### 分时电价下配电网优化运行的Python代码实现 分时电价是一种动态定价机制，旨在通过调整不同时段的电价来引导用户合理用电，从而平衡电力供需并减少高峰时段的压力。在配电网优化运行中，可以通过数学建模和优化算法求解最优调度方案[^2]。 以下是基于分时电价的配电网优化运行的一个简单Python代码示例： #### 1. 参数定义 ```python import numpy as np from scipy.optimize import minimize # 定义参数 T = 24 # 时间间隔数 (一天分为24小时) P_load = np.array([30, 32, 35, 38, 40, 45, 50, 60, 70, 80, 90, 100, 110, 120, 110, 100, 90, 80, 70, 60, 50, 45, 40, 35]) # 负荷功率 (单位: kW) price_electricity = np.array([0.1, 0.1, 0.1, 0.1, 0.1, 0.2, 0.3, 0.5, 0.7, 0.9, 1.0, 1.2, 1.3, 1.4, 1.3, 1.2, 1.0, 0.9, 0.7, 0.5, 0.3, 0.2, 0.1, 0.1]) # 不同时间段电价 ($/kWh) E_max = 50 # 储能最大容量 (kWh) P_charge_max = 10 # 最大充电功率 (kW) P_discharge_max = 10 # 最大放电功率 (kW) eta_c = 0.9 # 充电效率 eta_d = 0.9 # 放电效率 SOC_min = 0.1 * E_max # 最小 SOC SOC_max = 0.9 * E_max # 最大 SOC ``` #### 2. 目标函数 目标是最小化总购电费用： \[ \text{Minimize} \sum_{t=1}^{T} P_{\text{grid}, t} \cdot p_t \] 其中 \( P_{\text{grid}, t} \) 是从电网购买的电量，\( p_t \) 是第 \( t \) 小时时段的电价。 #### 3. 约束条件 - **能量守恒**: \[ P_{\text{load}, t} = P_{\text{grid}, t} + P_{\text{discharge}, t} - P_{\text{charge}, t} \] - **储能状态更新**: \[ \text{SOC}_{t+1} = \text{SOC}_t + \frac{\eta_c \cdot P_{\text{charge}, t}}{C_r} - \frac{P_{\text{discharge}, t}}{\eta_d \cdot C_r} \] - **储能上下限**: \[ \text{SOC}_{\min} \leq \text{SOC}_t \leq \text{SOC}_{\max} \] - **充放电功率限制**: \[ 0 \leq P_{\text{charge}, t} \leq P_{\text{charge}, \max} \quad \text{and} \quad 0 \leq P_{\text{discharge}, t} \leq P_{\text{discharge}, \max} \] #### 4. 编写优化模型 ```python def objective_function(x): """目标函数：最小化总购电费用""" grid_power = x[:T] charge_power = x[T:(2*T)] discharge_power = x[(2*T):(3*T)] cost = sum(grid_power[t] * price_electricity[t] for t in range(T)) return cost def constraints_func(x): """约束条件""" soc = [0] * (T + 1) # 初始化SOC数组 soc[0] = 0.5 * E_max # 初始SOC设为一半 grid_power = x[:T] charge_power = x[T:(2*T)] discharge_power = x[(2*T):(3*T)] cons_eq = [] # 等式约束 cons_ineq = [] # 不等式约束 for t in range(T): # 能量守恒方程 energy_balance = grid_power[t] + discharge_power[t] - charge_power[t] - P_load[t] cons_eq.append(energy_balance) # 更新SOC soc[t+1] = soc[t] + eta_c * charge_power[t] - discharge_power[t] / eta_d # SOC范围约束 cons_ineq.append(soc[t+1] - SOC_max) cons_ineq.append(SOC_min - soc[t+1]) # 充放电功率限制 cons_ineq.append(charge_power[t] - P_charge_max) cons_ineq.append(-charge_power[t]) cons_ineq.append(discharge_power[t] - P_discharge_max) cons_ineq.append(-discharge_power[t]) return cons_eq + cons_ineq # 变量初始猜测值 initial_guess = np.zeros(3 * T) # 设置边界条件 bounds = [(None, None)] * T + [(0, P_charge_max)] * T + [(0, P_discharge_max)] * T # 构造约束字典 constraints = { 'type': 'eq', 'fun': lambda x: constraints_func(x)[:T], # 等式约束部分 } result = minimize(objective_function, initial_guess, method='SLSQP', bounds=bounds, constraints=constraints) if result.success: optimal_grid_power = result.x[:T] optimal_charge_power = result.x[T:(2*T)] optimal_discharge_power = result.x[(2*T):(3*T)] else: raise ValueError("Optimization failed.") ``` #### 5. 结果展示 ```python print("Optimal Grid Power:", optimal_grid_power) print("Optimal Charge Power:", optimal_charge_power) print("Optimal Discharge Power:", optimal_discharge_power) ``` --- ###