Evaluation of the Effectiveness of Joint Use of Wood and Other Renewable Energy Sources in the Baikal Region

: This paper addresses the assessment of woody biomass resources in Russia and the Baikal region. The analysis of the literature demonstrates that the Baikal region has considerable amounts of waste from the logging, timber processing, and pulp and paper industries (up to 220 PJ). A review of utilization technologies for woody biomass demonstrates that the existing technologies based on biomass gasiﬁcation are promising for energy purposes. The gasiﬁcation of biomass for small-capacity power plants has some advantages compared to its combustion. This paper considers an autonomous power system that consists of photovoltaic converters, wind turbines, storage batteries, a biomass gasiﬁcation power plant, and a diesel power plant. A mathematical model used to optimize the system’s structure ﬁnds the minimum of the total discounted costs for the creation and operation of the system with some constraints met. Based on mathematical modeling, the cost-effectiveness of such a power supply system is assessed for different climatic zones of the Baikal region and the coastal area of Lake Baikal. The ﬁndings indicate that the optimal solution is the integration of various renewable energy sources in hybrid power systems. The proportion of energy sources of different types in the installed capacities is found. The study demonstrates that the optimal structure of the power system can provide signiﬁcant savings (the total discounted costs are reduced by almost 2.5 times compared to the option using a diesel power plant alone).


Introduction
The energy industry that fulfills the principles of sustainable development requires the minimization of emissions of pollutants generated by burning fossil fuels, including greenhouse gas emissions that negatively affect the climate. The most effective alternative to fossil fuel energy in terms of environmental performance is renewable energy sources (RES). Currently, more than a hundred countries are developing programs to support the adoption of renewable energy [1]. In some cases, the issue of creating energy systems based exclusively on renewable energy sources is raised [2].
Among RESs, solar and wind energy sources are developing at the fastest pace [1]. Their key feature is the random (stochastic) nature of power generation that depends on variable weather conditions. In this regard, they require either their capacity to be backed up by other energy sources or the use of energy storage units (batteries). Mutual redundancy also takes place in hybrid energy systems that include different types of RESs [3][4][5]. Solar and wind energy conversion technologies have recently become economically feasible, but problems remain in meeting end-user requirements for reliability and uninterrupted electric power supply. An important renewable energy source is woody biomass, the burning of which, first, recycles waste from the forest and wood processing industry and, second, does not change the balance of CO 2 in the atmosphere [6,7].
Maps image was used), the main part of the territory is colored green. This is the woodlands. The area of the Baikal region exceeds 1.55 million square kilometers (9.1% of the territory of the Russian Federation), and it is home to about 4.5 million people [14]. Almost half of the region's territory is in the Irkutsk region, where 2.4 million people live.
It is known that in the Baikal region multi-year average wind speeds (at a height of 10 m) are 2-6 m/s (they are the highest in the middle part of Lake Baikal), and the annual solar radiation incident on a horizontal surface ranges from 900-1000 kW·h/m 2 in the north to 1300-1400 kW·h/m 2 in the south [8].
One of the features of the region is its high forest cover. Forest area occupies nearly 64% of the territory of Buryatia, 70% of the territory of Zabaykalsky Krai, and 83% of the territory of the Irkutsk region [15]. For comparison, the forest cover ratio for the Russian Federation as a whole is 46.4% [16]. Forests are not only a source of timber and various products, they also perform essential ecosystem functions by helping to stabilize the composition of the atmosphere.
About 17% of Russia's total timber reserves are concentrated in the Baikal region, including 12% in the Irkutsk region [11]. The available significant timber reserves served as the basis for the timber industry. Enterprises of the sector produce industrial wood, lumber, pulp, cardboard, and paper. Table 1 shows the production volumes of the main timber products in Russia (logging and wood processing) in 2010-2017 [17][18][19]. Note: *-million tons. Sources: EMISS (Unified Interdepartmental Information and Statistical System) [17][18][19]. The area of the Baikal region exceeds 1.55 million square kilometers (9.1% of the territory of the Russian Federation), and it is home to about 4.5 million people [14]. Almost half of the region's territory is in the Irkutsk region, where 2.4 million people live.

Production Volumes of the Timber and Forestry Industry
It is known that in the Baikal region multi-year average wind speeds (at a height of 10 m) are 2-6 m/s (they are the highest in the middle part of Lake Baikal), and the annual solar radiation incident on a horizontal surface ranges from 900-1000 kW·h/m 2 in the north to 1300-1400 kW·h/m 2 in the south [8].
One of the features of the region is its high forest cover. Forest area occupies nearly 64% of the territory of Buryatia, 70% of the territory of Zabaykalsky Krai, and 83% of the territory of the Irkutsk region [15]. For comparison, the forest cover ratio for the Russian Federation as a whole is 46.4% [16]. Forests are not only a source of timber and various products, they also perform essential ecosystem functions by helping to stabilize the composition of the atmosphere.
About 17% of Russia's total timber reserves are concentrated in the Baikal region, including 12% in the Irkutsk region [11]. The available significant timber reserves served as the basis for the timber industry. Enterprises of the sector produce industrial wood, lumber, pulp, cardboard, and paper. Table 1 shows the production volumes of the main timber products in Russia (logging and wood processing) in 2010-2017 [17][18][19]. The Irkutsk region consistently ranks first among all Russian regions in the volume of logging (23-36 million m 3 /year, Table 2) with a share of 13-17% in all-Russian logging. In 2017, the Irkutsk region was also the leader in the production of lumber (4.8 million m 3 /year, or 18.6% of all-Russian production) [11]. In Buryatia and Zabaykalsky , 12, 1254 Krai, the number of enterprises for wood processing and production of related products is insignificant [20]. About 3.8 thousand tons of wood waste burns annually in fires in the Irkutsk region, causing significant environmental damage [21]. Disposal of this waste will help avoid littering of areas, forest fires, and pollution of surface water and groundwater, which will positively affect the environmental situation in the logging and wood processing areas.

Estimates of Woody Biomass Resources in Russia and the Irkutsk Region
According to current standards for waste generation [12,13], about 75-127 million m 3 (101 ± 26 million m 3 ) of wood waste is generated annually in Russia (Table 3). The standard value of waste generation for pulp and paper production (only bark is taken into account) is 0.54 m 3 /t, for wood pulp-1.83 m 3 /t. The most probable total estimate of the volume of waste wood is 90-110 million m 3 /year. Note: data on paper pulp and wood pulp are converted from tons to cubic meters according to the following ratios: 1 ton of cellulose = 4.52 m 3 , 1 ton of wood pulp = 2.62 m 3 [12,13]. Table 4 shows the results of estimating the amount of wood waste generated annually in the Baikal region at the most likely waste generation rates. The calculations used specific data on the balances of timber used in the Irkutsk region [15], which were interpolated to the other two entities of the region under consideration. The calculated standard values of wood waste generation assumed in Table 4 are for logging-0.33 (including branches and twigs, trunk tops, bark, and stumps), for sawmilling-0.80 (including sawdust, lumpy waste, bark, and chips), for plywood production-1.84 (including sawdust, lumpy waste, trimmings, cores, bark, chips), and for pulp production-0.12 (the volume factor of bark on pulpwood bolts). Notes: PP-plywood production, PPP-pulp and paper products.
The main resources of waste wood fuel are concentrated in the Irkutsk region; in Buryatia and Zabaykalsky Krai they are an order of magnitude smaller. The total volume of wood waste is about 19 million m 3 , including almost 90% in the Irkutsk region.
The bulk of waste is logging waste (13.4 million m 3 /year). With a heating value of 11-15 MJ/kg (for wet and naturally dried wood, respectively) [22] and a waste density of 850 kg/m 3 , its energy equivalent is 125-171 PJ, or 3-4 million tons of oil equivalent (toe). The energy equivalent of other waste products at a heating value of 9.5-11 MJ/kg and a waste density of 800 kg/m 3 is estimated to be 43-49 PJ, or 1.0-1.2 million toe. The total energy equivalent of wood waste is about 168-220 PJ (4.0-5.3 million toe).
A relatively new and promising product of wood waste processing is currently pellet fuels (pellets). Pellets are widely used in economically developed countries of Europe, America, and Asia for burning for heating purposes as a coal substitute (or together with it) and for electricity generation. Almost all Russian pellet producers export their products to the European Union, Japan, and South Korea.
Thus, the Baikal region has significant amounts of waste woody biomass (waste from logging, wood processing, and pulp and paper industry)-about 19 million m 3 /year or 5.6 million toe. It not only can but must be recycled and disposed of to prevent environmental and economic damage.
Management of this waste will help avoid littering of the areas, forest fires, and pollution of surface water and groundwater, which will have a positive effect on the environmental situation. Regional support programs are needed to more quickly adopt technologies of using wood waste.

Technologies of the Use of Wood for Energy Purposes
Electricity generation from biofuels is possible in two ways: either in a water Rankine cycle, which receives heat from the furnace to burn biofuel (including blended with coal [23,24]); or in Brayton and combined cycles, in which the fuel is the combustible gas obtained by pyrolysis or gasification of biofuel. The efficiency of the options depends to a significant extent on the capacity of the unit. As a rule, the water Rankine cycle is economically justified for capacities of the order of several MWs to several tens of MW [25,26]. It is difficult for gasification technologies to compete with combustion technologies in this area (although some authors suggest using gasification with small gas turbines [27][28][29]). However, for smaller capacities (up to 1 MW), which are of most interest in terms of creating autonomous energy systems, gasification turns out to be a promising way to obtain electricity from biofuels [26,30]. In some cases, it is possible to arrange the organic Rankine cycle, even at small capacity plants [31,32].
In this paper, we consider electricity production based on the gasification of biomass rather than its direct combustion. The reasons for this are higher efficiency of biomass for low power plants [33] and fewer technical problems associated with slagging and corrosion damage to equipment.
Production of liquid biofuels (e.g., stabilized pyrolysis liquids [34]) suitable for combustion in diesel generators (usually in a mixture with the specification fuel [35]) is not considered in this study, as more complicated process flow diagrams and chemicals are needed to produce such fuels.
The choice of gasification method and heat engine type depends on many factors. Biofuels generally have a low calorific value (compared to fossil fuels), which is why their thermochemical conversion does not allow achieving high temperatures. In this connection, the raw combustible gas obtained from the gasification of biofuels often contains significant amounts of tar products (up to several g/Nm 3 ), which can adversely affect the durability and reliability of gas engines (both internal and external combustion ones). Therefore, raw gas usually needs additional treatment (including filtration, adsorption, water flushing, and thermal purification [36]). Gasification processes are known that produce gas with a low content of tar products: for example, the downdraft process (tar content in the produced gas is of the order of tenths of g/Nm 3 ); and multi-stage processes (less than 0.1 g/Nm 3 ). Quality requirements for gas for internal combustion engines are given in [37]: according to these data, the tar content should not exceed 0.1 g/Nm 3 .
External combustion engines are less demanding in terms of gas purity, as the combustion of gas together with tar takes place in an external heat exchange chamber. In this case, gas combustion is preferable to heating by combustion products of biofuels because this reduces the pollution of heat exchange surfaces by fly ash. Nevertheless, the formation of tar deposits and their coking on the outer surface is not excluded. In addition, the engine power is limited by the intensity of the heat transfer. On the other hand, updraft gasification processes can be used, which are less sensitive to the moisture content of the feedstock [38,39]. The efficiency estimates for the Stirling engine running on biofuels are given in [27] (from 10% at 10 kW to 20% at 200 kW).
Internal combustion engines are generally more efficient, although maximum power is usually reduced by 20-30% with producer gas compared to a specification fuel (natural gas, diesel, or gasoline) [31,40,41]. Optimal operating modes are shifted to the area of lower air-flow rates, and due to the lower combustion temperature, nitrogen oxide emissions are reduced [42]. In [43], the thermal efficiency of about 35% with the combustion efficiency of 93-97% was achieved by burning gas with a tar content of about 20 mg/Nm 3 . However, there were condensation deposits on the piston rings despite the low tar concentration. In [37], the thermal efficiency of a gasoline engine running on producer gas was estimated at 15-20%. In [44], experimental studies have shown the maximum thermal efficiency of internal combustion engines of the order of 25%. Authors of [45,46] obtained the thermal efficiency of 19-22% at a power of 5 kW by using agricultural and household waste as fuel.
Thermal efficiency values of 12% to 24% (for power of 2-20 kW(e)) are given in [40]. Higher efficiency values are promised by manufacturers of gasification-based mini-CHPs [47] (about 30%, if one estimates it as the total efficiency of the plant). This is probably due to the scale effect: as the power increases, the efficiency tends to increase [48].
Engine exhaust gases are generally used for heating the air, and for drying and torrefying the fuel [49]. In multi-stage gasification processes, the heat of the exhaust gases is used to perform pyrolysis of biofuel [50]. As mentioned above, sometimes, this heat is used to implement the organic Rankine cycle. Finally, it can be used for house heating [38,51].
The fuel cells make it possible to significantly enhance the efficiency of electricity generation. This, however, requires thorough gas cleaning, not only from tar and particulate matter but also from some sulfur and nitrogen compounds. For example, in [52], the efficiency of a plant with a fuel cell and organic Rankine cycle at the exhaust is almost 55%. In [53], the combination of the Stirling engine and fuel cell at optimal gas distribution yields the efficiency of the plant of about 40%. With a fuel cell used without engines, the estimated efficiency of power generation is 30% [54][55][56][57]. The authors [58] conducted a three-day experiment on the operation of a fuel cell using the producer gas obtained from the multi-stage gasification of biofuel, with the cell efficiency of about 40%.
Combination with other renewable energy sources can, in some cases, increase the reliability of the energy supply. For example, a gasifier plant can operate in the baseload state, smoothing out power output dips in solar and wind installations (for example, due to the accumulation of combustible gas in dedicated storage facilities) [10,59,60]. Solar concentrators and thermal energy storage systems can be used to heat a gasification reactor [61,62], including operation in hybrid operating modes, when the blowing agent in excess heat is water steam, and in heat shortage, it is air [63].
According to estimates [64], the auxiliary needs of a gasification-based power plant are about 16-18% of the generated power. This energy is mainly used for fuel conditioning and compressor operation.
A summary of the data available in published research is shown in Figure 2. The bulk of the points indicate power plants using combustible gas in an internal combustion engine, but already at a capacity of about 1 MW(th), the efficiency values of such power plants are close to the limit (about 30%). Fuel cells, as mentioned above, demonstrate better performance but prove to be the most demanding in terms of operating conditions. Mini-GTUs in the power range of the order of 1 MW(th) are not superior to combustion engines in terms of their specifications, even though in the case of its capacity being of the order of 10 MW(th), they already prove more preferable. In this study, we consider a gasifier unit with a capacity of less than 1 MW(th) and assume that the resulting gas is used to power the internal combustion engine.
particulate matter but also from some sulfur and nitrogen compounds. For example, in [52], the efficiency of a plant with a fuel cell and organic Rankine cycle at the exhaust is almost 55%. In [53], the combination of the Stirling engine and fuel cell at optimal gas distribution yields the efficiency of the plant of about 40%. With a fuel cell used without engines, the estimated efficiency of power generation is 30% [54][55][56][57]. The authors [58] conducted a three-day experiment on the operation of a fuel cell using the producer gas obtained from the multi-stage gasification of biofuel, with the cell efficiency of about 40%.
Combination with other renewable energy sources can, in some cases, increase the reliability of the energy supply. For example, a gasifier plant can operate in the baseload state, smoothing out power output dips in solar and wind installations (for example, due to the accumulation of combustible gas in dedicated storage facilities) [10,59,60]. Solar concentrators and thermal energy storage systems can be used to heat a gasification reactor [61,62], including operation in hybrid operating modes, when the blowing agent in excess heat is water steam, and in heat shortage, it is air [63].
According to estimates [64], the auxiliary needs of a gasification-based power plant are about 16-18% of the generated power. This energy is mainly used for fuel conditioning and compressor operation.
A summary of the data available in published research is shown in Figure 2. The bulk of the points indicate power plants using combustible gas in an internal combustion engine, but already at a capacity of about 1 MW(th), the efficiency values of such power plants are close to the limit (about 30%). Fuel cells, as mentioned above, demonstrate better performance but prove to be the most demanding in terms of operating conditions. Mini-GTUs in the power range of the order of 1 MW(th) are not superior to combustion engines in terms of their specifications, even though in the case of its capacity being of the order of 10 MW(t), they already prove more preferable. In this study, we consider a gasifier unit with a capacity of less than 1 MW(th) and assume that the resulting gas is used to power the internal combustion engine.

Methods for Assessing the Economic Performance of Energy Systems with Renewable Energy Sources
The creation and operation of renewable energy sources, as well as hybrid energy systems that include them, can be considered as an investment project; to evaluate its economic feasibility one applies standard methods [65].
The criterion to judge the performance of an investment project is the net present value (NPV):Ê where R t and Z t are the outcomes and costs of the project in the year t expressed in monetary terms and d is the annual discount rate. The project outcomes are equal to the proceeds from the sale of the generated energy R t = p t Q t (p t is the price, Q t is the annual sales volume).
The key defining feature of solar and wind installations is the operation in an uncontrolled stochastic mode. In this regard, the following factors should be taken into account when evaluating the performance of wind turbines and analyzing the feasibility of their adoption: -Dependency of output on probabilistic characteristics; -Operation in an energy system that includes backup energy sources; - The ability to accumulate generated energy and its subsequent use during periods of idling operation.
For preliminary evaluations and comparisons of energy sources of different types, the cost of energy (in particular, electric power) is used [9,10,65]. The cost of energy is by definition equal to such a fixed price (p t = p = const) that yields the NPV (1) equal to zero. Then, it follows from (1) that: The cost of energy (2) is the minimum price at which the energy supply project is still feasible (Ê = 0); it is equal to per-unit costs (the ratio of total discounted costs to total discounted energy output). The best energy source is deemed to be the one that ensures the lowest cost of energy.
In the simplest case, the Formula (2) can be reduced to the form [65]: Here, k is specific investment, CF is the capacity factor, H = 8760 h/yr, CRF is the capital recovery factor, µ is annual fixed costs (as a percentage of capital expenditures), p F is the fuel price (tons of coal equivalent), and η is the efficiency. The last summand for wind and solar energy sources is zero, as the price of fuel for them is zero (they consume a free resource).
If necessary, Formula (3) can be transformed to take into account the terms of construction, operation, and dismantling of the energy source, co-generation of electricity and heat, energy losses and auxiliary energy costs, the escalation of the fuel price over time, and other factors [65].
The energy cost criterion is obtained by assuming that all of the energy produced is delivered to the consumer. Renewable energy sources with a stochastic mode of operation almost always operate in the energy system, which, by backing them up with controlled energy sources and storage batteries, makes it possible to provide a reliable energy supply to consumers. In hybrid energy supply systems, estimates of the cost of energy should be supplemented by taking into account the system effects that arise due to the presence of interconnections between energy sources of different types and energy storage facilities [65]. Such system effects are usually taken into account by applying dedicated mathematical models.
Mathematical modeling of energy systems with renewable energy sources has been the subject of a vast body of research [66][67][68][69][70][71][72][73][74][75][76][77][78]. In this case, the objects of research can be divided into two categories: large-scale use of renewable energy sources, operating together with centralized energy systems, and stand-alone local energy systems that include renewable energy sources along with controlled fossil fuel energy sources. In the latter case, energy storage and the interdependence of operating states of energy sources of different types play a more significant role.
The prospects for the large-scale use of solar and wind energy in the Mongolian part of the Gobi Desert are shown in a study by Otsuki [79]. Findings have established that the role of wind and solar power plants in total electricity production can be quite large, but the question of the transition to carbon-free energy is not raised.
Bogdanov and Breyer estimated the number of hours of installed capacity utilization of hybrid solar-wind installations and the prospective cost of the electricity they generate [80]. They demonstrated the possibility of creating an energy system of the region based only on renewable energy sources. However, an uninterrupted power supply in their process-flow diagrams is impossible without the use of hydroelectric power plants and biomass-fired power plants.
At present, along with the expansion of centralized power supply systems that include renewable energy sources, there is an increasing tendency to switch to a dedicated power supply based on distributed power generation [81]. In Russia and in the Baikal region, this can be facilitated by the location of consumers in remote and isolated areas. They receive power from diesel power plants, the delivery of fuel for which can have a complex multilink transport scheme, which is reflected in the cost of power generation. In this regard, the creation and implementation of highly efficient hybrid energy complexes, including wood biomass-fired power plants, is a relevant task.
The effectiveness of energy systems with RES is increased by the joint use of energy sources of different types and energy storage [67,68]. Hybridization of renewable energy resources can help to smooth out their variability and achieve a synergy effect, as some RES types complement each other [80], i.e., due to more accurate tracking of the load profile, the capacity factor of RES power utilization increases. In some areas of the world (Patagonia, the Atacama Desert, Tibet, the Horn of Africa, as well as areas on the borders of Libya, Niger, and Chad), hybrid wind-solar installations can operate with the number of hours of installed capacity utilization of about 6000-6500 h per year [80]. In Russia, conditions for the development of solar-wind energy are much more modest, primarily because of the relatively low incident solar radiation.
Energy plants based on pyrolysis and biomass gasification processes are used as part of hybrid energy systems with renewable generation to cover the shortage of generation by wind and solar plants [5,59]. This is due to the possibility of guaranteed power generation and the significant energy potential of biomass and wood waste. Biomass gasification can foster the replacement of expensive diesel generators, often used as part of stand-alone systems, particularly in order to provide power supply in the rural sector of developing countries [30,59,60].
Donskoi et al. demonstrated that the multi-stage gasification process, in which the pyrolysis and gasification stages are separated from each other, ensures favorable environmental performance. At the same time, the efficiency of multi-stage gasification is 10-20% higher than that of conventional single-stage processes [82]. Kozlov et al. in [9,83] reviewed the technologies of multi-stage gasification and demonstrated its advantages.
In [84], comparative studies demonstrate that hybrid systems containing RES based on wind energy and biomass gasification are more cost-effective than wind-diesel systems. In [85,86], it is concluded that the electricity generation by biomass gasification-based power plants is a preferable option for the power supply of remote and isolated rural areas in comparison with solar PV plants and even plans to expand the power grid.
The development of RES-based hybrid energy systems faces the problem of choosing RES types, the optimal structure of the energy system (the ratio of capacities of energy sources and storage devices included in the energy system), and algorithms of their operation. These system characteristics depend on the technical and economic performance of the energy sources, and the availability and energy potential of renewable energy resources in a given area. Some mathematical models are described in the published research to calculate RES potential and optimize the structure of the hybrid system, in particular, HOMER [73,81,87,88], TRNSYS [89][90][91], HOGA [92,93], and others [67,68,70,71,94]. The known approaches usually involve enumerating discrete structure variants and using a predetermined algorithm for switching energy flows.

Modeling Method Used in This Work
Our study relies on the mathematical model REM-2 (Renewable Energy Model) described in detail in [95]. In contrast to the well-known models (HOMER, HOGA, TRNSYS, and other models), it does not require an analysis of the structure options and a preliminary specification of the algorithm for switching energy flows between sources and storages. The optimal operating modes are determined based on GAMS (general algebraic modeling system) algorithms, given the random nature of solar energy and the variability of energy consumption conditions. This model finds the minimum of the objective function (the total discounted costs for the creation and operation of the system) under the balance of the secondary energy, primary energy consumption constraints, output energy production constraints, and variable constraints. For the energy system under study, we set the lists of primary energy sources J 1 , secondary energy carriers J 2 , and final types of energy J 3 .
The primary energy resources include all input energy (for example, liquid fuel for a diesel power plant or electrical power from a centralized power supply system); the final energy consists of energy consumed at a given point, as well as the energy that enters the overseas market (for example, synthetic liquid fuel or hydrogen ones).
The system comprises power installations (technologies) of the following two types: (a) energy conversion (transportation) and (b) energy (energy carriers) accumulation. Energy conversion installations converse primary and secondary energy into final and/or secondary energy of another type. Storage batteries accumulate secondary energy for subsequent use.
The power system operation is modeled with a time step ∆t; the variables with the index t = 0, 1, 2, . . . , T denote the corresponding moments of time. At moment t the power of the i-th energy conversion installation is equal to N it ≤ N i (where N i is an installed capacity). During operation, it is possible not only to change the current power of the installation but to switch it to a different mode (for example, a CHP can be switched from heating into a condensing mode of operation). At moment t, the i-th installation operates in the mode s it ∈ S i (where S i is a set of admissible modes).
For each energy conversion installation (i ∈ I), we set the following coefficients: α ij (s it ) is a specific (per unit of power) consumption of the j-th energy source in the mode s it ; β ik (s it ) is a specific production of the k-th energy type in the mode s it .
For example, if we consider a fossil fuel power plant, then β ik = 1 − δ, α ij = b, where δ is a share of auxiliary electricity consumption, b is specific fuel consumption per unit of electricity produced. For a solar power plant, we can set an arbitrary α (the energy source is unlimited and free) and determine coefficient β by operating characteristics depending on the mode s it (in this case, it is the intensity of solar radiation).
At moment t, the secondary energy reserve in the j-th energy storageis equal to Q jt ≤ Q j (where Q j is the capacity). For each storage technology (j ∈ J 2 ), the efficiency η j is preset and characterizes the energy losses in the battery.
In addition, for all technologies (i ∈ I ∪ J 2 ): k i are the specific investments (for generators-per unit of power, for battery-per unit of capacity), µ i are the annual fixed operating costs (share of capital investments), and ∆T i is a lifetime of the installation.
The mathematical problem statement is as follows: Find the minimum of the objective function under the primary energy consumption constraints; the final energy consumption constraints; the secondary energy balances; subject to the initial condition for t = 1, 2, . . . , T and s it ∈ S i . Here is the capital recovery factor at the annual discount rate d; H is the duration of the year in selected time units (for example, H = 8760 h/year); p j and P jt are the price and the maximum available volume of the primary energy resource, respectively; L jt is the final energy demand; X jt and Y jt are the secondary energy flows into and out of the energy storages, respectively; ∆Q jt is the secondary energy losses. The decision variables are the installed N i and current N it capacities of conversion energy installations, secondary energy reserves Q jt in the energy storages and their capacity Q j , energy flows X jt and Y jt , losses ∆Q jt , and controlled operating modes s it .
Stochastic modes of energy sources using renewable energy (for example, solar) cannot be optimized because they are determined by external environmental conditions and have preset values for the model.
The objective function (4) is the total (per year) discounted costs for the creation and operation of the system. For a given amount of energy supplied to final energy consumers, the minimum of Z corresponds to the maximum of the net present value.
The term ∆Q jt in Equation (7) accounts for possible (at certain moments) "excess" production of secondary energy. For example, it is sometimes more beneficial to employ a dump load to consume the excess energy of RES using a free resource (solar or wind) than to increase the battery capacity or reduce the installed capacity of the wind turbine.
The initial condition (12) imitates a random selection of the beginning of the simulation period on the time axis (to estimate a random value of the initially available energy resource, we use its most probable value, i.e., its arithmetic mean).

System Structure and Initial Data
We consider a stand-alone system, including photovoltaic cells (PVC or PV), wind turbines (WT), battery storage (BAT), an inverter (INV), a wood fuel gasification power plant (GPP), and a diesel power plant (DPP) as a backup and peak load power source (Figure 3). The GPP uses the technology of wood waste gasification and includes the following: a gasification module (gasifier to produce gas from wood waste); a tank for storing the produced synthesis gas (gas-holder); a generation module with a power generator running on this gas. resource, we use its most probable value, i.e., its arithmetic mean).

System Structure and Initial Data
We consider a stand-alone system, including photovoltaic cells (PVC or PV), wind turbines (WT), battery storage (BAT), an inverter (INV), a wood fuel gasification power plant (GPP), and a diesel power plant (DPP) as a backup and peak load power source (Figure 3). The GPP uses the technology of wood waste gasification and includes the following: a gasification module (gasifier to produce gas from wood waste); a tank for storing the produced synthesis gas (gas-holder); a generation module with a power generator running on this gas. The GPP uses either shredded wood waste or wood briquettes (pellets and pellet fuels) as fuel [11]. Thermochemical conversion of wood fuel into synthesis gas takes place in the gasifier. Syngas is a mixture of different gases, with the main combustible components being carbon monoxide and hydrogen.
The DPP is used as a backup and peak-shaving power source due to the limited maneuvering capacity of the GPP. The DPP is usually switched on at times when renewable energy generation is insufficient to cover the electric load and storage batteries are discharged.
The main factors determining the economic performance of renewable energy sources are the following: the potential and reserves of the corresponding natural The GPP uses either shredded wood waste or wood briquettes (pellets and pellet fuels) as fuel [11]. Thermochemical conversion of wood fuel into synthesis gas takes place in the gasifier. Syngas is a mixture of different gases, with the main combustible components being carbon monoxide and hydrogen.
The DPP is used as a backup and peak-shaving power source due to the limited maneuvering capacity of the GPP. The DPP is usually switched on at times when renewable energy generation is insufficient to cover the electric load and storage batteries are discharged.
The main factors determining the economic performance of renewable energy sources are the following: the potential and reserves of the corresponding natural resource; capacity and load profile; technical and economic performance of power plants; the price of wood fuel.
This study considers a variable load with a maximum of 1 MW and a capacity factor of 0.52. The maximum load is in the evening hours, at night the load is 10% of the maximum load. Such parameters are typical of small local energy systems in the Baikal region.
The technical and economic performance indicators of the system components [8][9][10][11]96,97] are shown in Table 5. Due to the volatility of the ruble exchange rate, capital expenditures are expressed in U.S. dollars (in fixed prices as of the beginning of 2020). In the previous work [10], based on the literature analysis, technical and economic indicators of power plants were set in the form of uncertainty intervals to factor in errors in some parameters. In this paper, we mostly focus on the dynamics of power systems and system effects and use the most probable average values of the parameters.
When forming options to be calculated, the task was to take into account the diversity of conditions of RES operation with a minimum number of points under consideration. Within the territory of the Baikal region, one distinguishes provisionally between three regions (south, center, and north) with their characteristic values of the number of maximum load hours and fossil fuel prices [8,96,97]. The average annual wind speed at a height of 10 m varied from 3 to 6 m/s (the highest speed is in the center), the annual solar radiation incident on a horizontal surface-from 1000 to 1400 kW·h/m 2 . Note: *-as a percentage of capital expenditures; **-USD/kW·h.
Meteorological data on the solar radiation and wind speed for this research were taken from reference books on climate and used according to the approach developed in [8].
The price of woody biomass is determined by a significant number of factors specific to a given area. Most of the wood fuel resources are concentrated in the northern parts of the country, with much less in the south [11]. For the calculations, we assumed the typical regional value of the price of wood fuel of 50-90 USD/toe.

Calculation Results and Discussion
The calculation results for the optimal structure of the power supply system for different climatic zones, taking into account the above-described differences in the prices of wood fuel and the characteristics of wind and solar radiation, are shown in Table 6 and Figures 4 and 5. The results obtained provide evidence on the feasibility of PVs only in the southern areas of the Baikal region (with solar radiation incident on a horizontal surface of above 1200-1250 kW·h/m 2 ), and GPPs and WTs prove feasible in all climatic zones. The share of WTs in the energy system is at its maximum in the center and at its minimum in the northern and southern areas, where the average wind speed rarely exceeds 3 m/s. The role of GPPs is most prominent in the north, where the main wood fuel resources are concentrated, and the price of fuel chips is minimal. In all the considered options, the DPP plays the role of a peak shaving power source to ensure an uninterrupted power supply. The power generation structure for different energy sources is shown in Figure 4.   The operation of the optimized power supply system in dynamics is elucidated in Figure 5 (spring days in the north and south regions).
We consider energy flows of energy sources hour by hour. In the first approximation, this approach is adequate, as the biomass gasification power plants with small-capacity reactors have a start-up time for the gasifier of about 20 min; the ramping rate of 1%/min; and a minimum power load of 20%. These values, however, cannot be considered constant for all downdraft gasifiers, as they depend on the size of the reaction zone, fuel and air consumption, particle sizes, and others. In addition, a gas-holder will improve the reliability of the power supply and expand the power range covered by the gasifier (including in the area of low loads) [98][99][100].
In northern areas with cheap wood fuel, most of the generation comes from GPPs. The role of DPPs is reduced to short one-time switching on for flexible tracking of load growth in the absence of WT generation (Figure 5a). During the hours when the WT power exceeds the load power, the electric batteries are charged, and the gas-holder is filled (in the example considered herein, this takes place in the evening and at night). The BS charging and the gas-holder filling are shown in Figure 5 as negative values. During the day, the GPP power increases smoothly to the rated power, during some periods it operates together with the WT and with the discharged BS.
In the southern areas (Figure 5b), the power of the WT exceeds the load power (including at night), the storage batteries are charged, and the gas-holder is filled. The PVC starts generating electricity from sunrise until sunset. Within three hours, the BS is discharged and the GPP is switched on in the baseload operating state. As the load grows, at 7 a.m., the diesel power plant is switched on and subsequently changes its power, tracking the load profile. The DPP power is minimal during periods of simultaneous operation of the WT, PV, and GPP. During the evening load increase, when the PV and WT stop their generation, the GPP and the DPP operate until the next wind speed increase, after which they can be switched off, and the next cycle of battery charging begins. Figure 6 shows the calculation data for the conditions of Lake Baikal coast under fa- The results obtained provide evidence on the feasibility of PVs only in the southern areas of the Baikal region (with solar radiation incident on a horizontal surface of above 1200-1250 kW·h/m 2 ), and GPPs and WTs prove feasible in all climatic zones. The share of WTs in the energy system is at its maximum in the center and at its minimum in the northern and southern areas, where the average wind speed rarely exceeds 3 m/s. The role of GPPs is most prominent in the north, where the main wood fuel resources are concentrated, and the price of fuel chips is minimal. In all the considered options, the DPP plays the role of a peak shaving power source to ensure an uninterrupted power supply. The power generation structure for different energy sources is shown in Figure 4.
The operation of the optimized power supply system in dynamics is elucidated in Figure 5 (spring days in the north and south regions).
We consider energy flows of energy sources hour by hour. In the first approximation, this approach is adequate, as the biomass gasification power plants with small-capacity reactors have a start-up time for the gasifier of about 20 min; the ramping rate of 1%/min; and a minimum power load of 20%. These values, however, cannot be considered constant for all downdraft gasifiers, as they depend on the size of the reaction zone, fuel and air consumption, particle sizes, and others. In addition, a gas-holder will improve the reliability of the power supply and expand the power range covered by the gasifier (including in the area of low loads) [98][99][100].
In northern areas with cheap wood fuel, most of the generation comes from GPPs. The role of DPPs is reduced to short one-time switching on for flexible tracking of load growth in the absence of WT generation (Figure 5a). During the hours when the WT power exceeds the load power, the electric batteries are charged, and the gas-holder is filled (in the example considered herein, this takes place in the evening and at night). The BS charging and the gas-holder filling are shown in Figure 5 as negative values. During the day, the GPP power increases smoothly to the rated power, during some periods it operates together with the WT and with the discharged BS.
In the southern areas (Figure 5b), the power of the WT exceeds the load power (including at night), the storage batteries are charged, and the gas-holder is filled. The PVC starts generating electricity from sunrise until sunset. Within three hours, the BS is discharged and the GPP is switched on in the baseload operating state. As the load grows, at 7 a.m., the diesel power plant is switched on and subsequently changes its power, tracking the load profile. The DPP power is minimal during periods of simultaneous operation of the WT, PV, and GPP. During the evening load increase, when the PV and WT stop their generation, the GPP and the DPP operate until the next wind speed increase, after which they can be switched off, and the next cycle of battery charging begins. Figure 6 shows the calculation data for the conditions of Lake Baikal coast under favorable conditions for PV and WT (solar radiation incident on a horizontal surface of 1300 kW·h/m 2 per year and multi-year average wind speed of 5 m/s), winter and summer days. The price of diesel fuel is taken equal to 500 USD/toe of fuel equivalent, the fuel price for GPP is 50 USD/toe [8,10,11,96]. At night, the power of the wind turbine exceeds the load power, thus the electric batteries are charged. The gas-holder is also filled at night. The PV generates electricity from sunrise to sunset, operating both to cover the load as such and to charge the BS. The DPP is switched on at certain hours, tracking the load profile.
In winter days (Figure 6a), the DPP is switched on when the load increases and is switched off during periods of simultaneous operation of the WT, PV, and GPP. During the period of the evening load increase when the PV and WT stop their generation, the GPP and the DPP operate until the next wind speed increase, when the next cycle of bat- At night, the power of the wind turbine exceeds the load power, thus the electric batteries are charged. The gas-holder is also filled at night. The PV generates electricity from sunrise to sunset, operating both to cover the load as such and to charge the BS. The DPP is switched on at certain hours, tracking the load profile.
In winter days (Figure 6a), the DPP is switched on when the load increases and is switched off during periods of simultaneous operation of the WT, PV, and GPP. During the period of the evening load increase when the PV and WT stop their generation, the GPP and the DPP operate until the next wind speed increase, when the next cycle of battery charging begins.
During the summer day, the DPP can be switched off, the power of the PV increases, and the contribution of the WT decreases (Figure 6b). At certain hours (at night, in the morning, and in the afternoon), the load profile is completely covered by the output of the GPP. The BS is charged at night by the WT, during the day it is charged by the PV. As the load increases in the morning and evening hours, the electric batteries are discharged.
In this case, the optimal solution is the joint use of all of these types of RES, if necessary; in periods of increased load, the DPP is switched on (see Figure 6). At that, the main part of generation is provided by the GPP (more than 60%), the share of WT is about 18%, PV-12%, and the contribution of the DPP does not exceed 10%.
In addition, we conducted calculations with constraints on some technologies. Rejection of one of the components (PV, WT, or GPP) increases the cost of the system by no more than 5-20% ( Figure 7). Therefore, all the considered renewable energy sources (except for PV in areas with solar radiation of 1100 kWh/m 2 and below) in the hybrid power system are desirable, but the exclusion of any one of the components is not critical for the economic performance of the power supply system.  The most expensive option is without RES, i.e., when consumers are supplied with electricity from the DPP only (Figure 7). Improved economic performance, when using RES, is associated with saving expensive diesel fuel and reducing the installed capacity of the DPP: up to 90% of the maximum load when included in the system of WTs and PVCs, and up to 60%-GPP.
The most economical option is the unrestricted option, i.e., when the system includes RES of all the considered types. In this case, the total discounted costs are reduced by almost 2.5 times compared to the DPP option.
Calculations with a decrease in the load power (up to 1-10 kW) demonstrate that the share of solar cells increases in the optimal structure due to the change in specific capital investments in favor of solar cells.

Conclusions
Russia and the Baikal region have significant resources of woody biomass (waste from logging, timber processing, and pulp and paper industry). It not only can but must be recycled and disposed of to prevent both environmental damage (littering of areas, forest fires, and pollution of surface and groundwater) and economic damage (garbage fines, emission fees, and lost profits).
Summarizing the published research data attests to the fact that woody biomass utilization technologies based on multi-stage gasification are promising for energy use. The The most expensive option is without RES, i.e., when consumers are supplied with electricity from the DPP only (Figure 7). Improved economic performance, when using RES, is associated with saving expensive diesel fuel and reducing the installed capacity of the DPP: up to 90% of the maximum load when included in the system of WTs and PVCs, and up to 60%-GPP.
The most economical option is the unrestricted option, i.e., when the system includes RES of all the considered types. In this case, the total discounted costs are reduced by almost 2.5 times compared to the DPP option.
Calculations with a decrease in the load power (up to 1-10 kW) demonstrate that the share of solar cells increases in the optimal structure due to the change in specific capital investments in favor of solar cells.

Conclusions
Russia and the Baikal region have significant resources of woody biomass (waste from logging, timber processing, and pulp and paper industry). It not only can but must be recycled and disposed of to prevent both environmental damage (littering of areas, forest fires, and pollution of surface and groundwater) and economic damage (garbage fines, emission fees, and lost profits).
Summarizing the published research data attests to the fact that woody biomass utilization technologies based on multi-stage gasification are promising for energy use. The combination of woody biomass gasification-based plants with the plants that make use of solar and wind energy can increase the reliability of the energy supply. At the same time, the plant running on wood waste smoothes out power output dips in solar and wind installations.
This paper considers a stand-alone power system that includes renewable energy sources of different types: photovoltaic cells (PV), wind turbines (WT), battery storage (BS), an inverter (INV), a wood fuel gasification-based power plant (GPP), and a diesel power plant (DPP) as a backup and peak load shaving power source. The optimization mathematical model developed by the authors was used to study this system.
Based on mathematical modeling, we evaluated the economic performance of the stand-alone power supply system with RES for different climatic zones of the Baikal region and the Lake Baikal coastal area. We determined the optimal structure of the power supply system and the operating states of its components: generation, storage, and consumption of energy.
It is demonstrated that in the central and southern regions of the Baikal region it is feasible to use wind turbines together with photovoltaic cells and gasification-based plants, in the northern regions -wind turbines together with GPPs with their capacity backed up by the DPP.
The findings indicate that the optimal solution for the coast of Lake Baikal is the joint use of renewable energy sources. Rejection of any one of the components (PV, WT, or GPP) leads to an increase in the total cost of creating a power supply system. The optimal structure of the energy system with RES reduces costs compared to the option of a diesel power plant alone by about 2.5 times.

Data Availability Statement:
The data presented in this study are available in the article.