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
PW = 12 kW, and the power of PV is
PPV = 39.2 kW. In [
7], the dependencies
PPV(
t) and
PW(
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
PPVR and WG installed power
PWR to peak load power
PL is
PPVR:
PWR:
PL = 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
PPVR and the energy capacity
WBR of SB. However, the obtained values of
PPVR and
WBR are somewhat overestimated. The ratio of
PPVR and
WBR to the peak load power
PL is
PPVR:
WBR:
PL = 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.
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
PLIM 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
IPV [
8,
9,
14,
15]. DC/DC3 has bilateral conductivity and provides charge/discharge of SB with the specified value of current
IB. 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
PPVR = 1 kW and the WG type [
25] at the power
PWR = 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 shows the values of the average monthly PV generation per day
WPVAVD, as well as by time intervals (
WPV23,
WPV34,
WPV56) in Kyiv. There are similar data for WG
WWAVD (
WW24,
WW56,
WW62). 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
PW of WG, a typical dependence [
26]
of the output-conditional unit WG power
on wind speed
was used, which has the form:
where
PW,
PWR is the current and rated value of WG power, respectively;
ν,
νR is the current and rated value of wind speed, respectively;
νMIN is starting wind speed;
νMAX 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]
PLC(
t) =
ρPL(
t) (
ρ, the coefficient of power increasing;
PL(
t), the basic load schedule, according to
Figure 2). At the same time,
PLC =
PLg +
PC (
PLg), load power, which is provided from grid electricity (
PLg ≤
PLIM),
PC, is the load added power, which is provided due to the energy of RES and SB). When calculating, we accepted that
PLIM is equal to the peak load power
PL = 200 W.
The added power value can be determined as
PC(
t) =
PL(
t)(
ρ – 1) [
8]. If to determine the value
PC(
t) in the daytime (interval (
t2,
t6))
PC26(
t) =
ρPL26(
t) –
PLIM, then, respectively, the RES energy
WC26, which is required to provide it, decreases
where
WL26 is the energy consumed according to the base load schedule,
.
The total energy
WR generated by PV and WG is [
6]:
where
m and
mP 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/
QR,
,
QR—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
WR26 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 (Δ
Q*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:
where
WgR26 is the reduction in energy consumption from the grid,
WC26 is the energy consumed by the added load, Δ
WB26 is the energy provided by the battery,
WB = UBCB is the energy capacity of SB,
UB is the voltage of SB,
CB is the capacitance of SB (Ah),
ηC is the efficiency of the converter, and
ηB is the efficiency of SB.
The value of
WgR26 > 0 may be during hours of high PV generation
tda, when
PR·ηC >
PC +
PB (
PB) =
UB·IB, the value of power for battery charging). The exception of generation to the grid is provided by the limitation of
PgR ≤
PLIM, which was achieved by controlling (reducing) PV power generation. The limiting case is
WgR26 =
PLIM·
tda [
8].
At night, the SB consumes energy:
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,
When there are a few variables (coefficients
mP,
m η WB), 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), 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
WgR26 = 0.
In the absence of WG generation (
WW26→0) and at the average monthly value of PV generation by (2):
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 (Δ
Q*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
WgR26 = 0 by (2) occurs when
We accept the value of
ρ = 1.6 when using WG for a speed of 3 m/s. The minimum value
WPV26 in the spring–summer–autumn period occurs in October (
Table 1); it corresponds to the minimal value of
mP = 0.568.
Due to the longer duration of the evening peak (4 h), the biggest value of
WC46 occurs in spring and autumn. To calculate
WB by (4), we used the minimum value of
WPV46 (March in
Table 1) at
WW46→0 and Δ
Q*46 = 80%; we achieved
WB = 662 Wh (Δ
WB46 = 478 Wh). This value is overstated when not accounting for
WW46.
Since the electricity generation into the grid is excluded, it is necessary to confirm the energy balance at night time (interval (
t6,
t2)):
where Wg62 is the energy consumed from the grid.
The maximum value is
WW62MAX =
PWMAX(
t2 −
t6) (maximum value WG generation power is
PWMAX = 1.1
PWR [
25]). In this case, the value
WW62MAX exceeds the load consumption, and there is no consumption from the grid, i.e.,
Wg62 = 0. The maximum value Δ
WB62 corresponds to Δ
Q*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]:
With low PV generation in winter (
WPV26→0) by (2):
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 WB by (4) for the December conditions, taking into account the generation of WG. We accept that the generation of RES WR46 is 0.5 from the average monthly value with the obtained values m and mP. In this case, WB = 572 Wh (ΔWB46 = 413 Wh). Under similar conditions for March, WB = 490 Wh (ΔWB46 = 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:
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:
The option for determining system parameters when
ρ = 1.6 in December is given in
Table 2. The values of
WB 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 mP = 0.568, and m = 15 at value ΔWB26 = 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
WB increases with increasing
mP 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:
To assess the efficiency, we used the coefficient of cost reduction for electricity [
8] (with one tariff rate and full use of RES energy):
where
is the total energy consumed by the load.
The values of kPV were estimated for June, and the value of kE was estimated for December with the average monthly generation of RES ΔWB26 = 0 and WgR26 = 1400 Wh. When changing mP from 0.568 to 1, the values of kPV decrease from 0.845 to 0.582 (1.45 times), as well as the values of kE, which decrease from 1.504 to 1.409 (by 1067 times). Thus, it is advisable to take the meaning of mP close to the minimum (6).
It can be accepted that mP = 0.568, m = 15 for the value ρ = 1.6. Furthermore, we chose the average value WB = 513 Wh (for March WB = 490 Wh, for December WB = 572 Wh). When recalculating, we used a ratio of PL/PPVR/PWR/WB = 1/2.84/0.334/2.565.
The calculated values of the parameters depending on the value
ρ are presented in
Table 3. 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
mP = 0.568, and
m = 15 when changing
ρ = 1.5–1.8 (
Table 4) without a night battery charge. In this case, with an increase in
ρ, the use of PV in comparison with
Table 3 increases, but
kE 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 Δ
Q*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
WR26P. In a general case:
We calculate the value ρ at WgR26 = 0 and ΔWB26 = 0. Then the following algorithm for setting the maximum value ρ is possible:
If ρ < 1.5, then we accept ΔWB26MAX (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 WgR26 at ΔWB26 = 0;
If 1.8 > ρ ≥ 1.7, then we accept ΔWB26 at ΔQ*26 = 15–20% and recalculate the value ρ ≤ 1.8;
If 1.7 > ρ ≥ 1.5, then we accept ΔWB26 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 WR26P. With low RES generation, the value of ρ is specified (decreases) by (14) at ΔWB26MAX for ΔQ*26 = 80% and WgR26 = 0.
Setting the graphs
PC(
t) and
Q*(
t) for the accepted value
ρ is carried out according to the forecast data
WR by intervals (
Figure 2). The technique can be used, which is similar to [
8]. The initial is a graph
P1C(
t) =
ρPL(
t) −
PLIM.
For the accepted value
ρ, we define:
If ΔWB26MAX ≥ ΔWB26 > 0 (ΔWB26MAX corresponds ΔQ*26 = 100 − Q*6, is accepted Q*6 = 20%), then Q*2 > Q*6 at ΔQ*26 = 100ΔWB26/WB·ηC·ηB. A night battery charge is necessary.
The reference start value
Q*2R is determined with values of Δ
Q*23 and Δ
Q*24:
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 WR23·ηC/W1C23 < 1.5 (W1C23, energy value for P1C(t)), then Q*2R = (100 − ΔQ*24) ≥ (Q*6 + Δ) (Δ ≥ 10%).
For the considered cases, the reference value of the added power is PC23 = P1C23.
With the high generation of RES in the morning (ΔQ*24 > 0, ΔQ*23 > 0, and WR23·ηC/W1C23 ≥ 1.5) several options are possible:
PC23 = P1C23 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;
PC23 = PLIM, 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 PLC23 ≥ (PC23 = PR23·ηC) ≥ P1C23, and the reference repeats the graph of RES generation when limited from below—P1C23 and top—PLC23. 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
PC34 on the interval (
t3,
t4) [
8]:
where Δ
Q*34 is determined by
Q*2R and Δ
Q*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
IB(
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
PC was determined by actual PV power generation as
PLC ≥
PC = (
PPV·ηC −
PB) ≥
P1C. The providing condition
PLC ≥
PC 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
mP = 0.568,
m = 10.05, and
WB = 513 Wh. When recalculating to a value of
PL = 5 kW, we achieved
PPVR = 14.2 kW,
PWR = 2.49 kW, and
WB = 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
Ud [
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 I1PV from MPPT or controller VCIPV;
Control by the charge of SB with the processing of taken value of current I1B from VCIB or fixed value;
Control by grid current Ig (reference of active power Pg) with the forming of the set value of the amplitude of grid current I1gm 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
P1C(
t) and
P1CLR(
t), which are determined by the accepted load schedule. The value
Pg is determined as
Pgi =
PLCi −
PCi (
PCi, the actual current value of the added load power;
PLCi, the active load power, which is determined by the measured values of load currents and phase voltages) at
PLIM ≥
Pgi ≥ 0. For a three-phase version with load balancing by grid phases and a power factor close to 1, there is a value
I1gm = √2
Pgi/3
Ugph (
Ugph—phase voltage). For
PC, there is a restriction:
PV operates in the MPPT mode under the following conditions:
If Q* ≥ Q*d and PLC > PC ≥ P1C. The current Ig (Pg) is set by the controller VCIg. SB current set as I1B = IBR (IBR = 0.2 CB—rated value), and its value is determined by IB(Q*);
If Q* < Q*d, then the SB current is set by VCIB, and the current of the grid is determined by the power Pg = PLC − PC.
The regulation of PV generation with restriction PR at the level of PR·ηC = PLC + PB is carried out at Q* ≥ Q*d. In this case, the reference of PV current is carried out by VCIPV, the SB current is set as I1B = IBR, and reference I1gm is constant I1gm = 0 at Pg = 0.
The discharge of SB with current reference by controller VCIB is possible at intervals (t2, t3), (t4, t5) at PR·ηC < PC, and on the interval (t5, t6)—with a given value of discharge current of SB.
If at Q* ≥ Q*d PLC = PLCR and PLC > PC + PB PV works with MPPT, then the current consumed from the grid (Pg) is set by controller VCIg. The current of SB is set as I1B = IBR, and its value is defined as IB(Q*).
A common situation is PLC ≠ PCR. If PLC < PLCR and Q* < Q*d, then power Pg = (PLC − PC) decreases; at Q* ≥ Q*d, the value of PC decreases and Pg = 0. If PLC > PLCR and Q* < Q*d, then, when VCIB operates, the charge current decreases, and SB can go into discharge mode. If PLC > PLCR 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
IB(
Q*) [
27], and in the case of the actual value
I1B >
IB(
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
Ud 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.