Solar–Wind System for the Remote Objects of Railway Transport Infrastructure

Abstract

The article deals with adding the power of a local object to a solar–wind system when consuming electricity from the grid within the power limit. The parameter’s calculation technique for the different values of degree of power increase was considered. The load schedule, the electricity consumption, use of installed power, boundary conditions of generation, and ensuring energy balance were taken into account. Furthermore, data from the renewable source’s generation archive for the location of the object were used. The control of the power consumed by the object was carried out on the taken values of added and total load power with binding to photovoltaic generation. The added power reference on some time intervals was carried out according to the actual renewable generation power value. This increases the degree of use of the battery capacity and energy from renewable sources. The reference of the added power with the state of battery charge formation was carried out according to the forecast. One cycle of deep battery discharge at the evening peak was used to extend the battery life. For the accepted conditions with the average monthly values of renewable energy sources generation with an increase in power by 1.6 times, there was a decrease in electricity consumption by 1.57–4 times.

1. Introduction

Recently, more and more attention has been paid to the use of systems with photovoltaic batteries (PV) and wind generators (WG) for the self-consumption of local objects (LO). Such systems are usually hybrid and connected to the AC distribution grid (DG). At the same time, along with ensuring energy saving, the problem of ensuring the reliability of the power supply is solved. The use of combined solar–wind (PV–WG) systems with a storage battery (SB) allows for increasing the degree of independence from weather conditions.

A possible application of PV–WG systems is to add LO power in the presence of a power limit for consumption from the DG. Such a solution can be used when the possibilities of power increase for the existing power line and grid equipment are exhausted. To a large extent, this applies to objects that are remote from the transformer substation. These can be objects of railway transport infrastructure. In this case, the implementation of the PV–WG system may be a more cost-effective solution than replacing the power transmission line and grid equipment. It is necessary to take into account the possibility of reducing the current costs of paying for electricity during the entire period of operation of the PV–WG system and the possibility to use of island mode in case of grid failures. Thus, the task of correctly determining the parameters of the system for the maximum use of the installed power of the equipment and reducing costs with effective energy management is urgent.

2. Literature Review and Problem Statement

Currently, large attention is paid to issues of the use of PV–WG systems, including systems that are used for the self-consumption of LO. A significant number of works are devoted to the optimization of technical and economic parameters of PV–WG systems [1,2,3,4,5]. This is usually undertaken for a specific location of the object, which confirms the importance of taking into account local values of RES generation, for example, for India [2], Great Britain [3], and Ukraine [6]. Optimization concerns the determination of the parameters of the PV, WG, and SB. At the same time, the generation of renewable energy sources (RES) is commensurate. So, in work [5], under maximum load power in the daytime of 12 kW, the power of WG is P_W = 12 kW, and the power of PV is P_PV = 39.2 kW. In [7], the dependencies P_PV(t) and P_W(t) are presented when there is the possibility of equalizing the total generation of RES energy during the day. Power generation in DG is considered in several works [1,3,7]. This reduces the cost of electricity consumption from the grid and simplifies the provision of power balance. The use of PV and WG of approximately the same power has a disadvantage. So, the generation of the system sharply reduces during no-wind weather. If the generation into the grid is not used, then the question of ensuring energy balance arises at a low night load. The option of using an auxiliary WG of lower power in a photovoltaic system (PVS) is considered in [6]. At the same time, the ratio of values of PV installed power P_PVR and WG installed power P_WR to peak load power P_L is P_PVR:P_WR:P_L = 3:0.36:1.

A solution to increasing the power of the object of railway transport infrastructure over the limit on consumption from the grid using PVS is considered in [8]. The considered implementation principles with reference to the added load power are focused on reducing the installed PV power P_PVR and the energy capacity W_BR of SB. However, the obtained values of P_PVR and W_BR are somewhat overestimated. The ratio of P_PVR and W_BR to the peak load power P_L is P_PVR:W_BR:P_L = 4.3:4:1. At the same time, the decrease in consumption costs in winter from 1.088 to 1.354 times is insignificant.

To implement a PV–WG system with the battery, a variant with a common grid inverter is usually considered [2,4,5,6]. Wide opportunities to improve the performance of the system are provided by the use of multifunctional grid inverters [9,10,11,12,13,14,15]. In this case, it provides a power factor close to 1 in a point of common coupling (PCC) to the AC grid, and the three-phase version [12,13,14,15] also provides the equalization of consumption by the phases in the grid.

For the maximum use of PV and WG energy, maximum power point tracking (MPPT) controllers are used. At the same time, the PV–WG system is provided a dump load [4] to reset excess energy. When excluding generation to the grid, a solution for PV with a switch from the maximum power mode to the regulation of the PV generation power looks appropriate [9]. In this case, the regulation of WG power can be avoided. The possibility of regulating the PV generation is also used in serial hybrid inverters [16] for PVS.

The effective management of PV–WG systems with energy storage devices is associated with the formation of the schedule of the SB charge degree using the short-term forecast of RES [6,17,18]. Recently, considerable attention has been paid to forecasting issues, and open web resources have appeared. For example, data of PV generation and wind speed forecast with the discreteness of 1, 0.5 h or less are presented in [19,20].

The central zone of Ukraine is characterized by a low wind speed of 3–5 m/s [21]. Approximately the same one is in Slovakia. In this condition, it is possible to use WG with a vertical axis. Such low-power wind turbines (up to 8 kW) are widely represented on the market for use in the domestic sector at design wind speeds of 3–7 m/s. It is possible to use them in combination with PVS as auxiliary sources with a power consumption of objects up to 30–100 kW.

The choice of parameters for the PV–WG system with a battery should be carried out using archival data on the generation of RES for specific conditions [6,8]. PV generation power data, including information on the average monthly energy values for the specified coordinate of the location of the object, are presented in [22]. Furthermore, this resource provides information on hourly wind speed. When electricity generation to the grid is excluded and there is no dump load, information on the average value of RES energy generation per day is not enough. There is a need to obtain information on the generation of RES at time intervals by the LO load schedule.

Experimental research of the efficiency of PV–WG systems with SB, including the principles of control and the redistribution of energy in the system, requires a lot of time and money. Therefore, mathematical modeling is widely used [9,14,23,24]. The simulation of a hybrid PVS system using a supercapacitor in the interval of the PV generation duration is considered in [24]. The modeling processes in the LO power supply system for the daily operation cycle using real archive data of RES generation to assess the system performance are presented in [6,8,18]. This implies the formalization of energy processes in the LO power supply system for the operating modes used. Naturally, the final criterion can only be an experiment. Nevertheless, modeling avoids dead-end solutions.

The use of the PV–WG system for increasing LO power enables a significant possibility for comparison with PVS. First of all, this concerns the possibility of reducing the consumption of electricity from the DG and reducing the installed power value of the equipment. A promising option for LOs with a predominance of daytime consumption is the option when the PV plays the main role, providing a large part of the electricity. WG generates around the clock and performs the function of equalizing the generation of electricity. In this case, the power of the WG can be significantly lower than the PV power. It becomes possible to reduce the installed PV power with a more complete use of its capabilities. The expansion of possibilities implies the emergence of additional conditions and restrictions, which requires additional study. From the standpoint of the use of RES energy, there are promising principles for managing the system with the given value of the added load power. Taking into account the introduction of an additional energy source, the issues of calculating the parameters and implementing control require further improvement.

The purpose of the article is to add LO power in the presence of a power limit for consumption while maximizing the use of the installed power of RES and reducing the consumption of electricity from the grid.

The main objectives of the research are as follows:

• To prepare data on the generation of RES, taking into account the load schedule of the LO by the archival data for the location of the LO;
• To justify the choice of system parameters taking into account the degree of power increase, boundary modes of RES generation, use of installed power of RES, and reduce the energy consumption from the grid;
• To develop the principles for implementing the management of the PV–WG system using a short-term forecast of RES generation;
• To perform research on system operation in the daily cycle for different weather conditions during the year using modeling.

3. Materials and Methods of Research

The substantiation of the choice of system parameters is made using the methods of the theory of electrical circuits. The calculation of the average monthly values of the RES generation energy was made according to the archival data for the location of the object. WG generation was determined for a specific device according to the manufacturer and wind speed. A specific object load schedule was used with the assignment of average power values for time intervals.

The initial prerequisite for improving the use of RES energy for consumption is the formation of a graph of the added load power of the object. This schedule is tied to the generation of a photovoltaic battery as the main source of energy and takes into account the power consumption limit from the grid. The contribution of the wind generator is significant only at low PV generation.

When determining the RES parameters, the boundary modes of RES generation in different periods of the year were taken into account, also taking into account the use of the installed power of PV and reducing the electricity consumed from the grid. The possibility of no wind was also taken into account. The possibilities of implementation with the maximum degree of increasing the power of the load depending on the RES generation, as well as with a constant coefficient of power increase during the year, were considered. When using a multifunctional grid inverter, the power factor is close to 1. This allows you to perform an analysis of energy processes in the system “grid—PV–WG system with battery—LO load” on active power, taking into account energy losses through efficiency. The battery model was designed to the manufacturer’s characteristics and charge modes. The generation of RES was estimated according to the average monthly energy values according to the load schedule. To achieve greater reliability for the calculated values of RES energy, archival data for 5 years were processed. When forming a graph of the state of charge SOC(t) of SB, a limitation DOD ≤ 80% was introduced with one deep discharge per day. The control system of the converter unit of the FV-VG system was made using a classical structure, maintaining a constant voltage in the DC link. During the modeling, the proven MATLAB software and real archival graphs of RES power generation were used. The energy process model uses calculated expressions for steady operating modes, taking into account changes in the modes of operation of the system at time intervals per day. The estimation of the reduction in electricity consumption during the year was performed for the selected days when the PV power generation schedule was close to the monthly averages.

4. Parameters Calculation and Control of the System

A variant of the system with the use of a grid multifunctional inverter VSI, which is common to RES [6,8], was considered (Figure 1). The generation of electricity into the grid was not used. On the LO, an additional load was used, and the total power of the load was increased above the limit P_LIM for the consumption of the grid. The structure of the converter unit of the PV–WG system included the DC voltage converter of PV (DC/DC2), the DC voltage converter of WG (DC/DC1), and the DC voltage converter of SB (DC/DC3). DC/DC1 ensured the operation of WG in maximum power mode and was not tied to the control of the main unit. DC/DC2 has two modes of operation: in maximum power point tracking (MPPT) mode and the mode with PV generation control at the reference of PV current I_PV [8,9,14,15]. DC/DC3 has bilateral conductivity and provides charge/discharge of SB with the specified value of current I_B. The control of the converter unit was carried out by the control system (CS) unit. Connection with the web resource for obtaining forecast data was provided by the Wi-Fi module, WFM. For consideration, the load schedule shown in Figure 2 was adopted.

To determine the parameters of the system, we used the calculation values of the average monthly energy generation of RES for time intervals (Figure 2) during the day [6], obtained from the archival data [22]. The location of the LO corresponds to the coordinates for Kyiv. The use of PV at the power P_PVR = 1 kW and the WG type [25] at the power P_WR = 1 kW at nominal wind speed values of 3 m/s and 4.5 m/s were considered. The WG of the vertical type was chosen using the bottom and top values of the diapason of the average wind speed for a given place (3–5 m/s).

Table 1. Indicators of average PV and WG energy generation.

Indicators	December	January	February	March	April	May	June	July	August	September	October	November
PV with power PPVR = 1 kW
WPVAVD, kWh	1.03	0.98	1.81	2.83	3.83	4.26	4.48	4.37	4.16	3.52	2.49	0.96
WPV23, kWh	0.21	0.166	0.31	0.55	0.52	1.15	1.17	1.13	1.08	0.56	0.33	0.22
WPV34, kWh	0.8	0.78	1.31	1.84	2.38	2.43	2.27	2.5	2.45	2.27	1.74	0.69
WPV45, kWh	0.021	0.038	0.16	0.32	0.84	0.53	0.63	0.61	0.53	0.72	0.39	0.03
WG with power PWR = 1 kW, vR = 3 m/s
WWAVD, kWh	21.072	20.84	19.84	21.406	18.603	16.549	17.77	16.55	15.794	18.316	17.72	18.956
WW62, kWh	9.5	9.4	9.05	8.638	7.38	5.583	5.611	5.38	5.27	7.16	7	8.27
WW26, kWh	11.572	11.44	10.79	12.768	11.223	10.966	12.159	11.17	10.524	11.15	10.72	10.68
WW46, kWh	6.168	6.175	5.76	6.239	5.547	5.39	5.861	5.457	1.195	5.29	5.239	5.524
WG with power PWR = 1 kW, vR = 4.5 m/s
WWAVD, kWh	14.00	13.38	11.91	13.91	11.98	9.14	10.03	9.39	8.55	10.32	10.54	12.33
WW62, kWh	6.26	5.88	5.128	5.1	3.69	2.66	2.616	2.644	2.432	3.44	3.78	5.264
WW26, kWh	7.73	7.47	6775	8804	7481	6484	7417	6748	6112	6877	6764	7,07
WW46, kWh	4.077	3.96	3.503	3.891	3.538	2.56	2.933	2.684	2.516	2.984	3.01	3.58

shows the values of the average monthly PV generation per day W_PVAVD, as well as by time intervals (W_PV23, W_PV34, W_PV56) in Kyiv. There are similar data for WG W_WAVD (W_W24, W_W56, W_W62). The calculation for PV was carried out for the period 2012–2016 and WG—for the period 2011–2016. To calculate the output electric power P_W of WG, a typical dependence [26] $P_W^{*}=f\left({\nu }^{*}\right)$ of the output-conditional unit WG power $P_W^{*}=P_W/P_{WR}$ on wind speed ${\nu }^{*}=\nu /{\nu }_R$ was used, which has the form:

$$P_W^{*}=\{\begin{array}{l}0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\nu }^{*}\le {\nu }_{MIN}/{\nu }_R,\\ {\left({\nu }^{*}\right)}^3,\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\nu }_{MIN}/{\nu }_R<{\nu }^{*}<1,\\ 1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\nu }^{*}=1,\\ -0.8216{\left({\nu }^{*}\right)}^2+2.1875{\nu }^{*}-0.3588,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1<{\nu }^{*}<1.33,\\ 1.1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1.33<{\nu }^{*}<{\nu }_{MAX}/{\nu }_R,\\ 0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\nu }^{*}>{\nu }_{MAX}/{\nu }_R.\end{array}$$

where P_W, P_WR is the current and rated value of WG power, respectively; ν, ν_R is the current and rated value of wind speed, respectively; ν_MIN is starting wind speed; ν_MAX is the maximum wind speed when the brake system is overstayed and WG stops.

We assumed that the value of power increases proportionally relative to the baseline load schedule [8] P_LC(t) = ρP_L(t) (ρ, the coefficient of power increasing; P_L(t), the basic load schedule, according to Figure 2). At the same time, P_LC = P_Lg + P_C (P_Lg), load power, which is provided from grid electricity (P_Lg ≤ P_LIM), P_C, is the load added power, which is provided due to the energy of RES and SB). When calculating, we accepted that P_LIM is equal to the peak load power P_L = 200 W.

The added power value can be determined as P_C(t) = P_L(t)(ρ – 1) [8]. If to determine the value P_C(t) in the daytime (interval (t₂, t₆)) P_C26(t) = ρP_L26(t) – P_LIM, then, respectively, the RES energy W_C26, which is required to provide it, decreases

$$W_{C26}=W_{L26}\left(\rho -1\right)-\left(W_{LIM26}-W_{L26}\right)<W_{L26}\left(\rho -1\right),$$

where W_L26 is the energy consumed according to the base load schedule, $W_{LIM26}=P_{LIM}\left(t_6-t_2\right)$.

The total energy W_R generated by PV and WG is [6]:

$$W_R=W_{PV}\cdot m_p+W_W/m,$$

(1)

where m and m_P are conversion coefficients for WG and PV power relative to the installed power 1 kW in Table 1, respectively.

With high daytime RES generation, the night charge SB is only used to accumulate excess energy, which is not used for load consumption. The value of the state of SB charge SOC or Q* = 100 Q/Q_R, $Q={\displaystyle \int I_{B}dt}$, Q_R—rated capacity, Ah. With the low daytime generation of RES, the night charge of the battery allows you to exclude energy consumption from the grid on the added load. For the process of the accumulation of excess RES energy W_R26 in the daytime followed by load consumption in the evening, we accounted for the reduced electricity consumption from the grid. To maximize the use of battery capacity at a high generation of RES, the initial value of Q*₂ can be taken at the level of the minimum Q*₆ and no night charge is required. Then the battery energy balance cycle for the twenty-four hours is reduced to a night charge (interval (t₆, t₂)) from WG and grid from Q*₆ to Q*₂ (ΔQ*₆₂ = Q*₂ − Q*₆), followed by discharge on the load from Q*₂ to Q*₆. The energy balance for the daily period (t₂, t₆) is as follows:

$$W_{PV26}\cdot m_p\cdot {\eta }_C+W_{W26}\cdot {\eta }_C/m+\mathsf{\Delta }{W}_{B26}-W_{C26}-W_{gR26}=0,$$

(2)

where W_gR26 is the reduction in energy consumption from the grid, W_C26 is the energy consumed by the added load, ΔW_B26 is the energy provided by the battery, W_B = U_BC_B is the energy capacity of SB, U_B is the voltage of SB, C_B is the capacitance of SB (Ah), η_C is the efficiency of the converter, and η_B is the efficiency of SB.

The value of W_gR26 > 0 may be during hours of high PV generation t_da, when P_R·η_C > P_C + P_B (P_B) = U_B·I_B, the value of power for battery charging). The exception of generation to the grid is provided by the limitation of P_gR ≤ P_LIM, which was achieved by controlling (reducing) PV power generation. The limiting case is W_gR26 = P_LIM·t_da [8].

Value ΔW_B26:

$$\mathsf{\Delta }{W}_{B26}=0.01\cdot W_B\left(Q_2^{*}-Q_6^{*}\right){\eta }_C\cdot {\eta }_B.$$

At night, the SB consumes energy:

$$\mathsf{\Delta }{W}_{B26}=\frac{0.01\cdot W_B\left(Q_6^{*}-Q_2^{*}\right)}{{\eta }_C\cdot {\eta }_B}.$$

(3)

The energy capacity of SB determines the maintenance of the added load functioning during the evening peak hours (t₅, t₆) and during the interval (t₄, t₅) when PV generation is significantly reduced. This is possible due to the charge of the SB on the day before Q*₄→100%. Respectively,

$$W_B=\frac{W_{C46}-W_{W46}\cdot {\eta }_C/m-W_{PV46}\cdot {\eta }_C\cdot m_p}{0.01\cdot \mathsf{\Delta }{Q}_{46}\cdot {\eta }_C\cdot {\eta }_B}.$$

(4)

When there are a few variables (coefficients m_P, m η W_B), the choice of its values is possible using successive approximations. We proceeded from several boundary conditions. Minimum PV generation takes place in winter (

Table 2. Calculated values of system parameters.

mP	1	0.9	0.8	0.7	0.6	0.568
m	34.4	26.5	21.6	18.1	15.7	15
ΔWB46, W	564	538	514	488	427	413
WB, Wh	781	745	711	676	592	572

), which is critical to providing the performance of the system. The exclusion of consumption from the grid to ensure the added load in the daytime is key. In this case, the value was W_gR26 = 0.

In the absence of WG generation (W_W26→0) and at the average monthly value of PV generation by (2):

$$m_P=\frac{W_{C26}-\mathsf{\Delta }{W}_{B26}}{W_{PV26}\cdot {\eta }_C}.$$

(5)

In the season’s spring–summer–autumn, PV energy generation increases significantly. The need to use the battery discharge in the morning peak is minimal (ΔQ*₂₆→0). To maximize the use of battery capacity, it is desirable to have a value of Q*₂ close to Q*₆. Excluding consumption from the grid when W_gR26 = 0 by (2) occurs when

$$m_P=\frac{W_{C26}}{W_{PV26}\cdot {\eta }_C}.$$

(6)

We accept the value of ρ = 1.6 when using WG for a speed of 3 m/s. The minimum value W_PV26 in the spring–summer–autumn period occurs in October (Table 1); it corresponds to the minimal value of m_P = 0.568.

Due to the longer duration of the evening peak (4 h), the biggest value of W_C46 occurs in spring and autumn. To calculate W_B by (4), we used the minimum value of W_PV46 (March in Table 1) at W_W46→0 and ΔQ*₄₆ = 80%; we achieved W_B = 662 Wh (ΔW_B46 = 478 Wh). This value is overstated when not accounting for W_W46.

Since the electricity generation into the grid is excluded, it is necessary to confirm the energy balance at night time (interval (t₆, t₂)):

W_W62·η_C/m + m_P·W_PV62·η_C + W_g62 = W_LC62 + ΔW_B62

(7)

where Wg62 is the energy consumed from the grid.

The maximum value is W_W62MAX = P_WMAX(t₂ − t₆) (maximum value WG generation power is P_WMAX = 1.1 P_WR [25]). In this case, the value W_W62MAX exceeds the load consumption, and there is no consumption from the grid, i.e., W_g62 = 0. The maximum value ΔW_B62 corresponds to ΔQ*₆₂ = 100 − Q*₆. We neglect the small generation of PV in the morning hours, then we find the condition of the exception of the generation into the grid [6]:

$$m\ge m_{MIN}=\frac{W_{W62}\cdot {\eta }_C}{W_{LC62}+\mathsf{\Delta }{W}_{B62}}.$$

(8)

With low PV generation in winter (W_PV26→0) by (2):

$$m=\frac{W_{W26}\cdot {\eta }_C}{W_{C26}-\mathsf{\Delta }{W}_{B26}}.$$

(9)

At ρ = 1.6 for December by (9), there is m = 13.98. It exceeds the value m = 8.5, obtained by (8). The value m = 13.98 is preliminary and needs clarification.

We determined the value of W_B by (4) for the December conditions, taking into account the generation of WG. We accept that the generation of RES W_R46 is 0.5 from the average monthly value with the obtained values m and m_P. In this case, W_B = 572 Wh (ΔW_B46 = 413 Wh). Under similar conditions for March, W_B = 490 Wh (ΔW_B46 = 354 Wh).

Consider the case when, with the average generation of RES, the added load during the day is provided without the consumption of electricity from the grid and without the discharge of the battery, then:

$$m=\frac{W_{W26}\cdot {\eta }_C}{W_{C26}-W_{PV26}\cdot m_p\cdot {\eta }_C}.$$

(10)

The value obtained for December is m = 15. The previously obtained m = 13.98 means an increase in WG power. Initially, an approach was adopted using WG as an auxiliary energy source; therefore, we accept m = 15.

The value ρ is calculated for the season when PV generation is minimal. In this case, it is December, then:

$$\rho \le \frac{W_{LIM26}+W_{R26}\cdot {\eta }_C+\mathsf{\Delta }{W}_{B26}}{W_{L26}}.$$

(11)

The option for determining system parameters when ρ = 1.6 in December is given in Table 2. The values of W_B were determined for December with an RES generation of 0.5 of the average monthly value.

For the accepted value of ρ = 1.6 with the average monthly indicators of RES generation in December, there are m_P = 0.568, and m = 15 at value ΔW_B26 = 0. That is, the night charge of the battery is not required. Using the night charge of the battery allows you to increase the value ρ. At Q*₂ = 100% and ΔQ*₂₆ = 80% is ρ ≤ 1.754. If the generation of RES will be lower than the average monthly by four times, then ρ ≤ 1.362.

The value of W_B increases with increasing m_P from 0.6 to 0.7 (16.7%) roughly proportionally—on 14.1%. An important issue is the installed PV power not being utilized at periods of high solar activity. For the estimation, we introduced the PV energy utilization factor, which by (2) is:

$$k_{PV}=\frac{W_{C26}+W_{gR26}-W_{W26}\cdot {\eta }_C/m-\mathsf{\Delta }{W}_{B26}}{m_P\cdot W_{PV26}\cdot {\eta }_C}.$$

(12)

To assess the efficiency, we used the coefficient of cost reduction for electricity [8] (with one tariff rate and full use of RES energy):

$$k_E=\frac{W_{LC}}{W_g}=\frac{W_{LC}}{W_{LC}+\mathsf{\Delta }{W}_{B26}/{\left({\eta }_C\cdot {\eta }_B\right)}^2-W_W\cdot {\eta }_C/m-m_P\cdot W_{PV}\cdot {\eta }_C},$$

(13)

where $W_{LC}=W_{LC62}+W_{C26}+P_{LIM}(t_6-t_2)$ is the total energy consumed by the load.

The values of k_PV were estimated for June, and the value of k_E was estimated for December with the average monthly generation of RES ΔW_B26 = 0 and W_gR26 = 1400 Wh. When changing m_P from 0.568 to 1, the values of k_PV decrease from 0.845 to 0.582 (1.45 times), as well as the values of k_E, which decrease from 1.504 to 1.409 (by 1067 times). Thus, it is advisable to take the meaning of m_P close to the minimum (6).

It can be accepted that m_P = 0.568, m = 15 for the value ρ = 1.6. Furthermore, we chose the average value W_B = 513 Wh (for March W_B = 490 Wh, for December W_B = 572 Wh). When recalculating, we used a ratio of P_L/P_PVR/P_WR/W_B = 1/2.84/0.334/2.565.

The calculated values of the parameters depending on the value ρ are presented in

Table 3. Calc ending on ρ.

P	1.5	1.6	1.7	1.8	2
mP	0.457	0.586	0.707	0.788	1
m	18.58	15	13.07	10.9	8.5
kPV	1	0.845	0.641	0.523	0.34
WB, Wh	415	513	625	716	914

. There is a significant deterioration in PV use and an increase in the values of the installed power of PV, WG, and SB at ρ > 1.7.

It is possible to use the option with m_P = 0.568, and m = 15 when changing ρ = 1.5–1.8 (

Table 4. Calculated parameters depending on ρ at m_P = 0.568, m = 15.

ρ	1.5	1.6	1.7	1.8
kE	1.557	1.504	1.46	1.42
kPV	0.908	0.845	0.771	0.774

) without a night battery charge. In this case, with an increase in ρ, the use of PV in comparison with Table 3 increases, but k_E insignificantly reduces (value for December). It is accepted that the RES generation corresponds to the average monthly. When generating RES below the average monthly, the night charge of the SB is used, and it is necessary to decrease value ρ and load upon reaching ΔQ*₂₆ ≥ 80%.

Thus, with the accepted values of the installed power of PV and WG, the system ensures operation without a significant deterioration in the parameters with the possibility of increasing the load within a sufficiently wide range. There are two options for using the system [8]: (a) with a value ρ that is defined by PV generation, which is applicable for the seasonal nature of the load; (б) with the selection of a constant value ρ.

For option (a) it is assumed that you can plan the load (ρ) according to the forecast for the next day W_R26P. In a general case:

$$\rho =\frac{W_{R26}\cdot {\eta }_C+\mathsf{\Delta }{W}_{B26}-W_{gR26}+P_{LIM26}}{W_{L26}}.$$

(14)

We calculate the value ρ at W_gR26 = 0 and ΔW_B26 = 0. Then the following algorithm for setting the maximum value ρ is possible:

• If ρ < 1.5, then we accept ΔW_B26MAX (at ΔQ*₂₆ = 80%) and recalculate the value of ρ with the possibility of increase;
• If ρ ≥ 1.8, then we accept restriction ρ = 1.8, obtained above, with the possibility of reducing consumption from the grid W_gR26 at ΔW_B26 = 0;
• If 1.8 > ρ ≥ 1.7, then we accept ΔW_B26 at ΔQ*₂₆ = 15–20% and recalculate the value ρ ≤ 1.8;
• If 1.7 > ρ ≥ 1.5, then we accept ΔW_B26 at ΔQ*₂₆ = 30–40% and recalculate the value ρ ≤ 1.8.

For option (b) with a constant value ρ, it is also corrected according to the forecast of RES generation for the next day W_R26P. With low RES generation, the value of ρ is specified (decreases) by (14) at ΔW_B26MAX for ΔQ*₂₆ = 80% and W_gR26 = 0.

Setting the graphs P_C(t) and Q*(t) for the accepted value ρ is carried out according to the forecast data W_R by intervals (Figure 2). The technique can be used, which is similar to [8]. The initial is a graph P¹_C(t) = ρP_L(t) − P_LIM.

For the accepted value ρ, we define:

$$\mathsf{\Delta }{W}_{C26}=\rho \cdot W_{L26}-W_{LIM26}-W_{R26P}\cdot {\eta }_C.$$

(15)

If ΔW_B26MAX ≥ ΔW_B26 > 0 (ΔW_B26MAX corresponds ΔQ*₂₆ = 100 − Q*₆, is accepted Q*₆ = 20%), then Q*₂ > Q*₆ at ΔQ*₂₆ = 100ΔW_B26/W_B·η_C·η_B. A night battery charge is necessary.

The reference start value Q*_2R is determined with values of ΔQ*₂₃ and ΔQ*₂₄:

$$\mathsf{\Delta }Q{*}_{23}=\frac{W_{R23}\cdot {\eta }_C-W_{C23}}{0.01\cdot W_B\cdot {\eta }_C\cdot {\eta }_B},\mathsf{\Delta }Q{*}_{24}=\frac{W_{R24}\cdot {\eta }_C-W_{C24}}{0.01\cdot W_B\cdot {\eta }_C\cdot {\eta }_B}.$$

If ΔQ*₂₄ ≤ 0, then Q*_2R = 100%. If ΔQ*₂₄ > 0 and ΔQ*₂₃ ≤ 0, then taking into account the SB discharge at the interval (t₂, t₃) we accept the value Q*_2R = (100 − ΔQ*₂₄) with some margin Q*_2R ≥ 40% If ΔQ*₂₄ > 0, ΔQ*₂₃ > 0 and W_R23·η_C/W¹_C23 < 1.5 (W¹_C23, energy value for P¹_C(t)), then Q*_2R = (100 − ΔQ*₂₄) ≥ (Q*₆ + Δ) (Δ ≥ 10%).

For the considered cases, the reference value of the added power is P_C23 = P¹_C23.

With the high generation of RES in the morning (ΔQ*₂₄ > 0, ΔQ*₂₃ > 0, and W_R23·η_C/W¹_C23 ≥ 1.5) several options are possible:

• P_C23 = P¹_C23 with a minimum discharge of the battery at the interval (t₂, t₃) and Q*_2R ≥ Q*₆ + 10. However, in this case, it is possible to charge the battery to almost 100% already at the interval (t₂, t₃). With high generation at the interval (t₃, t₄) the underutilization of RES energy is inevitable;
• P_C23 = P_LIM, which will limit the degree of charge of the SB at the interval (t₂, t₃). However, in this case, we found a deep discharge of the battery and the necessity for overstatement Q*_2R and, as a result, there is an underutilization of RES energy.

The preferred option is when P_LC23 ≥ (P_C23 = P_R23·η_C) ≥ P¹_C23, and the reference repeats the graph of RES generation when limited from below—P¹_C23 and top—P_LC23. In this case, the SB charge at the interval (t₂, t₃) is not carried out, and Q*_2R is set to equal Q*₆. RES generation on the interval (t₃, t₄) must be sufficient to charge the battery, and ΔQ*₃₄ ≥ 80%.

Value P_C34 on the interval (t₃, t₄) [8]:

$$P_{C34}=\frac{W_{R34}\cdot {\eta }_C-0.01\cdot \mathsf{\Delta }Q{*}_{34}^{}\cdot W_B\cdot {\eta }_C\cdot {\eta }_B}{\left(t_4-t_3\right)}\le P_{LC34},$$

where ΔQ*₃₄ is determined by Q*_2R and ΔQ*₂₃, which were obtained above.

Upon reaching the value Q* ≥ Q*_d (Q*_d = 90–92%), SB charge was carried out at a constant value of voltage [27]. In this case, the SB charge current was determined by the curve I_B(Q*), and its value reduces. This leads to a limitation of the battery’s ability to store energy. Upon at Q* ≥ Q*_d, the value of P_C was determined by actual PV power generation as P_LC ≥ P_C = (P_PV·η_C − P_B) ≥ P¹_C. The providing condition P_LC ≥ P_C was achieved by reducing the PV generation power.

When using WG for a speed of 4.5 m/s (Table 2) at a value of ρ = 1.6, it can be accepted that m_P = 0.568, m = 10.05, and W_B = 513 Wh. When recalculating to a value of P_L = 5 kW, we achieved P_PVR = 14.2 kW, P_WR = 2.49 kW, and W_B = 12.825 kWh. That is, we found an overestimation of the installed WG power by 1.49 times in comparison with WG on 3 m/s.

The system of automatic regulation of the converter can be achieved with voltage stabilization in the DC link U_d [6,8,9,15]. Three proportional-integral (PI) voltage controllers (VC) were used: VCI_PV forms the reference of PV current; VCI_B forms the reference of SB current; and VCIg forms the reference of current in the PCC.

Thus, we have three channels:

• Control by PV generation, provide processing of taken value of current I¹_PV from MPPT or controller VCI_PV;
• Control by the charge of SB with the processing of taken value of current I¹_B from VCI_B or fixed value;
• Control by grid current I_g (reference of active power P_g) with the forming of the set value of the amplitude of grid current I¹_gm from VCIg or fixed value.

One controller was always used, and the remaining currents were set. The WG control channel operates independently in the MPPT mode.

To the specified value, ρ corresponds to the values P¹_C(t) and P¹_CLR(t), which are determined by the accepted load schedule. The value P_g is determined as P_gi = P_LCi − P_Ci (P_Ci, the actual current value of the added load power; P_LCi, the active load power, which is determined by the measured values of load currents and phase voltages) at P_LIM ≥ P_gi ≥ 0. For a three-phase version with load balancing by grid phases and a power factor close to 1, there is a value I¹_gm = √2P_gi/3U_gph (U_gph—phase voltage). For P_C, there is a restriction:

$$P_C=\{\begin{array}{l}\le P_{LC},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_R{\eta }_C>P^1{}_C,\\ P^1{}_C,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_R{\eta }_C\le P^1{}_C.\end{array}$$

PV operates in the MPPT mode under the following conditions:

• If Q* ≥ Q*_d and P_LC > P_C ≥ P¹_C. The current I_g (P_g) is set by the controller VCI_g. SB current set as I¹_B = I_BR (I_BR = 0.2 C_B—rated value), and its value is determined by I_B(Q*);
• If Q* < Q*_d, then the SB current is set by VCI_B, and the current of the grid is determined by the power P_g = P_LC − P_C.

The regulation of PV generation with restriction P_R at the level of P_R·η_C = P_LC + P_B is carried out at Q* ≥ Q*_d. In this case, the reference of PV current is carried out by VCI_PV, the SB current is set as I¹_B = I_BR, and reference I¹_gm is constant I¹_gm = 0 at P_g = 0.

The discharge of SB with current reference by controller VCI_B is possible at intervals (t₂, t₃), (t₄, t₅) at P_R·η_C < P_C, and on the interval (t₅, t₆)—with a given value of discharge current of SB.

If at Q* ≥ Q*_d P_LC = P_LCR and P_LC > P_C + P_B PV works with MPPT, then the current consumed from the grid (P_g) is set by controller VCI_g. The current of SB is set as I¹_B = I_BR, and its value is defined as I_B(Q*).

A common situation is P_LC ≠ P_CR. If P_LC < P_LCR and Q* < Q*_d, then power P_g = (P_LC − P_C) decreases; at Q* ≥ Q*_d, the value of P_C decreases and P_g = 0. If P_LC > P_LCR and Q* < Q*_d, then, when VCI_B operates, the charge current decreases, and SB can go into discharge mode. If P_LC > P_LCR and Q* ≥ Q*_d, then we have a corresponding increase in consumption from the grid.

The changes in operating modes are carried out at time intervals and within the interval when a certain value reaches the set value. If Q* ≥ Q*_d, that SB current is determined by the charge curve I_B(Q*) [27], and in the case of the actual value I¹_B > I_B(Q*), then the controller VCI_B turns into saturation mode. In this case, the ability of the battery to store energy is limited. As a result, the VSI input voltage U_d increases, and when its threshold value is reached, the corresponding controller is switched. That is, we have two conditions for switching regulators with the exclusion of the influence of transient processes.

5. Mathematical Model

Modeling was performed in MATLAB at the level of active powers. Known approaches were used [6,8]. The operation of the system was considered in time as a set of steady modes represented by the corresponding calculated expressions. Changing (switching) modes were carried out by time intervals and the taken conditions. To estimate the reduction in electricity costs at a single tariff rate (take its value equal to 1), coefficient k_E = W_LC/W_g was used (W_LC, LO load energy per day; W_g, energy consumed from the grid).

The values of the powers P_LCR(t), P_LC(t), P¹_C(t), P_W(t), and the PV power in the MPPT mode P_PVM(t) are set in a tabular form. These values are the initial ones for the calculation, and the rest of them are defined through them. The time intervals are set by variables t₂₃, t₂₆, t₅₆, and t₆₂, taking value 1 at the appropriate time interval. The auxiliary variables are given switching conditions and restrictions of values:

$$\begin{array}{l}q=\{\begin{array}{l}1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Q*\ge Q{*}_d,\\ 0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Q*\hspace{0.17em}<Q{*}_d.\hspace{0.17em}\end{array}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}p\upsilon =\{\begin{array}{l}1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_R\cdot {\eta }_C\ge P^1{}_C,\\ 0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_R\cdot {\eta }_C\hspace{0.17em}<P^1{}_C.\hspace{0.17em}\end{array}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{l}_C=\{\begin{array}{l}1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_C\ge P_{LC},\\ 0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_C<P_{LC}.\end{array}\\ c=\{\begin{array}{l}1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_{LC}\ge P_R\cdot {\eta }_C\ge P^1{}_{C23},\\ 0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_{LC}<P_R\cdot {\eta }_C\hspace{0.17em}<P^1{}_{C23}.\hspace{0.17em}\end{array}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}h=\{\begin{array}{l}1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\left(P_{LC}-P_{LCR}\right)>0,\\ 0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\left(P_{LC}-P_{LCR}\right)\le 0.\hspace{0.17em}\end{array}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}m=\{\begin{array}{l}1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{I}_{B62R}\ge I_{B62MIN},\\ 0,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{I}_{B62R}<I_{B62MIN}.\end{array}\\ qc=\{\begin{array}{l}1,if{P}_C<P_{LC},\\ 0,if{P}_C\ge P_{LC}.\end{array},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}w=\{\begin{array}{l}1,\mathrm{if}{W}_{R23}\cdot {\eta }_C/W_{CB23}\ge 1.5,\\ 0,\mathrm{if}{W}_{R23}\cdot {\eta }_C/W_{CB23}<1.5.\end{array}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}r=\{\begin{array}{l}1,\mathrm{if}{P}_{R62}\cdot {\eta }_C>P_{LC},\\ 0,\mathrm{if}{P}_{R62}\cdot {\eta }_C\le P_{LC}.\end{array}\end{array}$$

(16)

To measure the values of Q*_t and Q*₅, the sample-and-hold circuit is used. The current value of RES power, taking into account the PV control:

$$P_R\cdot {\eta }_C=P_W\cdot {\eta }_C\cdot t_{62}+\left(P_R\cdot {\eta }_C\cdot \left(\overline{q}+qc\right)+\left(P_c+P_B\right)q\cdot lc\right)\cdot t_{26}.$$

(17)

At interval (t₅, t₆) there is a discharge of the SB with a given current value. The value P_C56 is set with the average value of SB voltage U_BAV [8].

The current value of added power:

$$\begin{array}{l}{P}_C=P_{LC}\cdot t_{62}+P^1{}_C\left(t_{23}\cdot \overline{w}+t_{34}\cdot \overline{q}+t_{45}\cdot \overline{p}\overline{\nu }\right)+P_{C56}\cdot t_{56}+\left(P^1{}_{C23}\cdot \overline{c}+P_{LC}\cdot \overline{c}\cdot lc+P_R\cdot {\eta }_C\cdot c\right)w\cdot t_{23}\\ +\left(\left(P_R\cdot {\eta }_C-P_B\right)\cdot q\cdot \overline{lc}+P_{LC}\cdot q\cdot lc\right)\cdot \left(t_{34}+t_{45}\right),\end{array}$$

(18)

where P_C56 = I_B56R·U_BAV + h(P_LC − P_LCR), $I_{B56R}=\frac{0.01\cdot C_B\cdot \left(Q{*}_5-Q{*}_6\right)}{\left(t_6-t_5\right)}$.

Active power consumed from the DG

$$P_g=\left(P_{LC}-P_C\right)\cdot t_{26}+\left(P_{LC}+P_B-P_R\cdot {\eta }_C\right)\cdot t_{62}.$$

(19)

The reference of SB current at the interval (t₆, t₂) [8]:

$$I_{B62R}=\frac{0.01\cdot C_B\cdot \left(Q{*}_2-Q{*}_t\right)}{\left(t-t_2\right)},$$

(20)

where Q*_t—measured value with hourly (or less) discreetness.

It should be taken into account that at P_R62·η_C > P_LC62, to ensure the power balance, the SB charge current value must be at least:

$$I_{B62MIN}=\frac{P_{R62}\cdot {\eta }_C-P_{LC62}}{U_B}.$$

Then

$$I_{B62}=\{\begin{array}{l}\ge I_{B62MIN},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_{R62}\cdot {\eta }_C\ge P_{LC62},\\ I_{B62R},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_{R62}\cdot {\eta }_C<P_{LC62}.\end{array}$$

(21)

The first condition is necessary if the battery charge is not required or if the current I_B62R is small.

In general, the value of SB current:

$$\begin{array}{l}{I}_B=t_{62}\cdot I_{B62}\left(\overline{r}+m\cdot r\right)+I_{B62MIN}\cdot \overline{m}\cdot r\cdot t_{62}+t_{25}\cdot \frac{P_R\cdot {\eta }_C-P^1{}_C}{U_B}\cdot \left(\overline{q}+qc\right)\\ +I_B\cdot \left(Q*\right)\cdot q\cdot \overline{qc}\cdot t_{25}+t_{56}\cdot \frac{P_{C56}}{U_B}.\end{array}$$

(22)

The battery model is implemented following [6,8].

6. Modeling Results

The values of k_E are presented in

Table 5. Coefficient reduction in cost of electricity consumed from the grid.

Months	December	January	February	March	April	May	June	July	August	September	October	November
kE	1.575	1.706	2.15	2.2	2.758	4.176	2.984	2.24	3.246	1.825	2.138	1.69

for the days selected by the archive when PV generation P_PV(t) by intervals of time corresponds to the average monthly values. The values ρ = 1.6, m = 15, m_P = 0.568 were set. WG generation is taken for the actually selected days.

The oscillograms of load power P_LC, added (inverter) power P_C, maximum power of RES P_RM, the actual power of RES with an account of PV regulation P_Rf, WG power P_W, the power consumed from the grid P_g, SB current I_B for 6 December 2014, are shown in Figure 3 for different values of Q*₂. In this case, PV energy generation corresponds to the average monthly values by time intervals. For the clarity of oscillograms, the scale is taken as 2 Q* and 10 I_B. The load P_LC is equal to the specified value P_LCR. In the case of Figure 3b, about 14.00 h (when Q* achieves value Q*_d), curve P_C is approaching and then repeats the curve P_R(t) at decreasing P_g. From Figure 3a k_E = 1.575, for Figure 3b k_E = 1.573. In this case, by (15) for the accepted value ρ = 1.6, there is $\Delta W_{B26}\le 0$; therefore, the value of Q*₂ has virtually no effect on k_E. Note that the difference in the calculated value k_E = 1.504 (Table 5) with what was obtained during the simulation k_E = 1.575 is a conditioned difference in values W_R for 06.12.2014 relative to the monthly average value W_RAV = W_PVAV + W_WAV.

In Figure 4a, the oscillograms for 06 December 2014, with a decrease in the RES generation by two times (k_E = 1.21, ρ = 1.5), and in Figure 4b with a decrease in the RES generation by 3.5 times (k_E = 1.1, ρ = 1.4), when ΔQ*₂₆ ≈ 80%, are presented.

The oscillograms for June Day (30 June 2013) at different values of P_C23 and P_LC = P_LCR are presented in Figure 5a; at P_C23 = 120 W (k_E = 2.496, ρ = 1.6) in Figure 5b; at P_C23 = 200 W (k_E = 2.588, ρ = 1.6) in Figure 5c; at P_LC = 320 ≥ (P_C23 = P_R23) ≥ P¹_C23 = 120 (k_E = 2.984, ρ = 1.6). Due to an increase in the degree of discharge of the SB at the interval (t₂, t₃), the value Q*₂ has to increase (discharge from 43% to 34%). At the same time, there is no significant improvement in the use of renewable energy. In the case of Figure 5c, there is almost complete use of RES energy.

The oscillograms for May Day (31 May 2013) at P_LC ≠ P_LCR are shown in Figure 6 (k_E = 4.145, ρ = 1.6). Due to the reduction in the load at lunchtime, there is an incomplete use of RES. In this case, the increasing k_E is connected to the fact that WG almost completely covers the night consumption of LO.

7. Discussion of the Research Results

The all-the-year-round increase in LO load power relative to the existing limit of power on consumption from the grid with the possibility of reducing the installed power of RES and the electricity consumed from the grid is achieved by:

• The use of a WG as the auxiliary energy source of lower power. WG is chosen according to the average wind speed for the place of the LO location. This enables reducing the energy consumption from the grid at night and increases the meaning of total RES generation in the winter period, decreasing the installed PV power;
• Binding to the PV generation of the base schedule of added power for the accepted load schedule, taking into account the power limit for consumption from the grid. This makes it possible to reduce the RES energy required for added power implementation and to reduce the energy capacity of the SB;
• Improvement of PV energy utilization is achieved by choosing an intermediate value of the degree of power increase;
• The determination of the PV–WG system parameters by the average monthly values of RES energy according to the time intervals of the accepted load schedule. At the same time, WG is considered an auxiliary source of energy, and the possibility of a complete absence of wind is taken into account. The conditions for ensuring the power balance at night are also taken into account;
• Setting the inverter power equal to the value of the added power by limiting the consumption of active power from the grid at the level of the set limit. The values of the added load power and the SOC values of the battery for time intervals are formed according to the predicted and actual RES power. At certain time intervals, the value of the added power is set according to the graph of the actual power of RES generation. This contributes to a more complete use of RES energy;
• The exclusion of battery charge from the grid at night when generating renewable energy at the level of the average monthly in the spring–summer–autumn period, which helps to reduce electricity consumption;
• Using one deep discharge of the battery in the evening. This reduces the number of battery discharge cycles, which increases its service life;
• The use of real archival data of renewable energy generation for different seasons of the year with the choice of a processing period of 5–6 years in modeling increases the degree of reliability of the results.

This article is a development of work [8], where the increase in LO power was considered using PVS with SB. When the degree of power increase is ρ = 1.6, the ratio of the installed power of PV, SB, and the peak power of the load is 4.3:4:1. That is, the installed powers of PV and SB are overestimated. At the same time, the reduction in electricity consumption in winter is minimal 1.088–1.354, and in summer—before 2.946. A feature of the considered solutions is the use of an auxiliary WG of lower power in the PV system, which provides a significant addition of energy in winter. When the ratio of the installed powers of RES and SB to the load power is determined, the task with three variables is solved. It is an added condition that ensures energy balance. As a result, decreasing the installed PV power by 1.51 times and the energy capacity of SB by 1.56 times at WG power of only 0.334 from load power is achievable. The reduction in energy consumption in winter is 1.575–2.15; in summer—up to 4.

Some limitations should be identified regarding the use of the obtained results:

• The main load of LO is in the daytime; the load power decreases during the night;
• The maximum values of the degree of power increase are achieved in the spring–summer–autumn period;
• When the power of RES generation significantly decreases relative to the average monthly values, it is possible to forecast the limitation of the increasing degree of power;
• The task of optimization regarding the determination of the values of the power increase factor (ρ) and the installed power of RES was not solved in this work. The used approach is somewhat simplified for assessing the possibilities;
• An assessment of the reduction in the cost of electricity was undertaken for one tariff rate and was somewhat simplified. When modeling, days were selected when the PV generation was close to the average monthly values for the corresponding intervals of the load schedule. At the same time, the WG generation was actual for these days and differed from the average monthly values;
• When modeling, the taken schedule of the power generated by RES was used and did not account for the possible change of forecast.

The development of this work focused on the automatization of calculating the data of the average monthly generation of RES, obtaining an integral assessment of cost reduction for the year, and improving the principles of implementing the control system.

8. Conclusions

The basic calculation data are the values of the average monthly RES generation for the accepted load schedule, obtained from archive data for 5 years for the location of the LO.

The taken variant of the reference of added power in the daytime enables reducing the required value of RES energy. With an increase in power by 1.6 times, there is a decrease in energy by 15–19%, which contributes to a decrease in the installed power of RES. The choice of system parameters from several conditions was proven. The key conditions are excluding the energy consumption from the grid on added power in the daytime, the coefficients of PV energy use and cost reduction for electricity consumption from the grid, and ensuring the energy balance in the nighttime.

With this technique for choosing the parameters, it is advisable to increase the power up to 1.7 times. It was shown that the system could operate without a significant deterioration in performance when the load deviates relative to the set value of power increase within large enough limits.

It was shown that when WG is chosen for an average wind speed for a place of LO location, the WG power can be less than the installed PV power by 5.51–8.33 times. At the same time, the ratio of the installed power of the PV, WG, the energy capacity of the SB, and the peak load power was P_PVR:P_WR:W_BR:P_L = 2.84:0.334:2.565:1 and P_PV:P_W:W_B:P_L = 2.84:0.498:2.565:1.

The principles of control realization with reference to the added power by the taken schedule of load tied to RES generation power and the state of SB charge were considered. The correction of the increasing power value and the state of the night charge of SB was carried out by forecasting the RES generation of the next day. A DOD limit of up to 20% was accepted, with one deep discharge per day. The description of the steady-state operating modes and their change in the process of the system functioning was formalized. The transient processes were not taken into account. A model of energy processes in the system for the daily operation cycle with an assessment of the possibilities for reducing the consumption of electricity from the grid was implemented. The simulation results show the possibility of reducing the cost of the electricity consumed from the grid from 1.57 times (winter) to 4.17 times (summer) with an average monthly generation of RES for one tariff rate and increasing power by 1.6 times. With a decrease in RES generation relative to the average monthly values in winter by 2 and 3.5 times, it is possible to increase power by 1.5 and 1.4 times while reducing electricity consumption by 1.2 and 1.1 times. Setting the added power during the morning peak hours according to the RES generation power schedule allows for reducing costs by up to 15% in the spring–summer–autumn seasons with an increase in the degree of use of RES energy.