This paper presents three methods for sizing the storage system. The first method sizes the storage system depending on the exported energy from the local grid (overproduction from the RES) and the imported energy from other interconnected power systems. The second method is where the import/export of the grid is monitored, as well as the price of electricity. The third method is created based on analysis of the first two approaches, where the best one is chosen, and coordination between the ESS and the PtG is performed. This is done so that a clear distinction can be made, whether adding a PtG to a system with ESS can further on improve the size of the storage system,

The network presented in Fig. 1, contains RES, wind turbines and photovoltaics. ESSPC needs to be supplied with electrical consumption data, grid parameters and weather data (wind speed and humidity) for some days. Through the weather data, different turbine and photovoltaic manufacturers can be reviewed for whether or not their production fits the area, both in production and whether the weather conditions are optimal for that technology.

Equation 12 presents how the power generation from all the RES in the network is obtained.

$$ {\mathrm{P}}_{\mathrm{G},\mathrm{G}}^{\left(\mathrm{m}\right)}={\mathrm{P}}_{\mathrm{G}\mathrm{n},\mathrm{WT}}^{\left(\mathrm{m}\right)}\ast {\mathrm{x}}_{\mathrm{n}}+{\mathrm{P}}_{\mathrm{G}\mathrm{N},\mathrm{PV}}^{\left(\mathrm{m}\right)}\ast {\mathrm{y}}_{\mathrm{n}} $$

(12)

Here, “m” refers to the given moment from the steady-state data. P_{G,G} is the power generated in the grid [MW], P_{Gn,WT} and P_{Gn,PV}, refer to the power produced by the wind turbines and the photovoltaics under the effect of the weather. To size the ESS, the number of RES installed in the grid needs to be varied. This is set through “x” and “y” in Eq. 12. Obtaining the optimal number of RES can be found by testing different combinations of RES and thus finding the most optimal ESS size.

$$ {\mathrm{P}}_{\mathrm{G},\mathrm{G}}^{\left(\mathrm{m}\right)}={\mathrm{P}}_{\mathrm{G}1,\mathrm{WT}}^{\left(\mathrm{m}\right)}\ast {\mathrm{x}}_1+{\mathrm{P}}_{\mathrm{G}2,\mathrm{WT}}^{\left(\mathrm{m}\right)}\ast {\mathrm{x}}_2+{\mathrm{P}}_{\mathrm{G}1,\mathrm{PV}}^{\left(\mathrm{m}\right)}\ast {\mathrm{y}}_1 $$

(13)

Equation 13 presents a case where two wind turbine technologies are tested and one photovoltaic technology. Each wind turbine and photovoltaic technology have a minimal and maximal number of installed units in the network, set by the user. Through varying ×1, ×2 and y, the power generation in the network for each combination for each period is found. After simulation of all possible results, the smallest ESS size is found and traced back to its RES combination.

### Sizing storage system with regards to the import/export

The first method for sizing the ESS is used with eqs. 14–16. Here, the ESS is sized only through using a percentage of the residual power in the given electrical network.

$$ {\mathrm{P}}_{\mathrm{IO},\mathrm{SS}}^{\left(\mathrm{m}\right)}={\mathrm{P}}_{\mathrm{R},\mathrm{G}}^{\left(\mathrm{m}\right)}\ast {\mathrm{R}}_{\mathrm{P}\mathrm{ER}} $$

(14)

P_{R,G} is the extra grid power, the difference between the generated and consumed power in the grid at data point “m”. R_{PER} is user-set and refers to what percentage of the residual power value must charge/discharge the ESS. When the residual power value is positive, the excess energy is transferred to other interconnected networks. A percentage (Rper) of that power is used for charging the storage system. When the residual energy in the grid is negative, a percentage (Rper) of the necessary electric power is supplied from the ESS. This way the ESS can support the local network, where the RES are installed. The power that is charged/discharged in the ESS is given by P_{IO,SS}.

After determining whether the storage system must perform a charging or discharging action, for that specific moment, the new ESS capacity can be found.

$$ {\mathrm{E}}_{\mathrm{CAP},\mathrm{SS}}^{\left(\mathrm{m}\right)}={\mathrm{E}}_{\mathrm{CAP},\mathrm{SS}}^{\left(\mathrm{m}\hbox{-} 1\right)}+{\mathrm{P}}_{\mathrm{I}/\mathrm{O},\mathrm{SS}}^{\left(\mathrm{m}\right)} $$

(15)

This action is performed for every data point, and the ESS charge state is updated for every data point. To obtain what the total storage capacity for the observed period must be, information is needed on the lowest and highest E_{CAP,SS} has reached for the entire dataset.

$$ {\mathrm{E}}_{\mathrm{CAP},\mathrm{SS}}=\max \left({\mathrm{E}}_{\mathrm{CAP},\mathrm{SS}}\right)\hbox{-} \min \left({\mathrm{E}}_{\mathrm{CAP},\mathrm{SS}}\right) $$

(16)

Equation 16 presents the total storage capacity for the entire dataset, given the current number of RES. An example is provided in Fig. 2. There, a specific size can be traced to each RES technology. The optimal number of RES for obtaining that ESS size is the combination of all RES that matches that specific size.

### Sizing storage system with regards to the import/export and the price of electrical power

The second method for sizing the ESS monitors the import/export power in the study grid and also oversees the price of electricity. Here, for every discharge action, the ESS must perform, the price of importing electricity from the interconnected network is also monitored. If the price of importing electricity into the studied grid is below a certain threshold, set by the researcher, the ESS performs no discharge action. On the other hand, when the price of importing electricity is too high, the test grid is supplied power through the ESS. For this method, another action must be performed before sizing the ESS, and that is to run the test grid through a power flow algorithm. This is done so that a more accurate model can be created, where the power loss in the grid is taken into account. For ESSPC, which is created in Matlab, the Matpower [13] toolbox is used. Equations. 17 to 24 present the explained method mathematically. Equation 17 is used in the event where the power that is generated in the grid (P_{G,G}) by the RES is greater than the total consumption (P_{C,G)} that is needed in the test grid at that point in time. In such an event, after accounting for the pre-set residual percentage, the ESS is charged P_{C,SS}. Because for MATPOWER, the ESS acts like a generator and a motor at the same time, in the event of charging the ESS, the generation of the ESS (P_{G,SS}) must be set to zero.

$$ {\mathrm{P}}_{\mathrm{C},\mathrm{SS}}^{\left(\mathrm{m}\right)}=\left({\mathrm{P}}_{\mathrm{G},\mathrm{G}}^{\left(\mathrm{m}\right)}\hbox{-} {\mathrm{P}}_{\mathrm{C},\mathrm{G}}^{\left(\mathrm{m}\right)}\right)\ast {\mathrm{R}}_{\mathrm{P}\mathrm{ER}} $$

(17)

$$ {\mathrm{P}}_{\mathrm{G},\mathrm{SS}}^{\left(\mathrm{m}\right)}=0 $$

(18)

If the power consumption is greater than the generation, and the price for importing power from the interconnected grid (P_{PRI,G}) is greater than the set power price limit (P_{PR,G}), it is determined that it is too expensive to import power, and as such the ESS supplies all the necessary power to the consumers.

$$ {\mathrm{P}}_{\mathrm{G},\mathrm{SS}}^{\left(\mathrm{m}\right)}=\left({\mathrm{P}}_{\mathrm{C},\mathrm{G}}^{\left(\mathrm{m}\right)}\hbox{-} {\mathrm{P}}_{\mathrm{G},\mathrm{G}}^{\left(\mathrm{m}\right)}\right)\ast {\mathrm{R}}_{\mathrm{P}\mathrm{ER}} $$

(19)

$$ {\mathrm{P}}_{\mathrm{C},\mathrm{SS}}^{\left(\mathrm{m}\right)}=0 $$

(20)

$$ {\mathrm{P}}_{\mathrm{P}\mathrm{R}\mathrm{I},\mathrm{G}}^{\left(\mathrm{m}\right)}>{\mathrm{P}}_{\mathrm{P}\mathrm{R},\mathrm{G}}^{\left(\mathrm{m}\right)} $$

(21)

In the event, where the price of electricity is low enough, the ESS does not perform any action.

$$ {\mathrm{P}}_{\mathrm{C},\mathrm{SS}}^{\left(\mathrm{m}\right)}=0 $$

(22)

$$ {\mathrm{P}}_{\mathrm{G},\mathrm{SS}}^{\left(\mathrm{m}\right)}=0 $$

(23)

$$ {\mathrm{P}}_{\mathrm{P}\mathrm{R}\mathrm{I},\mathrm{G}}^{\left(\mathrm{m}\right)}<{\mathrm{P}}_{\mathrm{P}\mathrm{R},\mathrm{G}}^{\left(\mathrm{m}\right)} $$

(24)

To find the size of the ESS, Eqs. 15 and 16 are used. Here P_{I/O,SS} is either P_{C,SS} or P_{G,SS}, depending on the action that the ESS must perform at that moment.

This method allows the researcher to make a more educated decision whether the RES are suitable for the current area based on information about how costly it is going to be to supply the test grid when the RES is not producing. It also allows for sizing the ESS, depending on the cost of importing electricity into the test grid, when the RES is not working.