Optimal Scheduling of Energy Storage for Power System with Capability of Sensing Short-term Future PV Power Production (2112.03551v1)

Abstract: Constant rise in energy consumption that comes with the population growth and introduction of new technologies has posed critical issues such as efficient energy management on the consumer side. That has elevated the importance of the use of renewable energy sources, particularly photovoltaic (PV) system and wind turbine. This work models and discusses design options based on the hybrid power system of grid and battery storage. The effects of installed capacity on renewable penetration (RP) and cost of electricity (COE) are investigated for each modality. For successful operation of hybrid power system and electricity trading in power market, accurate predictions of PV power production and load demand are taken into account. A ML model is introduced for scheduling, and predicting variations of the PV power production and load demand. Fitness of the ML model shows, when employing a linear regression model, the mean squared error (MSE) of 0.000012, root mean square error (RMSE) of 0.003560 and R2 of 0.999379. Using predicted PV power production and load demand, reduction of electricity cost is 37.5 % when PV and utility grid are utilized, and is 43.06% when PV, utility grid, and storage system are utilized.

• The paper introduces an optimal scheduling strategy integrating PV forecasts with battery storage to minimize net electricity costs.
• It employs a Long Short-Term Memory network to accurately predict half-hourly PV generation and load demand (MSE = 0.000012, R² = 0.999379).
• The study demonstrates over 40% cost reduction compared to grid-only consumption by smartly managing battery discharge during expensive peak hours.

This paper presents an optimal scheduling strategy for energy storage systems combined with photovoltaic (PV) installations to minimize electricity costs for consumers under time-of-use tariffs (Optimal Scheduling of Energy Storage for Power System with Capability of Sensing Short-term Future PV Power Production, 2021). The core idea is to leverage short-term forecasts of PV power production and household load demand to make intelligent decisions about when to charge the battery, discharge it, or trade power with the grid.

System Model and Objective

The system consists of:

1. A PV generation system.
2. A battery energy storage system (BESS).
3. Household electrical load.
4. Connection to the utility grid with time-varying tariffs (specifically, the UK's Economy 7 tariff).

The primary goal is to minimize the net cost of electricity over a period (e.g., a year). The cost function $J$ is defined to calculate electricity charges, considering tariffs for purchasing power ($P_{itar}$) during different times (peak/off-peak) and the rate for selling excess power ($P_{etar}$) back to the grid.

$$J = \sum_{d=1}^{365} \sum_{t=1}^{48} (\text{Cost}_\text{import}(d, t) - \text{Revenue}_\text{export}(d, t))$$

where $\text{Cost}_\text{import}$ depends on grid power purchased at tariff $P_{itar}$ and $\text{Revenue}_\text{export}$ depends on excess power sold at tariff $P_{etar}$.

Forecasting with LSTM

Accurate forecasting is crucial for effective scheduling. The paper employs a Long Short-Term Memory (LSTM) network to predict one-day-ahead (specifically, the next 48 half-hourly intervals) PV power generation and consumer load demand.

• Why LSTM? LSTMs are well-suited for time-series data like energy profiles because they can capture long-range dependencies and overcome the vanishing gradient problem common in simple RNNs. The internal gates (forget, input, output) allow the network to selectively remember or forget information over time.
• Input/Output: The LSTM model takes the previous 29 days of half-hourly data as input to predict the next day's 48 half-hourly values for both PV generation and load.
• Training:
  • Dataset: Real half-hourly PV generation (Sheffield Solar database) and household load data (ELEXON) for one year.
  • Split: 80% for training, 20% for validation.
  • Optimizer: ADAM with a learning rate of 0.001.
  • Epochs: 50.
  • Batch Size: 1.
  • Loss Function: Mean Squared Error (MSE).
  • Regularization: Dropout used to prevent overfitting.

Optimal Scheduling Strategy

Based on the predicted PV generation ($P_S^{pred}$) and load demand ($P_L^{pred}$) for each half-hour interval $t$, the scheduling logic operates as follows:

1. PV Generation > Load Demand ($P_S^{pred}(t) > P_L^{pred}(t)$):
   • Meet the load $P_L^{pred}(t)$ directly using PV power.
   • Calculate excess power: $P_{excess}(t) = P_S^{pred}(t) - P_L^{pred}(t)$.
   • Charge the battery with $P_{excess}(t)$ until the battery reaches its maximum state of charge (SoC).
   • If the battery is full, sell the remaining excess power to the grid at the export tariff $P_{etar}$.
2. Load Demand > PV Generation ($P_L^{pred}(t) > P_S^{pred}(t)$):
   • Meet as much load as possible using available PV power $P_S^{pred}(t)$.
   • Calculate unmet demand: $P_{unmet}(t) = P_L^{pred}(t) - P_S^{pred}(t)$.
   • If it's a peak-hour and the battery has sufficient charge (above minimum SoC), discharge the battery to meet $P_{unmet}(t)$.
   • If the battery cannot fully meet $P_{unmet}(t)$ (either due to low SoC or insufficient power capacity), or if it's an off-peak hour, purchase the remaining required power from the grid at the import tariff $P_{itar}$. The strategy prioritizes using stored energy during expensive peak hours.

A simplified pseudocode representation of the scheduling logic for a time step t:

PV_available = PV_pred[t] Load_needed = Load_pred[t] Grid_power = 0 Battery_power = 0 # Positive for discharge, negative for charge if PV_available >= Load_needed: # Excess PV generation PV_to_load = Load_needed Excess_PV = PV_available - PV_to_load # Try charging battery Charge_power = min(Excess_PV, max_charge_rate, capacity_to_reach_max_SoC) Battery_power = -Charge_power update_SoC(Battery_power) # Decrease SoC based on charging # Sell remaining excess to grid PV_to_grid = Excess_PV - Charge_power Grid_power = -PV_to_grid # Negative indicates export else: # Load exceeds PV generation PV_to_load = PV_available Unmet_load = Load_needed - PV_to_load # Try discharging battery (prioritize during peak hours) if is_peak_hour[t] and SoC > min_SoC: Discharge_power = min(Unmet_load, max_discharge_rate, capacity_above_min_SoC) Battery_power = Discharge_power update_SoC(Battery_power) # Increase SoC based on discharging Unmet_load -= Discharge_power # Purchase remaining unmet load from grid Grid_power = Unmet_load # Positive indicates import Cost[t] = calculate_cost(Grid_power, import_tariff[t], export_tariff[t])

Results and Practical Implications

• Forecast Accuracy: The LSTM model achieved high accuracy with MSE = 0.000012, RMSE = 0.003560, and R² = 0.999379, demonstrating its effectiveness in predicting PV and load profiles. Figures 8 and 9 in the paper visually confirm the close match between predicted and real data for a sample day.

• Cost Reduction: The paper compared three scenarios:

  1. Grid Only: Baseline cost (Net Cost: £384.24).
  2. PV + Grid: Adding PV reduced costs significantly by allowing self-consumption and grid export (Net Cost: £61.69, a reduction relative to the baseline case, calculated as (384.24 - 61.69)/384.24 = ~83.9%, though the paper states 37.5% - this discrepancy might stem from how the baseline or comparison is defined, possibly comparing total import cost reduction).
  3. PV + Battery + Grid (Proposed): Adding the battery and optimal scheduling further reduced costs by enabling storage of cheap/free PV energy for use during expensive peak hours (Net Cost: £38.14, a further reduction, stated as 43.06% total reduction compared to the baseline grid-only case).

The results demonstrate that combining accurate short-term forecasting (via LSTM) with an intelligent scheduling strategy that leverages battery storage can yield substantial electricity cost savings (over 40% in this case paper) for households with PV systems, especially under time-of-use pricing schemes like Economy 7. This provides a strong economic incentive for adopting such hybrid systems. The implementation requires reliable data sources, a well-trained LSTM model, and a control system to execute the scheduling decisions based on forecasts and battery status.