A multi-grade reactive power utilization evaluation method for distribution networks with high renewables

This paper proposes a multi-grade reactive power utilization evaluation strategy for distribution networks with high renewables to identify the devices with low-grade utilization efficiency. Firstly, a suitability assessment indicator is presented to quantify the mismatch degree between reactive power demand and compensation capacity in distribution substations, and then a Kantorovich distance-based scenario reduction method is used to obtain typical reactive power load curves from historical data. Furthermore, influence factors on reactive power planning are investigated for distribution networks with different penetration level of renewable energy sources. Finally, considering zonal differences in load types and network structures, a multi-grade utilization evaluation strategy is proposed to identify inefficient reactive power equipment under various operating conditions. Comparative case studies have validated the superior performance of the proposed strategy for better utilization of reactive power compensation equipment.

1 Introduction

With the increasing penetration of renewable energy sources (RESs) connected to distribution networks, reactive power imbalance and voltage fluctuation problems have become increasingly prominent due to the intermittency and fluctuation of RESs (Kroposki, 2017). Various reactive power compensation equipment, including capacitor banks, static var compensator (SVC) and static var generator (SVG), have been extensively used to improve the voltage profile and power loss of distribution networks (Li et al., 2005; Salih and Chen, 2015). However, affected by the stochastic bidirectional power flow, these reactive power compensation devices always fail to meet the fluctuating reactive power demand with low utilization efficiency (Jhala et al., 2019; Xu et al., 2017). So far, lots of power equipment utilization evaluation methods, such as load factor (He et al., 2018), capacity-load ratio (Rani et al., 2024) and life cycle utilization rate (Hu et al., 2015; Ye et al., 2018), have been reported to identify the transformers and electrical feeders with low-grade utilization efficiency (Shi et al., 2017; Utlu and Hepbasli, 2007a). With the high-level integration of RESs in distribution networks, utilization evaluation methods for reactive power compensation equipment have not been involved (Li et al., 2020; Magdy et al., 2018; Bejestani et al., 2014). Consequently, this study aims to offer insightful perspectives and discussions on the evaluation of multi-grade reactive power utilization in distribution networks with high shares of RESs.

The main contributions of this study are twofold as listed: (1) A suitability assessment indicator is presented to quantify the mismatch degree between reactive power demand and compensation capacity in distribution substations, and a Kantorovich distance-based scenario reduction method is used to obtain typical reactive power demand curves from historical data; (2) Influence factors on reactive power planning are investigated for distribution networks with different penetration level of renewable energy sources, and a multi-grade evaluation method is proposed for identifying reactive power compensation equipment with low utilization efficiency.

2 A suitability assessment indicator for reactive power equipment utilization

Due to issues with reactive power demand and voltage exceeding normal ranges in substations, it is necessary to propose a suitability assessment indicator to evaluate the degree of matching between reactive power allocation and reactive power demand (Liu et al., 2014). The suitability assessment indicator is defined as the ratio of the reactive power mismatch area to the area provided by compensation equipment (Li et al., 2005). The reactive power demand of a substation $Q_{\text{re}}\left(t\right)$ comprises three components (Kaloudas et al., 2017): the compensation capacity required by loads $Q_{\text{rl}}\left(t\right)$, the reactive power losses of the main transformer $Q_{\text{mt}}\left(t\right)$, and half of the charging power of the 110 kV transmission line $Q_{\text{cp}}$ caused by capacitance effect, as shown in Equations 1–3.

$Q_{\text{re}}\left(t\right)=Q_{\text{rl}}\left(t\right)+Q_{\text{mt}}\left(t\right)-\frac{1}{2}{Q}_{\text{cp}}=Q_{\text{rl}}\left(t\right)+Q_{\text{mt}}\left(t\right)-\frac{3}{2}\epsilon L_{110}(1)$

$Q_{\text{rl}}\left(t\right)=Q_{\text{md}}\left(t\right)+Q_{\text{ld}}\left(t\right)=P_{\mathrm{m}}\left(t\right)\tan \left(\arccos {\phi }_{\mathrm{m}}\right)+P_{\mathrm{l}}\left(t\right)\tan \left(\arccos {\phi }_{\mathrm{l}}\right)(2)$

$\begin{array}{l}{Q}_{\text{mt}}\left(t\right)=Q_{\text{hw}}\left(t\right)+Q_{\text{mw}}\left(t\right)+Q_{\text{lw}}\left(t\right)+Q_0=\frac{U_{k3}\%}{100}\frac{{P_{\mathrm{l}}}^2\left(t\right)+{Q_{\mathrm{l}}}^2\left(t\right)}{S_{\mathrm{N}}}+\frac{U_{k2}\%}{100}\frac{{P_{\mathrm{m}}}^2\left(t\right)+{Q_{\mathrm{m}}}^2\left(t\right)}{S_{\mathrm{N}}}\\ +\frac{U_{k1}\%}{100}\frac{{\left(P_{\mathrm{m}}\left(t\right)+P_{\mathrm{l}}\left(t\right)\right)}^2+{\left(Q_{\text{md}}\left(t\right)+Q_{\text{ld}}\left(t\right)+Q_{\text{mw}}\left(t\right)+Q_{\text{lw}}\left(t\right)\right)}^2}{S_{\mathrm{N}}}+\frac{I_0\%}{100}{S}_{\mathrm{N}}\end{array}(3)$

where $\epsilon$ is the charging power per unit length of the 110 kV overhead line, 0.034 Mvar/km; $L_{110}$ represents the length of the 110 kV overhead line; $Q_{\text{hw}}\left(t\right),Q_{\text{mw}}\left(t\right),Q_{\text{lw}}\left(t\right)$ denote reactive power losses of high-voltage, medium-voltage and low-voltage sides at time t, respectively; $Q_0$ presents the no-load loss of the main transformer; $U_{k1}\%,U_{k2}\%,U_{k3}\%$ define impedance voltage of high, medium and low sides, respectively; $S_{\mathrm{N}}$ is the rated capacity of the main transformer; $Q_{\text{md}}\left(t\right),Q_{\text{ld}}\left(t\right)$ stand for the reactive power compensation capacity required for medium-voltage and low-voltage sides at time t; $\cos {\phi }_{\mathrm{m}},\cos {\phi }_{\mathrm{l}}$ represent power factors on the medium-voltage and low-voltage sides; $P_{\mathrm{m}}\left(t\right),P_{\mathrm{l}}\left(t\right)$ present the active power load on the medium-voltage and high-voltage sides at time t; $I_0\%$ is the no-load current of the main transformer.

To reduce the computational costs for the 365 days-long analysis of historical data from the substation, a Kantorovich distance-based scenario reduction method is employed to generate a set of typical reactive power demand curves for calculating the suitability assessment indicator (do Prado and Qiao, 2018), as shown in Figure 1A. The Iterative Self-organizing Data Analysis Techniques Algorithm (ISODATA) is applied to group the 365 days of reactive power demand curves into distinct clusters (Lin et al., 2017; Li et al., 2024; Cao et al., 2024). For the i-th cluster set $W_i$ obtained by the clustering algorithm, the Kantorovich distance between two curves is defined as the product of their Euclidean distance and the proportion of each curve in relation to the total curves in set $W_i$. During each iteration, the curve $u_d^{\prime }$ with the minimum Kantorovich distance to the other curves is selected and added to the removal set ${W_i}^{\prime }$. Consequently, the number of curves in set $W_i$ decreases by one, while the number of curves in the removal set ${W_i}^{\prime }$ increases by one. To ensure that the sum of all curve proportions in set $W_i$ equals 1, the proportion of curve $u_d$, which is the adjacent to the removed curve $u_d^{\prime }$, is updated by incorporating the proportion of $u_d^{\prime }$ to the original value. These steps are repeated iteratively until each cluster set is reduced to a single representative curve (Golshani et al., 2017; Krishnamurthy et al., 2017).

Figure 1

Figure 1. Suitability assessment and multi-grade utilization evaluation of reactive power.

Based on the Kantorovich distance-based scenario reduction method described above, the set of demand curves is generated for enhancing computational efficiency and extracting the typical operating characteristics in the substation. Considering the discrete voltage regulation behavior of capacitors, a stepwise compensation curve can be generated based on capacitor switching taps and the average value between adjacent taps. The capacitor switching tap $T_{\mathrm{m}}^k$ is formed by the combination of the compensation capacities of individual capacitor units (Salih and Chen, 2015). Furthermore, the average value of adjacent $T_{{\mathrm{m}}^{\prime }}^k$ taps is the average value of the k-th $T_{\mathrm{m}}^k$ tap and the (k-1)-th $T_{\mathrm{m}}^{k-1}$ tap. If the demand curve $Q\left(t\right)$ lies within the interval $\left(T_{\mathrm{m}}^{k-1},T_{{\mathrm{m}}^{\prime }}^k\right]$, the corresponding tap is $T_{\mathrm{m}}^{k-1}$. If $Q\left(t\right)$ falls within the interval $\left(T_{{\mathrm{m}}^{\prime }}^k,T_{\mathrm{m}}^k\right]$, the corresponding tap is $T_{\mathrm{m}}^k$. Therefore, a stepwise compensation curve is obtained by analyzing the relationship between the demand curve and intervals of capacitor switching taps. The demand curve of the substation and the reactive power compensation curve are depicted by the black dashed line and the red solid line, respectively, as shown in Figure 1A. The area of reactive power mismatch is calculated as the area between these two curves, represented by the purple and orange areas. The suitability assessment indicator of the substation $E_{\text{match}}$ is quantified by calculating the mismatch area of each reactive power demand curve, weighted by the proportion of the curve v relative to the total annual reactive power demand, as illustrated in Equation 4.

$E_{\text{match}}={\displaystyle \sum _{v=1}^{N_v}}{\eta }_v{\alpha }_v={\displaystyle \sum _{v=1}^{N_v}}{\eta }_v\frac{{\int }_0^{96}\left|Q_{\text{supply},v}^t\right.-\left.Q_{\text{demand},v}^t\right|dt}{{\int }_0^{96}{Q}_{\text{supply},v}^{t}dt}(4)$

where ${\alpha }_v$ denotes the proportion of the mismatch area for the demand curve v to the area of reactive power capacity provided by compensation equipment; ${\eta }_v$ represent the proportion of the reactive power demand curve v relative to the total annual demand; $N_v$ presents the total number of the set of demand curves obtained based on the Kantorovich distance-based scenario reduction method; $Q_{\text{demand},v}^t$ and $Q_{\text{supply},v}^t$ represent the demand and the tap of compensation equipment for the curve v of the substation at time t, respectively.

3 Multi-grade reactive power utilization evaluation strategy for distribution networks

In recent years, some zones have faced challenges such as weak network structures, limited power supply capacity, inefficient reactive power compensation equipment, and a high idle rate of capacitors (Rani et al., 2024; Zhou et al., 2018; Keane et al., 2010; Keane and O’Malley, 2007). And existing standards primarily focus on individual standards such as reactive power allocation, power factor, and voltage qualification rate (Utlu and Hepbasli, 2007a; Utlu and Hepbasli, 2007b). Therefore, it is essential to establish a comprehensive and effective of the utilization evaluation strategy for reactive power compensation equipment in preventing prolonged equipment idleness and enhancing the utilization of reactive power compensation equipment. Moreover, the levels and fluctuations of reactive power demand in substations directly affect the utilization of reactive power compensation equipment (Qin et al., 2010). Considering characteristic factors such as power source and load types, grid structure, key parameters are presented to accurately analyze the reactive power demand of distribution networks with varying proportions of RESs, such as short-circuit capacity, voltage level, topology, and power factor, as shown in Figure 1B.

The utilization evaluation strategy of reactive power compensation equipment includes several key indicators: the suitability, the idle rate, the switching uniformity, and the capacity utilization rate. The suitability $E_{\text{match}}$ is the proposed concept in Equation 4. The idle rate $E_{\text{rdo}}$ is defined as the proportion of the idle time of reactive power equipment with respect to the total available operating time in Equation 5. The switching uniformity $E_{\text{rsu}}$ is presented to reflect the balance in the distribution of switching frequencies among reactive power equipment in Equation 6. The capacity utilization rate $E_{\text{rcu}}$ is defined in Equation 7.

$E_{\text{rdo}}=\frac{{\displaystyle \sum _{n=1}^{N_{\mathrm{c}}^{\text{idle}}}}{S}_n{T}_n}{{\displaystyle \sum _{m=1}^{N_{\mathrm{c}}}}{S}_m{T}_m}(5)$

$E_{\text{rsu}}=\frac{\sqrt{\frac{1}{N_{\mathrm{c}}}{\displaystyle \sum _{s=1}^{N_{\mathrm{c}}}}{\left(f_{\mathrm{c}}^s-\frac{1}{N_{\mathrm{c}}}{\displaystyle \sum _{s=1}^{N_{\mathrm{c}}}}\left(f_{\mathrm{c}}^s\right)\right)}^2}}{\frac{1}{N_{\mathrm{c}}}{\displaystyle \sum _{s=1}^{N_{\mathrm{c}}}}\left(f_{\mathrm{c}}^s\right)}(6)$

$E_{\text{rcu}}=\frac{{\displaystyle \sum _{i=1}^{N_{\mathrm{c}}}}{\displaystyle \sum _{j=1}^{365}}{\int }_0^{96}{Q}_{i,j}\left(t\right)dt}{{\displaystyle \sum _{m=1}^{N_{\mathrm{c}}}}\left(Q_{\text{rated}}^m{T}_m\right)}(7)$

where $N_{\mathrm{c}}$ represents the total number of capacitors in the zones; $f_{\mathrm{c}}^s$ denotes the total annual switching count of the equipment s; $N_{\mathrm{c}}^{\text{idle}}$ is the number of capacitors idle for over 24 h; $S_n$ and $T_n$ are the total capacities and hours of equipment idle for over 24 h, respectively; $S_m$ and $T_m$ are the total capacities and hours of all equipment during the evaluation period; $Q_{\text{rated}}^m$ presents the rated capacity of the equipment m; $Q_{i,j}\left(t\right)$ is the actual capacity of the equipment i in time t.

The capacity utilization rate is only a positive indicator. Therefore, it is necessary to normalize and align the directions of all indicators to ensure consistency in the evaluation process. A balanced and comprehensive method is employed to determine the weights of four indicators by combining the entropy weight method and the Criteria Importance Through Intercriteria Correlation (CRITIC) method. The Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is then used to rank the utilization efficiency based on the proximity of the evaluation objects to the ideal target (Arce et al., 2015). The final calculation results are converted to a 0–100 range with a linear scaling method, and rounded up to the nearest integer to obtain the utilization evaluation standards (Guo et al., 2013). Considering zonal differences in load types and grid structures, the demand for reactive power equipment utilization can generally be classified into four types: commercial areas, industrial areas, residential areas, and rural areas. The commercial areas exhibits stable daily load with prominent morning and evening peaks; the industrial areas has complex and volatile loads, significantly influenced by production schedules and equipment operation, resulting in high dynamic randomness; the residential areas shows obvious daily load fluctuations, with prominent morning and evening peaks and lower loads during midday and nighttime; the rural areas experience strong seasonal load fluctuations, significantly affected by external factors such as busy and slack farming seasons and climatic conditions. These distinct characteristics lead to regionalized reactive power demands in each area, posing different requirements for the configuration and utilization rates of reactive power equipment. The four types can be further subdivided into high or low proportions of RESs, thereby setting out multi-grade evaluation standards for the utilization rate of reactive power compensation equipment. The score for low efficiency in reactive power equipment utilization is defined as below 40. Thus, a multi-grade evaluation strategy can be employed for different zones to identify reactive power compensation equipment with low utilization efficiency, as shown in Figure 1C.

4 Case study

To highlight the advantages of the proposed reactive power demand calculation method in improving voltage compensation effectiveness compared to other traditional calculation methods, a 110 kV substation in Gansu Province, China, is selected as the study object for comparative analysis in terms of meeting voltage compliance requirements. The specific topology is shown in Figure 2A. The main transformer is of type SSZ10-31500/110. Branch 3-4 and branch 4-5 are both overhead lines (JL/G1A-120), with lengths of 42.8 km and 40.1 km, respectively. The power base value is set at 100 MVA, and the voltage limits for nodes are defined as 1.05 p.u. and 0.95 p.u. The voltage distribution results for the substation over a year are analyzed under three cases, as illustrated in Figures 2B–D: without capacitor compensation; with capacitor compensation based on the reactive power demand calculated by the traditional calculation method; with capacitor compensation referring to the reactive power demand obtained by the proposed method.

Figure 2

Figure 2. Topology and voltage distribution comparison for a 110 kV substation.

The per-unit voltage distribution without capacitor compensation is shown in Figure 2B. The results of node voltages falling below 0.95 p.u. indicate that the absence of reactive power compensation leads to voltage distribution noncompliance at the substation, thereby compromising the stability of the power system. Over-limit voltage issues persist at certain nodes in Figure 2C, indicating that the reactive power demand calculated by the traditional method as the capacitor compensation value improves overall voltage levels but fails to address variations in reactive power demand effectively. Additionally, the traditional method oversimplifies transformer losses and does not ensure the power factor remains within the acceptable range. The reactive power demand calculated by the proposed method in Equations 1–3 for capacitor compensation demonstrates all node voltages remain within the qualified range of 0.95–1.05 p.u., as shown in Figure 2D. In contrast to the traditional method, the proposed method precisely matches reactive power demand to enhance voltage compliance rates and operational stability, providing more reliable and scientifically grounded guidance for reactive power compensation. Consequently, the proposed method ensures that all node voltages simultaneously remain within the acceptable range, meeting both operational needs and voltage quality requirements.

Four cases are employed for analyzing various types of zones to further verify the effectiveness of the proposed suitability assessment indicator evaluation model. Case 1 and Case 4 apply the proposed ISODATA clustering method combined with the Kantorovich distance-based scenario reduction method. Case 2 employs only the ISODATA clustering method, while Case 3 applies the k-means method. Cases 1–3 adopt the proposed reactive power demand calculation method, whereas Case 4 implements the traditional method. The comparative results to evaluate suitability assessment indicators for various zone types are presented in Table 1.

Table 1

Table 1. Suitability assessment indicators for various zone types in four cases.

From the above table, Case 1 demonstrates significantly higher suitability in zone types compared to other cases. This indicates that the proposed evaluation model effectively captures reactive power demands by accounting for a wide range of operating conditions and power flow scenarios, accurately reflecting the matching degree between reactive power demands and compensation capacities under diverse scenarios, such as peak loads, valley loads, and seasonal fluctuations. Compared with Case 2 and Case 3, the proposed ISODATA clustering method demonstrates better performance in addressing irregular reactive power demand data and dynamically adjusting the number of clusters. Cases 2 and 3 both rely on a single or a few typical operating conditions for reactive power balance calculations, such as maximum or minimum load, simplifying the actual reactive power demand and resulting in generally lower calculation values. Compared with Case 4, Case 1 not only more accurately captures variations in reactive power demands of substations under diverse operating conditions and closely aligns with actual operating characteristics, but also identifies potential mismatch issues through higher suitability.

The suitability in the industrial zone is higher than other zones due to significant and complex load fluctuations driven by large inductive loads, such as motors and heavy machinery. Frequent equipment start-ups and shutdowns during production processes lead to rapid changes in load, causing large fluctuations in the reactive power demand curve. In contrast, residential zones exhibit relatively low overall loads with minimal fluctuations, resulting in a smooth reactive power demand curve and the lowest suitability among all zones. The suitability in commercial and rural zones falls between that of industrial and residential zones. Commercial zones demonstrate relatively high suitability but slightly lower than industrial zone. The load in commercial areas primarily comes from equipment such as lighting, air conditioners and elevators with smaller fluctuations than those in industrial zone. The load in rural areas is relatively dispersed with longer transmission lines. Particularly during agricultural production seasons, the application of irrigation systems and electric machinery leads to significant load fluctuations, increasing the suitability and causing sharp variations in demand.

In order to validate the effectiveness of the evaluation strategy for multi-grade reactive power utilization, three cases for a comparative analysis of zonal applicability are designed in the present study. Case 5 implements the proposed method described in this study. In Case 6, ignoring the impacts of renewable energy penetration and load types, each zone is scored and ranked separately with the same indicator weights. In Case 7, similar to Case 5, indicator weights are customized based on zonal characteristics, but all zones are scored and ranked together. This section selects eight distinct low-efficiency zones (A-H) identified from Case 1, representing high and low renewable energy penetration in commercial, industrial, residential, and rural areas. The utilization efficiency evaluation results for these areas under the other cases are shown in Table 2, with ranking scores provided in parentheses.

Table 2

Table 2. Zonal applicability of reactive power utilization and scores under different cases.

It can be observed that high proportions of RESs lead to significant fluctuations in reactive power demand, characterized by lower idle rates and higher values in other indicators. In Case 5, the customized weights tailored to zonal characteristics provide a balanced evaluation, thereby accurately reflecting the utilization efficiency across different zones. However, in Case 7, despite employing zonal-specific weights, the unified scoring and ranking approach introduces discrepancies in the relative rankings of certain areas, leading to some areas still exhibiting higher utilization rates. Notably, zones B, D, and F are identified as having high-efficiency reactive power equipment utilization rates under this approach. Compared to Case 5, identical weights for all zones neglects the varying emphasis on indicators across different areas, resulting in high utilization rates for zone A in Case 6.

5 Discussion and conclusions

A comprehensive overview of multi-grade reactive power utilization evaluation for distribution networks with high renewables is presented in this paper, the key findings of this paper can be summarized as follows: 1) The proposed suitability assessment indicator is presented to evaluate the degree of matching between reactive power allocation and demand under various typical operating conditions, reflecting actual reactive power demand characteristics and resulting in slightly higher suitability; 2) The multi-grade reactive power utilization evaluation strategy is established to accurately categorizes inefficient utilization rates of reactive power equipment in different zones, thereby providing valuable insights for the refinement of allocation strategies for reactive power equipment; 3) The further research will focus on diversified flexibility resources integration into active distribution networks.

Data availability statement

The data analyzed in this study is subject to the following licenses/restrictions: This study involves confidential information. Requests to access these datasets should be directed to Wanyan Zeng, 1452582007@qq.com.

Author contributions

MX: Writing–original draft, Investigation. WY: Writing–original draft, Conceptualization. WZ: Writing–original draft, Writing–review and editing, Methodology. TL: Writing–original draft. ZW: Writing–original draft. QD: Conceptualization, Data curation, Methodology, Writing–review and editing.

Funding

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.

Conflict of interest

Authors MX, WY, TL, and ZW were employed by Development Division of State Grid Gansu Electric Power Company.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The authors declare that no Generative AI was used in the creation of this manuscript.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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