# Increasing Technical Efficiency of Renewable Energy Sources in Power Systems

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## Abstract

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## 1. Introduction

_{p}is the value of the forecasted (predicted) hourly electricity generation of RES for the next day, and W

_{f}is the actual (“fact”) production of RES electricity during the same time.

## 2. Clarification of the Forecast Schedule of RES Generation by Means of Intraday Correction

_{p}or the actual value W

_{f}. It is possible to influence the actual generation of W

_{f}only in the direction of its reduction, which is not economically feasible. The actual power generation must be reduced only at the command of the transmission or distribution system operator when it is necessary to ensure the stability of the power system. Therefore, in normal EPS modes, it is possible to correct only the forecast values of electricity generation for a certain time $\Delta t$. The actual values of the generated electricity are approximated at the same time according to preliminary data from ASCEA.

_{1}, for example, ${\delta}_{1}\succ 0\hspace{0.17em}$ and ${\delta}_{1}\succ {\delta}_{per}$, the forecast must be reduced by k. Accordingly, the forecast will be ${W}_{p}=k{W}_{p}$, where $k=1-{\delta}_{1}\hspace{0.17em}\hspace{0.17em}$ and ${\delta}_{1}=({W}_{p}-{W}_{f1})/{W}_{f1}$. On point t

_{3}, for example, ${\delta}_{3}\prec \hspace{0.17em}$0 and ${\delta}_{3}\prec -{\delta}_{per}$, the forecast must be increased by k. Accordingly, the forecast will be ${W}_{p}=k{W}_{p}$, where $k=1-{\delta}_{3}\hspace{0.17em}$ and ${\delta}_{3}=({W}_{p3}-{W}_{f3})/{W}_{f3}$. If the difference between the forecasted and actual values is within the permissible range, i.e., $\left|\delta \right|\prec \left|{\delta}_{per}\right|$, then coefficient k = 1 and it is not necessary to correct the forecast values.

_{b}begins and ends i

_{e}PV power generation, where i is the current number of the hour. Further,

- −
- i = i
_{b}, the forecast error for the i-th hour is determined ${\delta}_{\mathrm{i}}=\frac{{w}_{\mathrm{i}}^{p}-{w}_{\mathrm{i}}^{f}}{{w}_{\mathrm{i}}^{f}}$; - −
- i = i + 1, the forecast error for the i + 1st hour is determined ${\delta}_{\mathrm{i}+1}=\frac{{w}_{\mathrm{i}+1}^{p}-{w}_{\mathrm{i}+1}^{f}}{{w}_{\mathrm{i}+1}^{f}}$.

## 3. Optimizing the Methods and Means of RES Reservation for Their Full Participation in the Control of the EPS Modes

_{res}for reservation ${P}_{res}(t)$ in (2) for unsustainable RES generation, then, taking into account currently possible reserving methods, the problem of minimization C

_{res}will be written as:

_{ch}(P

_{ch})—costs of reserving by electrochemical-type accumulators; C

_{h}(P

_{h})—costs of hydrogen technologies; C

_{b}(P

_{b})—costs associated with the use of biogas technologies as a reserve; C

_{s}(P

_{s})—costs of using the system reserve, which is actually compensation for maintaining the reserve at CHPS power units operating according to price bids; C

_{tl}(P

_{tl})—costs of capacity reserves of power transmission lines, which are necessary for the transportation of electricity from/to the place of connection of the reserve capacity to the EPS; C

_{c}(P

_{c})—costs of the implementation of the coordination of electricity generation and consumption schedules in the EPS; and P

_{ch}, P

_{h}, P

_{b}, P

_{s}, P

_{tl}, and P

_{c}—optimal capacity values determined from each of the reservation methods.

_{res}, then the components (3) ${C}_{\mathrm{i}}({P}_{\mathrm{i}})/{C}_{res},\hspace{0.33em}\mathrm{i}=\overline{1,\hspace{0.33em}m}\hspace{0.17em}\hspace{0.17em}$ (m is the number of members of the objective function) are the ‘’weighting’’ coefficients of the members of the function ${\pi}_{\mathrm{i}}$ and their sum is equal to one (normalization condition). In the theory of similarity [29], such dimensionless ‘’weighting’’ coefficients in the physical sense are criteria of similarity ${\pi}_{\mathrm{i}}\hspace{0.17em}$. Hence, the criterion method.

_{res}. In optimization theory, this is commensurability [32]. In accordance with the possibility of the method, a mathematical model is formed.

_{s}—the maximum capacity of the system reserve that can be used to balance RES generation (g

_{s}= 1/G

_{S}); and G

_{ch}—the maximum available capacity of electrochemical-type accumulators (g

_{ch}=1/G

_{ch}).

_{h}. The cost of using biogas to increase reserve capacity has a linear relationship. Provided that the system reserve is available and its cost is reduced, it will be used more and Ps will increase. The last component of the costs depends on the losses of electricity in the elements of the power grid.

_{rez}minimization problem from (3). In particular, these are costs for increasing the capacity of power transmission lines, which is considered sufficient at the initial stage, and costs for coordinating electricity generation and consumption schedules in the EPS, which are already partially used in electric grids. The last term of the objective function (4) reflects the costs of covering electricity losses, which are associated with the implementation of redundancy measures. At the same time, it is considered that the storage devices of the electrochemical type and the system reserve are located centrally.

_{i}. In our case, s = 7 − 4 − 1 = 2. According to the criterion method, we write the system of orthogonal and normalized (orthonormalized) equations for (4) relative to similarity criteria $\pi $ [31]:

**b**

_{0}—normalization vector; and

**b**

_{n}—vectors of discontinuity.

_{s}and electrochemical accumulators G

_{ch}(in (10), it depends on ${\pi}_{6}$ and ${\pi}_{7}$). The first component ${C}_{res*}$ from (10) is defined as

_{1},…, c

_{5}. As for the generalized coefficients C

_{1},…, C

_{5}, their influence on economically feasible power values ${P}_{ch*},\hspace{0.33em}{P}_{h*},{P}_{b*},\hspace{0.33em}{P}_{s*}$ and costs ${C}_{*}$ can be estimated by determining their values from the system of equations written according to the method of integral analogs from (4), taking into account (9) [33]:

_{res}to balance the RES generation schedule through reservation will increase by 6.2%.

## 4. An Example of Reducing Imbalances between Forecasted and Actual Generation by a Combination of Methods

_{1}), it is advisable to reduce this imbalance by accumulating energy, for example, in the form of hydrogen. Hydrogen can be produced directly at the PV if this possibility is provided by the appropriate installation; otherwise, it is necessary to buy the required amount of hydrogen as a service from another producer. The hydrogen option is appropriate because, when using, for example, electrochemical accumulators, we are limited by the need to convert the stored energy back into electrical energy. Meanwhile, in the case of hydrogen, there are more options, such as applications in other industries or in transport, or conversion into electricity. When the forecast at a certain time interval is greater than the “fact” (see Figure 6, point t

_{3}), then, after running the forecast refinement program, the forecast generation of the PV is corrected to be allowable under the condition $\delta \le {\delta}_{per}$.

^{3}of hydrogen or 50.56 kWh for 1 kg of hydrogen [36]. An amount of 250.5 MWh can be used to produce hydrogen, that is, M = 250.5/50.56 = 4954 kg of hydrogen per day. This hydrogen, if the power system is deficient in electricity generation, can be used to generate electricity and improve the balance of the EPS mode. If the energy system is in surplus, it is advisable to use hydrogen in other industries and in transport. The difference between the forecasted and actual generation of PV in the balancing group can be reduced with software by correcting the forecast, as shown in Figure 6.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ASCEA | Automated systems of commercial electricity accounting |

EPS | Energy power system |

PV | Photovoltaic power plant |

RES | Renewable energy sources |

WPP | Wind power plant |

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**Figure 3.**Algorithm of the program for the hourly correction of forecasting the power generation by PV.

**Figure 5.**Sensitivity of relative costs to changes in the power generation of biogas (red curve) and to changes in the power generation of hydrogen technologies (blue curve).

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**MDPI and ACS Style**

Smolarz, A.; Lezhniuk, P.; Kudrya, S.; Komar, V.; Lysiak, V.; Hunko, I.; Amirgaliyeva, S.; Smailova, S.; Orazbekov, Z.
Increasing Technical Efficiency of Renewable Energy Sources in Power Systems. *Energies* **2023**, *16*, 2828.
https://doi.org/10.3390/en16062828

**AMA Style**

Smolarz A, Lezhniuk P, Kudrya S, Komar V, Lysiak V, Hunko I, Amirgaliyeva S, Smailova S, Orazbekov Z.
Increasing Technical Efficiency of Renewable Energy Sources in Power Systems. *Energies*. 2023; 16(6):2828.
https://doi.org/10.3390/en16062828

**Chicago/Turabian Style**

Smolarz, Andrzej, Petro Lezhniuk, Stepan Kudrya, Viacheslav Komar, Vladyslav Lysiak, Iryna Hunko, Saltanat Amirgaliyeva, Saule Smailova, and Zhassulan Orazbekov.
2023. "Increasing Technical Efficiency of Renewable Energy Sources in Power Systems" *Energies* 16, no. 6: 2828.
https://doi.org/10.3390/en16062828