An optimization approach for primary frequency regulation reserve capacity considering frequency deviation for sending end of asynchronous interconnection system

Abstract

New materials and related new equipment are increasingly important to maintain the safety and stability of the asynchronous interconnection systems. DC lines equipped with Frequency Limit Controller (FLC) are able to quickly balance power fluctuation and limit frequency deviation. However, the frequency stability problem, especially in the sending end system characteristics of “large generation and small network”, still draws our attention for its significance to the gird. Based on the analysis of the primary frequency regulation principle of the power system and the impact of reserve configuration on frequency deviation in asynchronous interconnection, an optimization approach for primary frequency regulation reserve capacity, featured by the sequence quadratic programming, with the minimum quasi-steady-state frequency deviation, was proposed in this paper. The optimization idea of this approach is to arrange the reserve configuration in proportion to the unit’s adjustment coefficient and the dead zone, in order to prevent non-performance of some units while other units are sufficient. A numerical simulation indicated that, compared with the original scheme, the system frequency deviation was effectively reduced.

Keywords

Primary frequency regulation reserve capacity frequency deviation asynchronous interconnection system sequence quadratic programming numerical simulation

1. Introduction

With the development of new materials, new equipment and new technologies, the asynchronous interconnection system have gradually attracted great attention. Compared with the synchronous interconnection of the regional power grid, the asynchronous interconnection system is only interconnected via DC lines, so that the transmission of the AC fault between the sending end and the receiving end system is avoided from the network structure, and the short-circuit current is effectively limited [1, 2].

However, the frequency of the regional power grid remains a serious problem in the case of faults accrued in the sending and the receiving end system so that frequency stability becomes the main risk in the asynchronous connected power grids [3, 4]. Besides, compared with the receiving end power grid, there is a phenomenon of “large generation and small network” in the sending end system, and the network structure is relatively weak, which is more sensitive to frequency problems. In addition, the system operation mode has changed and the frequency control of the sending end system has changed greatly for the system originally interconnected by AC lines to be changed only through DC lines interconnection [5, 6]. When frequency fluctuations occur in the sending system, the mutual backup support capability between the sending end and the receiving end system is limited, which puts higher requirements on the reasonable arrangement of the reserve capacity of the primary frequency regulation, one of the important means of frequency control of the power system.

The configuration of the traditional primary frequency regulation reserve capacity is based on reliability considerations [7]. However, when the power market is rapidly developing, it is necessary to ensure the reliability while taking into consideration the economic benefit. Due to the large number, variety and performance of the units in the sending end system, the research on optimizing the primary frequency regulation reserve capacity of the unit at present is mainly carried out from two aspects: optimization model and solution algorithm, of the former there being two main research directions. Direction No 1 adopts the reliability index [8] or the economic index [9] as the objective function of the optimization model, and considers the system frequency stability requirement in the constraint to determine the reserve capacity. Direction No 2 adopts both reliability and economy as objective functions [10] for multi-objective optimization. The solution algorithm includes traditional optimization algorithm [11] and intelligent evolution algorithm [12, 13]. Through off-line analysis, under the premise that the maximum static frequency deviation of the system is not limited, the maximum active power allowed by each unit in the primary frequency regulation process is calculated, then adopted as a constraint to optimize the reserve configuration of each unit in order to minimize standby cost [14]. The existing research on the optimization of the primary frequency regulation of the sending end system mostly treats the frequency deviation as a constraint to optimize the economic benefit and reliability. However, the magnitude of the frequency deviation is of great significance to the security, stability and economy of the sending end of the asynchronous interconnection system. Therefore, it is necessary to add the frequency deviation to the objective function as the focus of the reserve capacity optimization.

To solve this problem, this paper proposed an optimization approach for primary frequency regulation reserve capacity which takes the frequency deviation in the sending end of the asynchronous interconnection system in order to optimize the primary frequency reserve capacity under the condition that the total rotation reserve is unchanged, that is, the number of online units is not changed, while the minimum frequency deviation is achieved. The sequential quadratic programming (SQP) [15] algorithm is used to solve the nonlinear optimization model. Finally, a numerical simulation research was made to verify the effectiveness of the proposed approach.

2. The frequency change and adjustment of power system

2.1 Analysis of frequency dynamic change process

Frequency is an important indicator for evaluating the power quality of power systems. In the following, the frequency response process is analyzed by taking the power shortage caused by the sending end system as an example. Figure 1 shows the frequency reduction response process when the sending end system is out of power. Such response is roughly divided into 3 stages according to the time scale [16].

Figure 1.

Schematic diagram of dynamic changes process of frequency.

In Fig. 1, $\Delta f_{\max}$ represents the maximum deviation of the transient frequency, $\Delta t_{\textit{sta}}$ represents the time required for the frequency to return to the quasi-steady state, and $\Delta f_{\textit{sta}}$ represents the quasi-steady-state frequency deviation.

Stage one: seconds scale: After the power disturbance occurs, the frequency responds quickly in a short time, the generator governor performs a frequency regulation, then the system power is balanced, and the frequency appears to be the minimum. This phase is a fast monotonic decline of frequency. If the measure is invalid at this stage, the frequency continues dropping and finally the system collapses. Therefore, the primary frequency regulation at this stage is most critical to ensure the stable operation of the system frequency.

Stage two: tens of seconds scale: The generator governor continues to perform a frequency regulation, however, due to the dead zone and governor’s own performance, this stage is subject to differential adjustment, and the frequency only recovers to a level slightly lower than the rated value, reaching a quasi-stable equilibrium state.

Stage three: minutes scale: The secondary frequency regulation of the system is activated, and the frequency is restored to the rated value or the specified value by further increasing the output of the unit.

It should be noted that when there is excess power in the sending end of the asynchronous interconnection system, the frequency adjustment measures act reversely, since the principle is basically the same, it will not be repeated here.

2.2 Analysis of system primary frequency regulation

To determine the change of frequency value caused by the system power imbalance, it is necessary to take into account the joint adjustment of both the system load and all the generator units in the system. Under the situation of a single load and a single unit, when the load increases by $\Delta P$ , the equilibrium power deviation of the system [17] is $\Delta P_{LD}$ , as shown in Eq. (1):

$\displaystyle\Delta P=\Delta P_{LD}+\Delta P_{G}=k_{LD}\Delta f{+}k_{G}(\Delta f% -a)$ (1)

Where $\Delta P_{LD}$ represents the amount of power change in load due to the frequency adjustment effect of the load; $\Delta P_{G}$ represents the increase in the output power of the generator units; $k_{LD}$ represents the frequency adjustment effect coefficient of the load; $k_{G}$ represents the static adjustment effect coefficient of the generator; $\Delta f=\left|{f_{N}-f_{2}}\right|$ indicates the frequency deviation of the system, of which $f_{N}$ and $f_{2}$ respectively represent the rated frequency of the system and the new equilibrium frequency after the system’s load fluctuations; $a$ represents the frequency regulation dead zone of the generator units.

According to Eq. (1), the system power is deficient due to the increase in load, and the system frequency is decreased. With generator units’ primary frequency regulation (increasing the output) and the load’s own power-frequency regulation (reducing the output), the system power is rebalanced.

For multi-generator complex systems, the power-frequency characteristics of the system is the sum of the power-frequency characteristics of all parallel units, that is, in order to cope with the system frequency change, the total output power of the unit is equal to the sum of the output power changes of each unit [18], as shown in Eq. (2):

$\displaystyle\Delta P=\Delta P_{1}+\Delta P_{2}+\cdots+\Delta P_{n}+\Delta P_{% L}=k_{G1}\cdot(\Delta f-a_{1})+k_{G2}\cdot(\Delta f-a_{2})\cdots+k_{Gn}\cdot(% \Delta f-a_{n})+k_{L}\Delta f$ (2)

Where $k_{Gi}$ represents the static adjustment effect coefficient of the $i$ -th unit, $i=1,2,\ldots,n$ ; $a_{i}$ represents the dead zone parameter of the $i$ -th unit; and $n$ represents the number of generator units in the system.

Appropriate deformation of the Eq. (2), the Eq. (3) is obtained:

$\displaystyle\Delta f=(\Delta P+(k_{G1}a_{1}+k_{G2}a_{2}+\cdots+k_{Gn}a_{n}))/% (k_{G1}+k_{G2}+\cdots+k_{Gn}+k_{L})$ (3)

It is noted that in the fraction of the Eq. (6), considering the dead zone parameter of generator unit is usually set to $\pm$ 0.033 Hz, a larger static adjustment effect coefficient of the unit will always make the numerator smaller than the denominator, thus leading to a smaller frequency difference. Likewise, this can also account for the more the units involved in frequency regulation, the smaller the frequency difference.

In short, Eq. (3) shows that when other parameters are fixed, a smaller dead zone parameter, a larger static adjustment effect coefficient of the unit, that is, a smaller difference coefficient (the reciprocal of the frequency regulation characteristic coefficient of the generator unit) and more the units involved in frequency regulation result in smaller frequency difference. By the way, the selection of the dead zone parameter should also consider their impact on the stability of the unit.

3. Impact of reserve configuration on frequency deviation in asynchronous interconnection

3.1 Total reserve capacity of primary frequency regulation

When the power imbalance occurs in the system, a larger primary frequency regulation reserve capacity of the unit guarantees better frequency regulation of the system [19]. However, due to the dead zone and action delay of the generator’s governor, the primary frequency regulation is hardly effective in stage one of the frequency dynamic change process when the system power fluctuates. Similarly, the reserve capacity produces little effect on the frequency change in the initial stage, though it creates certain impact on subsequent frequency changes.

3.2 Distribution location of primary frequency reserve capacity

The same primary frequency reserve capacity is distributed on the unit with different distances from the fault point, thus to differ the changes of system frequency [20]. However, in general, the distance between the distribution location of frequency regulation reserve units and the disturbance point has little effect on the overall system frequency, and a shorter distance suggests better adjustment.

3.3 Number of frequency regulation reserve distributed units

With identical rotating reserve capacity and different number of distributed units, the frequency adjustment effect is different [21]. In general, the more frequency regulation reserve distribution units require smaller active output of each unit, and achieve better system frequency.

3.4 DC transmission line Frequency Limit Controller (FLC)

FLC is vital for maintaining the frequency stability of asynchronous interconnection systems. Generally, the dead zone of FLC is set to 0.1 Hz [22]. Therefore, when the FLC is put into the sending end power grid, the primary frequency regulation reserve is only available in the range of 50 $\pm$ 0.1 Hz. It is non-economic to set too much reserve capacity. Therefore, when the FLC is put into operation, the requirement of the primary frequency regulation reserve capacity of the sending end power grid is adjusted to be able to separately bear the $N$ -1 power disturbance in the power grid, and the quasi-steady state frequency is restored to 50 $\pm$ 0.1 Hz.

3.5 Randomness of new energy sources

With the continuous increase of the new energy sources penetration rate in the sending end system, the impact of the randomness and fluctuation of the output of wind and photovoltaic power on the reserve capacity is becoming more prominent [23]. For the reserve capacity optimization model, this effect changes the failure mode of the system. At present, the biggest failure caused by the randomness of new energy sources is that the total output of concentrated new energy sources units suddenly drops to half of the rated power. Therefore, the most serious power disturbance variation of the system $\Delta P$ depends on the most serious case of the $N$ -1 fault of the original sending end system and the maximum output of new energy sources when dropping to half of the rated power [25]. As expressed in Eq. (4):

$\displaystyle\Delta P=\max(\Delta P_{\textit{origin}},\Delta P_{\textit{new}})$ (4)

Where $\Delta P_{\textit{origin}}$ represents the most serious case of the $N$ -1 fault of the original sending end system; $\Delta P_{\textit{new}}$ represents the maximum output of new energy sources becoming half of the rated power.

4. The mathematical model of primary frequency regulation reserve optimization approach

4.1 Reserve optimization objective function

Taking the unit shutdown, that is, the frequency decline caused by power fluctuation, as an example, the relationship between unit output and frequency [17] is shown in Fig. 2.

Figure 2.

Constraint of unit’s primary frequency regulation reserve capacity.

From Fig. 2 the unit’s primary frequency regulation reserve capacity is represented by Eq. (5):

$\displaystyle R_{i}=\left\{{{\begin{array}[]{ll}k_{Gi}(\Delta f+a)&a\leqslant% \left|{\Delta f}\right|\leqslant\Delta f_{i}\\ \overline{P_{i}}-P_{i}&\left|{\Delta f}\right|\geqslant\Delta f_{i}\\ \end{array}}}\right.$ (5)

Therefore, on condition $\Delta f\leqslant\Delta f_{i}$ , the maximum reserve of the unit is obtained as described in $R_{i\max}=\overline{P_{i}}-P<k_{Gi}(\Delta f-a)$ . Then the frequency deviation expression is changed from Eqs (3) to (6):

$\displaystyle\Delta f=-\frac{\Delta P-\sum\limits_{i\in M}{R_{i\max}}+\sum% \limits_{i\in N}{k_{Gi}a_{i}}}{\sum\limits_{i\in N}{k_{Gi}}+k_{L}}>\frac{% \Delta P+\sum\limits_{i=1}^{n}{k_{Gi}a_{i}}}{\sum\limits_{i=1}^{n}{k_{Gi}}+k_{% L}}$ (6)

In the formula, $M$ represents the unit whose reserve capacity is insufficient, while $N$ represents the unit whose reserve capacity is sufficient, and $M+N=n$ should be met; $R_{i\max}$ is the maximum primary frequency reserve capacity of the unit.

The equation shows that when the reserve of the unit is insufficient, the frequency difference increases, thus resulting in waste of reserve capacity of other units. Therefore, there is necessity to arrange reserve in proportion to the adjustment coefficient and the dead zone, to help reduce the frequency difference.

For each unit, according to the final quasi-steady-state frequency deviation $\Delta f_{\textit{sta}}$ , the actual called reserve is obtained from Eq. (7):

$\displaystyle R_{i}=k_{Gi}\cdot(\Delta f_{\textit{sta}}-a_{i})$ (7)

Equation (7) may be transformed into:

$\displaystyle\Delta f_{\textit{sta}}=\frac{R_{i}+k_{Gi}a_{i}}{k_{Gi}}=\frac{R^% {\prime}_{i}}{k_{Gi}}$ (8)

Due to the synchronicity of the system, on condition of the same frequency deviation for all units, Eq. (9) is obtained:

$\displaystyle\frac{R^{\prime}_{1}}{k_{G1}}=\frac{R^{\prime}_{2}}{k_{G2}}=% \cdots=\frac{R^{\prime}_{n}}{k_{Gn}}=\Delta f_{\textit{sta}}$ (9)

Equation (9) may be converted to Eq. (10):

$\displaystyle\frac{R^{\prime}_{i}}{\sum\limits_{i=1}^{n}{R^{\prime}_{i}}}=% \frac{k_{Gi}}{\sum\limits_{i=1}^{n}{k_{Gi}}}$ (10)

When the primary frequency reserve satisfies the Eq. (10), all the unit reserve is consistent and no waste is caused. At this time, under the circumstances that the total reserve amount is constant, the smallest frequency deviation of the system is obtained. However, with limitation from the unit output, line transmission capacity and economic benefit, Eq. (10) cannot be met in practice. So the objective function is:

$\displaystyle\min\sum\limits_{i=1}^{n}{\left|{\frac{R^{\prime}_{i}}{\sum% \limits_{i=1}^{n}{R^{\prime}_{i}}}-\frac{k_{Gi}}{\sum\limits_{i=1}^{n}{k_{Gi}}% }}\right|}=\min\sum\limits_{i=1}^{n}{\left|{\frac{R_{i}+k_{Gi}a_{i}}{\sum% \limits_{i=1}^{n}{(R_{i}+k_{Gi}a_{i})}}-\frac{k_{Gi}}{\sum\limits_{i=1}^{n}{k_% {Gi}}}}\right|}$ (11)

4.2 System active power balance constraint

Considering the new energy sources unit paralleling in the grid and the line power loss is ignored, the power balance constraint of the system is expressed by Eq. (12):

$\displaystyle\sum\limits_{i=1}^{n}{P_{i}+P_{w}=P_{L}}$ (12)

Where $P_{i}$ represents the actual power generation of unit $i$ ; $P_{w}$ and $P_{L}$ represents the power of new energy sources unit and system load.

4.3 Unit output constraint

$\displaystyle P_{i}^{\min}\leqslant P_{i}\leqslant P_{i}^{\max}$ (13)

Where $P_{i}^{\min}$ represents the minimum output constraint of the unit, and $P_{i}^{\max}$ represents the maximum output constraint of the unit.

4.4 Primary frequency reserve capacity inequality constraints

Equations (14) and (15) are the maximum reserve capacity constraints to be met by primary frequency regulation. Equation (16) depicts the minimum reserve capacity constraints to be met by primary frequency regulation, and at the same time to ensure economic benefit and security, the reserve capacity is spared up to 50% margin. Where $P_{iN}$ is the rated power of unit $i$ and $R_{\min}=\Delta P-\Delta f_{\textit{sta}}\cdot k_{LD}$ is the minimum reserve capacity. $\Delta P$ is obtained from Eq. (4).

$\displaystyle 0\leqslant R_{i}\leqslant P_{i}^{\max}-P_{i}$ (14) $\displaystyle R_{i}\leqslant 6\text{\%}\cdot P_{iN}$ (15) $\displaystyle R_{\min}\leqslant\sum\limits_{i=1}^{n}{R_{i}}\leqslant 1.5R_{\min}$ (16)

4.5 Network security constraint

$\displaystyle-P_{li}^{\max}\leqslant P_{li}\leqslant P_{li}^{\max}$ (17)

Where $P_{li}$ and $P_{li}^{\max}$ are the active power of the transmission line and the maximum transmission active power allowed respectively.

4.6 Solution algorithm

The objective function of the above model is nonlinear, Sequential Quadratic Programming (SQP) is often used to solve such problems due to its good convergence, strong boundary search ability, and high computational efficiency [21].

For general form of optimization problems:

$\displaystyle\min\,f(x)$ $\displaystyle\text{s.t.}\,g_{j}(x)=0\,\,j=1,2,\cdots,E$ (18) $\displaystyle\phantom{\text{s.t.}\,}h_{s}(x)\leqslant 0\,\,s=1,2,\cdots,F$

The sequential quadratic programming method is constructed by constructing a Lagrangian auxiliary function that satisfies the Karush-Kuhn-Tucher (KKT) condition.

$\displaystyle L(x,\alpha,\beta)=f(x)+\sum\limits_{j=1}^{p}{\alpha_{j}^{k}g_{j}% (x)}+\sum\limits_{s=1}^{m}{\beta_{s}^{k}h_{s}(x)}$ (19)

Where $\alpha_{j}^{k}$ and $\beta_{s}^{k}$ are the Lagrange multipliers corresponding to the $j$ -th equation and the $s$ -th inequality in Eq. (4.6), respectively. $k$ represents the number of iterations.

By implementing Taylor expansion at $x^{k}$ by $f(x)$ , $g_{j}(x)$ , and $h_{s}(x)$ , and carrying out quadratic approximation, we define a quadratic sub-problem that is equivalent to Eq. (4.6), as shown in Eq. (4.6).

$\displaystyle\min\frac{1}{2}d^{T}H_{k}d+\nabla f(x^{k})^{T}d$ $\displaystyle\text{s.t.}\,\nabla g_{j}(x^{k})^{T}d{+}g_{j}(x^{k}){=0}$ (20) $\displaystyle\phantom{\text{s.t.}\,}\nabla h_{s}(x^{k})^{T}d{+}h_{s}(x^{k})% \leqslant{0}$

Where $d=x-x^{k}$ , $H_{k}$ is generally the Hesse matrix of $f(x)$ at point $x^{k}$ , that is, $H_{k}=\nabla^{2}f(x^{k})$ . This formula is updated as follows [24]:

$\displaystyle H_{k+1}=H_{k}+\frac{q^{k}(q^{k})^{T}}{(d^{k})^{T}q^{k}}-\frac{(H% _{k})^{T}H_{k}}{(d^{k})^{T}H_{k}d^{k}}$ (21)

Where $q^{k}=\nabla_{x}L(x^{k+1},\alpha_{j}^{k+1},\beta_{s}^{k+1})-\nabla_{x}L(x^{k},% \alpha_{j}^{k},\beta_{s}^{k})$ .

Figure 3.

Flow chart of sequential quadratic programming algorithm.

The solution process is shown in Fig. 3. The optimal solution search direction involved in the figure is determined on the basis of the quasi-Newton method, and the symmetric positive definite iterative matrix is used as the direction matrix, according to which the objective function value is reduced by each iteration calculation while ensuring the positive definite of the direction matrix. After that, the inverse matrix of the Hesse matrix is approximated, thus avoiding the huge computational complexity of directly solving the Hesse inverse matrix.

5. Numerical simulation and verification

5.1 Case introduction

In this paper, the asynchronous interconnection of a provincial power grid and the main grid of China Southern Power Grid through only 7 DC lines is taken as an example, whose schematic diagram is shown in Fig. 4. The parameters of the 7 DC lines are shown in Table A1 of Appendix A.

Taking a provincial power grid as a typical representative of the sending end power gird of asynchronous interconnection system, its hydropower installed capacity is 61 631 MW, accounting for 73.7% of the total installed capacity (83 639 MW). In the mode with the minimum short circuit impedance value of wet season, the load is 18 200 MW, and the load models of induction motor and constant impedance are half each. The load regulation effect coefficient has a standard value of 1.2. In addition to meeting the local load of the province, other power is transmitted to the main network through DC lines, and the normal frequency of the system frequency is 50 Hz. The FLC control function of the DC lines rectification side converter station is put into operation, the action dead zone is $\pm$ 0.1 Hz, the power reduction limit is 50% of the rated power, and the upper limit is 20%. For the frequency regulation parameters of hydropower units and thermal power units, see Appendix A, Table A2. The receiving end system uses the data of the Southern Power Grid in the mode with the minimum short circuit impedance value of wet season in a certain year. All numerical simulation studies were performed in the power system transient simulation program PSD-BPA and the mathematical analysis software MATLAB.

Figure 4.

Schematic diagram of asynchronous operation of a provincial power grid and the main grid of China Southern Power Grid.

5.2 Calculation of optimization scheme

In view of the small capacity of a provincial power grid new energy sources at this stage, the installed capacity is up to 1 316 MW, which is 658 MW by reducing to half, while the maximum power shortage $N$ -1 fault of the provincial power grid is the full load trip of the power plant B with 700 MW units. According to Section 3.2.2 in this paper, the randomness of new energy sources has almost no effect on the primary frequency reserve of the unit that has been running online in a provincial power grid. However, the paralleling in of new energy sources may cause the original units to stop, and the system will reduce the total reserve capacity, and the wind turbines in this province will increase in the future, thus such impact cannot be ignored.

Based on the primary frequency reserve optimization model proposed in this paper, the sequential quadratic programming method is adopted to solve the problem on MATLAB platform. By calculation, the best total reserve capacity is 988 MW for primary frequency on condition that the provincial power grid is asynchronously interconnected. The reserve capacity before and after optimization of each online operation unit is shown in Appendix A, Table A2.

5.3 Effectiveness validation of optimization scheme

The backup plan before and after optimization is configured for a certain provincial power grid, and the largest single-unit trip in the province is set as the full-load trip fault of the single unit of power plant B. Using BPA software for numerical simulation calculation, comparing the effect of the system primary frequency regulation. Figure 5 shows the output of different units, Fig. 6 shows the frequency deviation of the sending end power grid, that is, the frequency of the provincial power grid, and Fig. 7 shows the transmission power of DC line 2. Moreover, the comparison of different back up schemes is presented in Table 1 according to the frequency evaluation index (The calculation method is detailed in Appendix B).

Table 1
Comparison of different backup schemes

	Original reserve scheme	Optimized reserve scheme	Increased percentage
Maximum deviation of transient frequency/Hz	$-$ 0.1461	$-$ 0.1469	$-$ 0.55%
Frequency deviation of quasi-steady state/Hz	$-$ 0.0735	$-$ 0.0672	8.57%
Recovery time of DC power/s	36.72	30.35	17.35%

Figure 5.

The output of different units under different backup schemes. a. The output of unit A.1; b. The output of unit K.2.

Unit A.1 is a class of units typically short of frequency regulation reserve capacity under the original reserve scheme, while in the optimization scheme, the frequency regulation reserve capacity increased by adjusting the output level in the steady state. As shown in Fig. 5a, in case of a failure, the optimized unit adjusted the frequency regulation reserve of about 3 MW to support the grid frequency. Unit K.2 belongs to another type of unit typically with sufficient frequency regulation reserve capacity in the original reserve scheme. In case of a fault, the actual frequency reserve called was far less than the set reserve level, resulting in reserve waste. While under the optimization scheme, its output level was adjusted to reduce its primary frequency reserve capacity. As shown in Fig. 5b, in the same fault condition, after the optimization, its primary frequency reserve capacity called was consistent with the original scheme, thus achieving full use of the backup.

Based on the numerical simulation curve of Figs 6 and 7 and Table 1, before and after optimization on the condition that only the power plant B trips, the quasi-steady-state frequency deviation was greatly reduced by 8.57%, thus improving the system stability and the unit reserve utilization rate. Moreover, the DC transmission power was restored to the rated value more quickly, reducing the impact on the receiving end system. The maximum deviation of transient frequency increased slightly, by only 0.55%, and the impact was limited. The main reason was that the power plant B unit increased from 700 MW to 718 MW, which caused a significant impact on the system, which called a certain time buffer to make primary frequency call reserve.

Figure 6.

Frequency deviation of the sending-end network under different backup schemes.

Figure 7.

Power transmitted by DC 2 under different backup schemes.

From the numerical simulation results above and Appendix Table A2, it can be concluded that only part of the reserve capacity participated in the primary frequency adjustment in the spinning reserve reserved by the unit, thus reducing the excessive reserve of the original primary frequency backup unit and increasing the primary frequency reserve of the unit not equipped with backup before. In this way, the number of units participating in the primary frequency regulation increased, and the unit reserve capacity distribution was made as proportional as possible, only to effectively reduce the quasi-steady-state frequency deviation of the system. This shows that the optimization scheme ensures a frequency regulation reserve for all the units running online, by adjusting the unit operating point of the steady-state situation in advance, so that in the case of a system failure, all the online units was to participate in primary frequency regulation and have high backup utilization, thus reducing the system frequency fluctuation as well as the total primary frequency reserve capacity after optimization. The reason is that the original scheme is configured according to the allowable frequency deviation of 0.2 Hz, and the optimization scheme considers the asynchronous interconnection factor, the actual called backup only acts within the 0.1 Hz deviation, which can avoid reserve waste. In addition, after the adjustment of the primary frequency regulation reserve scheme, although the maximum fault of the optimized sending end system is converted from 700 MW to 718 MW, the severity of the fault increases and the transient frequency increases slightly, but the quasi-steady-state frequency deviation is greatly reduced by 8.57%. And the DC lines can recover to the rated output more quickly, so the system with optimized reserve capacity is more resistant to the same power imbalance condition.

6. Conclusion

Focusing on the frequency stability problem in the asynchronous interconnection sending end system, this paper proposed an optimization approach for primary frequency regulation reserve capacity considering frequency deviation, to draw the following conclusions.

By analyzing the frequency adjustment process of a multi-unit complex system, it is concluded that a smaller dead zone, a smaller difference coefficient of the unit and more the units involved in frequency regulation result in smaller frequency difference.

The numerical simulation result of the example shows that the quasi-steady-state frequency deviation can be effectively reduced by the proposed model that minimizes the sum of the difference between the actual reserve capacity and the optimal reserve capacity of each unit. Besides, the DC lines can recover to the rated transmission power more quickly.

The optimization approach for primary frequency regulation reserve capacity proposed in this paper simplifies the receiving end system to a large load, and does not consider its dynamic performance. It is necessary to jointly discuss the sending end and receiving end systems in future research; Besides, the consideration of frequency deviation under different operating conditions is insufficient, only the typical working conditions are selected to verify the effectiveness of the adopted control strategy, and the operating conditions should be considered in the subsequent research to improve the rigor of the approach.

Footnotes

Acknowledgments

This research was funded by the Science and Technology Project of Yun-nan Power Grid Limited Liability Company (Research on the Co-ordinated Control Technology of Frequency and Voltage Regulation of Wind and Solar Power), grant number 0560002018030301XT00120.

Appendix A

Table A1

Asynchronous networking DC line parameters

Name	Voltage (kV)	Delivery power (MW)
DC line1 (double circuit)	$\pm$ 800	6400
DC line2	$\pm$ 800	5000
DC line 3	$\pm$ 500	5000
DC line 4	$\pm$ 500	3200
Back to back DC line 5	$\pm$ 500	2000
DC line 6	$\pm$ 500	3000

Table A2

A province’s power grid backup optimization scheme

Unit name	Rated power (MW)	Adjustment coefficient	Dead zone (Hz)	Original output (MW)	Optimized output (MW)	Original primary frequency reserve capacity (MW)	Optimized primary frequency reserve capacity (MW)
UnitA.1G	700	0.04	0.05	700	685.0	0	9
UnitA.2G	700	0.04	0.05	700	685.0	0	9
UnitA.3G	700	0.04	0.05	700	685.0	0	9
UnitA.4G	700	0.04	0.05	700	685.0	0	9
UnitA.5G	700	0.04	0.05	500	519.0	70	38
UnitA.6G	700	0.04	0.05	500	519.0	70	38
UnitB.10G	770	0.04	0.05	700	718.0	77	39
UnitB.11G	770	0.04	0.05	700	718.0	77	39
UnitB.12G	770	0.04	0.05	700	718.0	77	39
UnitB.13G	770	0.04	0.05	700	718.0	77	39
UnitB.14G	770	0.04	0.05	700	718.0	77	39
UnitB.15G	770	0.04	0.05	700	718.0	77	39
UnitB.16G	770	0.04	0.05	700	718.0	77	39
UnitB.17G	770	0.04	0.05	700	718.0	77	39
UnitB.18G	770	0.04	0.05	700	718.0	77	39
UnitC.9G	650	0.04	0.05	650	634.0	0	9
UnitC.8G	650	0.04	0.05	650	634.0	0	9
UnitC.7G	650	0.04	0.05	650	634.0	0	9
UnitC.6G	650	0.04	0.05	650	634.0	0	9
UnitC.5G	650	0.04	0.05	650	634.0	0	9
UnitC.4G	650	0.04	0.05	650	634.0	0	9
UnitC.3G	650	0.04	0.05	650	634.0	0	9
UnitC.2G	650	0.04	0.05	500	519.0	65	36
UnitC.1G	650	0.04	0.05	500	519.0	65	36
UnitD.1G	600	0.04	0.05	600	584.0	0	9
UnitD.2G	600	0.04	0.05	600	584.0	0	9
UnitD.3G	600	0.04	0.05	600	584.0	0	9
UnitD.4G	600	0.04	0.05	600	584.0	0	9
UnitE.1G	300	0.05	0.033	160	179.0	24	11
UnitE.2G	300	0.05	0.033	160	179.0	24	11
UnitE.3G	300	0.05	0.033	160	179.0	24	11
UnitF.1G	300	0.04	0.05	200	219.0	30	9
UnitG.1G	225	0.04	0.05	125	144.0	22.5	5
UnitG.2G	225	0.04	0.05	125	144.0	22.5	5
UnitH.1G	350	0.04	0.05	350	334.0	0	8
UnitH.2G	350	0.04	0.05	350	334.0	0	8
UnitH.3G	350	0.04	0.05	300	317.0	35	19

Table A2, continued
Unit name	Rated power (MW)	Adjustment coefficient	Dead zone (Hz)	Original output (MW)	Optimized output (MW)		Original primary frequency reserve capacity (MW)		Optimized primary frequency reserve capacity (MW)
UnitH.4G	350	0.04	0.05	250	269	.0	35		18
UnitI.1G	150	0.04	0.05	150	132	.0	0		6
UnitI.2G	150	0.04	0.05	100	118	.0	15		3
UnitJ.1G	175	0.04	0.05	175	157	.0	0		7
UnitJ.2G	175	0.04	0.05	175	157	.0	0		7
UnitJ.3G	175	0.04	0.05	175	157	.0	0		7
UnitJ.4G	175	0.04	0.05	175	157	.0	0		7
UnitJ.5G	175	0.04	0.05	120	138	.0	17	.5	2
UnitK.2G	105	0.04	0.05	80	95	.00	10	.5	3
UnitK.3G	105	0.04	0.05	80	95	.00	10	.5	3
UnitL.1G	225	0.04	0.05	200	211	.0	22	.5	5
UnitL.2G	225	0.04	0.05	200	211	.0	22	.5	5
UnitM.1G	400	0.04	0.05	400	384	.0	0		8
UnitM.G	400	0.04	0.05	400	384	.0	0		8
UnitM.G	400	0.04	0.05	400	384	.0	0		8
UnitN.1G	360	0.04	0.05	360	344	.0	0		8
UnitN.2G	360	0.04	0.05	360	344	.0	0		8
UnitN.3G	360	0.04	0.05	360	344	.0	0		8
UnitO.1G	360	0.04	0.05	360	344	.0	0		8
UnitO.2G	360	0.04	0.05	300	318	.0	36		18
UnitP.4G	600	0.04	0.05	600	584	.0	0		9
UnitP.3G	600	0.04	0.05	600	584	.0	0		9
UnitP.2G	600	0.04	0.05	600	584	.0	0		9
UnitP.1G	600	0.04	0.05	600	584	.0	0		9
UnitQ.4G	600	0.04	0.05	300	320	.0	60		34
UnitQ.5G	600	0.04	0.05	600	584	.0	0		9
UnitR	135	0.05	0.0325	100	117	.0	10	.8	6
UnitS	600	0.05	0.033	400	419	.0	48		35
Sum				28600	28600		1433	.3	988

Appendix B

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An optimization approach for primary frequency regulation reserve capacity considering frequency deviation for sending end of asynchronous interconnection system

Abstract

Keywords

1. Introduction

2. The frequency change and adjustment of power system

2.1 Analysis of frequency dynamic change process

3.1 Total reserve capacity of primary frequency regulation

3.2 Distribution location of primary frequency reserve capacity

3.3 Number of frequency regulation reserve distributed units

3.4 DC transmission line Frequency Limit Controller (FLC)

3.5 Randomness of new energy sources

4.1 Reserve optimization objective function

5.1 Case introduction

5.3 Effectiveness validation of optimization scheme

Table 1 Comparison of different backup schemes

Footnotes

Acknowledgments

Appendix A

Appendix B

References

Table 1
Comparison of different backup schemes