# Load forecasting for diurnal management of community battery systems

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## Abstract

This paper compares three methods of load forecasting for the optimum management of community battery storages. These are distributed within the low voltage (LV) distribution network for voltage management, energy arbitrage or peak load reduction. The methods compared include: a neural network (NN) based prediction scheme that utilizes the load history and the current metrological conditions; a wavelet neural network (WNN) model which aims to separate the low and high frequency components of the consumer load and an artificial neural network and fuzzy inference system (ANFIS) approach. The batteries have limited capacity and have a significant operational cost. The load forecasts are used within a receding horizon optimization system that determines the state of charge (SOC) profile for a battery that minimizes a cost function based on energy supply and battery wear costs. Within the optimization system, the SOC daily profile is represented by a compact vector of Fourier series coefficients. The study is based upon data recorded within the Perth Solar City high penetration photovoltaic (PV) field trials. The trial studied 77 consumers with 29 rooftop solar systems that were connected in one LV network. Data were available from consumer smart meters and a data logger connected to the LV network supply transformer.

## Keywords

Load forecasting Photovoltaic Battery Receding horizon optimization Neural network Wavelet Fuzzy inference## 1 Introduction

Community battery systems are shared by a small group of energy consumers to reduce the peak power demands, provide energy arbitrage or control the network voltages [1, 2]. Batteries have significant capital (CAPEX) and operating (OPEX) costs. The economic daily operation of energy storages requires an intelligent trade-off is made between energy supply cost savings versus the battery operational and capital costs. Any real time battery management optimization will rely completely upon daily forecasts of the aggregated customer loads and any local generation [3, 4, 5].

The optimum solution will contain a strong periodic component which reflects the daily demand profiles of customers and the diurnal variation in solar generation. A feature of community battery storage systems is the relatively small number of consumers which often falls into the range of 10 to 100. The load variability is higher than is observed in large electricity markets. Likewise, the number of embedded generators is smaller. As the generation is not as geographically distributed to the extent that may occur in a large power system the spatial smoothing is lower.

The battery cycle life costs of charging and discharging batteries are highly variable and depend strongly on the application. It can range from some cents to more than 1.00 $/kWh, exclusive of additional capital costs for inverters and grid connections [6, 7, 8]. Battery costs can be competitive for retail customers who calculate a return on a battery investment in terms of the retail costs of electricity [7]. In a network application, the battery costs will often exceed the costs of providing network solutions in a well serviced interconnected system. Remote, rural or island systems are an important exception. Many utilities have programs of research aimed at supporting the edge of the rural distribution grid [9, 10].

Electric vehicles have driven expansions in battery manufacturing at the scale of tens of gigawatts hours annually and retired electric vehicle batteries provide a new emerging lower-cost storage opportunity [11, 12]. BMW has recently announced it will offer a residential battery pack based on batteries recycled from its i3 EV series vehicles [11].

This paper will focus on the use of load forecasting to optimize the economic operation of community battery systems. The paper will be structured as follows. Firstly the use of a non-causal average is introduced as an optimum method of peak reduction. This process is inherently dependent upon a future knowledge of the network load and the need for load forecasting is introduced. The periodic nature of the daily or diurnal optimization is then discussed and the Fourier series is introduced as a compact method of representing the battery state of charge. Finally a generalized optimization method is introduced and some representative outcomes, based on data from the Perth Solar City trials, are presented.

## 2 Distribution network battery storage

## 3 Battery energy profile for peak reduction

*T*is the daily averaging period, 24 hours.

The non-causal average has no phase delay in the calculation of the average value but requires knowledge of the load for twelve hours into the future. Figure 1 shows the 24-hour average applied to the load profile. A battery energy storage system could be managed to charge and discharge at rates, allowing for battery and conversion losses, which result in the total transformer load that follows the averaged power. This method would focus on the minimization of the peak demand. It does not inherently include the other factors affecting the energy cost.

A key factor is the battery levelised cost of energy (LCOE) [8], which expresses the capital and operational costs, including losses, as a charge for each kilowatt-hour of energy exchanged. A practical control system that focuses on the day to day management of a battery requires two components: namely a forecasting system that can provide reasonable estimates of the load power, net of solar generation, over a forecast period and an optimization step that can find the minimum 24-hour energy cost.

*t*= 18 hours (6.00 p.m.). In this example a high peak demand charge was applied and the battery discharged at relatively high power during the period of peak energy demand. The battery energy is the integral of power and minimum state of charge, \(SoC_{ \hbox{min} }\) depends on the constant of integration in (3).

## 4 Representation of cyclic state of charge profiles

*SoC*(

*t*) profile. This determines the instantaneous charging power and ultimately the combined daily load profile and charges. The optimal solution can be specified as a daily vector of

*n*sample values of

*SoC*(

*t*) at regular time intervals:

All numerical optimization processes rely upon the repeated evaluation of a cost function at a proposed solution point subject to the problem constraints. Battery systems have constraints on the maximum and minimum states of charge and the charge and discharge power. A power constraint imposes an absolute difference constraint between each point within the \(\varvec{C}_{T}\) vector. Constraint checking increases the computational load during optimization. In some optimization methods such as genetic algorithms, the internal constraints between each point of the \(\varvec{C}_{T}\) vector are difficult to integrate with operations such as gene crossover during the generation of new candidate solutions.

*SoC*(

*t*) waveform using a vector of

*m*Fourier coefficients pairs such that [14]:

The coefficient *a*_{0} can be freely adjusted to set a minimum state of charge but does not contribute to the battery power.

## 5 Optimization cost functions

*r*(

*t*) and the grid power

*p*

_{ g }(

*t*):

In the this case the battery power is pure magnitude constraint as may be imposed by an interfacing converter but different constraints can be readily applied on charging and discharging. For some storages, such as flow batteries, battery power ramp rates may be applied.

## 6 Receding horizon optimization

The receding horizon approach relies on performing a sequence of 24-hour periodic optimizations that are updated on a periodic basis. The update period \(T_{s}\) is a design choice. In this example, a one hour update period is selected.

The key features receding horizon method are [14] that for each update period a 24-hour load profile is assembled using 12 forecasts at hourly intervals for the future load values and 12 historical load values. This is the current load value and the hourly loads eleven hours into the past. For the assembled 24-hour load profile, a direct search optimization is applied to find the battery state of charge profile, \(\varvec{C}_{F} \left( {kT_{s} } \right),\)that minimizes the daily energy cost. The new calculated profile is used to progressively update an averaged charge profile, \(\overline{{\varvec{C}_{F} \left( {kT_{s} } \right)}}\). The battery power is then controlled to follow the averaged charge profile. The allowable battery power will determine the rate at which the averaged profile may be permitted to change.

*α*is a low pass filter coefficient.

## 7 Forecast methods

The key to the performance of the battery optimization system is the availability of suitable forecasts of the power system load net of solar generation. Three approaches have been trialed including neural networks, wavelet neural networks and an adaptive networked based fuzzy inference system.

Mean prediction error

Prediction interval | Mean prediction error | ||
---|---|---|---|

NN (kW) | WNN (kW) | ANFIS (kW) | |

1 | 8.3 | 6.3 | 6.2 |

2 | 9.3 | 8.2 | 8.2 |

3 | 10.3 | 9.0 | 9.2 |

4 | 10.9 | 8.9 | 9.9 |

5 | 10.8 | 8.7 | 9.6 |

6 | 10.7 | 8.9 | 8.8 |

7 | 11.0 | 8.9 | 9.1 |

8 | 10.6 | 10.4 | 9.4 |

9 | 10.6 | 10.3 | 9.5 |

10 | 11.3 | 10.1 | 9.7 |

11 | 10.9 | 9.6 | 9.9 |

12 | 10.7 | 9.1 | 9.7 |

Mean of MAEs | 10.5 | 9.0 | 9.1 |

### 7.1 Neural networks

Neural networks have been widely applied for short term electrical load forecasting [15]. Twelve forecasts are required and twelve neural networks were individually trained to provide the load forecasts. Each network considered just one load forecast period. The network inputs are related to load, weather and time. The load related parameters are the current load, the load 24 hours ago and 168 hours ago and the average load over the past 24 hours. The weather related parameters are the dry bulb temperature the relative humidity and solar radiation. The Time/calendar parameters are the hour of the day, an integer representing the day of the week and an integer flag indicating if the day is a working day or holiday. The neural networks each have ten inputs and a hidden layer of 20 neurons. Training was undertaken using a mean absolute error (MAE) performance metric with the default MATLAB toolbox Levenburg-Marquardt algorithm [16].

### 7.2 Wavelet neural networks

The power system includes rapidly changing high-frequency loads such as thermostatically controlled appliances and low-frequency loads such general lighting. These have mixed timescales. The rapid and slow fluctuations in load profile cannot be captured adequately by one neural network. Wavelet analysis is a time-frequency joint representation of a signal which can be used to decompose a time domain signal to several other scales with different levels of resolution. The wavelet transformation requires the definition of a mother wavelet which embodies a set of specific characteristics that influence the frequency decomposition process. The choice of the appropriate mother wavelet depends on the type of application. In power systems, Daubechies (DB) mother wavelets are shown to be more effective than the other wavelets because they are orthogonal and do not cause any information loss [17, 18].

A combination of wavelet transform and neural network can bring up the benefits of having both approaches. In this paper, the past load measurement data from 1, 24 and 168 hours ago are decomposed into a low frequency component and three higher elements (level 4, DB4) [18]. The 12 decomposed load frequency signals and the other seven inputs used for the neural network in Section 7.1 are fed into a new neural network for training. The neural network (NN) element has 19 inputs and a hidden layer of 20 neurons. The Levenberg–Marquardt (LM) back-propagation algorithm was applied for training [18]. A total of 12 wavelet neural networks (WNNs are used to forecast the load for each of the specific future instants.

### 7.3 Adaptive network fuzzy inference system (ANFIS)

The ANFIS was firstly proposed by Jang in 1993 [19]. Two machine learning methods, fuzzy logic and neural networks, are integrated to overcome the drawbacks of neural networks and fuzzy logic systems. These are the limitations of neural networks with their representation of implicit knowledge and subjective and heuristic nature of fuzzy systems [20, 21, 22].

For each input, three Gaussian membership functions are assigned and the outputs of membership functions are linear. The Matlab toolbox ANFIS was used with a back propagation gradient descent optimization method to compute all parameters for building load forecasting models.

## 8 Predictive performance

## 9 Battery control simulations

Two practical applications of the forecast data are now considered. These are the use of the data in a peak demand reduction application and a periodic optimization application.

The top trace shows the load power and estimate of the non-causal average based on the WNN forecasts. The second trace is the difference between the average power estimate and the true averaged power shown in Fig. 1. The peak error is 9.5 kW and MAE is 2.4 kW. These are small relative to the battery power which has a peak of 81.3 kW and is shown in trace three. The final trace shows the resultant battery energy. The proposed control method reduced the peak load from 169.3 kW to 91.4 kW. This is close to the true averaged load peak of 89.0 kW.

*α*is set to 0.9.

The top trace is the original load waveform and the net power system loading. The second and third traces are the battery energy and power respectively. The periodic optimization process focuses on the total cost of energy supply which includes the battery wear cost. In order to reduce the battery costs, this example will not reduce the peak as strongly as the non-causal average result. The peak power is 117.6 kW and as expected this is higher than the 91.4 kW peak achieved in the earlier example.

The choice of the short Fourier coefficient vector length limits the higher frequency components of the battery energy profile. The highest harmonic, the fourth, corresponds to a six hour period. Fast changes in load demand are outside the effective bandwidth of the control system. The faster load components still appear in the power system loading. These are small and have very little impact in regard to energy or the peak demand. While it is possible to extend the length of the Fourier vector the improvements will be ultimately limited by the impact of the forecast errors within the optimization process.

## 10 Conclusion

This paper has demonstrated two community battery control methods both of which rely upon a future forecast of a distribution transformer load to adequately control the battery state of charge. The first battery management method is well suited to the control of the peak power demand. A 24-hour non-causal average provides a useful control target for a battery management system but requires a twelve hour future forecast. Three forecast methods, NN, WNN and ANFIS are compared. Of these the WNN and ANFIS systems achieve the better results. In this paper, twelve forecasts are made at one hour intervals. These are used together with load power samples in the previous twelve hours to calculate a moving 24-hour average. The averaging process significantly attenuates any forecasting errors and it is possible to generate a 24-hour forecast with low average errors. In this application, a MAE was less than 3% of the averaged peak load power.

The non-causal moving average system does not incorporate factors which influence the overall cost of energy and these include the battery wear costs and the impact of time of use tariff structures. This paper presents a periodic optimization method that determines an optimum periodic solution for any load profile over a 24-hour period. The cyclic solution for the battery state of charge is represented using Fourier coefficients.

The optimization process is embedded in a receding horizon battery control system. At each hour forecasts are made to develop a prospective 24-hour load profile. An optimization determines an optimal battery charge profile. The optimum profiles are progressively updated on an hourly basis with a twelve hour receding horizon. This approach is illustrated for a typical application with a two part energy and demand tariff.

## Notes

### Acknowledgements

The authors acknowledge the supply of consumption data collected under the Perth Solar City trial which is a part of the Australian Government’s $94 million Solar Cities Program. The authors also acknowledge the support of Western Power in supplying additional network data, models, technical reports and photographs.

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