Study on the Evolutionary Process and Balancing Mechanism of Net Load in Renewable Energy Power Systems

Abstract

With the rapid development of renewable energy sources such as wind and solar, the net load characteristics of power systems have undergone fundamental changes. This paper defines quantitative analysis indicators for net load characteristics and examines how these characteristics evolve as the proportion of wind and solar energy increases. By identifying inflection points in the system’s adjustment capabilities, we categorize power systems into low, medium, and high renewable energy penetration. We then establish adjustment models that incorporate traditional coal power, hydropower, natural gas generation, adjustable loads, system interconnections, pumped-storage hydroelectricity, and new energy storage technologies. A genetic algorithm is employed to optimize and balance the net load curves under varying renewable energy proportions, analyzing the mechanism behind net load balance. A case study, based on real operational data from 2023 for a provincial power grid in western China, which is rich in renewable resources, conducts a quantitative analysis of the system’s adjustment capability inflection point and net load balancing strategies. The results demonstrate that the proposed method effectively captures the evolution of the system’s net load and reveals the mechanisms of net load balancing under different renewable energy penetration levels.

1. Introduction

In recent years, the rapid development of new energy sources, particularly wind power and photovoltaics, has gradually established them as the primary power sources within power systems. As early as 2010–2015, China [1], the United States [2], and Europe [3] each proposed visions for constructing high-proportion new energy power systems by 2050, targeting penetration rates of 60%, 80%, or even 100%. With the increasing installed capacity and penetration of new energy sources, the operating characteristics of power systems have changed significantly. In particular, the volatility of net system load has increased, reflecting a substantial rise in the system’s demand for regulation capabilities [4]. To further promote the development of new energy sources, it is essential to conduct in-depth research on the evolution process and balancing mechanisms of the power system’s net load.

The net load of a power system is typically defined as the difference between the total load (including electricity demand from all users) and the variable generation from renewable energy sources such as wind and solar power [5,6,7,8]. The net load curve intuitively reflects system fluctuations and the flexibility requirements resulting from the combination of load and renewable energy characteristics. It serves as a key reference for studying the integration of renewable energy into the power system. Scholars worldwide have conducted extensive research on net load, exploring aspects such as net load characteristics, forecasting, and system flexibility assessment through net load analysis [4,9,10,11,12,13,14,15]. Common methods for net load analysis include machine learning algorithms, statistical approaches, and numerical simulations. In grids with high renewable energy penetration, models like Long Short-Term Memory (LSTM) and Support Vector Machines (SVM) are frequently used for net load forecasting [6,9]. Reference [4] proposes a net load forecasting method based on the gray system theory for systems with high renewable energy penetration. In reference [5], the net load carrying capability (NLCC) index is introduced to assess a generating unit’s contribution to system flexibility. However, a single index focused on generating units is insufficient to fully capture the net load fluctuation characteristics of systems with high renewable energy penetration. Existing studies lack comprehensive quantitative indicators for characterizing net load fluctuations, and there is insufficient research on the evolution of net load characteristics and balancing mechanisms at various stages of renewable energy development, particularly as the penetration rates of variable renewable energy increase.

This paper introduces a systematic quantitative indicator system for analyzing net load evolution in power systems with varying proportions of renewable energy. By defining boundaries based on the turning points of different types of regulating resources used to balance net load, power systems are classified into low, medium, high, and ultra-high renewable energy scenarios according to their regulation requirements. Models of representative regulating resources within the power system are developed. A scientifically designed fitness function integrates these resources, and a genetic algorithm (GA) is applied to optimize and balance the net load curves at different stages of renewable energy development. Genetic algorithms, known for their flexibility in adjusting parameters and superior performance in optimizing complex systems [16,17], have proven effective in power system studies, revealing the balancing mechanisms of net load at each stage. In conclusion, this paper proposes an innovative quantitative net load analysis indicator system, develops models for various regulating resources, and utilizes genetic algorithm optimization to allocate these resources. It also scientifically defines the stages of renewable energy development based on regulation requirements, providing insights into the mechanisms that balance net load in high-renewable energy systems.

In this paper, it is important to clarify that renewable energy refers specifically to variable sources such as wind and solar power, while controllable renewable sources, such as solar thermal and biomass power plants, are excluded from the scope of this study. The power systems analyzed are primarily located in resource-rich regions of China, including Northeast, Northwest, and North China, where coal, wind, and solar resources are abundant. These systems rely on a generation mix dominated by coal-fired power, hydropower, wind, and photovoltaic generation. Maintaining net load balance in these systems, given the high proportion of variable wind and solar energy, presents significant challenges.

2. Quantitative Analysis Indicators for Net Load Characteristics

2.1. Net Load Fluctuation Coefficient, NLfc

Defined as the ratio of the net load peak-to-trough difference to the original load peak-to-trough difference, this metric enables analysis of the relative magnitude of net load fluctuations. By evaluating this ratio, the amplitude of net load fluctuations can be quantified. A higher fluctuation coefficient signifies a greater impact of renewable energy integration on the system, as shown in (1).

$$N{L}_{fc}=\frac{∆L_{net}}{∆L_{total}}$$

(1)

where $N{L}_{fc}$ denotes the net load fluctuation coefficient, $∆L_{net}$ represents the net load peak-to-trough difference, and $∆L_{total}$ denotes the original load peak-to-trough difference.

The net load fluctuation coefficient ($N{L}_{fc}$) measures the amplitude of net load fluctuations relative to total load, indicating the overall stability of the system in response to renewable energy variability. A higher $N{L}_{fc}$ suggests that fluctuations in renewable energy significantly increase the system’s regulation difficulty and vulnerability, necessitating the integration of more flexible regulation resources.

2.2. Net Load Variation Coefficient, NLvc

The net load variation coefficient is defined as the ratio of the standard deviation of the net load to its mean. It is used to analyze the overall variability in the net load, where a high coefficient of variation indicates significant uncertainty in the net load, requiring more flexible regulating resources to maintain grid stability. The specific method for this is shown in (2).

$$N{L}_{vc}=\frac{{\sigma }_{L_{net}}}{{\mu }_{L_{net}}}$$

(2)

where $N{L}_{vc}$ denotes the net load coefficient of variation, ${\sigma }_{L_{net}}$ represents the standard deviation of the net load, and ${\mu }_{L_{net}}$ signifies the mean of the net load.

The net load variability coefficient ($N{L}_{vc}$) measures the uncertainty of the net load by calculating the ratio of the standard deviation to the mean. A higher $N{L}_{vc}$ indicates greater net load fluctuations, which increases the demand for regulation resources and presents a greater challenge for maintaining system balance.

2.3. Net Load Percentile Distribution, NLpd

Defined as the percentage distribution of the net load within different numerical ranges, this indicator comprehensively reflects the distribution of the net load across different levels, revealing the distribution and frequency of occurrence of the net load within each range. In this study, the net load is divided based on percentiles: 0%, 25%, 50%, and 75% of the maximum net load. The specific method for this is shown in (3).

$$N{L}_{pd}=\frac{n_i}{N_{total}}$$

(3)

where $N{L}_{pd}$ represents the net load percentile distribution, $n_i$ denotes the number of net load values within the percentile range, and $N_{total}$ denotes the total number of net load data sampling points.

The net load percentile distribution ($N{L}_{pd}$) reflects the distribution of the net load across different value ranges, helping to identify the operational characteristics of the system under varying load conditions. Frequent occurrences of high net load fluctuations indicate that additional regulation resources are needed within these ranges to prevent the power system from exceeding safe operating limits.

2.4. Net Load Rate of Change Index, NLrc

The Savitzky–Golay filter is applied to smooth the net load data and compute gradients [18]. This indicator is utilized to analyze the local variation characteristics of the net load. By comparing the ratio of the upward and downward trends in the net load change rate to the maximum original load value, the short-term volatility of the net load can be quantified. The specific method for this is shown in (4).

$$N{L}_{rc}=\frac{d{L}_{net}\left(t\right)}{dt}\times \frac{1}{L_{max}}$$

(4)

where $N{L}_{rc}$ denotes the net load rate of change index, $d{L}_{\mathrm{n}\mathrm{e}\mathrm{t}}\left(t\right)$ represents the derivative of the net load with respect to time, indicating the rate of change within the sampling interval, and $L_{max}$ is the maximum value of the original load.

The Savitzky–Golay filter is a digital filter used for data smoothing, which smooths data by fitting polynomials, aiming to preserve data features (such as peaks and valleys) while reducing noise [18]. The steps for smoothing data and computing gradients using the Savitzky–Golay filter are as follows:

• Selecting the window size and polynomial order:

Window size m: the number of data points considered by the filter (typically an odd number).

Polynomial order n: the order of the polynomial used for data fitting.

b.

Applying the Savitzky–Golay filter to smooth the data:

For each data point, fit a polynomial using its neighboring data points (based on the window size) and the selected polynomial order, and set the smoothed value of that point to the value of the polynomial at that point. This can be expressed by (5).

$$S_i={\sum }_{k=-\frac{m-1}{2}}^{\frac{m-1}{2}}{c}_k\cdot L_{i+k}$$

(5)

where $S_i$ is the smoothed value of the i-th data point, $L_{i+k}$ is the original data point, and $c_k$ is the coefficient precalculated based on the window size and polynomial order.

c.

Computing gradients:

After applying the filter to smooth the data, gradients of the smoothed data can be computed. The computation of gradients can be achieved through the difference method, where the difference between adjacent smoothed data points is divided by the time interval. For continuous time series data, the gradient $G_i$ can be expressed as (6).

$$G_i=\frac{S_i-S_{i-1}}{∆t}$$

(6)

where $∆t$ is the time interval between adjacent data points.

The net load rate of change ($N{L}_{rc}$) measures the magnitude of net load fluctuations over short time intervals, providing insights into the system’s ability to respond to rapid changes. A higher rate of change indicates a need for faster regulation capabilities to manage sudden spikes or drops in load. $N{L}_{rc}$ helps identify critical moments when an intervention in the system is most necessary, allowing for more effective regulation strategies.

3. The Evolution of Net Load

Based on the 2023 operational data from the Western Inner Mongolia Power Grid, which is rich in renewable energy resources with nearly 50% of its installed capacity coming from variable wind and solar energy, the generation curves for this region accurately reflect the local wind and solar conditions. The maximum utilization hours of the electrical load exceed 7000 hours, and the load remains relatively stable, making it an ideal case for analyzing the evolution of net load in power systems with different proportions of renewable energy. Using the day with the highest renewable energy generation as a typical case, the wind and solar generation data for that day are standardized. In this study, the daily generation data, sampled every 15 min (96 data points per day), are normalized by dividing them by the installed capacity, yielding the generation output ratio, as shown in (7).

$$x^{\prime }=\frac{x}{p}$$

(7)

where $x$ represents the original generation data, $p$ denotes the installed capacity of wind or solar power generation, and $x^{\prime }$ represents the generation output ratio.

By adjusting the installed capacity and generation output of wind and solar energy, net load curves for different proportions of renewable energy generation were obtained. These curves were then analyzed using the indicators proposed in Section 2. The wind and solar generation capacities were set at a ratio of 2:1, reflecting the current proportions of these energy source in the grid. Figure 1 illustrates the net load curves for proportions of renewable energy generation ranging from 0% to 100% of the total electricity consumption.

As the proportion of renewable energy generation increases, the net load curve declines and becomes significantly more volatile, displaying the characteristic “duck curve” shape, primarily due to the rise in the photovoltaic capacity [19]. When the proportion of wind and solar generation exceeds 70%, the net load turns negative. Furthermore, when wind and solar generation reaches 100% of the total electricity consumption, the area of negative net load far exceeds that of positive net load.

Using the quantitative analysis indicators for net load proposed in Section 2, values for the net load fluctuation coefficient, net load percentile distribution, net load rate of change index, and net load coefficient of variation were obtained, as shown in Figure 2, Figure 3, Figure 4 and Figure 5 and

Table 1. Quantitative analysis indicators for net load.

Proportion of Renewable Energy Generation	NLfc	NLvc	NLpd					NLrc
			100–75%	75–50%	50–25%	25%–0	<0
0%	1.00	0.02	1.00	0.00	0.00	0.00	0.00	274.85
10%	1.23	0.02	1.00	0.00	0.00	0.00	0.00	408.37
20%	1.62	0.04	1.00	0.00	0.00	0.00	0.00	561.59
30%	2.01	0.06	1.00	0.00	0.00	0.00	0.00	723.29
40%	2.41	0.08	0.73	0.27	0.00	0.00	0.00	884.98
50%	2.86	0.12	0.66	0.34	0.00	0.00	0.00	1046.68
60%	3.41	0.16	0.61	0.14	0.25	0.00	0.00	1208.37
70%	4.00	0.22	0.59	0.07	0.24	0.09	0.00	1370.07
80%	4.59	0.30	0.57	0.04	0.06	0.13	0.20	1531.76
90%	5.18	0.41	0.55	0.04	0.02	0.04	0.34	1693.46
100%	5.77	0.61	0.34	0.21	0.03	0.03	0.39	1855.15

.

As the proportion of renewable energy generation increases, the net load fluctuation coefficient, net load coefficient of variation, and net load rate of change index all show a consistent upward trend, while the net load percentile distribution becomes increasingly dispersed. These changes indicate a significant rise in both overall and local net load volatility as renewable energy penetration grows.

The analysis above is based on a wind-to-solar power generation capacity ratio of 2:1. Due to the distinct characteristics of wind and solar generation, varying installation ratios have a notable impact on the net load. An increased share of solar capacity further amplifies net load fluctuations. Therefore, it is insufficient to assess the level of renewable energy development in a power system solely based on the installed capacity or penetration rate. Figure 6 illustrates the net load curves for different wind and solar installation ratios under a 50% renewable energy generation scenario.

4. Mechanisms of Net Load Balancing

4.1. Impact of Variable Renewable Energy on Power System Balancing Mechanisms

Wind and solar power generation are characterized by high levels of variability due to fluctuating wind and sunlight conditions. As the installed capacity of wind and solar energy increases, this variability directly impacts the stability of the power grid. In traditional power systems, balancing mechanisms rely on conventional generators, such as coal and hydropower, to adjust their output and maintain the balance between supply and demand. However, with the growth of wind and solar energy, these traditional balancing mechanisms are becoming less effective.

Firstly, the output of wind and solar power is highly dependent on weather conditions, making it difficult for conventional power sources to adjust quickly enough to meet the fast-changing demand. Secondly, in systems with a high penetration of renewable energy, the load variability increases significantly, leading to greater uncertainty. With a high proportion of photovoltaic generation, the power system’s balancing mechanism increasingly depends on flexible energy storage systems to manage the frequent fluctuations in the net load curve [20].

To address these challenges, the power system must enhance its regulation capabilities on multiple levels. First, existing coal and hydropower units can be retrofitted to improve their flexibility. Second, energy storage systems, such as pumped hydro and battery storage, can play a critical role in regulating grid frequency and voltage. Finally, adjustable loads can contribute through demand response mechanisms, storing energy during periods of low demand and releasing it during peak periods, thereby smoothing the net load curve.

4.2. Modeling of Regulation Resources

In the power system, the main regulating resources include traditional thermal power plants, such as coal-fired, oil-fired, and gas-fired plants, along with adjustable hydroelectric stations, pumped storage plants, various new energy storage devices (excluding pumped storage), adjustable loads, and interconnection lines. The models for the participation of these regulating resources in system regulation are as follows.

1. Conventional Thermal Power Plants

Conventional thermal power plants have long been the primary energy source in power systems, providing the foundation for ensuring safe and stable grid operation. They have historically been the cornerstone of traditional power systems. Despite the rapid growth of wind and solar energy, conventional coal-fired plants will continue to play a crucial role in system regulation for some time. The model for thermal power plant participation in system regulation is presented in Equation (8)

$$\left\{\begin{array}{c}{F}_{G+}=min\left(P_{Gmax}-P_{G0},r_{G+}\cdot ∆t\right)\\ F_{G-}=min\left(P_{G0}-P_{Gmin},r_{G-}\cdot ∆t\right)\end{array}\right.$$

(8)

where $F_{G+}$ and $F_{G-}$ represent the upward and downward regulation capabilities of thermal power plants, $P_{Gmax}$ and $P_{Gmin}$ represent the maximum and minimum generation output, $P_{G0}$ represents the current generation output of thermal power plants, $r_{G+}$ and $r_{G-}$ represent the upward and downward ramp rates of coal-fired generating units, and $∆t$ represents the ramping time interval.

2. Adjustable Hydroelectric Stations

Adjustable hydropower stations are also a crucial regulation resource, with their ability to start, stop, and adjust output quickly, making them well suited to system regulation. They play a significant role in maintaining power system stability. The model for hydropower station participation in system regulation is provided in Equation (9).

$$\left\{\begin{array}{c}{F}_{H+}=min\left(P_{Hmax}-P_{H0},r_{H+}\cdot ∆t\right)\\ F_{H-}=min\left(P_{H0}-P_{Hmin},r_{H-}\cdot ∆t\right)\end{array}\right.$$

(9)

where $F_{H+}$ and $F_{H-}$ represent the upward and downward regulation capabilities of adjustable hydroelectric stations, $P_{Hmax}$ and $P_{Hmin}$ represent the maximum and minimum generation output of adjustable hydroelectric stations, $P_{H0}$ represents the current generation output of adjustable hydroelectric stations, $r_{H+}$ and $r_{H-}$ represent the upward and downward ramp rates of adjustable hydroelectric stations, and $∆t$ represents the ramping time interval.

3. Pumped Storage Power Stations

Pumped storage power plants play a critical role in modern power systems, particularly with the integration of high proportions of renewable energy. They balance supply and demand by storing excess electricity during periods of low demand and generating power during peak times. With their ability to respond rapidly to grid fluctuations, pumped storage facilities support the growth of renewable energy and contribute to grid stability. Currently, they are the most economical, mature, and reliable form of energy storage in power systems. The model for their participation in system regulation is shown in Equation (10).

$$\left\{\begin{array}{c}{F}_{S+}=min\left(P_{S+max},\frac{\left(S_t-S_{min}\right)}{∆t}\cdot {\eta }_{generation}\right)\\ F_{S-}=min\left(P_{S-max},\frac{\left(S_{max}-S_t\right)}{∆t}\cdot {\eta }_{pumping}\right)\end{array}\right.$$

(10)

where $F_{S+}$ and $F_{S-}$ represent the generation mode and pumping mode of pumped storage power stations, $P_{S+max}$ and $P_{S-max}$ represent the maximum generation power and maximum pumping power of pumped storage power stations, St represents the energy corresponding to the current water storage level, Smax represents the energy corresponding to the maximum water storage level, $S_{min}$ represents the energy corresponding to the minimum water storage level, ${\eta }_{generation}$ represents the generation efficiency, ${\eta }_{pumping}$ represents the pumping efficiency, and $∆t$ represents the time interval for generation or pumping.

4. New Energy Storage Devices

With the rapid growth of wind and solar energy, the role of emerging energy storage technologies in power systems has become increasingly prominent. Their fast regulation capabilities offer more flexible solutions for maintaining system stability and facilitating the integration of renewable energy. A model of the participation of emerging energy storage in system regulation is presented in Equation (11).

$$\left\{\begin{array}{c}{F}_{E+}=min\left(P_{E+max},\frac{SOC\cdot E_{max}}{∆t}\cdot {\eta }_{discharge}\right)\\ F_{E-}=min\left(P_{E-max},\frac{\left(1-SOC\right)\cdot E_{max}}{∆t}\cdot {\eta }_{charge}\right)\end{array}\right.$$

(11)

where $F_{E+}$ and $F_{E-}$ represent the discharge and charge modes of the new energy storage device, $P_{E+max}$ and $P_{E-max}$ represent the maximum discharge and maximum charge power of the energy storage device, $SOC$ represents the current state of charge of the energy storage device, $E_{max}$ represents the total energy capacity of the energy storage device, ${\eta }_{discharge}$ and ${\eta }_{charge}$ represent the discharge and charge efficiencies, and $∆t$ is the charging or discharging time interval.

5. Controllable Loads

Controllable loads are a crucial regulation resource in future power systems with a high share of renewable energy. In this context, it is essential to fully leverage the load-side regulation capacity. The model for controllable load participation in system regulation is provided in Equation (12).

$$\left\{\begin{array}{c}{F}_{L+}=min\left(∆P_{L-max},r_{L+}\cdot ∆t\right)\\ F_{L-}=min\left(∆P_{L+max},r_{L-}\cdot ∆t\right)\end{array}\right.$$

(12)

where $F_{L+}$ and $F_{L-}$ represent the upward and downward regulation capabilities of a controllable load, $∆P_{L-max}$ and $∆P_{L+max}$ represent the maximum power change limits for upward and downward adjustments of the controllable load, $r_{L+}$ and $r_{L-}$ represent the upward and downward regulation rates of controllable load, and $∆t$ is the regulation time interval.

6. Interconnection Lines

Interconnection lines between systems enable cross-regional power transmission, facilitating electricity exchange between grids. This helps balance supply and demand differences across regions, enhancing both the stability and flexibility of the power system. A model of the role of system interconnections in grid regulation is provided in Equation (13).

$$\left\{\begin{array}{c}{F}_{T+}=min\left(P_{Tmax}-P_{T0},r_{T+}\cdot ∆t\right)\\ F_{T-}=min\left(P_{T0}-P_{Tmin},r_{T-}\cdot ∆t\right)\end{array}\right.$$

(13)

where $F_{T+}$ and $F_{T-}$ represent the upward and downward regulation capabilities of interconnection lines, $P_{Tmax}$ and $P_{Tmin}$ represent the maximum and minimum transmission capacity limits of interconnection lines, $P_{T0}$ represents the current transmission power of the interconnection lines, $r_{T+}$ and $r_{T-}$ represent the upward and downward ramp rates of interconnection line power adjustment, and $∆t$ is the regulation time interval.

4.3. Turning Point in the Demand for Power System Regulation

As the proportion of renewable energy generation in the power system increases, the demand for system regulation rises, making an ample regulation capacity essential for the safe and stable operation of the system [15]. In scenarios with no or low renewable energy penetration, both overall and local net load fluctuations are minimal, and the regulation capabilities of traditional sources like thermal and hydroelectric power are sufficient to match the net load curve. However, as the share of renewable energy grows, coordinated efforts from power sources, the grid, loads, and energy storage become necessary to mitigate net load fluctuations. The turning point in regulation demand is closely linked to the level of renewable energy development.

Existing studies often measure renewable energy development using the penetration rate of capacity or energy [21,22,23,24]. However, relying solely on installed capacity or energy output is insufficient due to variations in load characteristics, resource availability, and grid structures across different power systems. Therefore, this paper categorizes the stages of renewable energy development based on the turning point in regulation demand. This approach allows for a more accurate analysis of system characteristics and serves as an effective supplement in assessing different levels of renewable energy integration.

Low-Proportion Renewable Energy Power System: Net load fluctuations are minimal, and regulation demand is low. Conventional regulation from thermal and hydroelectric sources is sufficient to meet this demand.

Medium-to-High-Proportion Renewable Energy Power System: Net load fluctuations increase, and traditional power sources continue to be the primary means of regulation. However, additional measures, such as enhancing system flexibility [20], are needed to meet growing regulation demands.

High-Proportion Renewable Energy Power System: As net load fluctuations rise further, loads and grid interconnections must participate in regulation. Pumped storage, new energy storage systems, and other storage facilities are introduced as supplemental resources. Power sources, the grid, loads, and storage collectively participate in system regulation.

Ultra-High-Proportion Renewable Energy Power System: Net load fluctuations are significant, and energy storage shifts from a supplemental to a primary regulatory role. The required scale of energy storage surpasses the combined regulation capacity of other resources.

4.4. Optimal Load Balancing Method Considering the Turning Point of Regulation Demand

The core function of traditional power systems is to maintain a balance between generation and consumption. With the integration of renewable energy, the primary objective shifts to meeting both load demand and incorporating renewable energy. Effective system operation now requires using various regulation resources to track and smooth the net load. By applying the regulation resource models from Section 4.2 and the concept of a turning point in the regulation demand from Section 4.3, an optimal net load balancing method is developed. This method prioritizes traditional power sources for regulation, followed by controllable loads and system interconnections. Once the regulation capacity of conventional sources is fully utilized, energy storage systems are employed. The goal is to determine the optimal combination of regulation resources to manage net load fluctuations. Due to the diversity and complexity of these resources, the optimization problem is nonlinear, multi-objective, and presents challenges in terms of the solution space.

Considering the robust parallel search capability of the genetic algorithm (GA), along with its flexibility in adjusting parameters such as population size, iteration count, crossover rate, and mutation rate [16,17], GA is used for optimization. Its dynamic adaptability and resistance to local optima make it suitable for solving this complex problem. This paper employs a novel approach by using GA to track the net load curve, incorporating a fitness function designed to optimize the use of multiple regulation resources, thereby revealing the evolution of regulation demand in power systems.

To prioritize achieving a specific proportion of new energy generation without curtailment while ensuring supply reliability, the adaptation function F is designed to maximize the tracking of the target net load by various regulation resources, considering their participation as a priority, as shown in (14).

$$\left\{\begin{array}{c}F=\alpha {\displaystyle \sum _{t=1}^T}max\left(0,N{L}_{target,t}-N{L}_{fit,t}\right)+\beta {\displaystyle \sum _{t=1}^T}|N{L}_{target,t}-N{L}_{fit,t}|+\Phi \\ \Phi =\gamma G+\phi H+ϵL+\rho T+\delta S+\theta E\end{array}\right.$$

(14)

where ${\sum }_{t=1}^{T}max(0,N{L}_{target,t}-N{L}_{fit,t})$ represents the cumulative curtailment of new energy, ${\sum }_{t=1}^T|N{L}_{target,t}-N{L}_{fit,t}|$ represents the cumulative tracking deviation; Φ is the penalty term set, where G, H, L, T, S, and E, respectively, represent the scale of the participation of thermal power, hydroelectric power, adjustable loads, system interconnection power control, pumped storage power stations, and new energy storage in the regulation; α, β, γ, φ, ϵ, ρ, δ, θ are corresponding penalty coefficients used to adjust the influence of each parameter, balancing different performance indicators, according to the overall net load tracking scheme for power optimization.

The specific tracking method is as follows:

First, determine the initial outputs ${P_t}_0$ at time t = 0 based on the overall adjustment range of the regulating resources:

$${P_t}_0=min\left(max\left(P_{{target}_{load\left[0\right]}},{\sum }_{r\in R}{P}_{min,r}\right),{\sum }_{r\in R}{P}_{max,r}\right)$$

(15)

where $P_{target\_load\left[0\right]}$ represents the initial value of the net load, r denotes the type of regulating resource, R represents the set of regulating resource types, $P_{min,r}$ denotes the minimum adjustment capacity of a certain type of regulating resource, and $P_{max,r}$ represents the maximum adjustment capacity of a certain type of regulating resource.

Next, iterate to calculate the output for each data point. For each time point t, adjust the output based on the difference between the target net load and the current output:

$$P_{difference}={P_{targe{t}_{l}oad}}_{\left[t\right]}-P_{t-1}$$

(16)

where ${P_{\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\mathrm{t}\_\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}_{\left[t\right]}$ represents the net load at time t, $P_{t-1}$ is the current output of the regulating resource at time t, and $P_{difference}$ is the difference between the target load and the current output of the regulating resource at the current time, used to determine how to adjust the output of the regulating resource to match the target load.

If $P_{difference}$ > 0, the ramping demand $P_{ramp}$ is:

$$P_{ramp}=min\left({\sum }_{r\in R}{R}_r,P_{difference}\right)$$

(17)

$$P_t=min\left(P_{t-1}+P_{ramp},\sum _{r\in R}{P}_{max,r}\right)$$

(18)

If $P_{difference}$ < 0, the ramping demand $P_{\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{p}}$ is:

$$P_{ramp}=max\left({\sum }_{r\in R}{R}_r,P_{difference}\right)$$

(19)

The output power of the regulating resource $P_t$ at time t is:

$$P_t=max\left(P_{t-1}+P_{ramp},\sum _{r\in R}{P}_{min,r}\right)$$

(20)

The flowchart of the net load balancing method is shown in Figure 7.

5. Case Study Analysis

Here, we present a case study analysis based on actual operation data from the western power grid in the Inner Mongolia Autonomous Region, China, in 2023. In this analysis, we apply the optimal net load balancing method proposed in Section 4 to examine the system’s transition points in adjusting capabilities at different stages of new energy development. The simulation platform used is MATLAB 2022b. Due to the inherent intermittency and variability of new energy sources, this study focuses on the day with the highest proportion of new energy generation. Data were collected at 15 min intervals, with the daily operation considered the smallest unit for system analysis. When the maximum daily new energy generation reaches a certain proportion, the system is deemed capable of accommodating that level of new energy generation.

5.1. System Main Parameters

The main parameters of the system, including system load, installed capacity, adjustable load regulation, and transmission line power regulation ranges, are shown in

Table 2. System load and regulation resource scale. (Unit: MW).

Load	Coal-Fired Power	Gas-Fired Power	Wind Power	Photovoltaic Power	Conventional Hydroelectric Power	Pumped Storage Hydroelectric Power	New Energy Storage	Adjustable Load	Interconnection Power Regulation
40,417	48,150	430	30,790	17,470	870	1200	2120	[–2000, 125]	[–500, 500]

.

The coal-fired power generation includes a self-use capacity of 10,000 MW, which lacks regulation capabilities. For the safe and stable operation of the system, the minimum operational capacity of coal-fired power generation should not be less than 25,000 MW. The available capacity of the pumped storage generation is fully utilized at 1200 MW. New energy storage facilities are paired with new energy power plants and are only used for the self-regulation of those plants, without participating in system-wide regulation. The adjustable load can be increased by 2000 MW and decreased by 125 MW. The tie line power can be adjusted within a range of ±500 MW based on operational requirements.

The upper and lower regulation limits for conventional power sources, pumped storage, and new energy storage are expressed as the ratio of their maximum and minimum generation capacities to their grid-connected capacity. The regulation rate is represented as the ratio of adjustable power per minute to grid capacity. The regulation capabilities of the tie line and adjustable load are based on actual operational data. The regulation capabilities of coal-fired power, gas-fired power, conventional hydroelectric power, pumped storage, and new energy storage are determined comprehensively based on the literature [25,26,27,28,29] and the system’s actual operating conditions, while the tie line and adjustable load capabilities are implemented according to the system’s operational requirements. Details are shown in

Table 3. Adjustment capabilities of different types of regulation resources.

Type	Coal-Fired Power	Gas-Fired Power	Conventional Hydroelectric Power	Pumped Storage Hydroelectric Power	New Energy Storage	Adjustable Load	Interconnection Power Lines
Regulation Upper Limit	100%	100%	100%	100%	100%	125 MW	500 MW
Regulation Lower Limit	55% (40%)	0	0	0	−100%	−2000 MW	−500 MW
Upward Ramp Rate	3%	5%	20%	20%	10%	100 MW	60 MW
Downward Ramp Rate	3%	5%	20%	20%	10%	100 MW	60 MW

.

5.2. Main Parameters Settings

Using the regulation resource model and the optimal net load balancing method proposed in Section 4, we analyze the net load balancing mechanism of the power system at different stages of new energy development. First, we normalize the load data for typical days of wind and photovoltaic power generation using (7) which is used to adjust the new energy generation to obtain net load curves under different proportions of new energy generation. Then, the regulation resource model (9–13), net load data, and the fitness function (14) are input into the GA to balance the net load. The main parameters are shown in

Table 4. Key parameters for optimal net load balancing.

Item	Parameter Name	Parameter Values
Genetic Algorithm (GA)	Population Size	50
	Gene Size	100
	Crossover Rate	0.8
	Mutation Rate	0.05
Penalty Coefficients	α, β	106, 104
	γ, φ, ϵ, ρ, δ, θ	Determined based on actual circumstances

.

The setting of α and β as large numerical values is intended to prioritize the accommodation of new energy and supply of load. The settings of other penalty coefficients mainly consider the priority of different regulation resources participating in the net load balancing at different stages.

5.3. Analysis of Net Load Balancing Mechanism in Different Stages of New Energy Development

Here, we analyze the transition from a 0% to a 100% new energy penetration rate in increments of 10%, considering the actual available capacity for new energy development in the region, with wind and photovoltaic power installation ratios assumed to be 1:1.

5.3.1. Low-Proportion New Energy Power System

At this stage, the proportion of new energy power is relatively low, and the conventional regulation capacity of traditional power sources is sufficient to meet the system’s regulation needs, balancing the net load. Without considering the addition of traditional power sources’ regulation capacity through technical means such as flexibility enhancement, other regulation resources are not involved. Considering energy saving and carbon reduction in the system, coal-fired power units are operated with minimal capacity, thus setting γ to 1, and φ, ϵ, ρ, δ, θ to 0. The calculation results are shown in

Table 5. Net load balancing data for low-proportion new energy power system (unit: MW).

New Energy Proportion	Involvement of Various Regulation Resources	Ability to Balance Net Load
0%	Coal-fired power 42500, Gas-fired power 100, hydroelectric power 400.	Yes
10%	Coal-fired power 39500, Gas-fired power 100, hydroelectric power 300.	Yes
20%	Coal-fired power 36000, Gas-fired power 100, hydroelectric power 400.	Yes
30%	Coal-fired power 31000, Gas-fired power 200, hydroelectric power 500.	No

.

Figure 8 shows that when the proportion of new energy power is between 0% and 20%, the regulation capacity of traditional power sources can effectively balance the net load. However, when the new energy proportion reaches 30%, the regulation capacity of traditional power sources is insufficient to balance the net load, failing to meet the system’s regulation needs. This results in unmet power demand during peak periods and challenges in integrating new energy during off-peak periods. Therefore, for this system, scenarios where the maximum single-day proportion of new energy power is 20% or less are considered to represent low proportions of new energy in the electricity system.

5.3.2. Medium-to-High-Proportion New Energy Power Systems

As the scale of new energy continues to grow, the conventional regulation capacity of traditional power sources becomes insufficient to balance the net load, pushing the system into the medium-to-high proportion of new energy stage. In this stage, traditional power sources require flexible transformations and other technological upgrades to enhance their regulation capacity, allowing them to meet the system’s regulation needs, while other regulation resources remain inactive. The flexible transformation referred to in this paper mainly refers to coal-fired power units, with the average minimum output decreasing from 55% to 40% after transformation. γ is set to 1, and φ, ϵ, ρ, δ, θ are set to 0. The calculation results are shown in

Table 6. Net load balancing data for medium-to-high-proportion new energy power system (unit: MW).

New Energy Proportion	Involvement of Various Regulation Resources	Ability to Balance Net Load
30%	Coal-fired power 31000, Gas-fired power 200, hydroelectric power 500.	Yes
40%	Coal-fired power 28000, Gas-fired power 200, hydroelectric power 400.	No

.

Figure 9 shows that the system, enhanced by retrofitting coal-fired power plants for greater flexibility, can meet the adjustment requirements of conditions with a proportion of new energy electricity below 30%. However, when the proportion of new energy electricity reaches 40%, the regulation capacity of traditional power sources becomes insufficient to meet these needs. Thus, for this system, a maximum single-day proportion of 30% new energy electricity represents a medium-to-high new energy power system.

5.3.3. High-Proportion New Energy Power Systems

Entering the high-proportion new energy phase, the traditional source-follow-load mode of the power system can no longer meet the system’s regulation requirements. It requires joint regulation by power sources, the grid, and loads, while energy storage facilities gradually become a necessary means of system regulation. However, the scale of energy storage facilities is still smaller than the combined regulation capacity of other resources. Considering energy conservation and carbon reduction, priority is given to minimizing the operation of coal-fired power plants, while pumped storage hydroelectric power stations and new energy storage facilities have lower priority in regulation. The adjustable load and interconnection power regulation are set with γ as 1, φ, ϵ, and ρ as 0, and δ and θ as 1.

Table 7. Net load balancing data for high-proportion new energy power system (unit: MW).

New Energy Proportion	The Scale of Regulation Resources Required to Balance the Net Load
40%	Coal-fired power 28000, Gas-fired power 200, hydroelectric power 500, adjustable load, and interconnection power regulation are included in the regulation.
50%	Coal-fired power 25000, gas-fired power 100, hydroelectric power 600, adjustable load, and interconnection power regulation fully participate. Pumped storage hydroelectric power 1200, and new energy storage 2400.
60%	Coal-fired power 25000, gas-fired power 200, hydroelectric power 400, adjustable load, and interconnection power regulation fully participate. Pumped storage hydroelectric power 1200, and new energy storage 2400.

provides the required regulation resource scale for balancing the net load after the system enters the high-proportion new energy phase.

When the proportion of new energy generation exceeds 40%, the system enters a high-proportion stage. Generation, grid, and load jointly participate in balancing the net load, and the scale of energy storage facilities rapidly expands. When the proportion of new energy generation reaches 60%, the scale of energy storage facilities approaches the total regulation capacity of other resources.

5.3.4. Ultra-High-Proportion New Energy Power Systems

When the proportion of new energy generation reaches 70%, the scale of energy storage surpasses the combined regulation capacity of other resources, becoming the primary regulation resource in the system. At this point, the system enters the ultra-high proportion of new energy stage. Coal-fired power plants operate at minimum capacity, while the priority of pumped storage hydroelectric plants and new energy storage in regulation decreases. Adjustable load and interconnection power regulation fully participate in system regulation. γ is set to 1, φ is set to 0, ϵ and ρ are set to −1, and δ and θ are set to 1. The configuration of regulation resources required to balance the net load is shown in

Table 8. Net load balancing data for ultra-high-proportion new energy power system (unit: MW).

New Energy Proportion	The Scale of Regulation Resources Required to Balance the Net Load
70%	Coal-fired power 25000, gas-fired power 200, hydroelectric power 100, adjustable load, and interconnection power regulation fully participate. Pumped storage hydroelectric power 1200, and new energy storage 16800.

.

An analysis of real grid operation data demonstrates the effectiveness and applicability of the proposed method in predicting power system regulation needs under high renewable energy penetration scenarios. The innovative application of the genetic algorithm shows excellent optimization in tracking net load fluctuations across different stages of renewable energy integration. The results indicate that as wind and solar power penetration increases to 30% and beyond, the net load fluctuations in the power system significantly intensify. Traditional power sources are unable to meet the growing regulation demands, requiring reliance on energy storage systems and adjustable loads to maintain grid stability.

An analysis of the western grid in the Inner Mongolia Autonomous Region, China, considering the current load structure, grid configuration, and conventional generation capacity, reveals that with a wind-to-solar installed capacity ratio of 1:1, different stages of renewable energy development can be identified based on the inflection points of regulation resources. Systems with new energy penetration below 20% are classified as low-proportion, 30% as medium-to-high, 40% to 60% as high-proportion, and 70% or more as ultra-high-proportion renewable energy systems.

6. Conclusions

This paper examines the net load of power systems, analyzing its evolution and balancing mechanisms as the proportion of renewable energy increases. The main conclusions are as follows:

Analysis Indicators: Four quantitative indicators—net load fluctuation coefficient, variability coefficient, percentile distribution, and rate of change index—are introduced to analyze the net load evolution at different stages of renewable energy development. As the share of renewable energy grows, both the fluctuation and variability coefficients increase significantly, the percentile distribution becomes more dispersed, and the rate of change across various time scales rises sharply.

Modeling Regulation Capabilities: The regulation capabilities of various adjustment resources are modeled, and power systems are classified based on the inflection points of regulation demand, offering a more effective method than traditional approaches that rely solely on renewable energy installation and penetration rates.

Net Load Fitting Method: Given the complexity, multi-objective nature, and dynamic changes within power systems, a net load fitting method is proposed. An adaptive function is designed to account for renewable energy curtailment, load supply requirements, and the prioritization of different adjustment resources. Using genetic algorithm optimization, the optimal configuration of adjustment resources to balance net load is determined.