1. Introduction
The imperative to achieve China’s “30·60” dual carbon goals necessitates transitioning toward modern power systems dominated by renewable energy. Wind and solar photovoltaics (PV) offer low-cost, zero-carbon generation pathways. However, their inherent stochasticity and volatility, compounded by large-scale uncoordinated charging of electric vehicles (EVs), exacerbate grid challenges: increased peak-valley load differences, degraded power quality, operational instability, and renewable curtailment. Effectively managing electric vehicle charging behavior is critical to mitigating these issues and enhancing renewable energy integration. Demand Response (DR) programs provide a strategic framework for leveraging electric vehicles as flexible grid assets. DR mechanisms are categorized as Price-Based Demand Response (PDR) and Incentive-Based Demand Response (IDR). While existing research often focuses on single-DR mechanisms (PDR or IDR) or single-stage scheduling, this work addresses the gap by proposing a holistic day-ahead and intra-day two-stage low-carbon economic-environmental dispatch model. This model explicitly incorporates the heterogeneous demand response characteristics of diverse electric vehicle charging modes and integrates a ladder-type carbon trading mechanism.
2. Source-Load Forecasting Framework (SSA-CNN-LSTM)
Accurate prediction of renewable generation (source) and load demand is paramount for effective scheduling. We employ a hybrid Sparrow Search Algorithm-Optimized Convolutional Neural Network-Long Short-Term Memory (SSA-CNN-LSTM) model, overcoming limitations of traditional methods (e.g., BP, Elman) in handling the complex, multi-variate, and time-series nature of modern grid data.
- CNN-LSTM Architecture: Processes raw data through layers: Input → Convolution (feature extraction) → Pooling (dimensionality reduction) → Fully Connected → LSTM (temporal pattern learning) → Output (prediction). See structural representation below:
CNN-LSTM(X) = LSTM(Pool(Conv(X))) - SSA Optimization: Enhances CNN-LSTM by optimizing hyperparameters (e.g., neuron count, initial learning rate). SSA simulates sparrow foraging behavior:
- Population Initialization:
X = [x_i,j](i=1..n sparrows, j=1..m parameters). - Fitness Evaluation:
F_x = [f(x_i)](Model prediction error). - Position Updates:
- Discoverers (Guiding Search):
X^(d+1)_i,j = { X^d_i,j · exp(-t/(α·iter_max)) if R2 < ST; X^d_i,j + Q·L otherwise }… (3) - Followers (Exploiting Discoveries):
X^(d+1)_i,j = { Q·exp((X_worst - X^d_i,j)/i²) if i > n/2; X_p^(d+1) + |X^d_i,j - X_p^(d+1)|·A⁺·L otherwise }… (4) - Scouts (Anti-Predation/Avoiding Local Optima):
X^(d+1)_i,j = { X_best^d + β·|X^d_i,j - X_best^d| if f_i > f_g; X^d_i,j + K·(|X^d_i,j - X_worst^d|/((f_i - f_w) + ε)) if f_i = f_g }… (5)
Whered=iteration,α,Q,R2,ST,A,K,βare algorithm parameters,f_i,f_g,f_ware individual, global best, and global worst fitness.
- Discoverers (Guiding Search):
- Parameter Tuning via SSA: Minimizes prediction error (e.g., MAPE, RMSE).
- Population Initialization:
- Forecasting Process:
- Data collection, cleaning, normalization.
- SSA parameter setup (Population=50, Iterations=10, ST=0.8, Discoverer ratio=20%).
- SSA optimizes CNN-LSTM parameters.
- CNN extracts spatial features from input data.
- LSTM processes feature sequences for temporal forecasting.
- Output next-day source/load predictions.
Table 1: Forecasting Model Performance Comparison (Wind Power Example)
| Model | MAPE (%) | RMSE (MW) | Improvement vs. SSA-CNN-LSTM |
|---|---|---|---|
| BP Neural Network | 5.27 | 0.73 | ↑2.96% (MAPE), ↑0.36MW (RMSE) |
| Elman Neural Network | 7.13 | 1.01 | ↑4.82% (MAPE), ↑0.64MW (RMSE) |
| CNN-LSTM | 4.22 | 0.70 | ↑1.91% (MAPE), ↑0.33MW (RMSE) |
| GA-CNN-LSTM | 2.91 | 0.38 | ↑0.60% (MAPE), ↑0.01MW (RMSE) |
| SSA-CNN-LSTM (Proposed) | 2.31 | 0.37 | – |
3. Electric Vehicle Demand Response Characterization
Recognizing diverse electric vehicle user needs is crucial for effective DR participation. We classify EVs into three modes based on their grid interaction flexibility during connection periods ([t_k,in, t_k,out]):
- Class A: Uncontrollable Charging:
- Users: Taxis, short-trip private EVs requiring guaranteed departure State of Charge (SOC). Power is fixed at rated charge (
P_ch^EV). No DR participation. - Model:
I_ch,k,t^EV = 1 ∀ t ∈ [t_k,in, t_k,out]; I_ch,k,t^EV = 0 otherwise… (6)P_k,t = P_ch^EVS_k,t = S_k,t-Δt + I_ch,k,t^EV * (η_ch * P_k,t * Δt) / S_k0 ≤ S_k,in ≤ S_k,out ≤ S_k^max
- Users: Taxis, short-trip private EVs requiring guaranteed departure State of Charge (SOC). Power is fixed at rated charge (
- Class B: Controllable Charging (V1G):
- Users: Typical private EVs willing to shift charging time for cost savings but avoiding battery degradation from discharging. Power can be modulated (
0 < P_k,t < P_ch^EV) but no V2G. - Model:
I_ch,k,t^EV = 1 ∀ t ∈ [t_k,in, t_k,out]; I_ch,k,t^EV = 0 otherwise… (7)S_k,t = S_k,t-Δt + I_ch,k,t^EV * (η_ch * P_k,t * Δt) / S_k - Constraints:
- Departure SOC:
0.95 * S_k^max ≤ S_k,out ≤ S_k^max… (8) - Power Balance (Time-shifting only):
0.95 * P_total^EV ≤ ΣΣ P_k,t ≤ P_total^EV… (9) - Minimum ON Duration (Protect Battery):
Σ x_t^ch ≥ T_min^ch(e.g., 15min) … (10)
- Departure SOC:
- Users: Typical private EVs willing to shift charging time for cost savings but avoiding battery degradation from discharging. Power can be modulated (
- Class C: Bidirectional Charging/Discharging (V2G):
- Users: EVs seeking maximal economic benefit (e.g., shared fleets). Enables charging during low prices and discharging during high prices (
P_k,tcan be negative). - Model:
I_ch,k,t^EV + I_dis,k,t^EV ≤ 1; =0 ∀ t ∉ [t_k,in, t_k,out]… (11)S_k,t = S_k,t-Δt + I_ch,k,t^EV * (η_ch * P_k,t * Δt) / S_k - I_dis,k,t^EV * (P_k,t * Δt) / (η_dis * S_k) - Constraints:
- Departure SOC:
0.95 * S_k^max ≤ S_k,out ≤ S_k^max… (12) - Discharge Depth Limit (Protect Battery):
S_k,t ≥ S_k^min(e.g., 0.2) … (13) - Maximum Mode Switches:
Σ |I_ch/dis,k,t+Δt^EV - I_ch/dis,k,t^EV| ≤ M(e.g., M=3) … (14)
- Departure SOC:
- Users: EVs seeking maximal economic benefit (e.g., shared fleets). Enables charging during low prices and discharging during high prices (
Table 2: Electric Vehicle Charging Mode Characteristics and Constraints
| Feature | Class A | Class B (V1G) | Class C (V2G) |
|---|---|---|---|
| Power Control | Fixed (P_ch^EV) | Modulated (0 < P < P_ch^EV) | Bidirectional |
| DR Participation | None | PDR, IDR (Charging Shift) | PDR, IDR (Charge/Discharge) |
| Primary Users | Taxis, Short-trip Private EVs | Standard Private EVs | Shared EVs, Fleet EVs |
| Key Constraints | Departure SOC | Departure SOC, Power Balance, Min ON Time | Departure SOC, Min SOC, Max Switches |
| Objective | Guaranteed Ready Time | Minimize Charging Cost | Maximize Economic Benefit |
4. Ladder Carbon Trading Model
To promote low-carbon operation and internalize environmental costs, a ladder carbon trading mechanism is integrated, specifically targeting thermal generation units (renewables have zero operational carbon).
- Free Allowance Allocation: Uses a baseline method:
E_qt = n * P_Lt… (15) wherenis the grid emission factor,P_Ltis predicted load. - Actual Carbon Emissions:
E_rt = Σ_i δ_i * P_Gi,t… (16) whereδ_iis the carbon intensity of uniti,P_Gi,tis its output. - Ladder Carbon Trading Cost (
C_t): Imposes progressively higher costs for exceeding free allowances:C_t = { K_c(E_rt - E_qt) if E_rt ≤ E_qt; K_c(E_rt - E_qt) if E_qt < E_rt ≤ E_qt + v; K_cv + (1+σ)K_c(E_rt - E_qt - v) if E_qt + v < E_rt ≤ E_qt + 2v; (2+σ)K_cv + (1+2σ)K_c(E_rt - E_qt - 2v) if E_qt + 2v < E_rt ≤ E_qt + 3v; (3+3σ)K_cv + (1+3σ)K_c(E_rt - E_qt - 3v) if E_qt + 3v < E_rt ≤ E_qt + 4v; (6+4σ)K_cv + (1+4σ)K_c(E_rt - E_qt - 4v) if E_rt > E_qt + 4v }… (17)
Wherev = λ * E_qt(interval length),K_cis base carbon price,σis price increase rate,λis allowance margin. - Total Carbon Cost:
F_T = Σ_t C_t… (18)
This mechanism incentivizes reducing high-carbon thermal output, particularly penalizing significant emissions exceeding baseline levels.
5. Day-Ahead & Intra-Day Optimal Dispatch Framework
Leveraging the principle that forecast accuracy improves with shorter time horizons and the complementary timescales of PDR (day-ahead) and IDR (intra-day), a two-stage optimization framework is proposed.
- Day-Ahead Stage (Time Scale: 1 hour):
- Inputs: Day-ahead forecasts (Wind, PV, Load, EV availability/Class).
- Outputs: 24-hour schedule for thermal unit commitment (ON/OFF), unit outputs, renewable dispatch, PDR signals, and day-ahead IDR commitments for B/C Class electric vehicles.
- Objectives: Minimize total system cost (
F_d^ad) and pollutant emissions (F_d^ad), combined into a weighted sum (F_ad = w1*F1_ad + w2*F2_ad; w1+w2=1). Key cost components:- Thermal fuel cost:
ΣΣ U_i,t (a_i P_Gi,t² + b_i P_Gi,t + c_i) - Thermal startup/shutdown cost:
ΣΣ [U_i,t(1-U_i,t-1) + U_i,t-1(1-U_i,t)] F_i - Ladder Carbon Trading Cost (
Σ C_t) - Day-Ahead IDR Cost:
F_cost^ch,ad * P_ch^DR,ad + F_cost^dis,ad * P_dis^DR,ad - Renewable Curtailment Penalty:
K_w(P_w^pre - P_w) + K_r(P_r^pre - P_r)
- Thermal fuel cost:
- Constraints: (See Section 4.1.2 in paper) Renewable limits, Thermal unit min/max output (
u_i,t P_min ≤ P_Gi,t ≤ u_i,t P_max), Ramp rates (|P_Gi,t - P_Gi,t-1| ≤ R_up/down), Min ON/OFF time, Spinning reserve (Σ min[R_up, (P_max - P)] ≥ τ_up^sys; Σ min[R_down, (P - P_min)] ≥ τ_down^sys), Power balance including EV loads (Eq. 26).
- Intra-Day Stage (Time Scale: 15 minutes, Rolling 4-hour window):
- Inputs: Intra-day rolling forecasts, fixed day-ahead decisions (Unit ON/OFF, PDR, Day-Ahead IDR).
- Outputs: 96-point (15-min) adjustments over 4-hour windows, rolled forward hourly. Focuses on fine-tuning unit outputs and activating intra-day IDR from B/C Class electric vehicles.
- Objectives: Minimize intra-day operating cost (
F_id) and emissions (F_id), combined (F_id = w3*F1_id + w4*F2_id; w3+w4=1). Costs exclude startup/shutdown and day-ahead IDR but include intra-day IDR cost (F_cost^ch,id * P_ch^DR,id + F_cost^dis,id * P_dis^DR,id) and updated curtailment penalties. - Constraints: (See Section 4.2.2) Renewable limits (using intra-day forecast), Thermal unit output (fixed commitment), Adjusted ramp rates (for 15-min intervals:
|ΔP| ≤ R_up/down / 4), Adjusted spinning reserve, Power balance including adjustments from day-ahead DR and intra-day IDR (Eq. 33).
This framework leverages PDR for coarse, day-ahead load shaping and unit commitment, while utilizing IDR and intra-day forecasts for fine-grained, rapid adjustments to handle forecast errors and short-term fluctuations, enhancing renewable integration and system stability. The participation of electric vehicles across different classes is fundamental to providing this flexibility.
6. Improved Multi-Objective Grey Wolf Optimizer (MOGWO)
The dispatch model is a complex, constrained, multi-objective (cost vs. emissions), non-linear optimization problem. We enhance the standard MOGWO algorithm to overcome limitations like local optima entrapment and slow convergence.
- Standard MOGWO:
- Hierarchy: Wolves ranked
α(best),β,δ,ω(worst). - Hunting: Guided by
α,β,δ. Positions updated relative to leaders:D_i = |C · X_p - X_i|… (Distance Vector)X_i(k+1) = X_p(k) - A · D_i… (Position Update) … (34, 35) - Coefficient Vectors:
A = 2a·R1 - a; C = 2·R2… (36) whereR1,R2~ U[0,1],adecreases linearly from 2 to 0.
- Hierarchy: Wolves ranked
- Proposed Improvements:
- Non-Linear Parameter
a: Replace linear decrease with exponential decay for better global exploration and local exploitation balance:a = 2 - (k / iter_max)^3 * 2… (37) - Survival-of-the-Fittest Population Update: After each iteration:
- Rank wolves by fitness (lower cost/emissions = better).
- Remove the worst
mwolves. - Generate
mnew random wolves to maintain diversity and escape local optima.mis dynamically sized:m = round(n * μ)… (38) wheren=population size,μ=update ratio (e.g., 0.1-0.3). Balances diversity (mlarge) and convergence speed (msmall).
- Non-Linear Parameter
The Improved MOGWO exhibits superior convergence characteristics and solution quality (Pareto front spread and dominance) compared to the standard version, as confirmed by case study results (Section 7).
7. Case Study and Results Analysis
A simulation based on a Northwest China regional system (20MW PV, 30MW Wind, multiple thermal units – parameters in Appendix) with 20,000 electric vehicles (A:50%, B:35%, C:15%) was conducted. EV parameters (travel distance N(3.2, 0.88²), start time N(17.6, 3.4²), end time N(8.92, 3.24²), 5 km/kWh, 7 kW charge/discharge power) and limits on DR participation (B/C: ≤30% PDR, ≤25% DA-IDR, ≤20% ID-IDR) were applied. Four scenarios were compared:
- Scenario 1 (S1): Baseline – No DR, No Carbon Trading.
- Scenario 2 (S2): Ladder Carbon Trading, No DR.
- Scenario 3 (S3): PDR & IDR (EV Flexibility), No Carbon Trading.
- Scenario 4 (S4): Proposed – PDR & IDR (EV Flexibility) + Ladder Carbon Trading.
7.1 Day-Ahead Dispatch Results:
*Table 3: Day-Ahead Scheduling Results Comparison*
| Metric | S1 | S2 | S3 | S4 | S4 vs S1 Improvement |
|---|---|---|---|---|---|
| Total Cost ($) | 64,434 | 62,850 | 60,786 | 58,929 | -5,505 (8.5%) |
| Start/Stop Cost ($) | 320 | 380 | 290 | 290 | -30 |
| Operational Cost ($) | 63,185 | 61,761 | 59,867 | 58,344 | -4,841 (7.7%) |
| PV Curt. Cost ($) | 235 | 143 | 120 | 102 | -133 (56.6%) |
| Wind Curt. Cost ($) | 694 | 461 | 198 | 39 | -655 (94.4%) |
| Carbon Cost ($) | 0 | 105 | 0 | -165 | – (Revenue) |
| PV Curt. Rate (%) | 6.13 | 3.75 | 3.13 | 2.84 | -3.29pp |
| Wind Curt. Rate (%) | 6.38 | 4.24 | 1.82 | 0.37 | -6.01pp |
| DA IDR Cost ($) | 0 | 0 | 311 | 319 | +319 |
| Pollutants (lb) | 7,932 | 7,558 | 7,292 | 7,126 | -806 (10.2%) |
- S1: High thermal output during peaks (causing high cost/emissions), high curtailment during valleys due to thermal minimum output constraints.
- S2: Carbon cost forces lower thermal output, reducing emissions and curtailment vs S1. However, increased thermal cycling (start/stop cost ↑60$) occurs due to renewable variability.
- S3: Electric vehicle DR shifts load, absorbing excess renewables during valleys and reducing thermal peak output. Significantly reduces curtailment and emissions vs S1, despite IDR cost.
- S4: Synergy of electric vehicle DR and carbon trading achieves the best performance. DR mitigates the thermal cycling induced by carbon trading (start/stop cost back to S3 level). Lowest cost, emissions, and curtailment. Carbon revenue is generated.
7.2 Intra-Day Dispatch Results:
*Table 4: Intra-Day Scheduling Results Comparison*
| Metric | S1 | S2 | S3 | S4 | S4 vs S1 Improvement |
|---|---|---|---|---|---|
| Total Cost ($) | 62,963 | 60,336 | 58,511 | 56,454 | -6,509 (10.3%) |
| Operational Cost ($) | 62,339 | 59,856 | 58,162 | 56,341 | -5,998 (9.6%) |
| PV Curt. Cost ($) | 49 | 22 | 15 | 10 | -39 (79.6%) |
| Wind Curt. Cost ($) | 575 | 360 | 88 | 32 | -543 (94.4%) |
| Carbon Cost ($) | 0 | 98 | 0 | -187 | – (Revenue) |
| PV Curt. Rate (%) | 1.28 | 0.58 | 0.41 | 0.26 | -1.02pp |
| Wind Curt. Rate (%) | 5.17 | 3.25 | 0.79 | 0.29 | -4.88pp |
| ID IDR Cost ($) | 0 | 0 | 246 | 258 | +258 |
| Pollutants (lb) | 7,785 | 7,456 | 7,143 | 6,937 | -848 (10.9%) |
- All scenarios benefit from improved intra-day forecast accuracy (reduced costs/curtailment/emissions vs DA stage).
- S1 & S2: Persistent curtailment issues, especially wind during valleys (spinning reserve constraints) and PV during ramps (thermal ramp constraints). S2 shows improvement over S1 due to carbon pressure.
- S3 & S4: Electric vehicle IDR provides crucial intra-hour flexibility, significantly alleviating thermal ramp and reserve pressures, leading to drastically lower curtailment. S4 leverages both IDR flexibility and carbon cost optimization for the best overall intra-day performance. The synergy minimizes unnecessary thermal output and maximizes renewable utilization.
- Overall S4 Performance (vs S1): Total Cost ↓10.3%, Pollutants ↓10.9%, PV Curtailment Rate ↓1.02pp, Wind Curtailment Rate ↓4.88pp. Achieves significant low-carbon economic benefits.
7.3 Algorithm Performance Validation:
- SSA-CNN-LSTM: Demonstrated superior forecasting accuracy (Lowest MAPE: 2.31%, Lowest RMSE: 0.37MW for wind) compared to benchmarks (Table 1).
- Improved MOGWO: Produced a superior Pareto front (Fig 16 vs Fig 15) compared to standard MOGWO – solutions are more spread (better diversity) and dominate standard MOGWO solutions (lower cost and emissions for comparable points). Extreme and compromise solutions (Table 4) confirm the improved algorithm finds better economic and environmental optima.
*Table 5: MOGWO Solution Comparison (Scenario 4 Intra-Day)*
| Algorithm | Solution Type | Pollutants (10³ lb) | Cost (10⁵ $) | Comment |
|---|---|---|---|---|
| Standard MOGWO | Economic Optimum | 7.2612 | 5.5323 | Higher cost than IMOGWO EnvOpt |
| Environmental Opt | 6.8445 | 5.8617 | Higher emissions than IMOGWO | |
| Compromise | 6.9527 | 5.6593 | Dominated by IMOGWO Compromise | |
| Improved MOGWO | Economic Optimum | 7.2858 | 5.5129 | Lower cost, Slightly ↑Emis |
| Environmental Opt | 6.8356 | 5.8941 | Lower emissions, ↑Cost | |
| Compromise | 6.9371 | 5.6454 | Better than Std MOGWO Comp. |
8. Conclusion
This research presents a comprehensive framework for low-carbon economic-environmental dispatch in modern power systems, effectively integrating large-scale electric vehicle participation. The key innovations and findings are:
- Enhanced Forecasting: The SSA-CNN-LSTM model significantly improves the accuracy of renewable generation and load demand predictions for both day-ahead and intra-day stages, providing a reliable foundation for scheduling decisions and mitigating source-load uncertainty.
- Granular EV Modeling: Classifying electric vehicles into three distinct charging modes (A: Uncontrollable, B: V1G, C: V2G) based on user needs and DR participation characteristics allows for a more realistic and effective utilization of EV flexibility within optimization models, capturing previously neglected potential.
- Two-Stage Optimization: The day-ahead (1h) and intra-day (15min rolling) scheduling framework effectively leverages the complementary timescales of PDR (planning) and IDR (rapid adjustment). This structure accommodates improved forecast accuracy over shorter horizons and harnesses the flexibility of electric vehicle DR to balance the system.
- Ladder Carbon Trading: Integrating a progressive carbon pricing mechanism internalizes environmental costs, strongly incentivizing the reduction of high-carbon thermal generation and promoting renewable integration, while generating revenue for low-carbon operators.
- Improved Optimization Algorithm: The enhanced MOGWO algorithm effectively solves the complex, constrained multi-objective dispatch problem, demonstrating superior convergence and solution quality compared to the standard version.
- Significant Synergistic Benefits: Case studies conclusively demonstrate that the simultaneous consideration of diverse electric vehicle DR capabilities (PDR and IDR across Classes B & C) and the ladder carbon trading mechanism (Scenario 4) yields the highest system-wide benefits:
- Cost Reduction: 10.3% decrease compared to the baseline (No DR, No Carbon Trading).
- Emission Reduction: 10.9% decrease in pollutants.
- Renewable Integration: Dramatic reduction in PV (1.02pp) and Wind (4.88pp) curtailment rates.
- Stability: Mitigation of thermal unit cycling stress induced by renewable variability or carbon constraints through electric vehicle flexibility.
This work provides a robust methodological foundation and demonstrates tangible benefits for achieving a low-carbon, economically efficient, and stable modern power system. Future research will extend this framework to real-time dispatch and explore multi-energy system integration, further enhancing grid resilience and sustainability through advanced electric vehicle grid services.