Improving Photovoltaic Power Management Efficiency in Three-Phase Prosumer Grids

Enhancing the Efficiency of Photovoltaic Power Flows Management in Three-Phase Prosumer Grids

Households equipped with photovoltaic (PV) systems play a significant role in reducing greenhouse gas emissions and combating global climate change. To maximize the advantages of clean solar energy, it is crucial to ensure its efficient utilization. This can be achieved by consuming all generated energy locally, either within the household or a microgrid community, thus minimizing losses during grid transportation and storage.

In this study, we introduce a method aimed at enhancing self-consumption by eliminating simultaneous bidirectional energy flows in the phase lines of a three-phase grid-tied household system, especially in instances of significant load asymmetry. We developed an Adaptive Power Flow Management (APFM) algorithm that distributes solar-generated energy across the household grid’s phase lines according to their respective loads and solar power generation levels.

Simulations based on real-world data demonstrated that the APFM algorithm effectively eliminated simultaneous active power import and export flows. Additionally, it ensured that all power exported from the household to the Distribution System Operator (DSO) grid remained symmetrical across all phase lines. Results from the simulations indicated that applying the APFM algorithm reduced daily energy imports and exports between the household and the DSO grid by an average of 27.5% during the spring–autumn period for a specific household. Moreover, this reduction in energy flow led to an average increase of 5% in self-consumption within the household grid, with peak improvements reaching 16.5%.

Keywords: photovoltaic; inverter control algorithm; three-phase prosumer grid; asymmetric phase line loads; self-consumption; adaptive power flow management; bidirectional power flow.

1. Introduction

The European Green Deal initiative, launched by the European Commission, aims to accelerate the adoption of renewable energy and promote energy efficiency to achieve climate neutrality by 2050. Energy efficiency, particularly in electricity, is vital for both environmental sustainability and economic growth. Households in Lithuania and other EU countries are key players in increasing renewable electricity adoption and have significant potential to enhance energy consumption efficiency in the future. Efficient management of self-generated energy supports sustainable development, leading to lower electricity costs and a substantial reduction in carbon footprints.

Over the last decade, the rapid adoption of photovoltaic (PV) installations has been driven by three main factors: technological advancements, cost reductions, and supportive government policies. However, the swift expansion of solar power plants introduces new challenges for grid operators and consumers alike. The inherent variability of photovoltaic electricity generation, influenced by fluctuating solar irradiation, becomes increasingly problematic as the installed capacity of solar plants grows. This expansion can lead to grid instability and frequent voltage fluctuations, frequency deviations, and a widening imbalance between supply and demand. Notably, most household devices are single-phase, which contributes to uneven load distribution across phase lines and results in voltage imbalances in the network. This issue becomes more pronounced as additional small single-phase solar power plants connect to the DSO grid, ultimately creating barriers to the further expansion of individual renewable generation capacity.

One effective solution to address generation imbalance is the implementation of high-capacity energy storage systems (ESS) to store excess energy. ESS help balance the mismatch between renewable electricity generation and consumption during the day, reducing load imbalances in the distribution grid when operating in on-grid mode. However, the high costs of many ESS types and their relatively rapid degradation often make initial investments unfeasible, which partly explains the limited adoption of ESS.

An alternative approach involves modifying individual energy consumption models to encourage the use of energy-intensive devices during peak daylight hours. Although technically straightforward and not reliant on energy storage, this approach requires behavioral changes from consumers, which can affect comfort and quality of life, making it less appealing for many users today.

Another viable solution to effectively address the supply-demand imbalance and increase self-consumption of locally generated electricity is the establishment of consumer communities. These communities integrate multiple neighboring consumers into a single large-scale microgrid, where one or more photovoltaic sources supply energy distributed among all members, leading to greater local consumption of generated energy. However, practical examples of such implementations are still rare, as establishing and maintaining these consumer community microgrids require substantial infrastructure investment and the creation of appropriate regulatory frameworks in each country. Given the current landscape, the rapid widespread adoption of community microgrids appears unlikely in the near future.

A solar inverter equipped with a load-sensitive control algorithm can also provide a solution to eliminate the imbalance in three-phase grids and enhance grid quality parameters. For instance, a study describes an inverter control method that adjusts voltage magnitude and addresses voltage unbalance through reactive power injections into the distribution grid. Another study presents a dual-mode inverter capable of both grid-following and grid-forming, featuring a hierarchical control structure incorporating power, voltage, and current control loops to regulate grid voltage and limit current under unbalanced conditions. However, many existing studies lack a detailed examination of real-life daily power flows between three-phase prosumers and the DSO grid under unbalanced conditions.

In this paper, we explore the challenges posed by load imbalance in individual prosumer systems and propose a solar inverter control algorithm. Our approach aims to fully mitigate simultaneous bidirectional power flows caused by load imbalances across phase lines in a prosumer’s household microgrid. We introduce a load-adaptive photovoltaic power redistribution strategy for three-phase microgrids and detail the development of an adaptive power flow management (APFM) algorithm.

2. Simultaneous Bidirectional Power Flows

Individual prosumers with solar power systems face additional challenges rarely discussed in the literature, including managing photovoltaic power flows in an unbalanced three-phase household grid. A typical structure of a grid-connected household system with its own solar plant is presented in Figure 1.

Data analysis from household grid smart meters reveals anomalies; even when a local photovoltaic system generates sufficient power to meet a household’s electricity demand, power may still be imported from the DSO grid. This occurs when phase lines in the household grid are asymmetrically loaded. In such cases, one heavily loaded phase line may import power while another exports excess power. Previous case studies have demonstrated that the annual overlap of imported and exported energy ranges from approximately 6% to 18%, with certain days showing overlaps exceeding 60%. The highest overlaps were observed in households with smaller installed capacities, decreasing as installed capacity increased.

Standard DSO smart meters only provide cumulative data at hourly intervals, limiting the ability to analyze power flows accurately over short periods. Our previous work examined power flow overlap using smart meters with one-second time resolution, revealing that roughly half of bidirectional energy flows resulted from asymmetric, time-varying phase loads in the three-phase household grid, while the other half emerged from changes in solar irradiation or the activation of high-power single-phase loads within an hour. Rapid fluctuations in grid loads can cause the ratio of imported to exported power to change multiple times per minute. Consequently, one-hour resolution measurements fail to capture these dynamics accurately. By using one-second resolution data, we can filter out the influence of slow-changing factors and identify that asymmetric phase loading remains the primary cause of simultaneous bidirectional power flows.

An earlier study proposed an asymmetric inverter to address load unbalance within phase lines. Standard solar string inverters, commonly used in small prosumer households due to their low cost and easy installation, typically operate in symmetric mode, distributing generated power evenly across all three-phase lines. However, advancements in inverter technology have led to hybrid solar inverters equipped with smart meters that can operate in asymmetric mode, distributing power unevenly across the three-phase household grid lines. Unfortunately, these hybrid solutions only partially enhance local photovoltaic energy utilization. If generated energy falls short, and one phase line’s load exceeds that of the other two, the hybrid inverter cannot completely eliminate simultaneous active power import and export flows.

This paper further investigates the unique challenges faced by individual prosumers and explores a potential solar inverter control algorithm aimed at fully addressing simultaneous bidirectional power flows caused by load imbalances across phase lines in the prosumer’s household grid.

3. Inverter Control Algorithm

The structure of a three-phase household grid includes a solar power plant, a three-phase inverter, and household loads, connecting to the DSO grid via a standard energy meter. The total power generated by the solar plant at the inverter’s output, excluding the small power consumed by the inverter itself, is expressed as:

[ P_{inv} = P_{inv L1} + P_{inv L2} + P_{inv L3} = \sum_{i=1}^{3} P_{inv L_i} ]

The total power consumed in the household is calculated as:

[ P_{cons} = \sum_{i=1}^{3} P_{cons L_i} ]

The total power connected to the DSO grid is:

[ P_{dso} = \sum_{i=1}^{3} P_{dso L_i} ]

Based on the situation, the power in each three-phase line connected to the DSO grid can either be supplied to the household grid (imported) or exported when the solar power plant generates excess power. If ( P_{dso L_i} > P_{inv L_i} ), energy is imported on the i-th line, and if ( P_{dso L_i} < P_{inv L_i} ), energy is exported. Therefore, a standard symmetric mode inverter can create situations where some phase lines import energy while others export it. To prevent this, the three-phase inverter should adaptively assess load changes on each household phase line over time and adjust power management for each inverter output phase line accordingly.

The APFM algorithm for solar inverters, developed by the authors, is illustrated in Figure 2. At each time reference period ( Δt ), the algorithm takes as input the power values for all three-phase line loads and the total inverter output power.

Initially, the power values of all three loads are sorted in ascending order:

[ P_{L_{max}} = max(P_{cons L1}, P_{cons L2}, P_{cons L3}) ]
[ P_{L_{med}} = med(P_{cons L1}, P_{cons L2}, P_{cons L3}) ]
[ P_{L_{min}} = min(P_{cons L1}, P_{cons L2}, P_{cons L3}) ]

Next, the phase line indices corresponding to these sorted power values are recorded. The imbalance of phase line loads is evaluated by the differences between the power values of the phase line loads:

[ diff_1 = P_{max} – P_{med} ]
[ diff_2 = P_{med} – P_{min} ]

The algorithm’s operation is divided into three cases based on the power generated by the solar power plant and the load consumption:

1. If ( P_{inv} ≤ diff_1 ), all generated power is directed to the most heavily loaded phase line.
2. If ( diff_1 < P_{inv} ≤ diff_1 + 2 \times diff_2 ), the generated power is distributed between the two most heavily loaded phase lines.
3. If ( P_{inv} > diff_1 + 2 \times diff_2 ), the power is distributed among all three-phase lines according to predefined rules.

The pseudocode of the proposed APFM algorithm is provided below:

1. Read the household load power data for each phase line and the total inverter output power.
2. Sort the phase load powers in descending order to determine the values for each phase line.
3. Define the indices corresponding to the sorted phase loads.
4. Calculate the differences between the power values of the phase line loads.
5. Based on the conditions, determine the new power values for each phase line.
6. Assign these new power values to the PV inverter outputs for each phase line.

This algorithm ensures that all energy provided by the inverter is primarily utilized for load balancing within the phase lines.

4. Simulation Results

The proposed algorithm was tested using real household data. A measurement system with two additional smart three-phase electricity meters was installed in a household grid powered by a solar power plant. These meters recorded average active power flows at one-second intervals. One meter measured bidirectional power on the edge of the DSO grid, while the other tracked power flows from the solar plant’s inverter outputs. Each measured data sample was transmitted to an SQL server in real time and stored for analysis.

The operation of the household grid was simulated using MATLAB/Simulink, both with and without the proposed APFM algorithm. During the simulation of the APFM algorithm, real three-phase output data from the household inverter and data from the lines connected to the DSO grid were used for each time interval. Using this data, the total power generated by the solar power plant and the consumption power in each phase line were calculated and processed by the APFM algorithm.

To evaluate the effectiveness of the APFM algorithm, simulated output data from the adaptive asymmetric mode inverter were compared with those from the measured symmetric mode inverter output over several days.

For visualization, the two most extreme cases (6 June and 15 April) were selected. The power flow profiles for these days are displayed, showing active power and time metrics. The results demonstrate that the household grid’s three-phase lines are unevenly loaded, with significant differences in power flows across the phase lines.

The comparison of imported and exported power flows illustrates how the inverter adjusts to changing loads in the grid. When the solar plant generates sufficient power, the imported power flows are nearly eliminated.

5. Discussion

The adaptive asymmetric inverter mode operating under the proposed APFM algorithm enables more efficient utilization of solar-generated energy within the household. This results in more energy being consumed locally, thereby reducing energy imports. The adaptability of the APFM algorithm allows it to control the inverter’s operation based on load variations in the household grid. Notably, any reduction in imported energy corresponds to an equal reduction in energy exported to the DSO grid, effectively minimizing simultaneous bidirectional power flows.

The research results demonstrate that employing the proposed APFM algorithm leads to an average reduction of 27.5% in imported energy. Furthermore, the adaptive asymmetric inverter mode was found to be more efficient at lower solar power generation levels. In contrast, the symmetric mode inverter tends to cause imbalances in the DSO grid during solar generation, failing to adapt to load variations. The proposed adaptive inverter mode significantly reduces phase line imbalances, resulting in a daily average imbalance of less than 1%.

6. Conclusions

The research indicates that simultaneous active power import and export flows in a three-phase prosumer household grid can be effectively eliminated by implementing the proposed APFM algorithm. This solution not only enhances the efficiency of solar energy utilization but also minimizes energy exchange with the distribution grid, thus improving grid capacity. The simulations showed a significant reduction in both imported and exported energy, along with improved self-consumption and self-sufficiency rates.

By adopting the APFM algorithm within hybrid solar inverters, households can achieve a more balanced and efficient use of locally generated solar energy, ultimately contributing to a more sustainable energy future.