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Energy storage is a potential alternative to conventional network reinforcement of the low voltage (LV) distribution network to ensure the grid's infrastructure remains within its operating constraints. This paper presents a study on the control of such storage devices, owned by distribution network operators. A deterministic model predictive control (MPC) controller and a stochastic receding horizon controller (SRHC) are presented, where the objective is to achieve the greatest peak reduction in demand, for a given storage device specification, taking into account the high level of uncertainty in the prediction of LV demand. The algorithms presented in this paper are compared to a standard set-point controller and bench marked against a control algorithm with a perfect forecast. A specific case study, using storage on the LV network, is presented, and the results of each algorithm are compared. A comprehensive analysis is then carried out simulating a large number of LV networks of varying numbers of households. The results show that the performance of each algorithm is dependent on the number of aggregated households. However, on a typical aggregation, the novel SRHC algorithm presented in this paper is shown to outperform each of the comparable storage control techniques.

As demand increases on the low voltage (LV) network due to changes in consumer behaviour and the electrification of transport and heating [

Two main methods for controlling a storage device are defined in the literature [

In this paper, we present algorithms using real-time data available from the network, to make a control decision for the storage device on the LV network, firstly incorporating demand forecasts into the control of DNO owned storage devices and then treating the demand as a stochastic element in the controller.

Using model predictive control (MPC), also known as receding horizon control (RHC) [

Stochastic optimization is a special subset of mathematical programming techniques that involves optimization under uncertainty. Wu

It is important to note that not only has it been shown in some cases that studying the demand as a stochastic process can improve performance, but also using a receding horizon can improve the performance of storage control. Hence stochastic receding horizon control [

This paper will present and compare MPC and SRHC controllers for the control of a single DNO owned storage on the LV network. The objective of the controllers are to gain the greatest possible peak reduction as measured at the LV substation. The algorithms will be comprehensively tested to verify their suitability for LV storage control by varying the number of individual domestic customers in a demand aggregation and testing the algorithms on large data sets, using real network data and, therefore, introducing real demand errors. This realistic demand error and varying aggregation size is important to study, due to the volatile nature and varying demand models on this part of the network. The smart meter data used in this work have been supplied by Ireland's Commission for Energy Regulation and is openly available on-line via the Irish Social Science Data Archive [

This work addresses the on-line peak reduction storage control problem as described in [_{s}_{s}τ_{S}_{s}_{S}_{S}_{S}_{min}_{max}_{S}_{S}

As described in the previous section, aggregated individual smart meter profiles, ^{i}_{A}_{A}

The objective of the research presented in this paper is to minimise the peak demand (_{A}_{A}

At each time step,

The controller is formulated as a model predictive control (MPC) problem. MPC, also known as receding horizon control, refers to a class of control methods that compute a sequence of decision-variable adjustments over a future time horizon iteratively based on an underlying optimization model [

The cost function used in this work is shown in _{A}_{S}

At the current time step, _{p}_{p}_{p}_{p}_{p}

The MPC problem is now formulated as a stochastic optimisation problem with a receding horizon [_{S}

The problem solved in this paper, incorporating the cost function introduced in the previous section, is shown in _{A}_{A}_{S}^{2}. The objective function in this form with the constraint

A scenario tree is used to approximate the continuous problem. Typically, these trees are developed based on heuristic rules used to develop potential future scenarios or selected using data based on the environment's historic behaviour; the latter is used in this work. The tree is formulated using the historic half hourly data, and the routes of potential future demand and their associated probabilities are found from this

_{S}^{n}_{S}^{r}_{AR}_{a}

As opposed to attempting to solve the continuous problem previously shown in

This can be expanded to:

The optimisation vector is given by:

The number of nodes per time step are selected by analysing the a priori data (_{D}^{d}_{T}^{×}^{N}^{1}^{×N}

1. Initialise:

_{D}, Nodes

_{Min}, Nodes

_{Max}

_{D}, d

_{Max}

_{Max}

Once the number of nodes per time step
_{max}_{size}_{D}_{D}^{d}_{T}^{×}^{N}_{b}_{b}_{b}_{max}^{1×}^{b}_{max}

This section will present results from the previously discussed deterministic and stochastic-based control algorithms. First, a specific case study will be presented; then, the MPC and SRHC algorithms will be tested on larger data sets of varying aggregation sizes. Throughout this section, the algorithms will be compared to two algorithms found in the literature and used to benchmark DNO owned storage devices [

The energy use of forty homes, recorded by smart meters, was aggregated to represent a realistic single phase of a feeder in the distribution network and validated against historical substation data. A period of 15 weeks was considered and split into 14 weeks of historical data; the forecasts were based on the first 14 weeks, and day one of week 15 is presented in _{size}_{max}_{min}_{p}_{min}_{max}

This section will show how the SOC varies as the horizon moves across a daily demand profile. Thirty daily household demand profiles have been aggregated (_{Size}_{size}_{max}_{min}_{P}_{S}

As discussed in Sections 4 and 5, the horizon size is an important parameter required in both algorithms presented in this paper. To compare the performance of the system _{size}_{A}_{max}_{A}

The MPC algorithm is now compared to a set-point control algorithm, where the set-point has been calculated from the previous day's demand profile. The two algorithms, MPC and set-point control, are run on the same demand profile using the same specification storage device. The results show the total number of times, as a percentage, that each algorithm achieved the greatest peak demand reduction across all simulations. Each aggregation size contains 7000 simulations, made up of 500 demand aggregations over 14 days randomly selected across a year's worth of data. The result for when the aggregation size is varied from five to 70 customers is shown in

All algorithms discussed in this paper are now compared. An aggregation size (_{size}_{max}

When compared to the smoother demand profiles found on the MV network, controlling energy storage systems on the LV network is challenging, due to the volatile and hard to predict nature of the LV network. As a result, more advanced control strategies are required for the LV network, and this paper has presented two such strategies: model predictive control (MPC) and stochastic receding horizon control (SRHC). Neither of these control approaches rely on perfect forecasts or fully accurate demand models, and the algorithms presented have been tested on real network smart meter data. The storage devices in this work are owned by the DNO and aim to achieve the greatest peak reduction on the LV network. Future work will study the impact of distributed generation in the distribution network on the control algorithms, as well as the impact of studying the effect of storage losses on the algorithms and the effect of using the energy storage control algorithms on network losses. The MPC controller incorporates a deterministic forecast, which allows the storage device to plan how to use the storage capacity throughout a pre-defined horizon size. The SRHC controller treats the demand as a stochastic process and formulates a scenario tree based on

The work has been carried out with Scottish and Southern Energy Power Distribution via the New Thames Valley Vision Project (SSET203 New Thames Valley Vision), funded by the Low Carbon Network Fund established by Ofgem.

The authors declare no conflicts of interest.

_{A}

Original demand profile

^{i}

_{A}

Demand profile of individual customer

Discrete time period

Finite samples _{A}

_{S}

Change in energy stored in the storage device at time

Maximum increase of energy storage capacity in one time step

Maximum decrease of energy storage capacity in one time step

^{≥0}

Storage device state of charge

_{max}

Maximum state of charge

_{min}

Minimum state of charge

Storage device standby losses

Storage device efficiency

_{size}

Demand aggregation size

_{A}

Demand profile treated as a random variable

Node

Route

Control signal _{S}

Demand at time

^{n}

Probability at time

Control signal vector _{S}

^{r}

_{AR}

Demand vector _{A}

Probability vector along route

_{Min}

Minimum number of nodes per time

^{Max}

Maximum number of nodes per time

Total number of routes used in the scenario tree

_{r}

Number of nodes in route

Set of nodes at time

Set of nodes in route

^{>0}

Day

_{T}

Total number of days in prior demand data

_{D}

^{d}

_{T}

^{×}

^{N}

Matrix of prior demand data

Five histograms showing the error distributions between the forecasted and actual demand in demand aggregation sizes of five, 10, 15, 25 and 35 individual demand profiles, respectively (from top to bottom). The forecasting methodology used to produce these errors can be found in the appendix of [

The model predictive control loop.

A scenario tree of five time steps with a varying number of nodes per time step. The probabilities of a specific node occurring are shown, as is the probability of the complete route occurring.

A specific example: (

(

(

Algorithm performance

Set-point control and MPC performance when varying the number of demand profiles aggregated.

Box plots showing the distribution of demand reduction achieved using algorithms (from left to right) MPC, SRHC, best possible demand reduction and set-point control.

Table showing the number of routes and the total number of nodes in the tree when using a 7.5-h horizon with a varying number of nodes in each time step.

1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 | 32,767 | 16,384 |

1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 | 4,782,969 | 7,174,453 |

1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 | 268,435,456 | 357,913,941 |

1 3 2 3 1 1 1 1 1 1 1 2 3 2 1 | 216 | 730 |

1 2 2 2 2 2 2 1 1 3 3 3 3 3 3 1 | 215,552 | 39,039 |