With the approaching “30·60” dual-carbon targets in China, the construction of a new power system dominated by new energy sources has become imperative. Wind power, photovoltaic power, and other renewable energy sources offer low generation costs and zero carbon emissions, representing an effective pathway to achieve these goals. However, the randomness and volatility of renewable energy generation, coupled with the large-scale disordered charging of electric cars, can exacerbate load peak-valley differences, degrade power quality, and complicate dispatch control, thereby threatening the stability and safety of the new power system. In some cases, it becomes necessary to curtail wind and solar power to ensure system reliability. How to guide electric cars to engage in orderly charging and discharging, reduce grid load fluctuations, and promote renewable energy absorption has become a focal issue.
China’s “Action Plan for Accelerating the Construction of a New Power System” proposes that electric cars can participate in demand response (DR) to achieve peak shaving and valley filling, thereby accelerating the development of the new power system. DR is categorized into price-based demand response (PDR) and incentive-based demand response (IDR). Current research on electric car participation in DR optimization scheduling primarily focuses on day-ahead scheduling based on day-ahead predictions. However, the randomness of electric car charging and the uncertainty of source-load outputs in the new power system often render day-ahead scheduling insufficient to meet charging demands. Day-ahead-intraday optimization scheduling can utilize intraday predictions that are closer to actual scenarios to correct errors from the day-ahead stage, enhancing the accuracy of electric car participation in power system optimization. Nevertheless, deviations between predicted and actual values of renewable energy and load introduce new challenges to day-ahead-intraday optimization scheduling.
Limited by current forecasting capabilities, the contradiction between prediction accuracy and scheduling foresight may hinder the system’s ability to adapt to changes. Therefore, improving the prediction accuracy of both source and load sides is crucial for realizing day-ahead-intraday optimization scheduling in the new power system. Commonly used prediction methods include time series, neural networks, and support vector machines. However, under the new power system, energy consumption patterns have diversified, and source-load characteristics have become more complex. Traditional methods struggle to ensure accuracy and stability. With advancements in artificial intelligence algorithms, new approaches have emerged. Convolutional neural networks (CNN) exhibit strong feature extraction capabilities for source-load data, while long short-term memory networks (LSTM) perform well in processing time-series data. Additionally, the sparrow search algorithm (SSA) can optimize model parameters, addressing the issue of manual parameter selection that often compromises prediction effectiveness. Thus, the SSA-CNN-LSTM prediction model can effectively enhance the prediction accuracy of both source and load sides.
Current day-ahead-intraday optimization scheduling for new power systems involving electric cars in China mostly employs either PDR or IDR individually for orderly charging and discharging. While this can reduce peak-valley differences and lower system costs to some extent, research simultaneously considering both PDR and IDR for electric cars remains scarce. PDR guides electric car owners to adjust charging and discharging based on electricity price mechanisms, offering advantages such as low cost and wide applicability, but it suffers from low调控精度 and slow response times. IDR incentivizes electric car owners to adjust charging and discharging through economic compensation, providing fast and precise responses. Therefore, PDR is suitable for day-ahead scheduling to guide electric car charging and discharging behavior and reduce peak-valley differences, while IDR is applicable for both day-ahead and intraday scheduling to precisely adjust electric car charging and discharging for rapid regulation. Simultaneously considering PDR and IDR leverages their complementary time scales, enabling reasonable scheduling in both day-ahead and intraday stages and better coping with renewable energy volatility and electric car charging load uncertainty. Moreover, existing studies have not fully considered the different charging characteristics of electric cars participating in DR, limiting the potential of electric car DR. Additionally, current dispatch models considering electric cars primarily focus on economic dispatch, neglecting the negative environmental impact of CO2 and other pollutant emissions from thermal power generation, which is detrimental to achieving dual-carbon goals. Introducing carbon trading into power system dispatch, along with pollutant emission constraints, can further reduce the environmental impact of fossil fuel power generation, laying the foundation for “dual-carbon” targets. However, current modeling of carbon trading mechanisms typically calculates carbon trading costs under a single carbon price, which is not conducive to balancing low-carbon and economic performance.
The multi-objective optimization scheduling model for the new power system considering electric cars is a nonlinear, multi-objective, and multi-constrained problem, and its solution directly affects the optimal operation of the power system. With the high penetration of renewable energy and electric cars, precisely solving the model has become challenging. In recent years, various artificial intelligence algorithms have been widely used in power system optimization scheduling, such as particle swarm optimization, genetic algorithms, and ant colony algorithms. These algorithms offer strong global search capabilities and adaptability but suffer from long search times and slow convergence. The multi-objective grey wolf optimizer (MOGWO) has advantages such as simple principles, good global search ability, and strong robustness. Compared to other intelligent algorithms, MOGWO shows clear advantages for solving multi-objective optimization scheduling models. However, to address its tendency to fall into local optima and slow convergence, improvements have been made.
In summary, this paper proposes a day-ahead-intraday two-stage low-carbon environmental economic dispatch method for the new power system, considering the different charging characteristics of electric cars. The SSA-CNN-LSTM prediction model is used to forecast source and load sides, reducing the impact of uncertainty on day-ahead-intraday optimization scheduling. Secondly, based on the Monte Carlo method to simulate electric car charging models, and comprehensively considering the charging characteristics of electric cars participating in DR, electric cars are categorized into three charging modes. With the optimal system total cost considering ladder-type carbon trading and pollutant emissions as objectives, a two-stage dispatch model for the new power system with different types of electric cars is constructed. The improved MOGWO algorithm is employed to solve the model. Finally, case studies using typical daily photovoltaic, wind power, and load data, and considering the demand response characteristics of different electric car charging modes, validate the advantages of the proposed method through comparative analysis of four operational scenarios.
Source-Load Prediction Based on SSA-CNN-LSTM
This paper employs the SSA-CNN-LSTM model for source-load prediction, as it possesses excellent feature extraction capabilities and proficiency in handling time-series data, making it more suitable for source-load prediction with多元化 and temporal characteristics.
The CNN-LSTM model consists of an input layer, convolutional layer, pooling layer, fully connected layer, LSTM layer, and output layer, as shown in the model structure diagram. First, raw data is input into the input layer. Next, the convolutional layer extracts important features from the data, followed by the pooling layer for data dimensionality reduction. The processed data is then fed into the fully connected layer for classification. Subsequently, it is input into the LSTM layer for data training. Finally, the predicted values are obtained through the output layer.
To address the issue that the CNN-LSTM prediction method does not optimize key model parameters, preventing further improvement in source-load prediction accuracy, the SSA is used to optimize the key parameters of CNN-LSTM. The design steps are as follows:
First, the sparrow population is represented by matrix $X$:
$$X = \begin{bmatrix}
x_{1,1} & x_{1,2} & \cdots & x_{1,m} \\
x_{2,1} & x_{2,2} & \cdots & x_{2,m} \\
\vdots & \vdots & \ddots & \vdots \\
x_{n,1} & x_{n,2} & \cdots & x_{n,m}
\end{bmatrix}$$
where $n$ is the number of sparrows, and $m$ represents the problem variable dimension.
The fitness of the sparrows is denoted by $F_X$:
$$F_X = \begin{bmatrix}
f([x_{1,1} & x_{1,2} & \cdots & x_{1,m}]) \\
f([x_{2,1} & x_{2,2} & \cdots & x_{2,m}]) \\
\vdots \\
f([x_{n,1} & x_{n,2} & \cdots & x_{n,m}])
\end{bmatrix}$$
In the equation, discoverers with high fitness values prioritize obtaining food during foraging and provide location information for the population, thus having a wider search range. The discoverer position update is as follows:
$$X_{i,j}^{d+1} = \begin{cases}
X_{i,j}^{d} \cdot \exp\left(-\frac{i}{\alpha \times iter_{\text{max}}}\right) & R_2 < ST \\
X_{i,j}^{d} + Q \cdot L & R_2 \geq ST
\end{cases}$$
where $X_{i,j}^{d}$ is the position of the discoverer at the $d$-th iteration, $d$ is the iteration number, $\alpha$ is a random number in (0, 1], $iter_{\text{max}}$ is the maximum number of iterations, $Q$ is a random number following a normal distribution, $L$ is a $1 \times m$ matrix with all elements being 1, $R_2$ is the warning value, and $ST$ is the safety value.
When discoverers find better food, other individuals join the competition for food. If they defeat the discoverer, they become joiners, and their position update is expressed as:
$$X_{i,j}^{d+1} = \begin{cases}
Q \cdot \exp\left(\frac{X_{\text{worst}}^{d} – X_{i,j}^{d}}{i^2}\right) & i > n/2 \\
X_{p}^{d+1} + |X_{i,j}^{d} – X_{p}^{d+1}| \cdot A^{+} \cdot L & \text{otherwise}
\end{cases}$$
where $X_{p}^{d+1}$ is the global best position at the $d+1$-th iteration, and $X_{\text{worst}}^{d}$ is the global worst position at the $d$-th iteration.
Sparrows at the edge of the group remain vigilant when perceiving danger to ensure group safety, expressed as:
$$X_{i,j}^{d+1} = \begin{cases}
X_{\text{best}}^{d} + \beta \cdot |X_{i,j}^{d} – X_{\text{best}}^{d}| & \text{if } f_i > f_g \\
X_{i,j}^{d} + K \cdot \left(\frac{|X_{i,j}^{d} – X_{\text{worst}}^{d}|}{(f_i – f_w) + \varepsilon}\right) & \text{if } f_i = f_g
\end{cases}$$
where $X_{\text{best}}^{d}$ is the current global best position, $\beta$ is the step size control parameter, $f_i$ is the fitness value of the current sparrow position, $f_g$ is the fitness value of the global best position, $f_w$ is the global worst fitness value, $K$ is a random number in [-1,1], and $\varepsilon$ is a small constant to avoid division by zero.
The specific steps for source-load prediction based on SSA-CNN-LSTM are as follows:
Step 1: Collect source-load data, remove abnormal data, fill in missing data, and then perform data normalization.
Step 2: Set parameters for the SSA algorithm: sparrow population size of 50, maximum iterations of 10, safety threshold of 0.8, and discoverer proportion of 20% of the population.
Step 3: Use SSA to optimize CNN-LSTM model parameters. Select the optimal number of neurons and initial learning rate for the CNN-LSTM model as the fitness function. The SSA algorithm calculates the optimal parameter configuration and assigns it to the CNN-LSTM model.
Step 4: CNN feature extraction. Input preprocessed load data into the CNN model. The data passes through the convolutional layer to extract local features. After the pooling layer reduces data dimensions, the feature sequence data from CNN is output.
Step 5: Input the feature sequence data extracted by CNN into the LSTM layer, and finally output the predicted values for the next day.
Analysis of Electric Car Demand Response Characteristics
In the process of electric cars participating in DR, the primary goal is to ensure that the electric car reaches the expected state of charge (SOC) when disconnecting from the grid to meet the owner’s driving needs. However, different owners have significant differences in charging mode requirements when participating in DR. Traditional charging modes for electric cars participating in DR often use standardized methods, ignoring the personalized charging needs of electric car owners in DR. To more accurately reflect the personalized charging characteristics of electric car owners participating in DR, this paper categorizes the charging modes of electric cars at grid connection into three types based on their charging characteristics: Mode A with unadjustable charging power, Mode B with adjustable charging power but no reverse charging, and Mode C with bidirectional V2G charging and discharging. Their mathematical models and constraints are as follows:
Mode A Charging
Mode A indicates that the electric car owner has a priority need for quick disconnection. Therefore, Mode A is suitable for owners with high requirements for charging duration, such as taxis or short-trip private cars. The electric car maintains rated charging power during grid connection, meaning the charging power is unadjustable and cannot participate in DR, until the electric car $k$ reaches the required SOC or the disconnection time. Its mathematical model is:
$$I_{ch,n,t}^{EV} = 1 \quad \forall t \in [t_{k,in}, t_{k,out}]$$
$$I_{ch,n,t}^{EV} = 0 \quad \forall t \notin [t_{k,in}, t_{k,out}]$$
$$P_{k,t} = P_{ch}^{EV}$$
$$0 \leqslant S_{k,in} \leqslant S_{k,out} \leqslant S_{k}^{max}$$
$$S_{k,t} = S_{k,t-\Delta t} + I_{ch,k,t}^{EV} \eta_{ch} \frac{P_{k,t}^{EV} \Delta t}{S_k}$$
where $P_{k,t}$, $S_{k,t}$, $I_{ch,n,t}^{EV}$ are the charging power, battery capacity, and charging flag (0-1 variable) of electric car $k$ at time $t$. $t_{k,in}$, $t_{k,out}$, $P_{ch}^{EV}$, $S_{k,in}$, $S_{k,out}$, $\eta_{ch}$, $S_k$, $S_{k}^{max}$ are the grid connection time, disconnection time, rated charging power, SOC at grid connection, SOC at disconnection, charging efficiency, battery capacity, and maximum battery capacity of electric car $k$, respectively.
Mode B Charging
Mode B indicates that the electric car owner hopes to save some charging costs by adjusting charging power during DR participation but does not want reverse discharging that could shorten battery life, such as ordinary household electric car owners. During grid connection, the power can be adjusted but not discharged in reverse. Owners can choose to charge when electricity prices are low and reduce charging when prices are high, thereby lowering charging costs while ensuring normal travel needs. Its mathematical model is:
$$I_{ch,n,t}^{EV} = 1 \quad \forall t \in [t_{k,in}, t_{k,out}]$$
$$I_{ch,n,t}^{EV} = 0 \quad \forall t \notin [t_{k,in}, t_{k,out}]$$
$$0 \leqslant P_{k,t} \leqslant P_{ch}^{EV}$$
$$S_{k,t} = S_{k,t-\Delta t} + I_{ch,k,t}^{EV} \eta_{ch} \frac{P_{k,t} \Delta t}{S_k}$$
Electric cars in Mode B participating in DR must meet the following constraints:
(1) To ensure the electric car reaches the owner’s minimum required SOC at disconnection time, ensuring normal driving, the electric car must satisfy the disconnection time capacity constraint:
$$0.95 S_{k}^{max} \leqslant S_{k,out} \leqslant S_{k}^{max}$$
(2) Mode B electric cars only shift on the time scale, and the total power before and after shifting remains unchanged, so power balance must be constrained:
$$0.95 P_{\text{total}}^{EV} \leqslant \sum_{t=t_{k,in}}^{t_{k,out}} \sum_{k=1}^{K} P_{k,t} \leqslant P_{\text{total}}^{EV}$$
where $P_{\text{total}}^{EV}$ is the disordered charging load of Mode B electric cars.
(3) To prevent frequent power adjustments from damaging the electric car battery life, the minimum continuous operation time must be constrained:
$$\sum_{t=1}^{t+T_{min}^{ch} – \Delta t} x_t^{ch} \geqslant T_{min}^{ch}$$
where $x_t^{ch}$ is the power adjustment status 0-1 variable at time $t$, and $T_{min}^{ch}$ is the minimum continuous operation time, set to 15 minutes.
Mode C Charging
Mode C indicates that the electric car owner hopes to minimize charging costs during DR participation, and the electric car can perform bidirectional V2G charging and discharging. Mode C is suitable for electric car users who wish to maximize economic benefits, such as shared electric cars. Mode C allows electric cars to charge when electricity prices are low and discharge when prices are high, reducing their own charging costs. However, the prerequisite for V2G is that the electric car must meet the expected SOC at disconnection time. For electric car $k$ in Mode C, its mathematical model is:
$$I_{ch,n,t}^{EV} + I_{dis,n,t}^{EV} = 1 \quad \forall t \in [t_{k,in}, t_{k,out}]$$
$$I_{ch,n,t}^{EV} + I_{dis,n,t}^{EV} = 0 \quad \forall t \notin [t_{k,in}, t_{k,out}]$$
$$-P_{ch}^{EV} \leqslant P_{k,t} \leqslant P_{ch}^{EV}$$
$$S_{k,t} = S_{k,t-\Delta t} + I_{ch,k,t}^{EV} \eta_{ch,k} \frac{P_{k,t} \Delta t}{S_k} + I_{dis,k,t}^{EV} \frac{P_{k,t} \Delta t}{\eta_{dis,k} S_k}$$
where $I_{dis,n,t}^{EV}$ is the discharging flag (0-1 variable) of electric car $k$ at time $t$, and $\eta_{dis,k}$ is the discharging efficiency of electric car $k$.
Electric cars in Mode C participating in DR must meet the following constraints:
(1) To ensure the electric car meets the owner’s minimum SOC requirement at disconnection time, the electric car must satisfy the disconnection time capacity constraint:
$$0.95 S_{k}^{max} \leqslant S_{k,out} \leqslant S_{k}^{max}$$
(2) To prevent deep discharge from affecting battery life, the discharge threshold capacity must be constrained:
$$S_{k,thr} \leqslant S_{k,t}, \quad P_{k,t} < 0$$
where $S_{k,thr}$ is the discharge threshold, set to 0.2.
(3) To prevent frequent switching between charging and discharging states from damaging battery life, assume the number of times an electric car switches charging and discharging states does not exceed $M$, set to 3 in this paper:
$$\sum_{t=t_{k,in}}^{t_{k,out}} |I_{ch,k,t+\Delta t}^{EV} – I_{dis,k,t}^{EV}| \leqslant M$$
Ladder-Type Carbon Trading Model and Source-Load Day-Ahead-Intraday Optimization Framework
This paper improves the low-carbon economic performance of the system through the source side using ladder-type carbon trading and the load side using DR to compensate for the limitations of ladder-type carbon trading in enhancing system low-carbon economic performance.
Ladder-Type Carbon Trading Model
This paper only considers the carbon trading cost of thermal power units. Photovoltaic and wind power generation, given their zero-carbon characteristics, do not participate in carbon trading. This paper uses the baseline method to determine free allocation quotas. For thermal power units with carbon emissions less than the free allocation quota, they can obtain economic benefits by selling excess carbon emission quotas in the carbon trading market. For thermal power units with carbon emissions exceeding the free allocation quota, a ladder price is implemented to control carbon emissions. The higher the carbon emissions, the higher the carbon trading cost. The ladder-type carbon trading cost is shown in equations (15)-(17).
$$E_{qt} = \eta P_{Lt}$$
$$C_t = \begin{cases}
K_c (E_r – E_{qt}) & E_r \leq E_{qt} \\
K_c (E_r – E_{qt}) & E_{qt} < E_r \leq E_{qt} + v \\
K_c v + (1 + \sigma) K_c (E_r – E_{qt} – v) & E_{qt} + v < E_r \leq E_{qt} + 2v \\
(2 + \sigma) K_c v + (1 + 2\sigma) K_c (E_r – E_{qt} – 2v) & E_{qt} + 2v < E_r \leq E_{qt} + 3v \\
(3 + 3\sigma) K_c v + (1 + 3\sigma) K_c (E_r – E_{qt} – 3v) & E_{qt} + 3v < E_r \leq E_{qt} + 4v \\
(6 + 4\sigma) K_c v + (1 + 4\sigma) K_c (E_r – E_{qt} – 4v) & E_r > E_{qt} + 4v
\end{cases}$$
$$\begin{cases}
E_r = \sum_{i=1}^{N} \delta_i P_{Gi,t} \\
v = \lambda E_{qt} \\
F_T = \sum_{t=1}^{T} C_t
\end{cases}$$
where $E_{qt}$ is the free allocation quota for thermal power units at time $t$, $\eta$ is the grid baseline emission factor, $P_{Lt}$ is the predicted load power at time $t$, $C_t$ is the carbon trading cost of thermal power units at time $t$, $K_c$ is the benchmark carbon trading price, $E_r$ is the carbon emissions of thermal power units at time $t$, $v$ is the carbon emission interval length, $\sigma$ is the carbon trading price growth rate, $N$ is the number of thermal power units, $\delta_i$ is the carbon emission intensity per unit electricity of thermal power unit $i$, $\lambda$ is the carbon allowance margin, and $F_T$ is the total carbon trading cost.
Source-Load Day-Ahead-Intraday Optimization Scheduling Framework
Based on the characteristic that source-load prediction accuracy improves as the time scale shortens, and comprehensively considering the charging characteristics of different electric cars participating in DR and the response time characteristics of PDR and IDR, a source-load day-ahead-intraday optimization scheduling framework is proposed. In the day-ahead stage, based on day-ahead prediction data of source and load, a 24-hour optimization scheduling plan with a time scale of 1 hour is established. This scheduling plan is issued from the dispatch center to various units, and the thermal unit commitment, PDR response, and day-ahead IDR response are taken as determined quantities into the intraday rolling scheduling stage. The day-ahead scheduling plan with a time scale of 1 hour helps PDR perform scheduling in the day-ahead stage, thereby reducing system costs caused by frequent start-stop of thermal units and improving the absorption rate of new energy. In the intraday stage, using intraday rolling prediction data of source and load, a 4-hour rolling optimization plan with a time scale of 15 minutes is established to correct the day-ahead scheduling plan. The intraday scheduling plan with a time scale of 15 minutes can more flexibly respond to fluctuations in renewable energy output and short-term load fluctuations, reduce wind and solar curtailment, and leverage the regulatory flexibility of IDR on the time scale.
Source-Load Day-Ahead-Intraday Low-Carbon Optimization Scheduling Model
Day-Ahead Optimization Scheduling Model
Objective Function
(1) Day-ahead economic objective function
The day-ahead stage takes the optimal total system cost as the economic objective function, including thermal unit coal consumption cost and start-stop cost, carbon trading cost, day-ahead IDR call cost, and wind and solar curtailment penalty cost.
$$F_1^{ad} = \sum_{t=1}^{T_1} \left\{ \sum_{i=1}^{N} U_{i,t} (a_i P_{Gi,t}^2 + b_i P_{Gi,t} + c_i) + \sum_{i=1}^{N} [U_{i,t}(1 – U_{i,t-1}) + U_{i,t-1}(1 – U_{i,t})] F_i + \sum_{i=1}^{N} C_t + F_{cost}^{ch,ad} P_{ch,t}^{IDR,ad} + F_{cost}^{dis,ad} P_{dis,t}^{IDR,ad} + K_W (P_{w,t}^{pre,1} – P_{w,t}) + K_R (P_{R,t}^{pre,1} – P_{R,t}) \right\}$$
where $F_1^{ad}$ is the day-ahead total system cost, $T_1$ is the day-ahead optimization scheduling period, $U_{i,t}$ is the on/off status of unit $i$ at time $t$, $a_i$, $b_i$, $c_i$ are the coal consumption cost parameters of unit $i$, $P_{Gi,t}$ is the output of unit $i$ at time $t$, $F_i$ is the start-stop cost of unit $i$, $F_{cost}^{ch,ad}$, $F_{cost}^{dis,ad}$ and $P_{ch,t}^{IDR,ad}$, $P_{dis,t}^{IDR,ad}$ are the day-ahead IDR compensation coefficients and day-ahead IDR response amounts for Mode B and Mode C electric cars, respectively, $K_W$, $K_R$ are the wind and solar curtailment penalty cost coefficients, $P_{w,t}^{pre,1}$, $P_{R,t}^{pre,1}$ are the day-ahead predicted wind and solar power, and $P_{w,t}$, $P_{R,t}$ are the actual wind and solar grid power.
(2) Day-ahead environmental objective function
The optimal pollutant emissions are taken as the environmental objective function.
$$F_2^{ad} = \sum_{t=1}^{T_1} \sum_{i=1}^{N} [\alpha_i P_{Gi,t}^2 + \beta_i P_{Gi,t} + \gamma_i + \zeta_i \exp(\lambda_i P_{Gi,t})]$$
where $F_2^{ad}$ is the day-ahead pollutant emissions, and $\alpha_i$, $\beta_i$, $\gamma_i$, $\zeta_i$, $\lambda_i$ are the pollutant emission parameters of unit $i$.
(3) Day-ahead comprehensive objective function
In the day-ahead optimization scheduling model, to comprehensively consider system economy and environmental protection, the day-ahead economic objective function and day-ahead environmental objective function are weighted summed to form the day-ahead comprehensive objective function.
$$F^{ad} = W_1 F_1^{ad} + W_2 F_2^{ad}$$
where $W_1$, $W_2$ are weight coefficients, satisfying $W_1 + W_2 = 1$. The weight coefficients can be adjusted according to scheduling objectives. This paper sets $W_1 = 0.5$, $W_2 = 0.5$.
Constraints
(1) Wind and solar power output constraints
$$\begin{cases}
0 \leq P_{w,t} \leq P_{w,t}^{pre,1} \\
0 \leq P_{R,t} \leq P_{R,t}^{pre,1}
\end{cases}$$
(2) Thermal unit output constraints
$$u_{i,t} P_{Gi}^{min} \leq P_{Gi,t} \leq u_{i,t} P_{Gi}^{max}$$
where $P_{Gi}^{min}$, $P_{Gi}^{max}$ are the minimum and maximum outputs of unit $i$.
(3) Thermal unit ramp constraints
$$\begin{cases}
P_{Gi,t} – P_{Gi,t-1} \leq U_{i,t} R_i^u \\
P_{Gi,t-1} – P_{Gi,t} \leq U_{i,t-1} R_i^d
\end{cases}$$
where $R_i^u$, $R_i^d$ are the upward and downward ramp rates of unit $i$, respectively.
(4) Thermal unit minimum on/off time constraints
$$\begin{cases}
(T_{i,t-1}^{on} – T_{i,min}^{on}) (U_{i,t-1} – U_{i,t}) \geq 0 \\
(T_{i,t-1}^{off} – T_{i,min}^{off}) (U_{i,t} – U_{i,t-1}) \geq 0
\end{cases}$$
where $T_{i,min}^{on}$, $T_{i,min}^{off}$ are the minimum on and off times of unit $i$, and $T_{i,t-1}^{on}$, $T_{i,t-1}^{off}$ are the continuous start and stop times of unit $i$ at time $t-1$.
(5) Spinning reserve constraints
$$\begin{cases}
\sum_{i=1}^{N} \min[R_i^u, (U_{i,t} P_{Gi,max} – P_{Gi,t})] \geq r_{sys}^{up,t} \\
\sum_{i=1}^{N} \min[R_i^d, (P_{Gi,t} – U_{i,t} P_{Gi,min})] \geq r_{sys}^{down,t}
\end{cases}$$
where $r_{sys}^{up,t}$, $r_{sys}^{down,t}$ are the upward and downward spinning reserves of unit $i$, and $P_{Gi,max}$, $P_{Gi,min}$ are the net output upper and lower limits of unit $i$.
(6) System power balance constraints
$$P_{ch,t} + P_{ch,t}^{DR,ad} + P_{load1,t} = P_{w,t} + P_{R,t} + P_{v2g,t}^{PDR,ad} + P_{v2g,t}^{IDR,ad} + \sum_{i=1}^{N} P_{Ji,t}$$
where $P_{ch,t}$ is the charging power of electric cars not participating in DR, $P_{ch,t}^{DR,ad}$ is the charging power of Mode B electric cars after participating in day-ahead PDR and IDR at time $t$, $P_{load1,t}$ is the day-ahead predicted basic load, $P_{v2g,t}^{PDR,ad}$, $P_{v2g,t}^{IDR,ad}$ are the net charging/discharging power of Mode C electric cars after participating in day-ahead PDR and IDR during period $t$, and $P_{Ji,t}$ is the net output of unit $i$ during period $t$.
Intraday Rolling Optimization Scheduling Model
Objective Function
(1) Intraday economic objective function
The intraday stage takes the optimal total system cost as the economic objective function. Compared to the day-ahead stage, the intraday stage does not consider thermal unit start-stop costs and day-ahead IDR costs, but intraday IDR total costs need to be considered. Additionally, due to changes in intraday prediction power, the expressions for wind and solar curtailment penalty costs are also different.
$$F_1^{id} = \sum_{t=1}^{T_2} \left\{ \sum_{i=1}^{N} U_{i,t} (a_i P_{Gi,t}^2 + b_i P_{Gi,t} + c_i) + \sum_{i=1}^{N} C_t + F_{cost}^{ch,id} P_{ch,t}^{IDR,id} + F_{cost}^{dis,id} P_{dis,t}^{IDR,id} + K_W (P_{w,t}^{pre,2} – P_{w,t}) + K_R (P_{R,t}^{pre,2} – P_{R,t}) \right\}$$
where $F_1^{id}$ is the intraday total system cost, $T_2$ is the intraday rolling optimization scheduling period, $F_{cost}^{ch,id}$, $F_{cost}^{dis,id}$ and $P_{ch,t}^{IDR,id}$, $P_{dis,t}^{IDR,id}$ are the intraday IDR compensation coefficients and intraday IDR response amounts for Mode B and Mode C electric cars, respectively, and $P_{w,t}^{pre,2}$, $P_{R,t}^{pre,2}$ are the intraday predicted wind and solar power.
(2) Intraday environmental objective function
The intraday stage takes the optimal pollutant emissions as the environmental objective function.
$$F_2^{id} = \sum_{t=1}^{T_2} \sum_{i=1}^{N} [\alpha_i P_{Gi,t}^2 + \beta_i P_{Gi,t} + \gamma_i + \zeta_i \exp(\lambda_i P_{Gi,t})]$$
where $F_2^{id}$ is the intraday pollutant emissions objective function.
(3) Intraday comprehensive objective function
To balance economy and environmental protection, weight coefficients are used for weighted summation to form the intraday comprehensive objective function:
$$F^{id} = W_3 F_1^{id} + W_4 F_2^{id}$$
where $W_3$, $W_4$ are weight coefficients, satisfying $W_3 + W_4 = 1$. This paper sets $W_3 = 0.5$, $W_4 = 0.5$.
Constraints
The intraday stage no longer considers unit commitment constraints. Since the intraday stage time scale is 15 minutes, related constraints also differ.
(1) Wind and solar power output constraints
$$\begin{cases}
0 \leq P_{w,t} \leq P_{w,t}^{pre,2} \\
0 \leq P_{R,t} \leq P_{R,t}^{pre,2}
\end{cases}$$
(2) Thermal unit ramp constraints
$$\begin{cases}
P_{Gi,t} – P_{Gi,t-1} \leq U_{i,t} R_i^u / 4 + P_{Gi,max} (1 – U_{i,t-1}) \\
P_{Gi,t-1} – P_{Gi,t} \leq U_{i,t} R_i^d / 4 + P_{Gi,max} (1 – U_{i,t})
\end{cases}$$
(3) Spinning reserve constraints
$$\begin{cases}
\sum_{i=1}^{N} \min[R_i^u / 4, (U_{i,t} P_{Gi,max} – P_{Gi,t})] \geq r_{sys}^{up,t} \\
\sum_{i=1}^{N} \min[R_i^d / 4, (P_{Gi,t} – U_{i,t} P_{Gi,min})] \geq r_{sys}^{down,t}
\end{cases}$$
(4) System power balance constraints
$$P_{ch,t} + \Delta P_{ev,t}^{DR,ad} + P_{ch,t}^{DR,id} + P_{load2,t} = P_{w,t} + P_{R,t} + P_{v2g,t}^{IDR,id} + \sum_{i=1}^{N} P_{Ji,t}$$
where $\Delta P_{ev,t}^{DR,ad}$ is the response amount of electric cars from day-ahead DR, $P_{ch,t}^{DR,id}$ is the charging power of Mode B electric cars after participating in intraday IDR during period $t$, $P_{load2,t}$ is the intraday predicted basic load, and $P_{v2g,t}^{IDR,id}$ represents the net charging/discharging power of Mode C electric cars after participating in intraday IDR during period $t$.
Improved Multi-Objective Grey Wolf Optimizer
The multi-objective grey wolf optimizer (MOGWO) has advantages such as simple structure, few adjustment parameters, good global search ability, and strong robustness. However, similar to other swarm intelligence algorithms, for nonlinear, multi-constrained, and multi-objective optimization problems, the traditional MOGWO algorithm has defects such as easily falling into local optima and slow convergence speed.
Traditional Multi-Objective Grey Wolf Optimizer
In the traditional MOGWO, the wolf pack is divided into four categories: α, β, δ, and ω, where the optimal solution is α, the suboptimal and general solutions are β and δ, and the remaining candidate solutions are ω. Hunting is led by α, β, δ, and ω performs global optimization based on α, β, δ. α, β, and δ are selected from the Archive using a roulette wheel method. The grey wolf population position update formula is as follows:
$$D_i(k) = |C \cdot X_p(k) – X_i(k)|$$
$$X_i(k+1) = X_p(k) – A \cdot D_i(k)$$
where $D_i(k)$ is the distance between the prey and the grey wolf, $k$ is the iteration number, $X_p(k)$ represents the position of the prey, $X_i(k)$ is the position of the grey wolf, and C and A are coefficient vectors.
The calculation method for vectors A and C is as follows:
$$\begin{cases}
A = 2a R_1 – a \\
C = 2 R_2
\end{cases}$$
where $R_1$ and $R_2$ are random numbers in [0,1], and $a$ decreases linearly from 2 to 0 during iterations.
Improved Multi-Objective Grey Wolf Optimizer
To address the defects of the traditional MOGWO algorithm, such as easily falling into local optima and slow convergence speed when handling multi-constrained, nonlinear multi-objective problems, the following improvements are made to the traditional MOGWO algorithm:
(1) In the traditional MOGWO algorithm, the parameter $a$ decreases linearly from 2 to 0 during iterations. Theoretically, $a$ close to 2 in the early stage enables global optimization, and close to 0 in the later stage enables faster convergence. However, in practice, MOGWO with linearly decreasing $a$ has poor global optimization effects and slow convergence speed. Replacing $a$ with equation (34) can improve the algorithm’s global search efficiency and enhance later convergence. Calculations show that the exponent of 3 works best.
$$a = 2 – \left( \frac{k}{k_{max}} \right)^3 \times 2$$
(2) Adopt a survival-of-the-fittest strategy to update the grey wolf population. The population is sorted according to their fitness values; individuals with higher fitness values are more superior. After each iteration, the m wolves with the lowest fitness are eliminated, and m new wolves are randomly generated to maintain population stability. The larger m is, the stronger the diversity of the algorithm. However, if m is too large, randomness increases, thus reducing the algorithm’s convergence rate; if m is too small, the algorithm easily falls into local optima. Therefore, m is expressed by equation (34).
$$m = [n \cdot (0.618 \cdot \eta), n \cdot \eta]$$
where $n$ is the number of grey wolves, and $\eta$ is the update比例系数.
The flowchart of the improved MOGWO algorithm is shown in the figure.
Case Study Analysis
Basic Data Description
The wind and solar power data used in this paper are from a photovoltaic power station and a wind power station in a certain region of Northwest China, with capacities of 20MW and 30MW, respectively. Thermal unit parameters are shown in the appendix. When the charging time is greater than the停留时间 or the charging time is less than the停留时间 and the initial SOC is less than 0.4, the electric car is set to Mode A charging. When the initial SOC is greater than or equal to 0.4, the proportions of the three types of electric cars are set to 0.5, 0.35, and 0.15, respectively. Relevant parameters of electric cars are shown in the appendix. Assume there are 20,000 electric cars in the system. The daily driving distance of electric cars approximately follows a normal distribution [3.2, 0.88²], the start charging time approximately follows a normal distribution [17.6, 3.4²], and the end time approximately follows a normal distribution [8.92, 3.24²]. The unit electricity consumption driving distance of electric cars is 5 km. The charging/discharging power is 7 kW·h. The number of electric cars connected in each time period is shown in Figure 4. The driving distance of electric cars is obtained by sampling from the daily driving distance density function, and then the initial SOC of the electric car can be calculated. Since the DR resources of electric cars are limited, assume that the response amounts of Mode B and C electric cars participating in day-ahead PDR and IDR do not exceed 30% and 25% of their total amounts, respectively, and the response amount of intraday IDR does not exceed 20% of their total amounts.
To verify the effectiveness of the source-load day-ahead-intraday low-carbon optimization scheduling for the new power system considering electric cars, this paper compares and analyzes the scheduling results under four different operation scenarios: (1) Without considering DR and ladder-type carbon trading; (2) Without considering DR, but considering carbon trading; (3) Considering DR, but not considering carbon trading; (4) Considering both DR and ladder-type carbon trading.
Case Study Results Analysis
Based on typical daily photovoltaic, wind power, and load data, Figure 5 shows the source-load power prediction using the SSA-CNN-LSTM model.
Day-Ahead Scheduling Analysis
From Table 1, it can be seen that in Scenario 1, since carbon trading and DR are not considered, to ensure the normal operation of the system, thermal units frequently start and stop and output at high levels during peak load periods, resulting in high system costs and pollutant emissions. During low load periods, due to thermal unit reserve constraints, wind and solar curtailment occur. Compared with Scenario 1, the total system cost, operating cost, solar curtailment penalty cost, wind curtailment penalty cost, and pollutant emissions in Scenario 2 are reduced by $1584, $1424, $92, $233, and 374 lb, respectively. By introducing ladder-type carbon trading, the output of thermal units is reduced, thus reducing wind and solar curtailment costs and pollutant emissions, but the start-stop cost increases by $60, due to the volatility of renewable energy generation and carbon trading causing frequent start-stop of thermal units. Scenario 3 introduces DR on the basis of Scenario 1. Its total system cost, start-stop cost, operating cost, solar curtailment penalty cost, wind curtailment penalty cost, and pollutant emissions are reduced by $3648, $30, $3318, $115, $496, and 640 lb, respectively, compared with Scenario 1. Through the DR mechanism, load-side peak shaving and valley filling are achieved. During low valley periods, adjusting electric car charging absorbs excess electricity, thereby utilizing excess wind and solar power. During peak periods, optimizing the charging and discharging behavior of electric cars reduces the output of thermal units, thereby reducing pollutant emissions. In Scenario 4, the total system cost, start-stop cost, operating cost, carbon trading cost, pollutant emissions, solar curtailment penalty cost, and wind curtailment penalty cost are reduced by $3921, $90, $3417, $270, $41, $422, and 432 lb, respectively, compared with Scenario 2. The carbon trading mechanism in Scenario 4 reduces the output of high-carbon emission thermal units. Additionally, by adjusting electric car load through DR, excess renewable energy output is absorbed during low valley periods, and the operation mode of thermal units is optimized during peak periods, improving the absorption of new energy.
| Scheduling Result | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 |
|---|---|---|---|---|
| Total System Cost ($) | 64434 | 62850 | 60786 | 58929 |
| Start-Stop Cost ($) | 320 | 380 | 290 | 290 |
| Operating Cost ($) | 63185 | 61761 | 59867 | 58344 |
| Solar Curtailment Cost ($) | 235 | 143 | 120 | 102 |
| Wind Curtailment Cost ($) | 694 | 461 | 198 | 39 |
| Carbon Trading Cost ($) | 0 | 105 | 0 | -165 |
| Solar Curtailment Rate (%) | 6.13 | 3.75 | 3.13 | 2.84 |
| Wind Curtailment Rate (%) | 6.38 | 4.24 | 1.82 | 0.37 |
| Day-Ahead IDR Cost ($) | 0 | 0 | 311 | 319 |
| Pollutant Emissions (lb) | 7932 | 7558 | 7292 | 7126 |
The day-ahead scheduling results for each scenario are shown in Figures 6-9.
As shown in Figure 6, in Scenario 1, due to the volatility of renewable energy and large-scale disordered charging of electric cars, during low valley periods, to ensure economic benefits, some wind and solar power need to be curtailed. During peak periods, the load peaks on top of peaks, and thermal units output at high power, resulting in high total system costs and pollutant emissions. As shown in Figure 7, Scenario 2 considers ladder-type carbon trading on the source side, improving the absorption of new energy and economic efficiency, but requires frequent adjustment of the start-stop status of thermal units. As shown in Figure 8, Scenario 3 considers DR on the load side, replacing thermal unit output during peak periods with wind and solar curtailment during load valley periods to reduce wind and solar curtailment phenomena. As shown in Figure 9, Scenario 4 further considers DR on the basis of Scenario 2. Using DR and ladder-type carbon trading can effectively reduce the power output of thermal units. At the same time, using the flexibility of DR can also avoid frequent start-stop of thermal units caused by carbon trading.
Intraday Scheduling Analysis
The intraday stage is based on the intraday prediction power of the source and load. The determined unit commitment, day-ahead PDR, and IDR plans from the day-ahead scheduling plan are expanded into 96 data points with a unit of 15 minutes and brought into the intraday plan. At the same time, an intraday scheduling plan for the next 4 hours is established for each rolling optimization, and each rolling optimization scheduling is connected into a continuous scheduling plan.
From Table 2, it can be seen that compared with the day-ahead stage, the system operating cost, solar curtailment rate, wind curtailment rate, and pollutant emissions in Scenario 1 are reduced by $846, 4.85%, 1.21%, and 147 lb, respectively. This is due to the improvement in source-load accuracy, optimizing the output of thermal units. However, due to the volatility of the source and load sides and the limitation of thermal unit ramp capability, especially during low valley periods, the spinning reserve constraints of thermal units lead to high wind and solar curtailment rates. In Scenario 2, the system operating cost, carbon trading cost, solar curtailment rate, wind curtailment rate, and pollutant emissions are reduced by $1905, $186, 3.17%, 0.99%, and 147 lb, respectively. Ladder-type carbon trading forces thermal units to reduce carbon emissions, thereby improving the absorption of new energy. However, due to the volatility of new energy, wind and solar curtailment still exist. In Scenario 3, the system operating cost, solar curtailment rate, wind curtailment rate, and pollutant emissions are reduced by $1705, 2.72%, 1.03%, and 149 lb, respectively. Although IDR requires certain compensation costs, by flexibly adjusting electric car load through IDR, the output of thermal units is reduced, further improving the absorption rate of new energy. In Scenario 4, the system operating cost, carbon trading cost, solar curtailment rate, wind curtailment rate, and pollutant emissions are reduced by $2003, $22, 2.58%, 0.08%, and 189 lb, respectively. Scenario 4, through the synergistic effect of improved source-load prediction accuracy, ladder-type carbon trading, and IDR, not only reduces unnecessary output of thermal units but also avoids wind and solar curtailment caused by the ramp and spinning reserve constraints of thermal units.
| Scheduling Result | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 |
|---|---|---|---|---|
| Total System Cost ($) | 62963 | 60336 | 58511 | 56454 |
| Operating Cost ($) | 62339 | 59856 | 58162 | 56341 |
| Solar Curtailment Cost ($) | 49 | 22 | 15 | 10 |
| Wind Curtailment Cost ($) | 575 | 360 | 88 | 32 |
| Carbon Trading Cost ($) | 0 | 98 | 0 | -187 |
| Solar Curtailment Rate (%) | 1.28 | 0.58 | 0.41 | 0.26 |
| Wind Curtailment Rate (%) | 5.17 | 3.25 | 0.79 | 0.29 |
| Intraday IDR Cost ($) | 0 | 0 | 246 | 258 |
| Pollutant Emissions (lb) | 7785 | 7456 | 7143 | 6937 |
The intraday scheduling results for each scenario are shown in Figures 10-13.
As shown in Figures 10 and 11, Scenarios 1 and 2 flexibly adjust the thermal units that are in the on state based on the characteristic that source-load power gradually improves as the time scale shortens, thereby realizing day-ahead-intraday optimization scheduling. However, due to low load power during low valley periods, the pressure on thermal unit spinning reserves still leads to wind curtailment issues in the system. The volatility of new energy leads to thermal unit ramp constraints, still causing solar curtailment issues in the system. As shown in Figures 12 and 13, Scenarios 3 and 4, through the flexibility of intraday IDR, can better alleviate the spinning reserve and ramp pressure of thermal units. Additionally, Scenario 4, by comprehensively considering ladder-type carbon trading and IDR, improves the low-carbon environmental performance and economy of the system.
In summary, through the comparison of different scenarios, the model proposed in this paper, Scenario 4, has good optimization effects. By considering DR and ladder-type carbon trading in day-ahead-intraday optimization scheduling, the effects on improving the utilization rate of wind and solar power and the low-carbon economic benefits of the system are more significant.
Algorithm Comparison
To evaluate the prediction accuracy of the SSA-CNN-LSTM model proposed in this paper, BP, Elman, CNN-LSTM, GA-CNN-LSTM, and SSA-CNN-LSTM models are selected for wind power prediction for the next 24 hours, and the prediction results are analyzed. This paper selects 24-hour wind power data from September to December 2020 in a certain region, with day type, temperature, wind speed, light intensity, and relative humidity as sample data. Typical daily wind power is selected for prediction, and mean absolute percentage error (MAPE) and root mean square error (RMSE) are selected as evaluation indicators for prediction accuracy. Their calculation formulas are shown in equation (36).
$$\begin{cases}
E_{MAPE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{L_i – \hat{L}_i}{L_i} \right| \times 100\% \\
E_{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (L_i – \hat{L}_i)^2}
\end{cases}$$
where $n$ is the number of samples, $L_i$ is the actual wind power, and $\hat{L}_i$ is the predicted wind power.
The MAPE and RMSE results of each model’s prediction results are compared in Table 3, and the wind power prediction graphs of each model are shown in Figure 14.
| Evaluation Indicator | MAPE (%) | RMSE (MW) |
|---|---|---|
| BP Neural Network | 5.27 | 0.73 |
| Elman Neural Network | 7.13 | 1.01 |
| CNN-LSTM Neural Network | 4.22 | 0.7 |
| GA-CNN-LSTM Neural Network | 2.91 | 0.38 |
| SSA-CNN-LSTM Neural Network | 2.31 | 0.37 |
As can be seen from Table 3, the proposed SSA-CNN-LSTM model has the smallest MAPE and RMSE values, and the prediction indicators are better than other models. Compared with the other four models, the MAPE value of the SSA-CNN-LSTM model is reduced by 2.96%, 4.82%, 1.91%, and 0.6%, respectively, and the RMSE value is reduced by 0.36 MW, 0.64 MW, 0.33 MW, and 0.01 MW, respectively. At the same time, it can be seen from Figure 14 that the prediction results of the SSA-CNN-LSTM model are closest to the actual power curve.
To verify the advantages of the improved MOGWO algorithm proposed in this paper compared with the traditional MOGWO algorithm, the Pareto front diagram of the intraday optimization scheduling of Scenario 4 is used for comparative analysis. Figures 15-16 show the Pareto front comparison diagrams solved by the two algorithms. It can be found that the non-dominated solutions of the traditional MOGWO algorithm are prone to fall into local optima, while the non-dominated solutions of the improved MOGWO algorithm are more evenly distributed, further illustrating that the improved MOGWO algorithm can achieve global optimization and improve convergence speed. In addition, through the data comparison of the solutions obtained by the two algorithms in Table 4, it can be seen that the improved MOGWO has a wider search area, and the solutions obtained by the improved MOGWO algorithm are significantly better than those of the traditional MOGWO algorithm.
| Algorithm | Target | Pollutant Emissions (10³ lb) | Economic Cost (10⁴ $) |
|---|---|---|---|
| Traditional MOGWO | Economic Optimal | 7.2612 | 5.5323 |
| Environmental Optimal | 6.8445 | 5.8617 | |
| Compromise Solution | 6.9527 | 5.6593 | |
| Improved MOGWO | Economic Optimal | 7.2858 | 5.5129 |
| Environmental Optimal | 6.8356 | 5.8941 | |
| Compromise Solution | 6.9371 | 5.6454 |
Conclusion
This paper uses the SSA-CNN-LSTM model to forecast source and load power for day-ahead and intraday stages, and proposes a low-carbon optimization scheduling model for the new power system that comprehensively considers multiple types of electric cars. This model not only utilizes the different demand response characteristics of electric cars and the flexibility of IDR but also combines the ladder-type carbon trading mechanism, fully exploiting the synergistic optimization potential of the source and load sides. It effectively alleviates the impact of renewable energy output fluctuations and large-scale disordered charging of electric cars on system stability. It also enhances the absorption level of renewable energy and reduces wind and solar curtailment. Through comparative analysis of optimization scheduling results under four operational scenarios, the optimization method proposed in this paper can significantly improve the low-carbon and economic benefits of the system. Compared with the baseline Scenario 1, the overall performance of the system is greatly improved. Among them, the total system cost is reduced by 10.3%, pollutant emissions are reduced by 10.9%, the solar curtailment rate is reduced by 1.02%, and the wind curtailment rate is reduced by 4.88%. In addition, through the day-ahead and intraday DR mechanisms, the flexibility of the system and its ability to cope with uncertainty are further enhanced, providing strong support for the rapid construction of the new power system.
Currently, this paper focuses on day-ahead-intraday optimization scheduling, but it can be further extended to real-time scheduling. Therefore, based on the work in this paper, the author can further study multi-time scale optimization scheduling of the new power system in the future to enhance the system’s ability to respond to emergencies and short-term fluctuations.