Study on Frequency Stability of an Independent System Based on Wind-Photovoltaic-Energy Storage-Diesel Generator

Abstract

Wind and photovoltaic power generation connected to the independent power system can save fuel, reduce carbon emissions, and provide significant economic and environmental benefits. Influenced by the characteristics of light resources and wind resources, the wind and photovoltaic output active power is characterized by volatility and randomness, which affects the frequency stability of the independent power system. In order to evaluate the frequency stability, in this paper, the simulation model of an independent power system is established, and the simulation model of a diesel generator, wind and photovoltaic are connected. Through droop calculation and Simulink simulation, the frequency characteristics of an independent power system under different working conditions are analyzed, and the maximum absorption capacity of wind and photovoltaic is studied. In an independent power system, when the new energy output is 25% of the total output, all the new energy output is cut off, the frequency drops by 0.5 Hz, and the frequency fluctuation is within the specified range.

1. Introduction

An independent power system is one of the important forms of distributed generation, which refers to the independent distribution and distribution system composed of an independent power supply, power load, distribution facilities, and monitoring and protection devices. An independent power system has flexible operation characteristics and can operate independently to meet the power supply demand of local areas. The independent power system is not connected to the external distribution system, and the independent power system uses its own independent power supply to meet the load power supply demand and ensure the power balance in the system. An independent power system can meet the power supply of remote areas, such as island and border defense to remote areas are difficult, improve power quality, and reduce the loss of power systems. An independent power system generally consists of renewable energy, an energy storage system and a conventional power supply. Routine power supply, including gas turbines and diesel generators, aims to provide relatively stable voltage and frequency support for the system [1].

The most prominent feature of the independent power system is from load control to frequency control, the adjustment system has met the requirements of static characteristics, good stability and dynamic response characteristics to ensure that in the case of load changes, the power system’s frequency automatically stays near the rated frequency, which requires the adjustment system to have a good frequency modulation ability. Because the independent power system is simple in structure, small in inertia, and there is no support for large-scale power systems, the problem of frequency stability is more prominent [2]. Frequency stability is an important factor in ensuring the safe and stable operation of the power system. The frequency abnormality or frequency collapse will bring extremely serious consequences to the power system itself and the power users. Therefore, it is very important work to develop a reasonable and effective control scheme for the frequency problem arising in the power system. The self-balance ability of the independent power system is poor, the load disturbance will change the frequency greatly, and the large disturbance will even lead to the frequency collapse of the power system, resulting in a large area of power failure in the regional network, so the frequency control has become the key to the operation of the independent system [3,4].

With the proposal of the dual-carbon target, in order to promote energy conservation and emission reduction, it is particularly important to give priority to the development and utilization of clean energy generation. Wind energy is a clean and renewable energy source, which is increasingly valued because it is rich in nature and completely emission-free [5]. Wind power generation has the advantages of energy conservation and emission reduction, a short construction cycle, good independence, obvious economic value and ensuring electricity demand, but it has the characteristics of randomness and instability. Solar energy is also a renewable resource with large reserves, low development cost, low carbon, environmental protection, and other characteristics; photovoltaic power generation also has the advantages of no fuel use, no pollutant emission, energy saving, environmental protection, simple system, flexible layout, and so on [6]. However, the intermittence and volatility of wind power and photovoltaic power generation systems will impact the operation of independent power systems, affect the frequency stability of power systems, and increase the difficulty of using wind energy and light energy [7]. Therefore, how to quickly realize the active power regulation to ensure the frequency stability of the system has become a hot topic in the current research. In order to study the frequency stability of the existing independent power system after connecting to the wind and photovoltaic systems, its stability energy needs to be analyzed. The allowable range of frequency deviation of a small capacity power system not exceeding 300 MW shall be limited to ±0.5 Hz [8]. The influence of wind-photovoltaic-energy storage on the frequency of small-capacity independent power systems shall be controlled within this range.

Independent systems mainly use gas turbines and fuel turbines to generate electricity. Document [9] established the gas turbine model and obtained the maximum penetration power of an independent power grid connected to wind power through PSCAD simulation, but access to photovoltaic and energy storage was not considered. Reference [10] simulates the frequency fluctuation caused by microgrid load switching under island operation through Simulink simulation. With the high permeability of the new energy grid connection, the frequency stability also gradually decreases, so the frequency stability is also gradually reduced, but it mainly studies the effect of the load change on the frequency. Reference [11] proposes a frequency control method of a 100% isolated, renewable energy power grid with model prediction control, used to maintain the power generation balance and thus ensure the stability of the system frequency, but it does not consider access to the wind. Reference [12] introduces the integral link in the control structure of traditional VSG (virtual synchronous generator) and combines damping torque in the PI controller. In the independent power system, the active output can automatically change with the load to realize the difference control of the frequency, but it does not consider access to new energy sources. By introducing the fuzzy sliding mode control method from reference [13], the influence of wind power being incorporated into the power system is reduced, and the stability of the original power system is guaranteed, but its main research is the access of wind. Reference [14] proposes a new frequency control strategy, namely, virtual inertia control based on an optimal robustness CDM (coefficient diagram method) controller to improve power system stability. Reference [15] proposes a robust PID (RPID) controller, which is the combination of a proportional-integral-derivative (PID) controller and a linear quadratic gaussian (LQG) controller. The RPID controller can effectually enhance frequency stability under the high proportion of new energy equipment access.

In order to study the frequency problem caused by the connection of the independent system with the wind-photovoltaic-energy storage, the mathematical model of the diesel generator set was established first, and then the active frequency characteristics of the diesel generator were analyzed. The relationship between the frequency variation and the output power of the diesel generator was obtained. The maximum wind and photovoltaic cut-out amount within the allowable range of the frequency was calculated by the relationship of the specific changes in the frequency of the power system after access to the wind-photovoltaic-energy storage, and finally, the application of Simulink simulation of the wind-photovoltaic-energy storage access to the power system. By comparing the results of mathematical calculation and simulation, we can finally prove that the frequency control method used in this paper can keep the frequency of a power system within the allowable range after the wind-photovoltaic-energy storage access, providing an important basis for the construction of the power system access.

2. Mathematical Modeling of Multi-Energy Power Generation Units

The original power generation equipment of an independent system is a diesel generator, and the frequency characteristics of the power system are determined by the frequency characteristics of the diesel generator. A diesel generator is the main power supply of the power system, which bears the benchmark power of the daily production load, and also plays the role of peak and frequency modulation. With access to the wind and photovoltaic systems and other equipment, the output of the diesel generator is also reduced. Wind fluctuation brings about the output fluctuation of the diesel generator, which leads to the frequency fluctuation of the diesel generator, and the frequency of the power grid also fluctuates accordingly. In the transient period, the output fluctuation can be obtained by the simplified model of the diesel generator and the power grid.

2.1. Mathematical Modelling of Wind Power

The wind output is the output power of the wind turbine. The ideal mathematical model is:

(1)$P_{\mathrm{wind}}=\frac{1}{2}\pi \rho C_{\mathrm{p}}{R}^2{v}^3$

Among,

(2)$C_{\mathrm{p}}=\frac{P_{\mathrm{u}}\rho v^{3}S}{2}=\frac{\Omega M\rho v^{3}S}{2}$

where ρ is the air density; P_u is the axial power of the wind wheel; S is the swept area; Ω is the wind speed; M is the torque of the wind wheel; C_p is the wind utilization coefficient; R is the blade radius; and v is the wind speed [16].

2.2. Mathematical Modeling of Photovoltaic Power

Photovoltaic output data can be calculated by Equation (3):

(3)$P_{\mathrm{s}}=\eta A{G}_{\mathrm{t}}\tau [1-0.0045(T_{\mathrm{c}}-25)]$

In the formula, Ƞ is the transfer efficiency; A is the surface area of the photovoltaic module; G_t is the total solar radiation; τ is the light transmittance of the photovoltaic module; and T_c is the operating temperature of the photovoltaic module of [17].

2.3. Mathematical Modeling of Energy Storage

Battery capacity is:

(4)$S=\frac{W}{U}\times \frac{D\prime }{{\eta }_1\times d}$

In Formula (4), W is the daily power consumption load in Wh; U is the DC voltage of the system in V; D’ is the continuous rainy days; Ƞ₁ is the inverter efficiency, according to the equipment selection, generally between 80% and 93%; d is the battery discharge depth, selected between 50% and 75% according to its performance parameters and reliability requirements. The energy storage battery can discharge power P_batt (t) available by Formula (5).

(5)$P_{\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{t}}(t)=\frac{E_{\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{t}}(t)-E_{\mathrm{m}\mathrm{i}\mathrm{n}\_\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{t}}}{\Delta T}$

where E_{batt (t)} is the energy stored by the energy storage module at time t; Emin_batt is the minimum power stored by the energy storage module; and ∆T is the time step.

2.4. Mathematical Modeling of the Diesel Generators

Considering the electromagnetic transient of the synchronous generator set, the wind and the rotor motion process, we establish the mathematical model of the synchronous generator, and its stator voltage equation is as follows:

(6)$\left\{\begin{array}{l}{u}_{\mathrm{d}}=X_{\mathrm{q}}{i}_{\mathrm{q}}-r_{\mathrm{a}}{i}_{\mathrm{d}}\\ u_{\mathrm{q}}={E^{\prime }}_{\mathrm{q}}-{X^{\prime }}_{\mathrm{d}}{i}_{\mathrm{d}}-r_{\mathrm{a}}{i}_{\mathrm{q}}\end{array}\right.$

The equation of the stator current for the synchronous generator:

(7)$\left\{\begin{array}{l}{i}_{\mathrm{d}}=\frac{{E^{\prime }}_{\mathrm{q}}-V_{\mathrm{s}}\cos \delta }{{X^{\prime }}_{\mathrm{d}}+X_{\mathrm{l}}}\\ i_{\mathrm{q}}=\frac{V_{\mathrm{s}}\sin \delta }{X_{\mathrm{q}}+X_{\mathrm{l}}}\end{array}\right.$

Voltage equation of the rotor excitation winding of the synchronous generator:

(8)$\frac{d{E^{\prime }}_{\mathrm{q}}}{d\mathrm{t}}=\frac{1}{{T^{\prime }}_{\mathrm{d}0}}\left[E_f-{E^{\prime }}_{\mathrm{q}}-\left({X^{\prime }}_{\mathrm{d}}-X_{\mathrm{q}}\right)\frac{{E^{\prime }}_{\mathrm{q}}-V_{\mathrm{s}}\cos \delta }{{X^{\prime }}_{\mathrm{d}}+X_{\mathrm{l}}}\right]$

Rotor motion equation of the synchronous generator:

(9)$\left\{\begin{array}{l}J\frac{d\Delta \omega }{dt}+D\left(\omega -{\omega }_{\mathrm{ref}}\right)=P_{\mathrm{m}}-P_{\mathrm{e}}\\ \frac{d\delta }{dt}=\omega -{\omega }_{\mathrm{ref}}=\Delta \omega \end{array}\right.$

where r_a is stator resistance; X_q is q-axis reactance; E’_q is q-axis transient electric momentum; T’_d0 is excitation winding time constant; E_f is stator excitation electromotive force; V_s is system voltage; X_l is transformer and line impedance; δ is the electric angle between the q-axis and x-axis; J is the rotational inertia of the rotor; D is the generator damping coefficient; P_m is mechanical power; P_e is electromagnetic power; ω is the angular frequency, ω_ref is the nominal angular frequency; and ∆ω is the amount of change in the angular frequency.

As Equation (9) knows, the speed of the synchronous generator is determined by the rotor equation of motion. The power balance relationship determines the speed of the synchronous generator, and the speed of the synchronous generator determines the frequency of the power grid. In order to study its rotational speed characteristics, the mathematical model of the excitation system of the diesel generator was established, as shown in Figure 1.

Among them, T₁ and T₂ are the time constants of the integrated amplification unit loop; K_p is the amplification factor of the proportional amplification circuit; and T_a is the time constant of the adaptation unit. The speed control system of the diesel generator is the main part of the diesel generator control system, which controls the speed of the diesel generator by controlling the diesel output signal. The simplified model of the diesel generators and speed control system is shown in Figure 2.

Specifically, K^* is the standard value of the power system; PI is the regulator of the secondary frequency modulation, which takes the frequency back to 50Hz; K is the diesel generator for maintaining the self-support diesel flow ratio; a, b and c are parameters reflecting the characteristics of the diesel fuel system; and W_F is the diesel flow output ratio. The system including the diesel generator set model is shown in Figure 3.

3. Frequency Stability Analysis

3.1. Principle of Independent System Droop Calculation

The grid frequency is determined by the frequency characteristics of the generator and the frequency characteristics of the load. The relationship between the frequency shift and load increase satisfies the droop calculation characteristic with a certain delay, as shown in the following equations [18]:

(10)$\Delta P^{*}=\frac{\Delta f^{*}{K}^{*}}{(1-e^{\frac{-t}{T}})}$

(11)$\Delta P^{*}=\frac{\Delta P}{P_0}\times 100\%$

(12)$\Delta f^{*}=\frac{\Delta f}{f_0}\times 100\%$

Formula ∆f* is the unitary value of the frequency change in the power system, K^* is the natural adjustment gain for the unitary, ∆P^* is the unitary value of the load variation, t is time in s, T is the time constant (s), ∆P is the load variation, P₀ is the total load, ∆f is the frequency variation and f₀ is the standard frequency of the grid.

3.2. Independent System Frequency Regulation Principle

The frequency characteristics of the power system are determined by the rotational speed of the diesel generator set. After deducting the power input of the excitation loss and the mechanical loss, the balance is maintained with the electromagnetic power, and the rotation speed of the diesel generator is maintained [19]. The change in load changes the electromagnetic power and then makes the power balance relationship, the speed of the diesel generator, the power grid frequency, and so on, change.

A diagram between angular velocity and power can be obtained from Equation (9), as shown in Figure 4.

In a stand-alone operating power system, the generator has a certain frequency regulation capability to support the frequency stability of the whole power system. The active frequency deviation feedback equation is shown in the following equation:

(13)$P_{\mathrm{m}}=P_{\mathrm{N}}-K_{\mathrm{d}}\Delta \omega$

where P_N is the rated power, and K_d is the feedback coefficient. This section is equal to the primary FM (frequency modulation) section, and its control block diagram is shown in Figure 5.

From Figure 5, it can be seen that the transient relationship between the amount of change in system power and the amount of change in angular velocity can be found using the superposition theorem as follows:

(14)$\Delta \omega =\frac{\Delta P}{D+K_{\mathrm{d}}}\left(1-e^{-\frac{D+K_{\mathrm{d}}}{J}\mathrm{t}}\right)$

In the equation, ∆P is the difference between the rated power and the electromagnetic power. When ∆P is zero, the stable angular frequency deviation of the system is zero. Since ω = 2πf, the system frequency deviation is zero. When the electromagnetic power of the generator changes, the generator output frequency changes exponentially, where K_d, D and J together determine the dynamic transition time of the frequency, while K_d and D jointly determine the offset of the system frequency at a steady state [20]. The simplified block diagram of the system after the introduction of secondary FM is shown in Figure 6 below.

The relationship between the system output frequency deviation and input power obtained from Figure 6 is:

(15)$\Delta \omega =\frac{s}{J{s}^2+\left(D+K_{\mathrm{p}}\right)s+K_{\mathrm{i}}}\Delta P$

From the final value theorem:

(16)$\underset{t\to \infty }{\lim }\Delta \omega =\underset{s\to 0}{\lim }s\Delta \omega =\underset{s\to 0}{\lim }s\frac{\mathrm{s}}{J{s}^2+\left(D+K_{\mathrm{p}}\right)s+K_{\mathrm{i}}}\Delta P=0$

In the formula K_p is the proportional coefficient of the PI controller, and K_i is the integral coefficient of PI controller. It can be seen that the steady state of the frequency is realized after the introduction of the PI controller.

4. Simulation Analysis

4.1. The Construction of Real Models

The independent power system studied in this paper includes the power generation platform and the load platform, and each power generation platform is connected to the power generation platform, which is connected by interconnection lines, with a total power generation capacity of 58.56 MW. The power system mainly includes cable, diesel generator set, transformer, load 4 class components and three voltage levels (6.3, 10.5 and 35 kV). They are connected in certain ways to form a complete network of power generation, transmission, distribution and electricity consumption [21]. The schematic topology of the power system is shown in Figure 7.

The power system consists of ten diesel generators and is divided into five diesel generator models. Its load is connected to the power generation platform, and the total load is 28.87 MW. Its basic parameters are shown in Table 1. The grid system composite Marine cable includes 10.5 and 35 kV Marine cable lines. The power grid system mainly includes 10 transformers connected between the three voltage levels of 6.5, 10.5 and 35 kV, corresponding to 4 nodes.

4.2. Simulation Analysis

According to Equation (10), the effect on the frequency amplitude when the load increases or decreases is simulated without considering the secondary frequency regulation of the system. When the load increases or decreases by 10%, the frequency decreases or increases by 0.2 Hz and when the load increases or decreases by 25%, the frequency decreases or increases by 0.5 Hz. The frequency change corresponding to the load change is shown in Figure 8.

According to Equation (15), the effect of load increase or decrease on the system frequency after considering the second frequency regulation of the system is shown in Figure 9. Therefore, under normal conditions, to ensure that the system frequency deviation is within the allowable range (±0.5 Hz), simultaneous removal of a large number of loads should be avoided.

We simulate the effect of output power fluctuations of wind and PV generation on frequency stability according to Equation (10). As an example, after complete disconnection of the wind and PV generation, the output power drops to 0. It is calculated whether the system frequency fluctuation at this point is within the allowable variation. The waveforms are shown in Figure 10 below.

According to Equation (15), the system frequency is shown in Figure 11 when the output power of the wind turbine and PV is decreased by 5%, 15% and 25%, respectively, after taking into account the secondary frequency regulation of the system.

According to Figure 11, when the permeability of new energy is 5%, the frequency decreases by 0.1 Hz, when the permeability is 15%, the frequency decreases by 0.3 Hz and when the permeability is 25%, the frequency decreases by 0.5 Hz. Therefore, the maximum penetration of new energy is 25%. The specific circumstances are shown in Table 2.

The allowable frequency range of China’s power system is ±0.5 Hz, and the standard value of grid frequency variation ∆f* is 0.01. According to Equation (10), the standard value of active power variation rate ∆P* of wind and PV generating units is 0.25. According to Equation (11), since the total load is 28.87 MW, the maximum active power value of wind and PV generating units is 7.2175 MW. The correspondence between the fluctuation amount and the new energy access amount is shown in Table 3.

According to the wind and PV resources near the independent power system, the active output of the selected wind turbine is 5 MW and the active output of the selected PV generator is 2 MW. The selected energy storage in this platform is 1 MW. When all 7 MW from wind and PV generators are removed, the frequency drops to near 49.5 Hz, and after the secondary frequency regulation, the system frequency returns to the rated value, which is consistent with the theoretical calculation results. The waveform diagram is shown in Figure 12 below.

Figure 13 shows the output power curves for the two wind-photovoltaic-energy storage. In Figure 13, the energy storage output power is maintained around 1 MW, and the PV output power is 0 MW from 0 to 60 s, which increases and then decreases from 60 to 180 s and 0 MW from 180 to 240 s. Figure 13 shows when the wind speed changes violently, the output power of the wind turbine also changes violently, while Figure 13b shows the wind speed change is relatively gentle, and the output power change in the wind turbine is also relatively gentle.

When the load does not change, the output power of the wind turbine, PV and energy storage is shown in Figure 13, then the output of the diesel generator is shown in Figure 14. The output power of the diesel generator in Figure 14a is relatively drastic, and the output power of the diesel generator in Figure 14b is relatively flat.

When the output power of the wind turbine and PV fluctuates, as shown in Figure 13, the system frequency also fluctuates, as shown in Figure 15. Compared with Figure 15b, the frequency fluctuation in Figure 15a is a little larger. However, the frequency is still kept within the allowable range of frequency after the secondary frequency regulation, thus ensuring the stable operation of the power system [22].

5. Conclusions

This paper models a multi-energy independent power grid platform, calculates the frequency change in the independent power system after the secondary FM control strategy and verifies the effectiveness of the control strategy with Matlab simulation. The typical output situation of the wind-photovoltaic-energy storage is fitted. The calculation results and simulation results show that after the wind-photovoltaic-energy storage is connected to an independent power system, the frequency of the platform can also be within the range of allowable fluctuations. After the introduction of wind power and photovoltaic generating units, the system can still operate stably, which provides a basis for the actual engineering design.

Author Contributions

Collecting and sorting data, C.H. and F.D.; analyzing and visualizing the data, G.W. and S.Z.; software validation, G.L. and Y.W.; writing—first draft, Y.W. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Conflicts of Interest

There are no potential competing interests in our paper. All authors have seen the manuscript and approved submission to your journal. We confirm that the content of the manuscript has not been published or submitted for publication elsewhere.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. The excitation system model of the diesel generator.

Figure 2. Speed control system and diesel generator model.

Figure 3. Diesel generator set model.

Figure 4. Transfer function of angular velocity and power.

Figure 5. Simple box diagram of the system with primary FM.

Figure 6. Simplified block diagram of the primary and secondary FM principle of the system.

Figure 7. Schematic diagram of a certain power system.

Figure 8. Frequency Change amplitude Calculation—Simulation Results.

Figure 9. Frequency Change amplitude Calculation—Simulation Results Considering the secondary FM.

Figure 10. Frequency variation caused by different penetration rates of wind turbine and PV.

Figure 11. Frequency variation caused by different penetration rates of wind turbine and PV considering the secondary FM.

Figure 12. The effect of the total wind and photovoltaic generator set resection on the frequency.

Figure 13. Wind-photovoltaic-energy storage output curve. (a) When the wind speed changes rapidly; (b) When the wind speed changes relatively gently.

Figure 14. Output curve of the diesel generator. (a) When wind-photovoltaic-energy storage output fluctuates relatively violently. (b) When wind-photovoltaic-energy storage output fluctuates relatively gently.

Figure 15. Influence of the wind-photovoltaic-energy storage output on frequency. Influence of the wind-photovoltaic-energy storage output on frequency. (a) When wind-photovoltaic-energy storage output fluctuates relatively violently. (b) When wind-photovoltaic-energy storage output fluctuates relatively gently.

Table 1

Basic information of the diesel generator and load of the electric power system.

Access Node	Gross Rated Capacity/MW	Number	Load/MW
1234	21.87.511.218.06	3223	10.7292.7435.7869.612

Table 2

Frequency drop caused by different penetration rates of wind turbine and PV.

Penetration Rate of Wind Turbine and PV	Frequency Drop/Hz
5%15%25%	0.10.30.5

Table 3

Correspondence between allowable frequency variation and new energy access.

Frequency Variation/Hz	The Amount of Active Change/MW
0.10.20.30.40.5	1.44352.8874.33055.7747.2175

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