The Capacity of Power of Biogas Plants and Their Technical Efficiency: A Case Study of Poland

Abstract

The size of a company is a fundamental factor that can influence its efficiency. In larger companies, economies of scale are a key consideration. The objective of this study was to evaluate the technical efficiency of agricultural biogas plants differentiated according to their capacity of power. The study included 43 agricultural biogas plants, which were divided into three groups according to their capacity power: group I, <0.5 MW; group II, 0.5–1 MW; group III, ≥1 MW. In order to assess the technical efficiency of agricultural biogas plants under the research, the Data Envelopment Analysis (DEA) method was applied. It was found that the largest biogas plants were the most efficient. However, the technical efficiency of the smallest biogas plants was not statistically significantly different from that of the largest biogas plants. This indicates that small entities can achieve the technical efficiency at a satisfactory level. For this reason, in the development policy of agricultural biogas plants, the optimal solution is the coexistence of large and small facilities. The smallest biogas plants were more sensitive to changes in the macroeconomic environment than other biogas plants. This may suggest a need to pay more attention to energy policy mechanisms to stabilize their performance in periods of disadvantageous macroeconomic conditions.

1. Introduction

The economic efficiency of businesses is a fundamental determinant of their competitiveness, their capacity for growth, and the smooth functioning of their current activities. Moreover, it is a crucial aspect from both an economic and a social perspective. Consequently, the factors that influence economic efficiency remain a significant area of research. In light of the rapid changes occurring in the economic environment and the challenges facing economies, it is imperative to conduct ongoing evaluations of management efficiency issues. Furthermore, agricultural biogas plants require ongoing evaluation. This is particularly the case in the countries where the agricultural biogas sector is at its early stages of development and where the potential for production is yet to be fully realized [1,2,3,4,5,6]. Such analyses are of particular utility in the design of appropriate mechanisms and policy tools for the development of the sector.

The development of agricultural biogas plants in Poland was initiated by the adoption of relevant legislative solutions concerning energy law and environmental protection in 2005. The inaugural agricultural biogas plant was established in 2005, and by 2023, there were 119 biogas producers in Poland that generated 795.61 GWh of electricity and 374.09 million m³ of agricultural biogas [1]. With a project to develop this type of installation, it was envisaged that around 2000 agricultural biogas plants should be in operation in 2020 [7]. It is clear that there is a significant discrepancy between the development plans for this sector and reality. This prompts the question of why the agricultural biogas sector has not experienced the anticipated dynamic development. Comparing the scale of development of the agricultural biogas plants in Poland to other European Union countries, it is clear that Poland is not using its potential. The largest biogas producers in the EU-27 are countries such as Germany (in 2023, the power generation capacity was 7119 MW, representing 61.4% of the EU-27 capacity), Italy (1429 MW—12.3%), France (580 MW—5%), Czech Republic (383 MW—3.3%), Spain (272 MW—2.3%), Netherlands (256 MW—2.2%), Belgium (205 MW—1.8%), Austria (166 MW—1.4%), Denmark (125 MW—1.1%), and Finland (116 MW—1%), and outside the EU-27 countries, the world’s largest biogas producers are Great Britain (1953 MW), China (1490 MW), the USA (1941 MW), Brazil (509 MW), Canada (283 MW) and Ukraine (123 MW) [8]. In 2023, Poland’s power generation capacity was 292 MW, representing a 2.5% share in the EU-27’s total power generation capacity. In comparison to the outcomes observed in the EU-27, this represents a relatively favorable outcome. However, the potential for biogas production in Poland is considerably more substantial [9,10,11].

Investment in agricultural biogas plants requires an appropriate level of economic efficiency that is acceptable for investors. The factors determining the efficiency of agricultural biogas plants are multifaceted. Among these factors, there are those related to technical aspects (technologies used and their efficiency, feedstock types, operational parameters, biogas and fertilizer utilization strategies, and demand-oriented biogas supply) [12,13,14], the level of investment costs and high investment risk, operating costs, especially the costs related to substrate acquisition [15,16,17,18], as well as the electricity and certificate prices [3]. These are the factors that have a direct impact on the economic calculus. In addition to this group of factors, non-economic benefits related to public goods should also be sought. The extensive literature indicates that the biogas sector fits into a model of a circular bioeconomy, which allows achieving the goals related to the Sustainable Development Goals (SDGs), particularly in terms of decarbonizing certain sectors of the economy, reducing greenhouse gas emissions, and reducing organic waste [19,20,21]. In addition, it has a positive impact on rural development, creates additional jobs, maintains the vitality of rural areas, creates additional value added by farmers, provides additional income for farmers, and promotes the modernization and restructuring of agriculture [22]. It is also noteworthy that a considerable number of agricultural biogas plants are situated on livestock farms. This allows the utilization of livestock manure in energy production, thereby reducing the energy consumption costs. Furthermore, these farms are able to benefit from the production of digestate, which enables a reduction in mineral fertilization costs [1,23,24,25,26].

In the research on the operation of agricultural biogas plants, the issue of management efficiency is a frequent topic. These studies highlight the size of biogas plants as one of the main factors determining the management efficiency, but they also consider the issue in the context of centralization or decentralization of this type of facility, transport costs, and balancing the distance between suppliers and consumers [1,3,27,28,29,30,31]. This issue is still relevant, especially in countries such as Poland, where the agricultural biogas sector is at an early stage of development. Furthermore, economies of scale are an ongoing issue in research and have important implications for the development policy of specific economic sectors. Therefore, our study aimed at assessing the technical efficiency of agricultural biogas plants differentiated according to their capacity of power.

The issue of measuring business efficiency is one of the main problems in analyzing and diagnosing the situation of enterprises. Various methods can be used to measure the efficiency of enterprises. They are most often classified into three groups: quotient indicators, parametric methods, and non-parametric methods. A non-parametric approach, the Data Envelopment Analysis (DEA) method, was used in our research. This method is commonly used in the evaluation of business efficiency. It is particularly useful when considering a production technology that produces more than one product from more than one input [32,33,34,35].

2. Literature Review

The achievement of high levels of performance is a pivotal factor in the success of any given organization. It is, therefore, crucial to understand the factors that influence performance and identify why some organizations are operating efficiently or inefficiently. DEA is a frequently used method to evaluate the productivity of individual companies (DMU—Decision-Making Unit) [36]. DMUs are homogeneous entities (farms, companies, banks, universities, hospitals) with some decision autonomy, engaging in a production process, receiving a specific set of inputs, and transforming it into a specific set of outputs. The DEA models use a set of input and output to calculate an efficiency score for a given DMU. Efficiency is given by the quotient of the weighted sum of outputs to the weighted sum of inputs. The efficiency score for a given DMU is used to compare other DMUs under consideration [37,38]. This approach also enables the comparison of DMUs with markedly disparate structures, nature of outputs and inputs, and unobservable elements derived from inputs and outputs, without the necessity of making restrictive assumptions about the parameters of the production process [39]. DEA is an applicable technique to evaluate, compare, and rank the relative efficiency of DMUs [40].

DEA models are often used to assess the efficiency of organizations in the energy sector. In a study conducted by Madlener et al. [38], a DEA model was employed to assess the relative performance of 41 agricultural biogas plants in Austria in terms of economic, environmental, and social criteria. These authors suggest extending the assessment of the efficiency of agricultural biogas plants with multi-criteria decision analysis (MCDA), emphasizing that DEA is the tool generally used to evaluate the efficiency of decision-making units (DMUs). Moreover, they emphasize that the DEA models are particularly useful in the enterprise management process, and the MCDA model should rather be used as a complementary technique. Similarly, in the study by Datkov and Effenberger [41], the DEA and MCDA models were applied to evaluate 10 Bavarian biogas plants. In the research by Cierpiał-Wolan et al. [42], the DEA model with constant returns to scale was used to analyze the efficiency of biogas plants. The DEA model was also applied to evaluate the efficiency of the biogas project subsidy policy [43]. In addition to the analysis of relative performance, another important aspect is the analysis of intertemporal productivity changes. This is made possible by analyzing the changes in total factor productivity (TFP) based on the DEA–Malmquist index. The Malmquist index was used in the Rácz and Vestergaard study [44]. In this study, the analysis of changes in total factor productivity was conducted for 19 agricultural biogas plants in Denmark. The results obtained regarding changes in the Malmquist index indicated the need for changes in the energy policy and a greater focus on investment subsidies. Similarly, in the study by Eder et al. [45], the DEA–Malmquist index was used to assess changes in the productivity of 65 Austrian biogas plants from 2006 to 2014. It was found that the exploitation of returns to scale, a major driver of productivity growth and technical change, is rather low. In turn, in a review article, Mardani et al. [46] demonstrated the usefulness of different DEA models for assessing energy efficiency. Sueyoshi et al. [47], in a review article covering 693 articles, demonstrated the possibility of using DEA models to assess energy and environmental efficiency. The literature review conducted on the use of DEA models indicates that these are commonly used models for performance assessment in the energy sector. To the best of our knowledge, there is a gap in the use of DEA models to assess the efficiency of agricultural biogas plants.

By concentrating production in large factories, processors are able to take advantage of economies of scale, reducing costs and increasing market share [48]. Large-scale production allows standardization, a reduction in the number of actors in supply chains, which should consequently lead to improved technical and economic efficiency. Although the centralized production system is characterized by cost-efficiency, it may nevertheless lead to an increase in risk due to the limited flexibility of large enterprises to adapt quickly to changes in the economic environment, significant fixed costs, and possible greater negative externalities [49].

The scale of production is also an important issue in the development of agricultural biogas plants. The identification of advantages and disadvantages associated with centralization or decentralization of agricultural biogas plants is an important issue for the development strategy of this sector. Research indicates that both strategies have their advantages and disadvantages. Raven and Gregersen [50], when analyzing the development of the biogas plant sector in Denmark, highlighted the benefits of the centralized biogas plant concept. However, the success of this approach required the involvement of many actors. First, the ministries involved adopted a bottom-up strategy and encouraged interaction between different social groups. This helped to create a broad social network that supported the development of the centralized biogas plant and focused on interactive learning. Many of the benefits that are now recognized emerged from this bottom-up approach through the participation of many actors (e.g., centralized storage, reduction in the use of artificial fertilizer, reduction of transport miles). A study by Raven and Gregersen [50] also drew attention to the continuity in development policy in the long term. Investments in biogas plants require large financial investments, which results in a long payback period. Interruptions to the support program may, therefore, have a detrimental impact on the viability of such investments. The fact that many advantages have been recognized from the operation of large-scale centralized biogas plants has stimulated ministries, farmers, researchers, and biogas plant suppliers to continue improving the centralized biogas plant. Plant improvement enabled a process of diversification after the mid-1990s in Denmark. Subsequently, the farm-scale biogas plants were reintroduced, in particular, due to a temporary investment grant and an increase in the average farm size. This also indicates that investments in biogas plants located at farms necessitate a substantial production scale on the farm and collaboration with other large farms to ensure an adequate supply of substrates [17,23,51,52]. In addition, with an increase in the size of the plant, the investment costs per kW of capacity fall, but the rate of this fall decreases as the size of the biogas plant increases [29]. The size of the biogas plant must also be adapted to the planned and achievable substrate amount. The excessive size of agricultural biogas plants in relation to the possibility of obtaining sufficient substrate in close proximity leads to higher costs, especially for transport, capital intensity, and investment, which reduces the economic efficiency of such investments [51,53,54]. The issue of substrate availability not only shows the importance of the location of the biogas plant but also the optimal size of the biogas plant determined by local substrate availability [29].

Decentralizing the energy supply system with a larger number of smaller agricultural biogas plants can benefit rural development, especially in developing countries. These benefits are mainly related to additional income in rural areas, the provision of cheaper energy, the reliability of energy supply, and thus increased energy security for rural communities. It is also noted that such distributed energy systems may generate certain social dilemmas related to concerns about the safety of the technologies used or the ownership of the biogas plants and the profits generated. It is important to implement an appropriate strategy at the stage of planned investments, involving all potential stakeholders, local conditions, social and political power relations, and economic circumstances. However, there is no doubt that decentralized energy generation and distribution systems can lead to long-term sustainability [55].

The profitability of biogas plants also depends on policy tools that support the development of this sector [1,56,57]. Investment subsidies are important here; these are often subsidies for small facilities that improve their economic efficiency and make them profitable. In addition, progressive electricity prices may also be applied. This changes the operating conditions for biogas plants, making the conditions unequal and often favoring small biogas plants [29]. Such subsidies need to be justified and are most often explained in terms of economic, social, and environmental benefits [1,58].

However, scholars increasingly argue that there is no one best system that fulfills our economic, environmental, and social preferences. The answer exists in plural since there is no single best solution. Socio-economic systems should be optimized in terms of the context where they are used. Hence, it depends on the local context which system is to prevail and what the ratio between centralized and decentralized energy infrastructure systems is to be [59]. The research we have conducted deals with the impact of the size of agricultural biogas plants on their management efficiency in microeconomic terms. We do not consider the efficiency of the studied biogas plants in the broader context of efficiency in terms of environmental, social, and macroeconomic costs and benefits. Economic efficiency in a broad sense is important from a social point of view, but microeconomic efficiency is most important for the functioning of companies. Without a level of microeconomic efficiency that satisfies investors, it is difficult to imagine the functioning of companies.

3. Materials and Methods

This study encompassed all agricultural biogas plants that were operational in Poland between 2019 and 2023 (there were 93 agricultural biogas plants in 2019 and 119 biogas plants in 2023). These biogas plants met the following conditions: 1. Operate continuously in the years 2019–2023. 2. These are separate objects in terms of organization, which means they are independent objects. Biogas plants that are part of the organizational structures of other companies were excluded. This exclusion results from the fact that such biogas plants do not publish separate financial statements, which means that it is not possible to assess their economic efficiency. 3. Published financial statements during the period under review. To ensure the accuracy of the analysis, the financial statements were reviewed, and companies with deficiencies and errors in the financial statements were removed from the study. The study also excluded agricultural biogas plants with both losses and negative equity in their financial statements (5 biogas plants), i.e., plants with serious financial problems. These are companies where serious management errors have been made, and it can be assumed that these organizations are in a state of liquidation or restructuring. The inclusion of these organizations would significantly distort the assessment of the remaining biogas plants. Excluding them allows an assessment of the efficiency of biogas plants that do not have such serious financial problems. Ultimately, 43 agricultural biogas plants were qualified for the research. The researched agricultural biogas plants were divided into three groups according to their capacity power: group I, <0.5 MW; group II, 0.5–1 MW; and group III, ≥1 MW. The structure of the analyzed biogas plants is presented in Table 1.

In order to assess the efficiency of the researched agricultural biogas plants, the Data Envelopment Analysis (DEA) method was employed. The DEA is a non-parametric method for evaluating the relative effectiveness of the decision-making units (DMUs) [60]. The DEA analysis allows the identification of the most efficient objects and the determination of the efficiency frontier (production possibilities frontier) based on these. This frontier serves as a reference point for evaluating the efficiency of the remaining objects, and it also suggests avenues for enhancing their technical efficiency (TE). The DEA method permits the evaluation of efficiency in systems that generate more than one output using more than one input. TE is calculated according to the following formula [61]:

$TE={\displaystyle \frac{{\sum }_{i=1}^l{\mu }_{i,j}Y}{{\sum }_{i=1}^k{\gamma }_{i,j}X}}$

where,

• j—number of the tested units from a group of n units (j = 1, …, n),

• l—number of outputs (l = 1, …, n),

• k—number of tested inputs (k = 1, …, n),

• Y—output,

• X—input,

• µ_i,j—weigths i-output j-unit,

• γ_i,j—weigths i-input j-unit.

• TE is the quotient of the aggregated values of outputs and inputs, that is to say, the quotient of weighted outputs by weighted inputs.

By aggregating multiple outputs and multiple inputs, the resulting TE score allows the assessment of the effectiveness of individual decision-making units (DMUs). The analysis of the efficiency of agricultural farms using the DEA method was carried out using the following set of inputs: x₁—raw materials and consumables used, this input was adopted due to its fundamental importance in the production process; x₂—employee benefit expense, this input reflects the level of involvement of the labor factor in the production process; x₃—the value of fixed assets represents the level of capital employed in the production process; and output: y₁—total operating revenue. The selection of inputs and outputs was also contingent upon the availability of data within the financial statements of the agricultural biogas plants under examination. Therefore, total operating revenues were used as output; as the financial statements report aggregated total operating revenues, it is not possible to obtain information on the structure of revenues broken down into revenues from the sale of electricity, heat, or certificates of origin.

An output-oriented model with constant returns to scale was used to analyze efficiency [62]. The calculations were performed using the DEAP program [63]. In the case of n objects utilizing k inputs to yield l outputs, the data pertaining to the inputs and outputs can be represented in the form of a matrix of dimension n × (k + l) [64]:

(1)$\begin{array}{cccc}\hfill [& \begin{array}{ccc}{x}_{11}& \cdots & x_{1k}\\ ⋮& ⋮& ⋮\\ ⋮& ⋮& ⋮\\ x_{n1}& \cdots & x_{nk}\end{array}& \begin{array}{ccc}{y}_{11}& \cdots & y_{1l}\\ ⋮& ⋮& ⋮\\ ⋮& ⋮& ⋮\\ y_{n1}& \cdots & y_{nl}\end{array}& ]\hfill \\ & \underset{\mathrm{input}}{︸}& \underset{\mathrm{output}}{︸}& \end{array}$

In order to evaluate the technical efficiency of a specific established facility N (1 ≤ N ≤ n), a series of conditions will be formulated with regard to the outputs and inputs obtained by that facility in relation to other decision-making units. The objective of the model is to achieve a proportional reduction in expenditure without a reduction in output. From a mathematical perspective, this can be expressed as follows [64]:

$$\begin{gathered} \underset{{\lambda }_1,\dots ,{\lambda }_n}{min}\theta \\ {\lambda }_1,\dots ,{\lambda }_n\ge 0 \end{gathered}$$

(2)$\left.\begin{array}{c}{\lambda }_1{y}_{11}+\cdots +{\lambda }_n{y}_{n1}\ge y_{N1}\\ ⋮\\ {\lambda }_1{y}_{1l}+\cdots +{\lambda }_n{y}_{nl}\ge y_{Nl}\end{array}\right\}\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{s}\mathrm{r}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}$

(3)$\left.\begin{array}{c}{\lambda }_1{x}_{11}+\cdots +{\lambda }_n{x}_{n1}\le \theta \cdot x_{N1}\\ ⋮\\ {\lambda }_1{x}_{1k}+\cdots +{\lambda }_n{x}_{nk}\le \theta \cdot x_{Nk}\end{array}\right\}\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{s}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{b}\mathrm{y}\mathrm{a}\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{o}\mathrm{f}x$

The model presented above offers the following solution:

$$\begin{gathered} {\lambda }_i=0i\ne N \\ {\lambda }_N=1 \\ \theta =1 \end{gathered}$$

In the absence of a solution for which θ ≠ 1, the decision object is deemed to be effective. In contrast, the value 1 − $\theta$ illustrates the extent to which the inputs can be diminished without a corresponding reduction in the outputs.

The subsequent analysis employed a non-parametric methodology based on the Malmquist productivity index to assess the year-on-year changes in biogas plant efficiency over the period 2019–2023. The Malmquist Index is a tool that assesses the impact of changes in technical efficiency and changes in the technological capability frontier on change in total factor productivity. The Malmquist Index (total factor productivity—tfpch) for object A, which characterizes the change in total factor productivity level between period t and t + 1, is determined by the following formula [65]:

(4)$M_{t,t+1}\left(A\right)={\displaystyle \frac{E^{t+1}\left(A_{t+1}\right)}{E^t\left(A_t\right)}}\sqrt{{\displaystyle \frac{E^t\left(A_t\right)}{E^{t+1}\left(A_t\right)}}·{\displaystyle \frac{E^t\left(A_{t+1}\right)}{E^{t+1}\left(A_{t+1}\right)}}}$

where: ${\displaystyle \raisebox{1ex}{$E^{t+1}\left(A_{t+1}\right)$}\!\left/ \!\raisebox{-1ex}{$E^t\left(A_t\right)$}\right.}$—changes in technical efficiency (effch); $\sqrt{{\displaystyle \raisebox{1ex}{$E^t\left(A_t\right)·E^t\left(A_{t+1}\right)$}\!\left/ \!\raisebox{-1ex}{$E^{t+1}\left(A_t\right)·E^{t+1}\left(A_{t+1}\right)$}\right.}}$—changes in the technological capability frontier (technological change -techch); $E^{t+1}\left(A_{t+1}\right)$—technical efficiency of the entity for data for the t + 1 period and technology in period t + 1; $E^t\left(A_t\right)$—technical efficiency of the entity for data for the t period and technology in period t; $E^t\left(A_{t+1}\right)$—technical efficiency of the entity for data for the t period and technology in period t + 1; $E^{t+1}\left(A_t\right)$—technical efficiency of the entity for data for the t + 1 period and technology in period t.

The Malmquist index value exceeding 1 will indicate an increase in total factor productivity (TFP); a value below 1 will indicate a decrease in total productivity; and a value of 1 will indicate no change in productivity. In order to calculate the Malmquist productivity indices, the same set of variables was employed as in the case of analyzing the efficiency of agricultural biogas plants using the DEA method.

Owing to a lack of normal distribution, which was tested using the Shapiro–Wilk test, the analysis of variance (ANOVA) Kruskal–Wallis test was used to compare technical efficiency between the separate groups of agricultural biogas plants studied. Post hoc analysis for Kruskal–Wallis ANOVA was performed by using a multiple comparison test (Dunn test). The Wilcoxon test was used to assess the non-randomness of changes in selected variables over time. All statistical calculations were performed using STATISTICA 13.3 PL (StatSoft, Krakow, Poland) software. The significance level was set at p < 0.05.

4. Results

4.1. Technical Efficiency of the Analyzed Agricultural Biogas Plants

By evaluating the technical efficiency of the studied agricultural biogas plants differentiated in terms of power capacity using the DEA method, the measures of technical efficiency were obtained (Table 2). The maximum possible value to determine the level of technical efficiency is 1. An object that achieves a value of 1 is characterized by the most efficient use of its resources. On the other hand, if the technical efficiency index is below 1, it means that with a given level of resources, the level of effects can be increased. Table 2 presents basic statistics regarding the technical efficiency indicators for individual years of the analysis period. In 2019, 2020, 2021, and 2023, statistically significant differences in technical efficiency were identified between the tested biogas plants at the level of p < 0.05. Additionally, in 2022, statistically significant differences were observed, albeit at the level of p < 0.1. The differences were mainly between group III and group II biogas plants. In 2019, the highest technical efficiency was observed in the largest biogas plants (group III), with statistically significant differences being noted only between biogas plants from group III and group II (p = 0.0331) (Table 3). The technical efficiency of the biogas plants from group I in 2019 did not differ statistically significantly from the other two groups (Table 3). In 2020, statistically significant differences were noted only between group I and group II—p = 0.0657 (p < 0.1) (Table 3). In 2021, statistically significant differences were noted between group II and group III—p = 0.0194; the technical efficiency of biogas plants from group I did not statistically significantly differ in 2021 from the other groups (Table 3). In 2022, statistically significant differences (p < 0.1) were also noted only between the biogas plants from group II and group III—p = 0.0574 (Table 3). In 2023, statistically significant differences (p < 0.1) were also noted only between biogas plants from group II and group III—p = 0.0542 (Table 3).

When analyzing the distribution of technical efficiency indicators (Table 4) in individual years, it should be noted that the facilities with low efficiency below 0.5 predominate. The fewest such facilities were in 2021 and 2022. The better situation of biogas plants recorded in this period resulted from the particularly high energy prices in this period [1,3,66]. It is also noticeable that the lowest percentage of biogas plants with the lowest technical efficiency indicators was recorded in the largest biogas plants (group III). This also confirms the previous considerations indicating that this group is characterized by higher technical efficiency than the other groups. It is also noticeable that the fewest plants with the lowest technical efficiency were in 2021 and 2022 in group I and group III. In addition, there was a clear decrease in the share of least efficient facilities in these two groups. No such decrease was recorded in the group of medium-sized biogas plants (group II). This indicates that the smallest and largest entities were best able to exploit the good energy situation.

4.2. Changes in Total Factor Productivity (Malmquist Index) of Investigated Agricultural Biogas Plants

Table 5 presents an assessment of changes in the level of efficiency of the biogas plants under study, employing the Malmquist index, with its decomposition into two components: technical efficiency change (effch) and technological change (techch). This assessment is provided for each year. In 2020, the largest changes in total factor productivity (tfpch > 1.0) were noted in medium-sized biogas plants (group II; mean 1.47—increase of 47%; median 1.17—increase of 17%); in the largest biogas plants, no significant changes in total productivity were noted (mean 1.10—increase of 10%, median 1.01—increase of 1%). In the smallest biogas plants, a decrease in total factor productivity was noted (mean 0.96—decrease of 4%, median 0.61—decrease of 39%). In all groups of biogas plants, a decrease in technological change (techch) indicators was recorded, but an increase in technical efficiency change (effch) indicators was noticed. In the year 2021, compared to 2020, only biogas plants from the smallest group showed the greatest increase in total factor productivity, and this was achieved mainly due to changes in technical efficiency change (effch). In all groups of agricultural biogas plants, the technological change (techch) indicator was below 1, which means there was a decrease in technological possibilities. The next year 2022, compared to 2021, was particularly favorable for all groups of biogas plants; a significant increase in the Malmquist index (tfpch) was recorded in every group, and this was mainly due to the improvement in the technological change (techch) indicator, i.e., the change in production (technological) capabilities, and not a change in the way biogas plants use the resources available within the available technologies (effch). In 2023, positive changes in total factor productivity were recorded for the largest biogas plants, and in this group, they were caused by changes in technological capabilities (techch). The weakest results in 2023 were recorded for the smallest biogas plants (group I), and this was mainly due to very low values of technical efficiency change (effch). This analysis indicates that the best year was 2022, a year of exceptionally favorable electricity prices. Next, changes in the Malmquist index over time were analyzed (Table 6). In the largest (group III) and medium-sized (group II) biogas plants, changes in the Malmquist index between periods were statistically significant (p < 0.05). For the smallest biogas plants (group I), statistically significant changes in the Malmquist index were only recorded for the 2021/2020 period compared to the 2020/2019 period (p = 0.0425), while for the 2022/2021 period compared to the 2021/2020 period, the changes were statistically significant but at a lower significance level of p < 0.1 (p = 0.091). This may indicate the high sensitivity of the smallest biogas plants to the macroeconomic environment, especially electricity prices.

5. Discussion

There is a noticeable advantage in the technical efficiency of biogas plants with the largest capacity power (group III) over other biogas plants, with statistically significant differences being noted mainly between these biogas plants (group III) and the medium-sized biogas plants (group II). In turn, the smallest biogas plants (group I) achieved technical efficiency that did not differ statistically significantly from the largest (group III) and medium-sized biogas plants (group II). This allows us to state that despite the small size of operations, it is possible to achieve efficiency at the level of larger facilities. This may result from the fact that smaller biogas plants are located near the sources of raw material or are objects operating on farms. This facilitates access to cheap raw materials for processing, reduces transport costs, and allows more flexible management of these objects. The studies on the economic efficiency of biogas plants emphasize the significant impact of the costs of obtaining raw materials on their economic results [67,68]. Moreover, small agricultural biogas plants operating on farms also have greater opportunities to sell digestate due to their proximity to recipients. In the studies conducted by Wall and Schneeberger [29], the significance of biogas plant size on efficiency was highlighted. It was observed that the average cost per kWh exhibited a notable decline initially as the size of the biogas plant expanded. However, the rate of decline in average costs subsequently diminished considerably. The relationship between the electrical efficiency and electrical capacity behaved in a similar way: the initial rate of increase in electrical efficiency is significantly higher than the later. This indicated that large biogas plants had a higher efficiency, but the rate of change in efficiency was decreasing. In turn, in the study by Havrysh et al. [69], it was clearly indicated that large agricultural biogas plants were preferable due to low specific investment costs and acceptable production costs. In the study by Kusz et al. [1], it was also pointed out that it was necessary to include certain benefits that were not always reflected in the income calculation in the profitability calculation of such facilities. These may be benefits for the farm, allowing lower electricity costs or fertilization costs. This is not always fully reflected in the economic results, especially for small agricultural biogas plants located at the farm. Our research indicates that small agricultural biogas plants can operate with technical efficiency similar to larger facilities.

The literature on this subject also points to the issue of public support, which may be important, especially for small biogas plants, in ensuring the economic efficiency of the investment [1,23,51,70,71]. Our own research lacks the information on grants obtained as support for investments. However, this could have had a significant impact on improving the efficiency of biogas plants, especially small ones.

It can also be noticed that medium-sized facilities (group II biogas plants) are characterized by the lowest level of technical efficiency, statistically significantly different from the group of the largest biogas plants; however, no clear statistically significant differences were noted in comparison to the smallest biogas plants. This may indicate that the technologies used in medium-sized biogas plants are not suitable for the scale of production. The theory of scale economics indicates the need to adapt the technology to the scale of production in order to optimize average costs [72,73]. Inappropriate technology combined with too small a scale of production causes an efficiency gap. The obtained results may indicate that the optimal solution for the development policy of biogas plants is the coexistence of large and small objects. This opinion is also confirmed by other studies, where attention was paid to the possibility of developing both decentralized (dispersed, small biogas plants) and centralized large biogas plants [59]. This is mainly determined by local requirements. It not only ensures the effective conduction of such operations but also allows for dispersion and decentralization of these facilities, which can contribute to increased energy security.

The revenues of agricultural biogas plants depend mainly on the prices of electricity and the prices of certificates of origin [23]. It is worth emphasizing that researchers also noted that macroeconomic factors, such as prices of energy, energy stock price bubbles, inflation, financial crises, and the growth of gross domestic product, were important for determining the profitability of renewable energy source production [74,75,76,77,78,79]. In our own research, changes in the Malmquist index over time were noted. The greatest improvement in efficiency was noted from 2021 to 2020 and from 2022 to 2021. This was a period of particularly high electricity prices, which clearly influenced the improvement in the efficiency of the agricultural biogas plants studied. Similar results were also obtained in the research by Kusz at al. [1], where a positive impact of electricity prices on the economic results was found. This confirms the importance of macroeconomic factors, especially energy prices, in shaping the economic situation of agricultural biogas plants. In addition, this period is also associated with global crises related to military conflicts that adversely affect energy security. In light of these considerations, it should also be noted that the development of agricultural biogas plants makes the national energy system independent from global energy markets, reducing the risk of losing energy security. For this reason, agricultural biogas plants are an important element in ensuring energy security [10,80,81,82]. In our own research, it was also found that the smallest biogas plants were more sensitive to changes in macroeconomic conditions. Statistically significant differences in the Malmquist index in this group were recorded only from 2022 to 2021 and from 2021 to 2020. In the remaining two groups, statistically significant differences in total factor productivity were recorded throughout the entire period under study. More favorable changes occurred in the largest biogas plants. However, this requires further research due to the short analysis time.

6. Conclusions

The technical efficiency of agricultural biogas plants is crucial for the development of this sector and for ensuring its sustainability. One of the key policy issues in the development of agricultural biogas plants is the question of what the optimal size for biogas plants is. This is also related to the issue of locating such objects and their centralization or decentralization. The fundamental question that arises here is how the technical efficiency of agricultural biogas plants changes with increasing plant size. In our research, the nonparametric DEA method was used to assess the technical efficiency of agricultural biogas plants. The analyzed agricultural biogas plants were divided into three groups depending on the electric capacity power. Statistically significant differences were found in the technical efficiency of agricultural biogas plants. The largest biogas plants were the most efficient organizations. Their technical efficiency was statistically significantly higher than that of medium-sized biogas plants. No statistically significant differences in technical efficiency were found between the smallest agricultural biogas plants and the largest and medium-sized agricultural biogas plants. This indicates that small objects can achieve technical efficiency at a satisfactory level. For this reason, in the development policy of agricultural biogas plants, the optimal solution is the coexistence of large and small objects.

The response of biogas plants to changes in the macroeconomic environment also varied. In the analyzed period, there were changes in the level of energy prices caused by global crises related to military conflicts. In Poland, these changes were caused by the conflict in Ukraine. Our own research shows that changes in the macroeconomic environment had a greater impact on the smallest biogas plants than on other biogas plants. This may indicate that small biogas plants are less economically robust and that greater focus is required on energy policy mechanisms to ensure their stability in less favorable macroeconomic conditions. Further research is required, particularly with regard to the analysis of trends over an extended period of time.

It is acknowledged that our research is limited by a lack of detailed analyses of the production technologies employed, average production costs, an examination of the impact of the structure of the substrates utilized, transport costs, and system efficiency. This is due to the lack of access to this data. This requires in-depth research. In our opinion, it would be useful to use the case study method for the most technically efficient biogas plants and for the organizations that achieve the lowest level of technical efficiency. In this way, it is possible to obtain detailed information about the reasons for success and the mistakes made.

Author Contributions

Conceptualization, D.K., T.N. and B.K.; methodology, D.K. and T.N.; software, D.K. and T.N.; validation, D.K., T.N. and B.K.; formal analysis, D.K., T.N. and B.K.; investigation, D.K., T.N. and B.K.; resources, D.K., T.N. and B.K.; data curation, D.K. and T.N.; writing—original draft preparation, D.K., T.N. and B.K.; writing—review and editing, D.K., T.N. and B.K.; visualization, D.K., T.N. and B.K.; supervision, D.K.; project administration, D.K.; funding acquisition, D.K., T.N. and B.K. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Tables

Table 1

The structure of the analyzed agricultural biogas plants.

Biogas Plant Group	Number of Biogas Plants	%
I	7	16.3
II	19	44.2
III	17	39.5
Total	43	100.0

Source: own study.

Table 2

Technical efficiency indicators of the surveyed biogas plants and result of the Kruskal–Wallis test for the period 2019–2023.

Characteristics	Groups			p-Value
	I	II	III
2019
mean	0.22	0.23	0.40	0.0394
median	0.23	0.16	0.28
Q1 *	0.14	0.10	0.19
Q3 *	0.34	0.20	0.53
Skewness	−0.20	2.12	1.31
2020
mean	0.31	0.38	0.57	0.034
median	0.19	0.32	0.35
Q1	0.14	0.18	0.30
Q3	0.35	0.60	0.96
Skewness	2.31	0.94	0.40
2021
mean	0.62	0.44	0.67	0.018
median	0.57	0.33	0.68
Q1	0.35	0.25	0.55
Q3	1.00	0.67	0.79
Skewness	0.30	1.00	-0.08
2022
mean	0.51	0.41	0.64	0.063
median	0.39	0.34	0.71
Q1	0.22	0.17	0.41
Q3	1.00	0.56	1.00
Skewness	0.64	0.99	-0.16
2023
mean	0.46	0.23	0.45	0.048
median	0.33	0.16	0.33
Q1	0.16	0.13	0.22
Q3	0.79	0.23	0.62
Skewness	0.40	3.18	0.86

* Q₁—the first quartile (25th percentile); Q₃—the third quartile (75th percentile). Source: own study.

Table 3

The p-value for the multiple comparisons of the variable: technical efficiency indicators for the period 2019–2023.

DMU	Group I	Group II	Group III
2019
Group I		1	0.8299
Group II	1		0.0331
Group III	0.8299	0.0331
2020
Group I		1	0.0657
Group II	1		0.1289
Group III	0.0657	0.1289
2021
Group I		0.2987	1
Group II	0.2987		0.0194
Group III	1	0.0194
2022
Group I		1	0.8947
Group II	1		0.0574
Group III	0.8947	0.0574
2023
Group I		0.4099	1
Group II	0.4099		0.0542
Group III	1	0.0542

Source: own study.

Table 4

Distribution of technical efficiency (TE) in biogas plants [%].

Range	Total	Group I	Group II	Group III
2019
Less than 0.5	83.72	100	89.47	70.59
0.5 ≤ TE < 0.7	6.98	-	5.26	11.76
0.7 ≤ TE < 0.8	-	-	-	-
0.8 ≤ TE < 0.9	-	-	-	-
0.9 ≤ TE < 1	2.33	-	5.26	-
TE = 1	6.98	-	-	17.65
	100	100	100	100
2020
Less than 0.5	69.77	85.71	73.68	58.82
0.5 ≤ TE < 0.7	2.33	-	5.26	-
0.7 ≤ TE < 0.8	6.98	-	10.53	5.88
0.8 ≤ TE < 0.9	2.33	-	5.26	-
0.9 ≤ TE < 1	9.3	-	5.26	17.65
TE = 1	9.3	14.29	-	17.65
	100	100	100	100
2021
Less than 0.5	46.51	42.86	68.42	23.53
0.5 ≤ TE < 0.7	20.93	14.29	15.79	29.41
0.7 ≤ TE < 0.8	11.63	14.29	-	23.53
0.8 ≤ TE < 0.9	-	-	-	-
0.9 ≤ TE < 1	-	-	-	-
TE = 1	20.93	28.57	15.79	23.53
	100	100	100	100
2022
Less than 0.5	55.81	57.14	68.42	41.18
0.5 ≤ TE < 0.7	11.63	14.29	15.79	5.88
0.7 ≤ TE < 0.8	6.98	-	-	17.65
0.8 ≤ TE < 0.9	6.98	-	10.53	5.88
0.9 ≤ TE < 1	-	-	-	-
TE = 1	18.6	28.57	5.26	29.41
	100	100	100	100
2023
Less than 0.5	79.07	57.14	94.74	70.59
0.5 ≤ TE < 0.7	2.33	-	-	5.88
0.7 ≤ TE < 0.8	4.65	28.57	-	-
0.8 ≤ TE < 0.9	-	-	-	-
0.9 ≤ TE < 1	-	-	-	-
TE = 1	13.95	14.29	5.26	23.53
	100	100	100	100

Source: own study.

Table 5

Change in Malmquist index (from year to year; previous year = 1).

Statistics	Group I			Group II			Group III
	effch	techch	tfpch	effch	techch	tfpch	effch	techch	tfpch
2020/2019
mean	1.91	0.60	0.96	2.36	0.66	1.47	1.63	0.69	1.10
median	1.43	0.66	0.61	2.00	0.69	1.17	1.46	0.71	1.01
Q1	0.45	0.41	0.27	1.20	0.61	0.80	1.15	0.60	0.87
Q3	1.63	0.70	1.14	3.20	0.71	2.03	1.88	0.71	1.11
Skew	2.38	−1.01	1.99	0.86	−0.39	0.49	1.12	−0.02	2.58
2021/2020
mean	2.92	0.71	2.12	1.50	0.85	1.12	1.71	0.83	1.19
median	2.54	0.69	1.76	1.52	0.78	0.86	1.00	0.70	0.77
Q1	1.60	0.64	1.11	0.78	0.61	0.63	0.77	0.56	0.61
Q3	4.20	0.87	2.20	2.00	1.14	1.29	2.61	0.85	1.45
Skew	1.21	0.18	2.07	1.83	1.15	1.60	0.96	1.52	0.99
2022/2021
mean	0.81	1.86	1.43	1.12	1.34	1.50	1.05	1.42	1.48
median	0.95	1.62	1.62	0.98	1.33	1.53	1.00	1.36	1.36
Q1	0.39	1.38	0.90	0.50	1.16	0.54	0.67	1.27	0.86
Q3	1.04	2.30	1.86	1.52	1.60	2.46	1.06	1.50	1.71
Skew	−0.12	1.31	−1.05	0.92	0.40	0.35	1.57	1.33	0.83
2023/2022
mean	1.28	1.21	0.84	0.77	1.82	1.26	0.76	1.56	1.13
median	0.49	1.27	0.46	0.55	1.71	0.93	0.62	1.64	1.23
Q1	0.33	1.25	0.38	0.29	1.34	0.56	0.33	1.28	0.55
Q3	2.02	1.58	1.24	0.96	2.24	1.55	1.09	1.72	1.64
Skew	2.00	−1.98	1.58	2.07	0.39	1.76	0.27	0.78	0.52

effch—technical efficiency change; techch—technological change; tfpch—total factor productivity change (Malmquist Index). Source: own study.

Table 6

The p-value of the Wilcoxon test for comparisons of the indicator: total factor productivity (Malquist Index) in the analyzed period (from period to period).

Period	Group I	Group II	Group III
2020/2019	0.4630	0.0329	0.0003
2021/2020	0.0425	0.0015	0.0003
2022/2021	0.0910	0.0486	0.0005
2023/2022	0.3980	0.0100	0.0003

Source: own study.

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