Method of Multi-Energy Complementary System Participating in Auxiliary Frequency Regulation of Power Systems

Abstract

This research investigates a grid with two areas interconnected by a high-voltage direct-current (DC) link. One of the areas, called the sending-end region, has intermittent renewable generation and frequency stability issues. To address the lack of frequency-regulation (FR) resources in the sending-end region of the interconnected grid, the participation of hydroelectricity–photovoltaics and pumped storage complementary systems (HPPCSs) in auxiliary frequency-regulation (AFR) services is studied in the context of the construction of the electricity market. Firstly, the HPPCS participating in AFR services considering DC modulation is modeled by combining the operational characteristics of the actual power station. Taking the purchase cost of auxiliary service as the objective function, the optimum allocation of FR scheduling demand is achieved by the proposed method. The simulations confirm that the proposed method of HPPCS participation in the AFR service of the sending-end grid can effectively maintain the frequency stability of the regional interconnected grid while ensuring optimal economic efficiency. The proposed method provides the optimal scheduling solution for multiple energy resources participating in the AFR service of the grid.

1. Introduction

In response to the existential threat to humanity caused by climate change and global warming, the development of renewable energy generation technology has become a crucial decision for countries worldwide in addressing energy issues [1,2,3]. According to the latest data from the International Renewable Energy Agency (IRENA) [4], the global installed capacity of renewable energy generation reached 3381.76 GW in 2022, with hydropower accounting for 39.69% and solar power accounting for 30.01% of the total capacity. In recent years, for large-scale regional grids with a high proportion of energy delivery, the frequency stability problem caused by the power imbalance within the grid and the nonlinear time-varying characteristics of the system have gradually become more prominent [5,6]. Traditional thermal power-plant frequency regulation exhibits drawbacks such as slow responses and limited ramping capability; it is thus unable to meet the stability and FR demand of the grid [7]. To ensure the stable operation of interconnected regional power systems, the integration of various flexible energy sources into the grid is required [8,9,10].

In order to fully utilize the FR resource within the grid, the method of renewable-energy generation system participation in AFR has gradually been focused on and developed by many countries [11,12]. The output of new energy generation is characterized by significant stochasticity and intermittency [13]. The large-scale grid connection of the single photovoltaic power-generation system not only fails to meet the demand for its stable participation in AFR but also brings challenges to the stable operation of the grid [14]. Hydropower and pumped storage units are high-quality grid-internal FR resources, featuring the advantages of controllable output, rapid adjustment capability of unit startup-shutdown and generation output [15,16]. To smooth out the fluctuating characteristics of photovoltaic generation, pumped storage units can be considered to be combined with cascading hydropower and photovoltaic systems to form the HPPCS [17]. On one hand, HPPCSs participating in AFR can increase the available frequency-regulation resource capacity within the grid, enhancing system frequency stability. On the other hand, utilizing the adjustable characteristics of hydropower and pumped storage units to compensate for the random output of photovoltaics can reduce power-generation-system output fluctuation and promote the large-scale consumption of renewable energy [18].

Within the electricity market environment, the reasonable and effective promotion of the AFR service market operation can not only increase the enthusiasm of generating units to provide FR service but also enhance the improvement in the FR performance of the units, thereby reducing the cost of purchasing FR services [19,20]. In recent years, scholars have proposed methods for various types of energy systems participating in AFR services. With the goal of minimizing purchasing costs, a market-clearing mechanism for renewable energy producers participating in auxiliary services of the power system is constructed in [21]. Considering the uncertainty of renewable energy and market price, the method of joint operation for multiple types of energy systems, such as wind farms and photovoltaics, in the energy and ancillary services market is researched in [22]. In [23,24,25], the method of energy storage participating in FR is proposed, and capacity optimization allocation and the control method of energy storage participating in FR are designed. The output characteristics of different types of electric energy storage devices are compared and the economy of their participation in FR auxiliary services is analyzed in [26]. In [27], the participation of energy storage for electric vehicles in the market bidding and optimized allocation methods for ancillary services are proposed, which enhances the response capability of electric vehicles participating in AFR services. Furthermore, the closed-loop vehicle-to-grid (V2G) control method is proposed in [28], which simultaneously realizes the function of FR and charging for the electric vehicle. Regarding the frequency stable control of the grid, a coordinated frequency-control method based on situational awareness for wind power and high-voltage direct-current (HVDC) participation is proposed in [29], which improves the frequency-response characteristics of the sending-end grid through variable objective optimal control. In [30], a frequency stability-control method based on model predictive control is proposed, which is applicable to the microgrid containing multiple types of energy resources. However, this method increases the cost of FR due to the need for additional sensors and communication devices. A frequency-prediction method for the grid based on the Spearman correlation coefficient and light gradient boosting machine (LightGBM) is proposed in [31], which can assist the system in achieving dynamic frequency stability control. In [32], a frequency stability improvement method based on frequency trajectory planning is proposed, which can provide inertia and damping support for the system by controlling the inverter. However, it cannot be directly applied to the AFR control of regional interconnected HVDC transmission systems.

The method for AFR service and FR control for the grid are discussed from different perspectives in the above study, mainly involving the optimal scheduling of traditional FR resources and some new energy resources. However, the market clearance method for HPPCSs with more energy types participating in AFR has not yet been analyzed in the current research. Additionally, there is a lack of research on methods for multi-energy complementary systems participating in AFR services within a regional interconnected grid. Therefore, under the FR market environment, improving the system frequency stability by fully utilizing the controllability of the HPPCS and rationally utilizing the FR resource within the interconnected grid is worthy of further study. To address these gaps, the method of HPPCSs participating in AFR services of the sending-end grid is proposed. The contribution of this paper can be concluded as follows.

(1) Considering asynchronously interconnected DCs as the in-network FR resource, the response model of the HPPCS participating in an AFR service is constructed, which provides a modeling reference for the FR method research of multi-energy complementary systems participating in asynchronous interconnected sending-end systems.

(2) The market-clearing method of the HPPCS participating in the AFR service at the sending end of the interconnected grid is designed. The proposed method can realize the economic allocation of FR demand within a regional interconnected grid while maintaining the frequency stability of the grid.

The rest of this paper is organized as follows. In Section 2, the response model for HPPCSs participating in AFR services is built. A market-clearing method for HPPCSs participating in AFR services is proposed in Section 3. In Section 4, the effectiveness of the proposed AFR method is validated through simulation. Finally, the conclusions are drawn in Section 5.

2. Modeling of HPPCS Participating in AFR Service

2.1. Frequency-Response Modeling for AFR Service

A schematic diagram of the HPPCS is shown in Figure 1, and its output is bundled and sent through an external delivery channel, which is controlled by the grid scheduling.

In order to clarify the response characteristic of HPPCSs participating in AFR, a sending-end system of the interconnected regional grid connected by a DC line is taken as the object of study in this section. In this paper, high-voltage DC transmission based on a line commutated converter (LCC-HVDC) is used. The frequency regulation of the interconnected regional grid is mainly composed of primary FR and secondary FR. In referring to [33], the schematic diagram of the FR process of the regional interconnected grid sending-end system can be obtained as shown in Figure 2 (wherein Δf denotes the frequency deviation of the regional grid; ΔP_L denotes the variation of the load; ΔP_M denotes the variation of the active regulation of the generator unit; and ΔP_FLC denotes the power change of DC AFR).

Based on Figure 2, the frequency-response model of the sending-end grid containing multiple AFR resources can be established as shown in Figure 3. In this section, the following reasonable simplification is adopted in modeling. For the automatic generation control (AGC), the structure of the power plant side is ignored, the calculation of area control error (ACE) signal and controller for the main station is retained, and the model of the thermal unit is supplemented [34], which can be used to allocate command according to the calculation results of the AFR market.

As shown in Figure 3, the model of hydro, photovoltaic, pumped-storage and thermal power-generating units and the DC line is included, and the subscripts h, p, s and t denote the sequence number of hydro, photovoltaic, pumped-storage, and thermal power-generating units, respectively. R denotes the regulation coefficient; E_ACE denotes the active power deviation signal of the send-end grid; ΔP_C denotes the control command output by the AGC controller; β denotes the frequency deviation factor of the system; λ denotes the allocation factor of the generator power of the AGC signal, which can be allocated based on the calculation result of the AFR service; D denotes the equivalent damping coefficient of the system; and T_sys denotes the equivalent inertia constant of the system.

The frequency-power modulation of the DC within the inter-area in Figure 3 is realized through the frequency limit controller (FLC) of the AC/DC converter station of the DC link. Using the frequency deviation signal of the AC system, the FLC can change the DC power reference to quickly regulate the transmitted active power, which is, in turn, used to offset the power imbalance and improve the frequency response of the system. Using an FLC is an important DC modulation method, which can assist in frequency regulation using FR resources in the grid. The control block diagram of an FLC commonly used in engineering practice is shown in Figure 4 [35]. The input signal of the controller is the frequency deviation ∆f, which enters the PI controller after going through the limiter, low-pass filter, and frequency-difference dead-zone limiter. Then, it passes through the limiter of controller output power. Finally, the deviation signal of system frequency is transformed into the command signal of DC power adjustment. In Figure 4, F_max and F_min denote the upper and lower limit of frequency deviation of FLC, respectively; T_r denotes the inertia time constant; K_r denotes the amplification coefficient of the measurement link; and P_max and P_min denote the regulating limit of active power for FLC.

As shown in Figure 4, the control process of the FLC of the send-end system is carried out by the following equation.

$$\Delta {\dot{P}}_{\mathrm{f}}=\frac{K_{\mathrm{r}}}{T_{\mathrm{r}}}\Delta f_c-\frac{1}{T_{\mathrm{r}}}\Delta P_{\mathrm{f}}$$

(1)

$$\Delta {\dot{P}}_{FLC}=(K_{\mathrm{I}}-\frac{K_{\mathrm{P}}}{T_{\mathrm{r}}})\Delta P_{\mathrm{f}}+\frac{K_{\mathrm{r}}{K}_{\mathrm{P}}}{T_{\mathrm{r}}}\Delta f$$

(2)

2.2. Calculation of ACE Signal and Frequency Deviation

In response to fluctuation in the balance of active power in the sending-end region, the output state of the AGC unit within the area is changed by adjusting the reference setting value of the load and thus realizing the FR. The input signal of the AGC controller is the area control error (ACE) of the control area, and the output signal is the power adjustment amount of the generating unit. The control objectives of the AGC system are different, and the calculation method of the ACE signal is also different. In this paper, the commonly used frequency-deviation control method of the contact line in the actual system [36] is taken as the basis of the study. Through making the ACE signal 0, the control objective of maintaining the stability of the regional grid frequency is achieved by the AGC controller, so as to guarantee the power of the interconnected power-grid contact line at the given value.

As can be seen from Figure 3, after interconnecting the regional grid, the ACE signal of the interconnected grid area contains the system frequency deviation and the power change of the DC contact line ΔP_FLC. The frequency-active regulation capability of the grid is increased after the access of the HPPCS. In order to fully utilize the FR resources in the grid, the HPPCS can be involved in the calculation of the ACE signal to provide AFR services. The ACE signal of the send-end grid consists of the product between the system frequency deviation and the frequency deviation factor as well as the power deviation of the DC contact line, which can be defined as:

$$E_{\mathrm{ACE}}=\beta \Delta f+\Delta P_{FLC}$$

(3)

Within the regional grid, frequency regulation is realized through the governor-primary motor. When the power disturbance in the system occurs, resulting in frequency deviation, the power regulation is completed by changing the output of the primary motor in the generating unit of HPPCS. Combined with Figure 3, it is found that the frequency deviation of the regional grid at this point can be written as:

$$\Delta \dot{f}=-\frac{D}{T_{sys}}\Delta f+\frac{1}{T_{sys}}(\Delta P_{M,h}+\Delta P_{M,p}+\Delta P_{M,s}+\Delta P_{M,t}-\Delta P_{FLC}-\Delta P_L)$$

(4)

3. Research on the Method of HPPCS Participating in AFR Service

3.1. Overview of the AFR Ancillary Services Model

In order to fully utilize the FR resources within the regional power-grid system and improve the positivity of multi-type FR resources to participate in the frequency modulation auxiliary service, the HPPCS is incorporated into the AFR service in this section. Also, the economic scheduling method of the FR resource applicable to the grid containing the HPPCS is developed, so as to achieve the economic and effective scheduling for the FR resources of the system.

An AFR service, as an important part of the auxiliary service of the power system, plays an indispensable role in the safe, stable, and economic operation of the system. In developed countries, the development of the power market is relatively mature. In this section, the basic framework and process of the U.S. PJM AFR service are selected [37,38]. Combined with the operational property of the interconnected system, the participation of the HPPCS in the AFR service method of the send-end system is established.

The units participating in the bidding for AFR services are required to provide the mileage quotation, capacity quotation, and declared capacity of the unit, which is checked by the organizing department for access. The scheduling agency then provides the demand for FR capacity based on the actual operation of the grid, while the generating units participate in the bidding based on the capacity declaration, so as to determine the combined supply scheme for the FR service providers. On the premise of meeting the constraint of stable operation for the grid, clearing is carried out with the objective of achieving an optimal economic dispatch cost for the purchaser of AFR services. The combination of units providing AFR services and the corresponding bidding capacity of each unit are obtained to realize the economic allocation of FR demand.

3.2. Cost Calculation of AFR Service

In this section, the AFR service method is proposed. According to the FR capacity demand, whether the existing FR capacity in the current cycle meets the FR demand is judged; also, the regulation capacity participated in by the HPPCS and the asynchronous interconnected DC are determined. It is set that each unit participating in the bidding only participates in the auxiliary FR service and is retained with a certain regulation capacity. We take 15 min as the calculation cycle for rolling transaction calculations and minimizing the economic cost of purchasing auxiliary services as the objective function and determine the amount of power allocation of the units participating in the bidding of FR services. It is taken as the active regulation capacity of the unit in this scheduling cycle to realize the coordinated dispatch of the FR resources in the network and the optimal economic allocation of the FR demand capacity. The constructed objective function is as follows [39,40]:

$$\min M={\displaystyle \sum _{i=1}^{N_{\mathrm{g}}}{s}_i(k)[P_{\mathrm{c},i}{R}_{\mathrm{c},i}(k)+P_{\mathrm{m},i}{R}_{\mathrm{m},i}(k)]}+{\displaystyle \sum _{j=1}^{N_{\mathrm{dc}}}{C}_{\mathrm{dc}}[\Delta P_{\mathrm{dc},j}(k)]}$$

(5)

where M denotes the cost required for purchasing AFR service; k denotes the kth scheduling cycle; N_g denotes the number of AGC units participating in the bidding at the send-end grid; s_i(k) denotes the comprehensive FR performance coefficient of the ith generating unit, which is calculated and defined as shown in Equation (6), and the larger the value of s_i denotes the better FR performance of the unit; P_c,i and P_m,i denote the capacity offer and mileage offer of the ith generator unit, respectively; R_c,i(k) and R_m,i(k) denote the values of FR capacity and FR mileage bid by generator unit i in the kth calculation cycle; R_m,i(k) can be expressed as the product of the bidding FR capacity, R_c,i(k), and the actual mileage dispatch coefficient α_i; C_dc denotes the regulation cost function of the DC contact line; and ΔP_dc,j(k) denotes the active power regulation of the DC contact line j in the calculation period k.

The execution status of the control command by the AGC unit is described by the comprehensive FR performance coefficient s_i(k), which is mainly composed of three aspects: command regulation speed, command response delay, and control accuracy. s_i(k) can be defined as follows [39]:

$$\left\{\begin{array}{l}{s}_i(k)={\alpha }_1{s}_1(k)+{\alpha }_2{s}_2(k)+{\alpha }_3{s}_3(k)\\ s_1(k)=\frac{v_i}{v_N}\\ s_2(k)=1-\frac{t_i-0.5}{t_N}\\ s_3(k)=1-\frac{{\gamma }_i}{{\gamma }_N}\end{array}\right.$$

(6)

where the indicator s₁(k) reflects the speed of the AGC command response rate of the generating unit, the indicator s₂(k) reflects the delay of the actual command execution of the generating unit, and the indicator s₃(k) indicates the accuracy of the command execution of the generating unit. v_i denotes the actual regulating rate of the generating unit; v_N denotes the standard regulating rate of the generating unit; t_i denotes the delay of the command execution of the generating unit; t_N denotes the delay time of the standard response; γ_i and γ_N denote the actual execution error and the standard allowable error of the unit command, respectively; α_j denotes the weighting coefficient.

The constraints mainly consist of the following:

(1) Dynamic balance constraint of power within the regional grid.

$$\Delta P_{\mathrm{uc}}(k)={\displaystyle \sum _{i=1}^{N_{\mathrm{g}}}{R}_{\mathrm{c},i}(k)+}{\displaystyle \sum _{j=1}^{N_{\mathrm{dc}}}\Delta P_{\mathrm{dc},j}(k)}$$

(7)

where ΔP_uc(k) denotes the FR demand capacity of the send-end grid; and the right side of the equation denotes the AGC unit bidding capacity and DC regulation capacity. This equation indicates that the active power is balanced in each calculation cycle, which means that the combination of the bidding capacity of the unit meets the FR capacity demand in such a cycle.

(2) Power transfer constraint of the system.

The power of the HPPCS and DC system participating in the AFR service needs to be within the allowable range of that power modulation capability.

$$\Delta P_{HPSCS,j}^{\min }(k)\le \Delta P_{HPSCS,j}(k)\le \Delta P_{HPSCS,j}^{\max }(k)$$

(8)

$$\Delta P_{\mathrm{dc},j}^{\min }(k)\le \Delta P_{\mathrm{dc},j}(k)\le \Delta P_{\mathrm{dc},j}^{\max }(k)$$

(9)

where $\Delta P_{HPSCS,j}^{\min }(k)$ and $\Delta P_{HPSCS,j}^{\max }(k)$ denote the upper and lower limit of the amount of active adjustment allowed by the HPPCS to participate in AFR service; $\Delta P_{\mathrm{dc},j}^{\min }(k)$ and $\Delta P_{\mathrm{dc},j}^{\max }(k)$ denote the upper and lower limit of the amount of active adjustment allowed by the DC system to participate in AFR services. In the actual system, the upper and lower limit can be reasonably set by the operation and scheduling personnel in combination with the near-area line flow constraint, operation history data, regulation performance of converter station equipment, and experience of the operation personnel, which is declared to the scheduling center.

(3) Capacity constraint of FR for the system.

$${\displaystyle \sum _{i=1}^{N_{\mathrm{G}}}{R}_{\mathrm{c},i}(k)\le R_{\mathrm{c},\mathrm{sys}}}$$

(10)

where R_c,sys denotes the total declared amount of send-end grid FR resources participating in the auxiliary FR services.

(4) Power output constraint of the AGC bidding unit.

$$P_{\mathrm{g},i}^{\min }\le R_{\mathrm{c},i}(k)+P_{\mathrm{g},i}(k-1)\le P_{\mathrm{g},i}^{\max }$$

(11)

where $P_{\mathrm{g},i}(k-1)$ denotes the active output of the bidding unit i in the last cycle; $P_{\mathrm{g},i}^{\min }$ and $P_{\mathrm{g},i}^{\max }$ denote the active minimum output and the maximum output limit of the unit.

(5) FR capacity constraint of the AGC unit.

$$0\le R_{\mathrm{c},i}(k)\le R_{\mathrm{c},i}^{\max }$$

(12)

where $R_{\mathrm{c},i}^{\max }$ denotes the FR capacity limit of the unit.

In an asynchronously interconnected send-end grid, the cost of DC participation in the auxiliary FR service is considered as the FR service provided by the recipient system through the DC modulation that makes the DC power change. Since DC interconnects both grid systems at the send end and receive end, using an analogy of the bidding units, this cost can be offered by the receiving system and paid uniformly according to the scheduling agency of the service purchaser. Referring to the idea of reference [41], the power of DC modulation is modeled equivalently using unit combination modeling, and the power variation of the DC contact line is equated using the power variation of the equivalent generating unit. Therefore, the cost function C_dc can be expressed as:

$$\left\{\begin{array}{l}{C}_{\mathrm{dc}}=({\eta }_f+{\eta }_{\mathrm{co}2})\cdot Q(\Delta {\overline{P}}_{\mathrm{G}})\\ Q(\Delta {\overline{P}}_{\mathrm{G}})=(a^2\Delta {\overline{P}}_G+b\Delta {\overline{P}}_{\mathrm{G}}+c)\end{array}\right.$$

(13)

where η_f and η_co2 denote the coal price and environmental pollution cost of the equivalent generating unit; Q denotes the coal consumption of the equivalent unit due to the power change; a, b and c denote the generator consumption characteristic coefficient. The selection of parameters for the calculation of the operating cost of the equivalent generating unit is determined by the recipient system based on the estimated capacity of the DC AFR service and the corresponding equivalent unit.

3.3. Research on Clearance Scheduling Method

When entering the real-time scheduling clearance stage, clearance is performed once during each scheduling period. The grid control center sends the FR command demand capacity to the organizer of AFR. The ordering is completed according to the comprehensive FR performance of the bidding unit. Based on the order of comprehensive FR performance from high to low, the bidding unit can be scheduled sequentially until the bidding FR capacity meets the current scheduling capacity demand, which is called the traditional scheduling method.

For the send-end system of the interconnected grid, due to the deterioration of the system frequency-response characteristic, the AFR service strategy proposed in this section focuses on the effect of improving the system frequency. The power regulation of the HPPCS responds quickly and accurately, which is a high-quality FR resource. Based on the above analysis, the scheduling principles established in this section are as follows. In this scheduling cycle, if there is a situation where power can be called, under the premise of meeting the specific scheduling capacity, the reasonable allocation of FR resources can improve the frequency response in different time periods of this scheduling cycle. At the same time, for the time periods with high scheduling capacity demand, the HPPCS and DC capacity are preferentially used to participate in regulation so as to optimize the frequency-response situation during the whole cycle.

In summary, in this section, the response characteristics of the system frequency in the different real-time scheduling time periods during the whole calculation cycle are optimized by reasonably allocating the FR capacity of the HPPCS and DC system according to the scheduling command. The flowchart of the optimization method for the clearance scheduling is shown in Figure 5.

3.4. Service Process for HPPCS Participating in AFR

Based on the above, the method of HPPCS participation in AFR services is proposed in this paper, for which a flow block diagram is shown in Figure 6. Firstly, based on the demand capacity of the system FR, combined with the declared capacity of the current system, it can be judged whether HPPCS and DC are needed to participate in the AFR services. If the FR demand is not satisfied, the HPPCS is required to participate in the AFR service to meet the FR capacity demand. Secondly, based on the status of the application offer of each bidding unit, the declared capacity and the comprehensive FR performance of the unit, the objective function is solved to determine the bidding combination by taking the optimal cost for purchasing FR service as the objective function. Finally, the operating point of the unit in the grid is determined based on the clearance method and scheduling requirement. Commands are determined during the scheduling cycle, and the scheduling scheme of the unit is executed, thus obtaining the optimal FR resource combination scheme, realizing the reasonable allocation of the FR capacity for the unit and balancing the FR demand in real-time.

4. Simulation Result and Analysis

4.1. Overview of the Simulation Model

In order to verify the effectiveness of the proposed method in this paper, a two-area power grid was built on the Matlab/Simulink platform as shown in Figure 7. Area 1 and Area 2 of the AC system are connected by the DC link in asynchronous operation. Among them, the AC system of Area 1 contains four generating units: G1–G3 are hydroelectric, photovoltaic, and pumped-storage generating units with an installed capacity of 600 MW, which together constitute the HPPCS; and G4 is thermal unit of reheat with installed capacity of 600 MW, which is coal-driven steam power plant. The units of Area 1 are equipped with AGC control. The AC system in Area 2 contains two generators, namely G5 and G6, with capacities of 1100 MW and 1200 MW, respectively. In this paper, the equivalent generator set parameters required for DC regulation cost calculation are set up in accordance with thermal generators with an installed capacity of 100 MW. The parameters for the AGC unit model and DC cost calculation are shown in

Table 1. The parameters for the AGC unit model and DC cost calculation.

Symbol	Value	Symbol	Value
β/(pu/Hz)	0.44	$P_{\mathrm{g},p}^{\max }$/pu	0.9
Tsys/s	17	$P_{\mathrm{g},s}^{\min }$/pu	0
D/pu	0.0015	$P_{\mathrm{g},s}^{\max }$/pu	0.9
$P_{\mathrm{g},t}^{\min }$/pu	0.6	a/(t/pu2)	19.4
$P_{\mathrm{g},t}^{\max }$/pu	0.8	b/(t/pu)	367
$P_{\mathrm{g},h}^{\min }$/pu	0	c/(t/pu)	5.63
$P_{\mathrm{g},h}^{\max }$/pu	0.9	ηf/($/t)	60
$P_{\mathrm{g},p}^{\min }$/pu	0	ηco2/($/t)	30

.

In this paper, it is set that both HPPCS units in Area 1 and networked DC participate in the AFR service market bidding. The unit declaration bidding information can be obtained by referring to [42], as shown in

Table 2. Bidding information for different FR resources.

Types of Unit	Declared Capacity/MW	Capacity Quotation/(yuan/MW)	Mileage Quotation/(yuan/MW)	Comprehensive FR Performance Coefficient	Mileage Dispatch Coefficient
Hydroelectricity	60	2.5	5	3.3	3
Photovoltaic	60	2	4	3.3	3
Pumped storage	60	1.5	3	3.3	3
Thermal electricity	110	3.5	7	4	3

. Using the YALMIP and CPLEX toolbox of the Matlab2016a platform, the simulation is carried out for building and solving the optimization model established in Section 3. Using the modeling language of YALMIP, the objective function, constraints, and decision variables can be defined in the software platform. Subsequently, using the built-in function provided by YALMIP, the AFR market-clearing model can be solved by calling the CPLEX statement in YALMIP. In addition, in this research, the coefficient of FR performance s_i is regarded constant for photovoltaics. However, during the night period, s_i is zero.

4.2. Analysis of FR Market Clearance

4.2.1. Cost of FR Service

In one calculation cycle, the FR capacity demand of the interconnected grid send-end system is 280 MW, which exceeds the declared capacity of the traditional thermal power units, so it is necessary to provide part of the capacity using the HPPCS to meet the capacity demand. Using the YALMIP and CPLEX toolbox of Matlab, the market clearing can be completed by solving the optimization model established in Section 3. Then, the clearing result of solution 1 can be obtained, which is as shown in

Table 3. Clearance results for AFR services.

Clearance Solution	FR Resource	Hydroelectricity	Photovoltaic	Pumped Storage	Thermal Electricity	DC
Solution 1	Bidding capacity/MW	40	40	40	110	50
	Bidding ratio	0.67	0.67	0.67	1	0.5
Solution 2	Bidding capacity/MW	40	40	40	60	100
	Bidding ratio	0.67	0.67	0.67	0.55	1

. In order to verify the FR effect of interconnected DC, solution 2 is set up as the comparison in the simulation, which enhances the capacity of DC participating in AFR while keeping the capacity of HPPCS participation in auxiliary FR service unchanged. The cost expense of AFR services for solution 1 and solution 2 is shown in Table 3.

As shown in Table 3 and

Table 4. The cost of AFR services.

Clearance Solution	Clearing Capacity Price/(yuan/MW)	Clearing Mileage Price/(yuan/MW)	Total FR Cost/yuan
Solution 1	4	7	33,875.7
Solution 2	4	7	38,864.1

, both of the clearing solutions can meet the FR capacity requirement. The cost of each FR resource is shown in Figure 8. Taking into account the market-clearing cost of the bidding unit, the total cost of purchasing FR ancillary service for solution 1 is RMB 33,875.7. The bidding capacity of the thermal unit in solution 2 is reduced by 50 MW, resulting in reduced revenue for the thermal unit. Also, considering the cost of the bidding units, the corresponding FR cost of this option is RMB 38,864.1, which is about 14.7% higher than the total FR cost of solution 1. The equivalent DC regulation capacity of solution 2 is higher, and the regulation cost of this solution is increased to some extent due to additional transmission line loss.

4.2.2. Centralized Scheduling of FR Demand

In order to verify the influence of the bidding capacity of HPPCS participation in AFR services on the system frequency regulation, it is assumed that there is centralized scheduling of FR demand during the scheduling period. Namely, at a certain moment in time, the centralized scheduling demand is 130 MW. Meanwhile, solution 3 with a single thermal unit participating in an AFR service is added as a comparison group. The proportion of the output of each resource to the FR demand for the different solutions and the frequency deviation curve of the grid are shown in Figure 9 and Figure 10.

As can be seen from Figure 10, when solution 1 and solution 2 are adopted, the frequency deviation of the system can be restored to 0. This proves that the solution of an HPPCS with an interconnected DC participating in an AFR service can maintain the frequency stability of the regional grid.

Meanwhile, it can be observed that the maximum value of the system frequency deviation of solution 2 is 0.043 Hz, and that of solution 1 is about 0.056 Hz. Compared with clearing solution 1, a higher proportion of DC participation is available in solution 2. During the system response period of 50~150 s, the adjustment time of the frequency deviation of solution 2 is shorter, and the frequency reset is more rapid, which achieves a better regulation effect than solution 1. In terms of FR cost, according to Table 4, the bidding capacity of the thermal power unit corresponding to solution 2 is reduced, and the cost of DC FR increases. Although the AFR cost of solution 2 is higher, the FR stable-control effect for solution 2 is better. Based on the above analysis, it is known that the higher the proportion of interconnected DC participation, the better the FR stable-control effect. For this reason, we can consider allocating certain extra costs to the system to buy higher-quality FR resource services. This kind of solution can not only satisfy the FR demand but also enhance the motivation of high-quality resources participating in AFR services.

In addition, in order to analyze the necessity of HPPCSs with interconnected DCs participating in FR, the frequency deviation curve of the grid is given when using solution 3, where the HPPCS does not participate in the AFR services. When solution 3 is adopted, the maximum frequency deviation of the system is about 0.07 Hz. In the steady state, the system frequency cannot return to normal and there is still a frequency deviation of 0.024 Hz. The main reason for this is that when a single thermal unit participates in an AFR service, the FR resource within the grid is insufficient to meet the FR demand. It is shown in the above analysis that the joint participation of DCs and HPPCSs in AFR services can effectively relieve the pressure of FR in grid and supplement the FR reserve capacity. The AFR solution with HPPCS participation can maintain the frequency stability of the regional grid under high scheduling demand.

4.2.3. Decentralized Scheduling of FR Demand

In order to analyze the impact of different FR capacity scheduling methods on the frequency response of the system under different clearing solutions, it is set that after entering the scheduling stage, the bidding capacity is scheduled in two time periods based on the result of the market clearing. Each scheduling demand capacity is 110 MW and 75 MW, corresponding to scheduling period 1 and period 2, respectively. Also, it is assumed that the comprehensive FR performance of the FR unit is kept unchanged. The traditional scheduling method based on the integrated FR performance factor is selected for comparison, and the scheduling scheme of different clearance solutions is shown in

Table 5. The scheduling scheme of different clearance solutions.

Scheduling Period	Solution 3	Solution 4
Period 1	Thermal electricity 110 MW	HPPCS 90 MW AC 20 MW
Period 2	HPPCS 75 MW	Thermal electricity 75 MW

. Among them, solution 3 is the traditional thermal-power priority scheduling method, and solution 4 is set to assign priority to the HPPCS participating in the scheduling during the scheduling hours with high FR demand. The method of load perturbation superposition is adopted in the simulation to emulate the actual unbalanced power of the system during the scheduling period. The perturbation is applied sequentially in each scheduling period.

The frequency deviation curve of the system under different scheduling modes is shown in Figure 11. In scheduling period 1, with higher demand capacity, the maximum frequency deviation is 0.028 Hz and 0.018 Hz for solution 3 and solution 4, respectively. Compared with the traditional scheduling method, when using the method of HPPCSs priority participating in scheduling, the system frequency deviation decreases less, the range of fluctuation during the adjustment period is smaller, and the adjustment process is more rapid. In scheduling period 2, the maximum frequency deviation of solutions 3 and 4 remain basically the same. The dynamic response of solution 3 is faster, and the time for the frequency to recover stability is shorter. Meanwhile, it can be observed from Figure 11 that the frequency deviation of solution 4 is smaller than that of solution 3 during the whole scheduling period.

The above analysis shows that overall performance is better when the HPPCS with interconnected DC participates in scheduling with priority. This is because the power regulation capability of HPPCS and interconnected DC system is faster, and the accuracy is higher than the conventional FR unit. During periods of high scheduling demand capacity, the HPPCS with interconnected DC is supplemented as the FR demands power in time. These high-quality FR resources can not only effectively reduce the rate of frequency deviation change but also lower the frequency drop rate. For this reason, for the regional interconnected grid, the HPPCS and interconnected DC system can be reasonably arranged to participate in AFR services with priority during the scheduling periods of high FR demand, which can contribute to improving the frequency-response characteristics for the system in the overall scheduling cycle.

5. Conclusions

The interconnection of the regional grid through DC transmission is an important development trend in current large-capacity long-distance power transmission. In order to improve the frequency stability of the regional interconnected grid with DC participation, a method for the HPPCSs participating in AFR services is proposed in this paper. The conclusion of this paper can be summarized as follows:

(1) Combining the FR processes of the regional interconnected grid sending-end system, the modeling of the HPPCS participating in AFR services is built. The calculation of the ACE signal and frequency deviation for the system is analyzed.

(2) To effectively and rationally utilize the FR resource in a high-penetration renewable-energy integrated grid, the solution model for FR resource allocation for a regional interconnected sending-end system is built with the goal of minimizing the cost of AFR services. The means of calculating the cost of the FR resource is analyzed.

(3) The process of the clearing scheduling method is designed, which fully considers the regional AFR capacity demand and regulation cost. Using the YALMIP toolbox and CPLEX toolbox of the Matlab platform, the proposed clearing scheduling method is implemented by simulation examples. It is proved by simulation examples that the low-cost acquisition of high-quality AFR service resources can be achieved by the proposed method while ensuring the frequency stability of the regional interconnected grid.