+1}^{\mathrm{dho}}=[t+1,t+8].$$
• At time $t+2$, a third EV joins with:

  $$N_3^{\mathrm{conn}}=8.$$
  Hence:

  $$W_{t+2}^{\mathrm{dho}}=max\{N_1^{\mathrm{conn}},N_2^{\mathrm{conn}},N_3^{\mathrm{conn}}\}=8.$$

  $$T_{t+2}^{\mathrm{dho}}=[t+2,t+10].$$

As shown in Figure 3, the DHO window adapts over time—from 6 intervals at time t, to 7 at $t+1$, and 8 at $t+2$—ensuring that all connected EVs are effectively integrated into the optimization framework.

6. Adaptive Electricity Pricing Model for PEVs in Microgrids

The adaptive pricing framework aims to optimize electricity price signals for PEVs, specifically, the charging price $C^{\mathrm{ch}}\left(t\right)$ and discharging price $C^{\mathrm{dis}}\left(t\right)$, to minimize the total operational cost of the microgrid over a scheduling horizon $[0,T]$. This cost includes the energy procurement cost from the external grid and the compensation paid to PEV owners for participating in grid services.

Unlike conventional ToU-based approaches, the proposed model is co-optimized with the DHO scheduling strategy. This tight integration ensures that dynamic EV availability directly influences price adaptation, which has not been explicitly addressed in prior adaptive/rolling-horizon studies such as [37].

The objective function is formulated as:

$$\underset{C^{\mathrm{ch}}\left(t\right),C^{\mathrm{dis}}\left(t\right)}{min}{\int }_0^T\left(C^{\mathrm{grid}}\left(t\right)+C^{\mathrm{PEV}}\left(t\right)\right)\mathrm{d}t,$$

(45)

where $C^{\mathrm{grid}}\left(t\right)$ is the real-time cost of purchasing electricity from the utility grid, and $C^{\mathrm{PEV}}\left(t\right)$ represents the total compensation paid to PEV owners for charging and discharging services.

The grid procurement cost at time t is:

$$C^{\mathrm{grid}}\left(t\right)=C^{\mathrm{ToU}}\left(t\right)·P^{\mathrm{grid}}\left(t\right),$$

(46)

where $C^{\mathrm{ToU}}\left(t\right)$ is the time-of-use (ToU) tariff set by the utility, and $P^{\mathrm{grid}}\left(t\right)$ is the power imported from the grid.

The compensation to PEVs is:

$$C^{\mathrm{PEV}}\left(t\right)=C^{\mathrm{ch}}\left(t\right)·P^{\mathrm{ch}}\left(t\right)-C^{\mathrm{dis}}\left(t\right)·P^{\mathrm{dis}}\left(t\right),$$

(47)

where $P^{\mathrm{ch}}\left(t\right)$ and $P^{\mathrm{dis}}\left(t\right)$ are the aggregate charging and discharging powers of PEVs at time t.

6.1. Dynamic Pricing Model Based on Operational Modes

6.1.1. Normal Operation Mode

When the net load satisfies $P^{\mathrm{NL}}\left(t\right)\le P^{\mathrm{cri}}$, where $P^{\mathrm{cri}}$ is the microgrid’s critical import threshold, the system operates under normal conditions. The PEV charging and discharging prices follow the ToU tariff:

$$C^{\mathrm{ch}}\left(t\right)=C^{\mathrm{ToU}}\left(t\right),C^{\mathrm{dis}}\left(t\right)=C^{\mathrm{ToU}}\left(t\right).$$

(48)

In simulations, $P^{\mathrm{cri}}$ was set to 80% of the feeder’s rated import limit, consistent with [37].

6.1.2. Peak-Demand Mode

When $P^{\mathrm{NL}}\left(t\right)>P^{\mathrm{cri}}$, the system enters peak-demand mode to reduce grid stress. The adaptive pricing model imposes a penalty $\varphi$ for charging and an incentive $\psi$ for discharging:

$$C^{\mathrm{ch}}\left(t\right)=C^{\mathrm{ToU}}\left(t\right)+\varphi ,C^{\mathrm{dis}}\left(t\right)=C^{\mathrm{ToU}}\left(t\right)+\psi ,$$

(49)

where $\varphi$ and $\psi$ are operator-defined coefficients based on market signals and system needs.

For reproducibility, this study uses $\varphi =0.1$ CNY/kWh and $\psi =0.2$ CNY/kWh, calibrated through sensitivity analysis. These values reflect realistic penalty/incentive margins in the Chinese ancillary services market, ensuring that V2G participation remains profitable despite battery aging costs.

6.1.3. High Renewable-Generation Mode

When the output from distributed energy resources (DERs), denoted $P^{\mathrm{DER}}\left(t\right)$, exceeds demand, the system encourages PEV charging to absorb surplus energy. The adaptive prices are:

$$C^{\mathrm{ch}}\left(t\right)=min\left(C^{\mathrm{SMP}}\left(t\right),{\displaystyle \frac{C^{\mathrm{SMP}}\left(t\right)+C^{\mathrm{ToU}}\left(t\right)}{2}}\right),$$

(50)

$$C^{\mathrm{dis}}\left(t\right)=min\left(C^{\mathrm{SMP}}\left(t\right),C^{\mathrm{ToU}}\left(t\right)\right),$$

(51)

where $C^{\mathrm{SMP}}\left(t\right)$ is the system marginal price (SMP).

This ensures that charging incentives are always bounded by market-clearing prices, thus avoiding arbitrage anomalies. For case studies, SMP values were drawn from the Guangdong day-ahead market (ranging 0.25–0.65 CNY/kWh). Sensitivity of results to SMP fluctuations is quantified in Appendix A.2.

Overall, the novelty of this pricing model lies in: (i) the explicit integration with the DHO window, enabling horizon-aware pricing, and (ii) the parameterized structure ($\varphi$, $\psi$, $P^{\mathrm{cri}}$, SMP bounds) that facilitates reproducibility and benchmarking against ToU-only schemes and advanced DRL-based policies.

7. Impact of Forecast Errors and Model Comparison

The accuracy of forecasts, particularly for distributed energy generation (DES), electric vehicle (EV) behavior, and grid prices, plays a critical role in the performance of microgrid-optimization systems. In this section, we compare the forecasting performance of different models and quantify the impact of forecast errors on system performance.

7.1. Comparison of Forecasting Models

Table 4. Comparison of forecasting models: RMSE and MAE.

Model	RMSE	MAE	Forecasting Approach	Strengths and Weaknesses
Persistence	X	X	Assumes the future will be the same as the last known value	Simple, minimal computation but poor performance in volatile systems, no trend adaptation
ARIMA	X	X	Uses past values to model time-series data, assumes stationarity and autocorrelation	Suitable for linear trends but struggles with non-stationary data
Proposed	X	X	Uses deep learning to capture nonlinear dependencies and temporal patterns	Can capture complex dynamics, adapts to changing conditions but requires more data and computational resources

presents a comparison of the forecasting models used in this study, including persistence, ARIMA, and the proposed LSTM model. The comparison is based on two widely used point-error metrics: Root Mean Square Error (RMSE) and Mean Absolute Error (MAE).

7.2. Impact of Forecast Errors on System Performance

Forecast errors, especially in DES generation (e.g., PV and wind) and EV behavior (e.g., arrival and departure times), can significantly affect the microgrid optimization. Below we summarize the key impacts and quantify them based on sensitivity analysis of the forecasting models.

7.2.1. Net Energy Cost (NEC)

Forecast errors in DES generation and EV charging/discharging behavior lead to suboptimal energy trading decisions. An overestimate or underestimate of generation or load results in higher grid energy imports or exports, increasing operating costs.

Quantitative Effect: Small forecast errors (e.g., 2–5%) in DES generation or EV scheduling can lead to an increase of 2–5% in the net energy cost (NEC), primarily due to over-reliance on grid energy during low DES output periods.

7.2.2. Peak Demand Cost (PDC)

Errors in forecasting EV arrivals and departures lead to inaccurate peak-demand predictions. An overestimate of EV availability may prevent sufficient discharging during peak demand periods, resulting in higher penalties.

Quantitative Effect: Forecast errors in EV behavior (e.g., 10–15%) can increase peak demand penalties by 3–7%, particularly during high-price intervals.

7.2.3. Battery-Degradation Cost

Inaccurate forecasts of EV charging/discharging schedules cause inefficient battery usage, increasing degradation. Charging or discharging when not optimal leads to faster wear and tear.

Quantitative Effect: Forecast errors in EV state-of-charge (SoC) predictions can increase battery-degradation costs by 5–10% due to unnecessary or inefficient charging cycles.

7.2.4. Renewable Energy Curtailment

Overestimation of renewable generation can result in excess energy that cannot be properly stored or used, leading to unnecessary curtailment, especially in high-penetration renewable systems.

Quantitative Effect: Overestimation of renewable generation by 5–10% can lead to a 20% increase in curtailment, depending on the flexibility of the system’s storage and load.

7.2.5. System Stability

Continuous forecasting errors may degrade the optimization process’s stability, as the system fails to adapt adequately to real-time changes in renewable generation and load conditions.

Quantitative Effect: Forecast errors increase the risk of violating operational constraints (e.g., SoC limits, grid capacity), which may cause up to 10% degradation in system performance.

7.3. Forecast Error Propagation and Sensitivity Analysis

Forecast errors in one component (e.g., DES generation) can propagate and impact other parts of the system, such as EV scheduling, energy costs, and grid interactions. Larger forecast errors introduce higher uncertainty, forcing the optimization algorithm to adopt conservative strategies that increase operational costs (e.g., more grid imports, unnecessary energy storage).

We performed a sensitivity analysis to assess how various levels of forecast errors (e.g., 5–15% in DES generation or EV behavior) degrade the system’s overall performance. The results showed that forecast inaccuracies lead to up to 15% higher operating costs, primarily due to suboptimal energy scheduling, higher peak demand penalties, and inefficient battery utilization.

The dynamic horizon optimization (DHO) approach is designed to adapt to real-time updates, including forecasts of DES generation, EV arrivals, and grid prices. However, as demonstrated, forecast errors can still negatively affect the system’s performance. The LSTM-based forecasting model outperforms simpler models like persistence and ARIMA in capturing nonlinear dynamics and adapting to changing conditions. Nonetheless, minimizing forecast errors remains crucial for improving the accuracy and cost-effectiveness of the optimization process [38,39].

7.4. Error Plot: Predicted vs. Actual Values

We present the error plot (Figure 4), comparing the predicted and actual values for the NREL dataset. The plot below illustrates how closely the predicted values match the actual data, and it highlights the error between them.

In addition to the error plots, we have included the following quantitative metrics to validate the effectiveness of our forecasting module:

• Normalized Root Mean Square Error (nRMSE): This metric normalizes the RMSE by dividing it by the range of the observed data. It provides a standardized measure of forecasting accuracy across different datasets.
• Kolmogorov-Smirnov (KS) Test: The KS test is used to compare the distribution of the forecasted values with the observed data, assessing the goodness of fit.

Table 5. Quantitative validation metrics for NREL dataset.

Metric	Value	Phase
nRMSE	0.12	Testing
KS Test Statistic	0.05	Testing

presents the results of the nRMSE and KS test for both the training and testing phases of the LSTM model on the NREL dataset.

These quantitative metrics demonstrate the high forecasting accuracy of our LSTM-based model. The nRMSE value indicates a relatively low error compared to the data range, while the KS test statistic suggests that the forecasted values closely match the observed data distribution.

8. Case Study and Performance Evaluation

This section presents a comprehensive case study assessing the performance of the proposed dynamic horizon optimization (DHO) and adaptive pricing model in a microgrid integrated with PV and wind energy sources. As shown in Figure 1, the microgrid comprises four vehicle-to-grid enabled charging stations, each supporting a heterogeneous fleet of PEVs with different power ratings and battery capacities (see

Table 6. PEV charging station and fleet specifications.

EV Stations	${\mathit{P}}_{\mathbf{max}}^{\mathbf{ch}}$ (kW)	PEV Model	Battery Capacity (kWh)
EVCS#1	9.6	EV1	25
EVCS#2	13.2	EV2	32
EVCS#3	19.6	EV3	35
EVCS#4	13.2

). The renewable energy mix includes PV panels and wind turbines with the following specifications: the wind turbines have a rated power of 50 KW, a rated wind speed of 12 m/s, a cut-in wind speed of 3 m/s, and a cut-out wind speed of 25 m/s.

To demonstrate the effectiveness of our approach, we compare the proposed method against a conventional rolling horizon MPC framework and a scenario-based Stochastic MPC (SMPC) baseline. While more advanced baselines such as deep reinforcement learning (DRL) or other complex methods exist, these are typically computationally intensive and less practical for day-ahead market participation in microgrids with limited computing resources [11]. We therefore focus on MPC as a practical baseline but include a discussion in Appendix A highlighting scalability considerations relative to DRL and acknowledge the comparison to DRL as important future work.

The critical peak demand threshold $L_{\mathrm{peak}}^{\mathrm{crit}}$ is set at 150 $\mathrm{k}$$\mathrm{W}$, corresponding to the lowest observed historical monthly peak load. This value was validated by sensitivity analysis across 12 months of data to ensure robustness. The penalty ($\varphi =0.1$ CNY/kWh) and incentive ($\psi =0.2$ CNY/kWh) parameters in the adaptive pricing model were tuned such that PEV charging is discouraged during grid stress events while still ensuring net profitability for EV owners.

8.1. Comparative Analysis with Stochastic MPC

We implemented a scenario-based Stochastic MPC (SMPC) baseline that explicitly accounts for forecast uncertainty through multiple generation and demand scenarios. The SMPC achieves slightly better cost performance (2–3% improvement) in high-uncertainty conditions due to its scenario-based robustness, it requires 3.5x more computation time than our proposed DHO framework. This demonstrates the practical value of our approach: the DHO provides a favorable trade-off, achieving 85–90% of the economic benefits of SMPC with significantly lower computational burden, making it more suitable for real-time applications with limited computing resources.

8.2. Utility Pricing and Adaptive EV Pricing Strategy

The pricing strategy is foundational to the MG-EMS operation. During off-peak hours (23:00–07:00), when electricity prices are lowest, the system prioritizes charging. Conversely, during on-peak periods (11:00–17:00), with the highest rates, discharging is encouraged to reduce grid burden. Mid-peak intervals use moderate pricing to maintain operational flexibility. The specific Time-of-Use (ToU) rates for summer and winter are detailed in

Table 7. ToU electricity prices and time periods (CNY/kWh).

Time Period	Summer	Winter	Time Interval
Off-Peak	0.532	0.574	23:00–07:00
Mid-Peak	0.820	0.878	07:00–11:00, 17:00–23:00
On-Peak	1.208	1.274	11:00–17:00

.

Figure 5 presents a comprehensive view of the 24-h forecast of load demand, renewable generation, and electricity pricing schemes. Photovoltaic output peaks around midday, while wind power exhibits stochastic fluctuations. The proposed adaptive pricing algorithm dynamically adjusts the real-time charging $C^{\mathrm{ch}}\left(t\right)$ and discharging $C^{\mathrm{dis}}\left(t\right)$ prices in response to these net load conditions, lowering prices to encourage charging during renewable abundance and increasing them to incentivize V2G discharge during high demand.

The figure also compares the utility-defined System Marginal Price (SMP), which varies continuously between $0.26$ and $0.63$ CNY/kWh, against the stepwise ToU tariffs.

Table 8. Charging $C^{\mathrm{ch}}$ and discharging $C^{\mathrm{dis}}$ prices by seasons (CNY/kWh).

Scenario	${\mathit{C}}^{\mathbf{ch}}$		${\mathit{C}}^{\mathbf{dis}}$
	Winter	Summer	Winter	Summer
ToU Pricing	0.57–1.27	0.53–1.21	0.57–1.27	0.53–1.21
Proposed Pricing	0.60–1.20	0.55–1.15	0.80–1.50	0.75–1.45

further contrasts the price ranges for both ToU and the proposed adaptive model across seasons. Our model offers finer granularity, with EV charging costs ranging from $0.6$ to $1.2$ CNY/kWh and discharging prices from $0.8$ to $1.5$ CNY/kWh, providing stronger financial incentives for grid-supportive behavior.

8.3. PEV Scheduling and State-of-Charge Results

The core of the DHO strategy’s effectiveness is demonstrated in the scheduling of individual PEVs. Figure 6, Figure 7, Figure 8 and Figure 9 illustrate the adaptive scheduling and state-of-charge (SoC) evolution for EVs across all four stations, comparing the baseline against the DHO-based strategy.

The results, summarized in

Table 9. PEV fleet specifications and final state of charge comparison.

EVCS	EV	${\mathit{P}}_{\mathbf{max}}^{\mathbf{ch}}$ (kW)	Battery Capacity (kWh)	Initial SoC (%)	Baseline Final SoC (%)	DHO Final SoC (%)
EVCS#1	EV1	9.6	25	20	50	55
	EV2	9.6	32	30	85	90
	EV3	9.6	35	25	75	85
EVCS#2	EV1	13.2	25	10	35	40
	EV2	13.2	32	20	65	70
	EV3	13.2	35	30	70	75
EVCS#3	EV1	19.6	25	12	38	44
	EV2	19.6	32	22	68	74
	EV3	19.6	35	28	72	80
EVCS#4	EV1	13.2	25	18	33	39
	EV2	13.2	32	24	60	66
	EV3	13.2	35	32	68	72

, show a consistent and significant improvement in final SoC achieved through DHO optimization. For instance:

• At EVCS#1, EV1’s SoC increased from 50% (baseline) to 55% (DHO).
• At EVCS#2, EV2 reached 70% SoC with DHO, outperforming the 65% baseline.
• Similar gains of 4% to 6% were observed across EVs at EVCS#3 and EVCS#4.

This uniform improvement is a direct result of the DHO framework’s ability to coordinate high-power charging strategies adaptively during optimal periods, ensuring higher energy delivery to each vehicle.

8.4. Performance Metrics and Cost–Benefit Analysis

The improvements in scheduling directly translate to superior system-wide performance and economic gains.

Table 10. Summary of microgrid performance metrics.

Metric	Value
Peak Load $L_{\mathrm{peak}}$	150.3 kW
Total Operational Cost	7934.4 CNY
Average PEV Utilization Rate	78.5%
PV Utilization Rate	92.1%
Wind Utilization Rate	85.4%

summarizes the key high-level metrics, showing effective peak load regulation and high utilization rates for renewables and PEVs.

A detailed cost-benefit analysis, presented in

Table 11. Cost comparison between baseline and DHO-based scheduling.

Metric	Baseline	DHO-Based
Total Charging Cost	$8.74$ CNY	$7.64$ CNY
Average Cost per kWh	$0.205$ CNY/kWh	$0.180$ CNY/kWh
Final Average SoC	74 %	$86.5$ %
EV Discharging Revenue	$0.00$ CNY	$1.15$ CNY
Net Economic Gain	–	$12.6$ % reduction

, reveals the stark economic advantage of the DHO approach. It achieved a reduction in total charging cost from $8.74$ CNY to 7.64 CNY and a lower average cost per kWh. The strategy also generated 1.15 CNY in V2G discharging revenue, leading to a net economic gain equivalent to a 12.6% cost reduction. Furthermore, the final average SoC across the fleet improved from 74% to 86.5%.

A more granular cost–benefit breakdown over a 7-day horizon showed that V2G discharging generated 1320 CNY in revenue, while the modeled battery-degradation cost (using the semi-empirical model from [15]) was 820 CNY, yielding a net benefit of 500 CNY. This supports our claim that V2G revenues can outweigh degradation costs under the proposed adaptive pricing+DHO framework. Sensitivity analysis confirmed this finding for battery-degradation coefficients varying ±20%.

The strategy’s benefits extend beyond economics:

• Emissions: A $6.2$ % reduction in net CO₂ emissions was achieved by shifting demand to periods of high renewable generation.
• Grid Stability: As shown in Figure 10, the DHO strategy reduced peak demand from 170 kW (baseline) to 130 kW, effectively eliminating grid stress during critical periods.
• Battery Health: The DHO’s constraints on depth-of-discharge and SoC cycling minimized degradation. The slight increase in wear cost ($0.03$ CNY) was vastly outweighed by V2G revenue.

8.5. Computational Performance and Scalability

A critical advantage of the proposed DHO is its computational efficiency, which is essential for real-world deployment. Implemented in Gurobi [40], the MILP formulation was solved on a standard workstation. For a 24-h horizon with 96 time steps, the average solver time was 18.4 s per scheduling window, which is practical for real-time operation.

To rigorously test scalability, we benchmarked the DHO against conventional fixed-horizon MPC and a Rule-Based strategy across microgrids of varying sizes (10 to 200 PEVs). The results, detailed in

Table A1. Computational benchmarking and scalability analysis.

Scale	Avg. No. of PEVs	Strategy	Avg. Solve Time (s)	Total Cost Reduction vs. RB (%)	Peak Demand Reduction vs. RB (%)	Final Avg. SoC (%)
Small	10	RH-MPC	2.35	8.2	19.1	92.5
		DHO	1.28	10.1	21.7	4.8
Medium	50	RH-MPC	9.84	11.5	21.3	91.7
		DHO	4.76	14.2	24.5	93.5
Large	200	RH-MPC	42.77	12.8	22.1	90.2
		DHO	19.65	7.1	25.9	2.1

in Appendix A, demonstrate that the DHO reduces computation time by 45–55% while simultaneously improving solution quality (cost and peak demand reduction) as the system scales. This performance advantage is a key differentiator from more computationally intensive methods like DRL.

However, we acknowledge that these scalability tests use simulated loads and stylized arrival patterns, and the absence of network constraints (voltage, transformer capacity, feeder limits) represents a significant limitation. Our results should therefore be interpreted as demonstrating computational scalability rather than immediate real-world applicability, which requires incorporating these constraints in future work.

8.6. Comparative Analysis of Pricing Strategies

To empirically validate the performance of the proposed adaptive pricing strategy, a comparative analysis was conducted against two benchmark schemes:

• Standard Real-Time Pricing (RTP): This benchmark reflects a common market-based approach where PEVs pay or are paid the actual system marginal price (SMP) at each time interval, i.e., $C^{\mathrm{ch}}\left(t\right)=C^{\mathrm{dis}}\left(t\right)=C^{\mathrm{SMP}}\left(t\right)$. This represents a principled, market-driven baseline.
• Fixed Premium/Discount Pricing: This simpler heuristic charges a fixed premium of $0.15$ CNY/kWh over the ToU tariff for charging and offers a fixed discount of $0.10$ CNY/kWh from the ToU tariff for discharging, regardless of system conditions. This tests whether conditional adjustments based on system state provide tangible benefits.

The proposed DHO framework was simulated under identical microgrid and EV fleet conditions using all three pricing strategies. The key economic and operational performance metrics are summarized in

Table 12. Comparative performance of different pricing strategies.

Performance Metric	RTP	Fixed Premium	Proposed
Total Microgrid Cost (CNY)	1256.4	1187.2	1153.8
Avg. PEV Charging Cost (CNY)	34.21	31.50	29.89
PEV V2G Revenue (CNY)	28.95	24.81	26.33
Peak Demand (kW)	145	138	130
Battery Aging Cost (CNY)	0.88	1.05	0.95
Comp. Time (s)	124.5	118.2	121.7

and visualized in Figure 11.

The results, as shown in Figure 11, demonstrate the practical value of the proposed conditional pricing strategy. While the RTP benchmark benefits from direct market price signals, it results in the highest operational costs (+8.9% vs proposed) and peak demand (+11.5% vs proposed) due to the absence of explicit grid-supportive incentives. The Fixed Premium approach reduces costs but proves suboptimal, generating 5.8% less V2G revenue and causing 10.5% higher battery degradation than the proposed method due to its inflexible incentives.

Our proposed method achieves the best balance across all metrics, reducing total costs by 8.2% versus RTP and 2.8% versus Fixed Premium pricing. More importantly, it demonstrates how simple conditional logic—dynamically coupling price signals with real-time grid constraints—can yield significant benefits: discouraging consumption during peak periods ($P^{\mathrm{NL}}\left(t\right)>P^{\mathrm{cri}}$) while encouraging V2G discharge and renewable absorption during surplus conditions ($P^{\mathrm{DER}}\left(t\right)>P^{\mathrm{L}}\left(t\right)$).

This analysis confirms that while not a full market design optimization, the proposed transparent pricing heuristic provides measurable economic and operational benefits over common alternatives. This positions it as a valuable contribution for practical implementations where computational tractability and operational simplicity are prioritized alongside performance.

9. Conclusions

This paper has presented a dynamic horizon optimization (DHO) framework with adaptive pricing for real-time energy management in renewable-powered microgrids. The proposed strategy dynamically adjusts control horizons based on EV connection patterns and system states, while a heuristic pricing mechanism couples time-of-use tariffs with system marginal prices to incentivize vehicle-to-grid (V2G) operations.

Simulation results demonstrate the operational effectiveness of the approach, showing a 23.5% reduction in peak load, 12.6% lower charging costs, and a 12.5% increase in average final State of Charge. The framework also achieves a 6.2% reduction in carbon emissions while incorporating battery-degradation constraints. The results suggest a potential trend toward reduced battery degradation under the applied semi-empirical model, though these specific longevity benefits require experimental validation.

10. Future Work

We emphasize that our study has several important limitations that should be addressed in future work. The scalability analysis uses simulated data and stylized patterns rather than real-world datasets, and the absence of network constraints (voltage regulation, transformer loading, feeder capacity) represents a significant simplification. Our claims of “real-world applicability” are therefore tempered, and we position this work primarily as a proof-of-concept demonstrating the potential of the DHO methodology.

The study positions the DHO framework as a practical alternative to more complex methods like deep reinforcement learning or bilevel optimization, particularly for implementations where computational tractability and interpretability are prioritized. Future work will focus on: (1) enhancing the pricing mechanism through stochastic optimization techniques to better handle forecast uncertainties; (2) experimental validation of the battery-degradation model against laboratory cycling tests; (3) expanding the framework to multi-node distributed energy systems; (4) incorporating network constraints including voltage stability and feeder capacity limits; and (5) incorporating robust cybersecurity measures for V2G infrastructure protection.