Optimal Scheduling of Power Systems with High Proportions of Renewable Energy Accounting for Operational Flexibility

Abstract

The volatility and uncertainty of high-penetration renewable energy pose significant challenges to the stability of the power system. Current research often fails to consider the insufficient system flexibility during real-time scheduling. To address this issue, this paper proposes a flexibility scheduling method for high-penetration renewable energy power systems that considers flexibility index constraints. Firstly, a quantification method for flexibility resources and demands is introduced. Then, considering the constraint of the flexibility margin index, optimization scheduling strategies for different time scales, including day-ahead scheduling and intra-day scheduling, are developed with the objective of minimizing total operational costs. The intra-day optimization is divided into 15 min and 1 min time scales, to meet the flexibility requirements of different time scales in the power system. Finally, through simulation studies, the proposed strategy is validated to enhance the system’s flexibility and economic performance. The daily operating costs are reduced by 3.1%, and the wind curtailment rate is reduced by 4.7%. The proposed strategy not only considers the economic efficiency of day-ahead scheduling but also ensures a sufficient margin to cope with the uncertainty of intra-day renewable energy fluctuations.

1. Introduction

There has been a rapid development in renewable energy, specifically in wind power and photovoltaics. According to the International Renewable Energy Agency’s report, in the upcoming power system, it is anticipated that the penetration of renewable energy to the power system will increase to 85% by the year 2050 [1]. Promoting energy transition is an important way to achieve the strategic goal of “carbon peaking and carbon neutrality” [2,3]. However, due to the random and intermittent nature of renewable energy, the high penetration of renewable energy seriously affects the safe and stable operation of a power system.

Improving power system operational flexibility is an important way to enhance system stability and reliability [4]. Different countries around the globe have varying interpretations of power system flexibility. According to the International Renewable Energy Agency, power system flexibility refers to the capability of reacting to changes in the supply and demand sides, while ensuring the safe and stable operation of the power system within the operational constraints [5]. Energy Innovation Policy and Technology LLC defines flexibility as the ability of a power system to respond to changes in supply and demand across different time scales ranging from seconds to seasons [6].

To address the potential adverse effects associated with the integration of renewable energy resources into the power grid, various strategies are being implemented. The conventional energy’s complementary feature, such as wind, water, gas and thermal power is utilized [7]. In the high-proportion renewable energy power system, it is difficult to effectively respond to rapid net load changes only using reserve capacity, thus resulting in increased hazards to grid security [8]. The literature [9] proposed a flexibility evaluation method using the system-regulation demand as the goal. The literature [10] evaluates flexibility by scoring different types of flexibility resources. The flexibility supply and demand across multiple time scales is analyzed in [11]. The probability of upward and downward flexibility and the expectation of insufficient flexibility on different time scales are calculated. However, the above-mentioned studies focus on the evaluation of power system flexibility. Due to the uncertainty of renewable energy, the real-time scheduling of a power system regarding flexibility needs more research.

In order to reduce the adverse effects of renewable energy uncertainty, a large number of optimization models based on a multi-time scale are proposed. A scheduling model of multi-time optimization considering wind power uncertainty and demand response is proposed in [12]. It verifies the importance of coordinated scheduling across multiple time scales. The distributed power flow controllers are used in [13]. And a day-ahead and real-time optimization model is proposed to reduce the system operation cost. The multiple time scale optimization models improve the system operation safety, but these studies fail to consider power system flexibility. The available system flexibility resources and demand are not taken into account. Several different types of flexibility resources are modeled in [14], and an integrated energy system optimal scheduling strategy considering multi-energy flexibility is proposed. But the constraint of the flexibility index is ignored and flexibility resources and demands on different time scales are not quantified and used.

Compared with electrochemical energy storage, which cannot meet the long-term energy demand, hydrogen energy storage is attracting more and more attention due to its characteristics of low carbon, fast response speed and long-term energy storage. In recent years, demonstration projects of hydrogen production using electrolytic water using renewable energy have been carried out in many countries [15]. An optimal scheduling model of hydrogen energy storage [16] is studied to participate in the demand-response program. The photovoltaic output power characteristics and hydrogen production process [17] is considered, and an energy management scheme for a hydrogen production system with photovoltaic generation is proposed. The fundamental framework of a solar and wind generation system equipped with hydrogen energy storage is studied in [18]. The study demonstrates that the hydrogen energy storage can minimize the fluctuations of the output power of renewable energy. However, the above literature only considers the reliability and low-carbon characteristic of hydrogen energy storage. These studies do not quantify the flexibility offered by hydrogen energy storage and fail to utilize the fast regulation capacity of hydrogen energy storage in the scheduling of power systems with high-proportion renewable energy across multiple time scales.

Currently, most of the research on optimization models for multiple time scales fails to consider the establishment of safety margin indicators for the system and ignores the volatility of renewable energy on different time scales. Moreover, the flexibility of resources and demands on different time scales are not quantified, making it impossible to accurately evaluate the flexibility of multiple energy sources within the system. The literature [19] considers the flexibility of the system on multiple time scales but fails to establish safety margin indicators. The relationship between the flexibility of various energy sources is considered in [20], and penalties are used for insufficient flexibility. However, the safety margin constraints of the system are ignored. Research on hydrogen energy storage primarily focuses on its application in renewable energy integration and low carbon emissions. The ability to enhance the system flexibility of hydrogen energy storage is overlooked. The flexibility of the demand response in intra-day and day-ahead dispatch is considered in [21]. But the flexibility of energy storage is ignored. Most of the studies have not considered the safety margin indicators for the power system, which makes it difficult to accurately evaluate the flexibility of multiple energy sources within the system.

To address these issues, this paper proposes a flexibility-dispatch-optimization method for high-penetration renewable energy power systems. Firstly, various flexibility resources, such as pumped hydro energy storage, hydrogen storage, and electrochemical storage, as well as the flexibility demands of the power system, are quantified and modeled. Next, in the day-ahead scheduling, flexibility index constraints and the balance between 1 h-scale flexibility resources and demands are considered, providing a certain margin for flexible operation and determining the unit start-up and shut-down plans for the intra-day operation. Based on the day-ahead scheduling plan, adjustments are made to the output of different devices to accommodate power fluctuations on a 15 min time scale, followed by rolling optimization to smooth out rapid power fluctuations on a 1 min time scale. Through simulation studies, the proposed dispatch strategy is verified, and the system flexibility demands under different wind power penetration rates are analyzed.

2. Flexibility Resources and Demand on Multiple Time Scales

2.1. Flexibility Demand

The flexibility demand of power system $F_{\mathrm{NE},t}$ can be represented as the system adjustment capacity required to cope with the changes of net load $L_t$, which depends on the fluctuations of load $P_{\mathrm{NL},t}$ and renewable energy $P_{\mathrm{RE},t}$ as follows:

$$F_{\mathrm{NE},t}=P_{\mathrm{NL},t+1}-P_{\mathrm{NL},t}$$

(1)

$$P_{\mathrm{NL},t}=L_t-P_{\mathrm{RE},t}$$

(2)

where $P_{\mathrm{NL},t}$ and $P_{\mathrm{NL},t+1}$ are the system net load at time t and time t + 1, respectively.

The evaluation of system flexibility includes two types: the upward flexibility demand (UFD) and downward flexibility demand (DFD). The demand for flexibility is calculated on varying time scales. Figure 1 illustrates the schematic diagram of flexibility demands.

As renewable energy penetration increases, the peak-to-valley difference and the volatility of the net load curve experience a notable increase. The limited adjustment ability of conventional power generators is difficult to meet the soaring flexibility demand in power systems with a high proportion of renewable energy. When the system flexibility is not enough, load shedding or renewable energy curtailment may occur. Therefore, it is necessary to install more flexibility resources and optimize the operation of multiple flexibility resources to provide enough flexibility.

2.2. Flexibility Resources

The flexibility resources of a power system include coal-fired power units (CFPUs), combined cycle gas turbines (CCGTs) after flexibility transformation, rapid regulation gas turbines (RRGTs), adjustable hydropower stations (AHSs), pumped storage stations (PSSs), battery energy storage systems (BESSs), and hydrogen energy storages (HESs). The system flexibility is related to the time scale, the operation state of each unit and the regulation characteristics of units. Flexibility resources can be categorized into upward flexibility resources (UFRs) and downward flexibility resources (DFRs). In this section, the flexibility of each controllable unit is analyzed, and the adjustment capacity models of the controllable units under different time scales [22,23,24], as shown in

Table 1. Flexibility resources involved in regulating the time scale.

		0 min	15 min	1 h
Thermal power unit	RRGT
	CCGT
	CFPU
Hydroelectric power unit	AHS
	PSS
BESS
HES

, are established.

As shown in Table 1, a RRGT can provide flexible resources for a 1 min time scale and 15–60 min time scale. A CCGT can provide flexible resources with a time scale of 15~60 min. A CFPU can only provide flexible resources with a time scale of 1 h. An AHS and various types of energy storage (PSS, BESS, and HES) provide flexibility for 1 min timescales and 15–60 min timescales.

(1) Flexibility of conventional thermal power units

Thermal power units can be classified into gas-fired units and coal-fired units. Gas-fired units have high flexibility and usually participate in short-term power adjustment within hours. Coal-fired units with flexibility modification can participate in hourly-level power adjustment.

Fast-response gas turbine units, represented by single-cycle gas units, participate in short-time scale regulation. Their flexibility is constrained by their ramp-up and ramp-down rates, as well as their maximum and minimum output power as follows:

$$F_{\mathrm{G},+}=\min \{P_{\mathrm{G},\max }-P_{\mathrm{G},0},\Delta t\times r_{\mathrm{m},+}\}$$

(3)

$$F_{\mathrm{G},-}=\min \{P_{\mathrm{G},0}-P_{\mathrm{G},\min },\Delta t\times r_{\mathrm{m},-}\}$$

(4)

where $P_{\mathrm{G},\max }$, $P_{\mathrm{G},\min }$ and $P_{\mathrm{G},0}$ represent the maximum power output, minimum power output and the present power output of the unit, respectively; $r_{\mathrm{m},+}$ and $r_{\mathrm{m},-}$ represent the upward ramp rate and downward ramp rate of the unit, respectively. For single-cycle gas turbines, the upward and downward ramp rates are generally 6–10% and 8–12% of the unit’s rated capacity per minute, respectively; $\Delta t$ represents the length of the ramping period.

In the intermediate time scale, CCGT can offer flexibility, in addition to RRGT. Equations (3) and (4) can be used to calculate the flexibility of gas-fired units. The CCGT has ramp-up and ramp-down rates of about 3% and 4% of the rated capacity per minute, respectively.

In the long-time scale, in addition to the combined cycle gas turbine unit that operates online, flexibility adjustments can also be made through the start-up and shutdown of gas turbine units and adjustment of coal-fired units that have been transformed for flexibility. Among them, the adjustment characteristics of the coal-fired units are shown in Equations (3) and (4), while the size of the flexibility resources provided by the start-up and peak shaving of gas turbines is related to the unit capacity.

$$\begin{array}{l}{F}_{\mathrm{G},+}=P_{\mathrm{SG},\max }\\ F_{\mathrm{G},-}=P_{\mathrm{SG},0}\end{array}$$

(5)

where $P_{\mathrm{SG},0}$ and $P_{\mathrm{SG},\max }$ represent the current power output and maximum power output of the gas turbine units, respectively.

(2) Flexibility of adjustable hydropower station

AHSs are capable of participating in power regulation on various time scales throughout a day. However, due to the limit of upstream water flow, they generally serve as peak-load-regulation resources during dry seasons. Equations (3) and (4) also illustrate the flexibility offered by hydropower units. The ramping rate of hydropower is usually 20~40% of the rated capacity per minute. Expected output power determines the maximum output power of hydropower units, while forced output power determines their minimum output power.

(3) Flexibility of hydrogen energy storage

As a flexibility power source, hydrogen energy storage has the characteristics of no pollution, diverse energy conversion and application methods and a fast response speed, etc. The flexibility of hydrogen energy storage is

$$\begin{array}{l}{F}_{\mathrm{HSS},+}=\min \{P_{\mathrm{HSS},+,\max },\frac{{\sigma }_{\mathrm{EH}}{k}_{\mathrm{ved}}(S_t^{\mathrm{HSS}}-S_{\min }^{\mathrm{HSS}})}{\Delta t}\}\\ F_{\mathrm{HSS},-}=\min \{P_{\mathrm{HSS},\text{-},\max },\frac{k_{\mathrm{ved}}(S_{\max }^{\mathrm{HSS}}-S_t^{\mathrm{HSS}})}{{\sigma }_{\mathrm{HE}}\Delta t}\}\end{array}$$

(6)

where $P_{\mathrm{HSS},+,\max }$ and $P_{\mathrm{HSS},\text{-},\max }$ represent the maximum discharge and charging power of HES, respectively; $S_{\max }^{\mathrm{HSS}}$ and $S_{\min }^{\mathrm{HSS}}$ represent the upper and lower limits of HES capacity, respectively; $S_t^{\mathrm{HSS}}$ represents the hydrogen storage tank capacity at time t; ${\sigma }_{\mathrm{HE}}$ and ${\sigma }_{\mathrm{EH}}$ represent the energy conversion efficiency of the electrolytic device and the fuel cell, respectively; $k_{\mathrm{ved}}$ represents the volumetric energy density of hydrogen gas under standard hydrogen storage tank conditions.

(4) Flexibility of pumped storage station

$$\begin{array}{l}{F}_{\mathrm{storage},+}=\min \{P_{\mathrm{storage},+,\max },\frac{S_t-S_{\min }}{\Delta t}\}\\ F_{\mathrm{storage},-}=\min \{P_{\mathrm{storage},\text{-},\max },\frac{S_{\max }-S_t}{\Delta t}\}\end{array}$$

(7)

where $P_{\mathrm{storage},+,\max }$ and $P_{\mathrm{storage},\text{-},\max }$ represent the maximum output power and input power of PSS, respectively; $S_{\max }$ and $S_{\min }$ represent the upper and lower limits of PSS capacity, respectively; $S_t$ represents the current stored energy of the PSS.

(5) Flexibility of battery energy storage

Battery energy storage can be applied to power adjustment on multiple time scales such as a within−15 min time scale and 15–60 min time scale. The flexibility provided by battery energy storage can be quantified using Equation (7).

3. Flexibility Resource Scheduling Based on Multi-Time Scale

This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation and the experimental conclusions that can be drawn.

3.1. Day-Ahead Unit Commitment Based on the Flexibility Index

The day-ahead unit commitment model aims to minimize the operational costs of the power system while enhancing the penetration levels of renewable energy and power supply reliability. The total operational cost includes penalty costs for renewable energy curtailment and load shedding and the depreciation cost of the BESS. The objective function can be written as follows:

$$\begin{array}{l}\min f_1={\displaystyle \sum _{t=1}^{24}(f_{\mathrm{G},t}+f_{\mathrm{erss},t}+f_{\mathrm{Q},t}+f_{\mathrm{load},t})}\\ \{\begin{array}{l}{f}_{\mathrm{G},t}={\displaystyle \sum _{i=1}^{N_{\mathrm{G}}}[(a_i{P}_{\mathrm{G}i,t}^2+b_i{P}_{\mathrm{G}i,t}+c_i)+}{S}_i(1-u_{\mathrm{G}i,t-1})u_{\mathrm{G}i,t}]\\ f_{\mathrm{erss},t}={\displaystyle \sum _{i=1}^{N_{\mathrm{erss}}}{k}_{\mathrm{erss},s}{P}_{s,i,t}^{\mathrm{erss}}}\\ f_{\mathrm{Q},t}=k_{c,\mathrm{REG}}(P_{\mathrm{REG},t}^{\mathrm{pre}}-c)\\ f_{\mathrm{load},t}=k_{\mathrm{c},\mathrm{load}}{P}_{\mathrm{loss},t}\end{array}\end{array}$$

(8)

where $f_1$ is the total system operation cost; $f_{\mathrm{G},t}$ and $f_{\mathrm{erss},t}$ represent the cost functions of conventional units and energy storage power stations (including pumped storages, battery energy storages and hydrogen storage), respectively; $f_{\mathrm{Q},t}$ and $f_{\mathrm{load},t}$ represent the penalty costs of renewable energy generators and load, respectively; $N_G$ represents the number of conventional units; $P_{\mathrm{G}i,t}$ represents the output power of the thermal power unit i at time t; $a_i$, $b_i$ and $c_i$ represent the parameters of the cost function of the coal-fired unit i; $S_i$ represents the startup and shutdown cost parameters of the thermal power unit i; $u_{\mathrm{G}i,t}$ represents the state of the thermal power unit i at time t; when $u_{\mathrm{G}i,t}$ is 1, it denotes that the unit is in operation state; when $u_{\mathrm{G}i,t}$ is 0, it denotes that the unit is in shutdown state; $N_{\mathrm{erss}}$ is the number of energy storage stations; $k_{\mathrm{erss},s}$ represents the operation and maintenance cost parameters of the energy storage station per unit; s represents the type of energy storage system; when s is ‘1’, it represents PSS, ‘2’ represents BESS and ‘3’ represents HES; $P_{s,i,t}^{\mathrm{erss}}$ represents the current output power of energy storage i at time t; $k_{c,\mathrm{REG}}$ represents the penalty cost coefficient for curtailing renewable energy; $P_{\mathrm{REG},t}^{\mathrm{pre}}$ is the predicted power output of the renewable energy station at time t; $k_{\mathrm{c},\mathrm{load}}$ is the penalty coefficient of load shedding; $P_{\mathrm{loss},t}$ is the loss of load at time t.

The constraints are as follows:

(1) Power balance constraints

$${\displaystyle \sum _{i=1}^{N_{\mathrm{G}}}{P}_{\mathrm{G}i,t}+}{P}_{\mathrm{REG},t}+{\displaystyle \sum _{i=1}^{N_{\mathrm{erss}}}{P}_{s,i,t}^{\mathrm{erss}}}=L_t-P_{\mathrm{loss},t}$$

(9)

(2) Constraints of conventional units

$$P_{\mathrm{G}i,t}^{\min }\le P_{\mathrm{G}i,t}\le P_{\mathrm{G}i,t}^{\max }$$

(10)

where $P_{\mathrm{G}i,t}^{\max }$ and $P_{\mathrm{G}i,t}^{\min }$ represent the maximum and minimum limits of the output power of the thermal power unit i, respectively.

(3) Constraints of conventional units’ ramp rates:

$$\{\begin{array}{l}{P}_{\mathrm{G}i,t}-P_{\mathrm{G}i,t-1}\le u_{\mathrm{G}i,t}{R}_i\\ P_{\mathrm{G}i,t-1}-P_{\mathrm{G}i,t}\le u_{\mathrm{G}i,t-1}{R}_i\end{array}$$

(11)

where $R_i$ represents the ramp rate of the conventional units i.

(4) Renewable energy output constraints

$$0\le P_{\mathrm{REG},t}\le P_{\mathrm{REG},t}^{\mathrm{pre}}$$

(12)

(5) Operation constraints of energy storage stations

① Pumped storage station

$$\{\begin{array}{l}{y}_{\mathrm{hc},t}^{\mathrm{water}}{P}_{\mathrm{hc}}^{\min }\le P_{\mathrm{hc},t}^{\mathrm{water}}\le y_{\mathrm{hc},t}^{\mathrm{water}}{P}_{\mathrm{hc}}^{\max }\\ y_{\mathrm{hf},t}^{\mathrm{water}}{P}_{\mathrm{hf}}^{\min }\le P_{\mathrm{hf},t}^{\mathrm{water}}\le y_{\mathrm{hf},t}^{\mathrm{water}}{P}_{\mathrm{hf}}^{\max }\\ y_{\mathrm{hc},t}^{\mathrm{water}}+y_{\mathrm{hf},t}^{\mathrm{water}}\le 1\\ V_{t+1}^{\mathrm{water}}=V_t^{\mathrm{water}}+({\eta }_{\mathrm{p}}{P}_{\mathrm{hc},t}^{\mathrm{water}}-P_{\mathrm{hf},t}^{\mathrm{water}}/{\eta }_{\mathrm{g}})\Delta t\\ V_{\mathrm{pump}}^{\min }\le V_t^{\mathrm{water}}\le V_{\mathrm{pump}}^{\max }\end{array}$$

(13)

where $P_{\mathrm{hc}}^{\max }$ and $P_{\mathrm{hc}}^{\min }$ represent the upper and lower limits of the pumping power of the PSS, respectively; $P_{\mathrm{hf}}^{\max }$ and $P_{\mathrm{hf}}^{\min }$ are the upper and lower limits of the generating power of the PSS, respectively; $y_{\mathrm{hc},t}^{\mathrm{water}}$ and $y_{\mathrm{hf},t}^{\mathrm{water}}$ is a 0–1 variable representing the operation state of the PSS (i.e., generating or pumping); ${\eta }_{\mathrm{p}}$ represents the conversion coefficient of generating power; $V_t^{\mathrm{water}}$ represents the storage volume of the PSS cistern at time t; ${\eta }_{\mathrm{g}}$ represents the conversion coefficient of pumping; $V_{\mathrm{pump}}^{\max }$ and $V_{\mathrm{pump}}^{\min }$ represent the upper and lower limits of the water volume stored for the PSS, respectively.

② Battery energy storage

$$\{\begin{array}{l}{P}_{\min }^{\mathrm{cha}}\le P_{\mathrm{ch},t}\le P_{\max }^{\mathrm{cha}}\\ P_{\min }^{\mathrm{dis}}\le P_{\mathrm{dis},t}\le P_{\max }^{\mathrm{dis}}\\ E_{\mathrm{ESS}}^{\min }\le E_{\mathrm{ESS},t}\le E_{\mathrm{ESS}}^{\max }\\ E_{\mathrm{ESS},t+1}=E_{\mathrm{ESS},t}+{\eta }_{\mathrm{ch}}{P}_{\mathrm{ch},t}-\frac{P_{\mathrm{dis},t}}{{\eta }_{\mathrm{dis}}}\end{array}$$

(14)

where $P_{\max }^{\mathrm{cha}}$ and $P_{\min }^{\mathrm{cha}}$ represent the upper and lower limits of the power of charge of the BESS, respectively; $P_{\max }^{\mathrm{dis}}$ and $P_{\min }^{\mathrm{dis}}$ represent the upper and lower limits of the discharging power of the BESS, respectively; $E_{\mathrm{ESS},t}$ represents the stored energy of the BESS at time t; ${\eta }_{\mathrm{ch}}$ and ${\eta }_{\mathrm{dis}}$ represent the efficiency parameter for the charging and discharging process of the BESS; $E_{\mathrm{ESS}}^{\max }$ and $E_{\mathrm{ESS}}^{\min }$ represent the upper and lower limits of the stored energy of the BESS.

③ Hydrogen energy storage

$$\{\begin{array}{l}{\eta }_{\mathrm{EH}}=\Delta t\cdot {\sigma }_{\mathrm{EH}}/k_{\mathrm{ved}}\\ {\eta }_{\mathrm{HE}}=k_{\mathrm{ved}}{\sigma }_{\mathrm{HE}}/\Delta t\\ V_{t+1}^{\mathrm{HES}}=V_t^{\mathrm{HES}}+P_{\mathrm{H},t}^{\mathrm{cha}}{\eta }_{\mathrm{EH}}-P_{\mathrm{H},t}^{\mathrm{dis}}/{\eta }_{\mathrm{HE}}\\ 0\le V_t^{\mathrm{HES}}\le V_{\max }^{\mathrm{HES}}\\ 0\le P_{\mathrm{H},t}^{\mathrm{cha}}\le P_{\max }^{\mathrm{cha}}{b}_{\mathrm{H},t}^{\mathrm{cha}}\\ 0\le P_{\mathrm{H},t}^{\mathrm{dis}}\le P_{\max }^{\mathrm{dis}}(1-b_{\mathrm{H},t}^{\mathrm{cha}})\end{array}$$

(15)

where $\Delta t$ is the scheduling time step; ${\eta }_{\mathrm{EH}}$ represents the volume of hydrogen produced via electrolysis per unit of electric power in $\Delta t$; ${\eta }_{\mathrm{HE}}$ represents the electric power generated per unit volume of hydrogen in $\Delta t$; $V_t^{\mathrm{HES}}$ and $V_{t+1}^{\mathrm{HES}}$ represent the amount of hydrogen stored in the hydrogen storage tank at time t and t + 1, respectively; $V_{\max }^{\mathrm{HES}}$ represents the capacity of the hydrogen storage tank; $P_{\mathrm{H},t}^{\mathrm{cha}}$ and $P_{\mathrm{H},t}^{\mathrm{dis}}$ represent the consumption and generating power of the HES, respectively; $P_{\max }^{\mathrm{cha}}$ and $P_{\max }^{\mathrm{dis}}$ represent the maximum consumption and generating power of the HES, respectively; $b_{\mathrm{H},t}^{\mathrm{cha}}$ represents a binary variable; when HES is charged at time t, $b_{\mathrm{H},t}^{\mathrm{cha}}$ is 1; otherwise, the value is 0.

(6) Adjustable hydropower station

$$\{\begin{array}{l}{P}_{\mathrm{kt},t}^{\min }\le P_{\mathrm{kt},t}\le P_{\mathrm{kt},t}^{\max }\\ P_{\mathrm{kt},t}-P_{\mathrm{kt},t-1}=R_{\mathrm{kt}}\\ P_{\mathrm{kt},t-1}-P_{\mathrm{kt},t}=R_{\mathrm{kt}}\end{array}$$

(16)

where $P_{\mathrm{kt},t}^{\max }$ and $P_{\mathrm{kt},t}^{\min }$ represent the upper and lower limits of AHS power; $P_{\mathrm{kt},t}$ is the output power of the AHS at time t; $R_{\mathrm{kt}}$ represents the ramping rate of the AHS.

(7) Flexibility constraint

① Flexibility supply and demand balance

$$\{\begin{array}{l}\min \{F_t^{\mathrm{su}}-F_t^{\mathrm{du}}\}\ge 0\\ \min \{F_t^{\mathrm{sd}}-F_t^{\mathrm{dd}}\}\ge 0\end{array}$$

(17)

where $F_t^{\mathrm{su}}$ and $F_t^{\mathrm{sd}}$ represent the upward and downward flexibility resources available at a given time t, respectively; $F_t^{\mathrm{du}}$ and $F_t^{\mathrm{dd}}$ represent the upward and downward flexibility demands at a given time t, respectively; the flexibility resources of the system need to exceed the flexibility demands at every time step.

② Flexibility margin constraint

The reasonable and practical evaluation indicators for flexibility are crucial for the allocation of flexibility resources and optimization of the operation in power systems with a high proportion of volatile power sources. In this paper, the flexibility margin is adopted as the indicator to evaluate the regulating capability of flexibility resources. The flexibility margin is defined as follows:

$$\{\begin{array}{l}{E}_{\mathrm{flex}}=\frac{{\displaystyle \sum _{i=1}^N\Delta F_{\mathrm{flex},i}}}{P_{\mathrm{res}}}\\ \Delta F_{\mathrm{flex},i}=F_i-D_i\end{array}$$

(18)

where $\Delta F_{\mathrm{flex},i}$, $F_i$ and $D_i$ represent the flexibility margin, resources and demand of the entire system at time step i, respectively; the flexibility resource of the system is defined as the sum of all flexibility resources in the system; $P_{\mathrm{res}}$ represents the total capacity of renewable energy of the system.

The flexibility margin needs to be larger than a threshold to ensure sufficient flexibility resource for the flexibility demand within a day. The flexibility margin constraint is as follows:

$$\{\begin{array}{l}{E}_{\mathrm{flex}}\ge E_{\mathrm{flex}}^{\min }\\ E_{\mathrm{flex}}^{\min }=\max \{(P_{\mathrm{res},t}^{\mathrm{forecast}}-P_{\mathrm{res},t}^{\mathrm{real}})/P_{\mathrm{res}}\}\end{array}$$

(19)

where $E_{\mathrm{flex}}^{\min }$ represents the minimum flexibility margin index of the power system; $P_{\mathrm{res},t}^{\mathrm{forecast}}$ represents the predicted renewable energy output at time t, and $P_{\mathrm{res},t}^{\mathrm{real}}$ represents the actual renewable energy output at time t. The value of the flexibility margin index is closely linked to the error of the day-ahead prediction of renewable energy.

To calculate the prediction error coefficient, the forecast data and actual data of wind power and photovoltaic generation from the previous day are analyzed. The error rate between the predicted data and actual data is calculated at each time point. The maximum error rate among all time points is taken as the error coefficient for renewable energy for that day.

3.2. Multi-Time Scale Optimal Scheduling for Flexibility Resources

The multi-time scale optimal scheduling method includes the day-ahead scheduling with a time scale of 1 h, the intra-day rolling scheduling with a time scale of 15 min and the intra-day real-time scheduling with a time scale of 1 min. The day-ahead optimal scheduling strategy determines the unit commitment scheme and the hourly output power of the dispatchable devices. The intra-day rolling scheduling uses the short-term prediction data of renewable energy generation and load to optimize the power scheduling plan every 15 min. The intra-day real-time scheduling modifies the output power of the devices with fast response ability, such as BESSs, adjustable hydropower stations, pumped storage stations and fast-response gas turbine units every 1 min based on the ultra-short-term prediction data. Figure A1 in Appendix A displays the process of multi-time-scale optimal scheduling.

3.3. Intra-Day Rolling Scheduling Model

The intra-day rolling scheduling optimizes the output power of dispatchable devices using a 15 min time scale. The unit commitment scheme employed is consistent with the day-ahead scheduling.

3.3.1. Objective Function

Similar to the day-ahead scheduling, the objective function for intra-day rolling optimization is to minimize the cost of operating the system, which can be expressed as follows:

$$\min f_2={\displaystyle \sum _{t=1}^{24}(f_{\mathrm{G},t}+f_{\mathrm{erss},t}+f_{\mathrm{Q},t}+f_{\mathrm{load},t})}$$

(20)

Compared with the day-ahead scheduling model, the objective function of the intra-day rolling model does not consider the start-up cost of thermal power units.

3.3.2. Constraints

The constraints for the intra-day rolling model are identical to those of the day-ahead scheduling model. However, the start-up and shutdown constraints of thermal power units are ignored since the unit commitment scheme is already determined in the day-ahead scheduling plan.

3.4. Intra-Day Real-Time Scheduling Model

For intra-day real-time scheduling, prediction data with a time scale of 1 min over the future 15 min is incorporated to adjust the output power of devices with fast-response ability.

3.4.1. Objective Function

The scheduling on a 1 min time scale requires very fast response ability of the devices. Thus, coal-fired units and combined-cycle gas turbine units do not participate in the scheduling at this time scale. The devices scheduled on a 1 min time scale include rapid-regulation gas turbines, adjustable hydropower stations, pumped storage stations, battery energy storages and hydrogen storages. In order to guarantee low operation costs, the real-time scheduling plan should follow the intra-day rolling scheduling as much as possible. The objective function of real-time scheduling is as follows:

$$\min f_3={\displaystyle \sum _{t=1}^{15}(\Delta f_{\mathrm{RQ},t}+\Delta f_{\mathrm{erss},t}+f_{\mathrm{Q},t}+f_{\mathrm{load},t})}$$

(21)

where $\Delta f_{\mathrm{RQ},t}$ is the adjustment cost of rapid-regulation gas turbines; $\Delta f_{\mathrm{erss},t}$ is the adjustment cost of energy storages.

$$\{\begin{array}{l}\Delta f_{\mathrm{RQ},t}={\displaystyle \sum _{i=1}^{N_G}\Delta k_{\mathrm{rq}}\Delta P_{\mathrm{RQ},t}}\\ \Delta f_{\mathrm{erss},t}={\displaystyle \sum _{i=1}^{N_{\mathrm{erss}}}\Delta k_{\mathrm{erss},s}\Delta P_{s,i,t}^{\mathrm{erss}}}\\ f_{\mathrm{Q},t}=k_{c,\mathrm{REG}}(P_{\mathrm{REG},t}^{\mathrm{pre}}-P_{\mathrm{REG},t})\\ f_{\mathrm{load},t}=k_{\mathrm{c},\mathrm{load}}{P}_{\mathrm{loss},t}\end{array}$$

(22)

where $\Delta k_{\mathrm{rq}}$ and $\Delta k_{\mathrm{erss},s}$ correspond to the cost parameter for gas turbines and energy storages, respectively; $\Delta P_{\mathrm{RQ},t}$ and $\Delta P_{s,i,t}^{\mathrm{erss}}$ represent the output power adjustment of rapid-regulation gas turbines and energy storages compared to the intra-day rolling scheduling.

3.4.2. Constraints

Since coal-fired units and combined cycle gas turbines do not participate in intra-day real-time scheduling, their output power remains the same as that with intra-day rolling scheduling. The operation constrains of coal-fired units and combined cycle gas turbines are not considered in the real-time scheduling. The operational constraints in the intra-day rolling scheduling are identical to those in real-time scheduling, with the exception of the start-up and shutdown constraints for thermal power units, since the unit commitment scheme is determined in the day-ahead scheduling.

4. Case Studies

4.1. System Parameters

The simulation is conducted on a provincial power system of China with its load data scaled down to 10% of its original value. The capacity of renewable energy is set as 50% (high proportion) of the maximum load in the simulation. Two typical scenarios of wind, solar and load curves are shown in Appendix A Figure A2 and Figure A3. Appendix A

Table A1. Thermal power unit parameters.

Unit Number	Node	Pmax/MW	Pmin/MW	a/b/c/($/(MWh)2)/($/(MWh))/$	Ramp Rate/(MW/h)	Startup Cost/$	Minimum Startup Time/h
1	30	550	50	0.00024/25.53/615.40	50	84.79	5
2	31	400	50	0.00031/22.31/610.74	200	70.65	5
3	32	325	50	0.00101/14.88/339.85	55	79.13	5
4	33	350	50	0.00056/18.16/321.48	40	70.65	5
5	38	300	50	0.00028/20.48/367.40	150	36.74	5
6	39	600	50	0.00069/27.78/918.51	80	127.18	5

displays the thermal power unit parameters and other relevant parameters. Other devices are two 50 MW/(2.5 × 10⁵ m³) hydrogen storage stations, two 50 MW/200 MWh battery energy storages, two 100 MW/400 MWh pumped storage stations, two 400 MW adjustable hydropower stations, four 500 MW wind farms and three 200 MW photovoltaic power stations. The relevant cost coefficients are as follows: 28.26$/(MWh) for the wind curtailment penalty cost, 14.13$/(MWh) for the photovoltaic curtailment cost, 8.48$/(MWh) for the pumped storage operating cost, 15.54$/(MWh) for the energy storage operating cost, 4.14$/(MWh) for the hydrogen storage operating cost. Other system parameters are set as ${\sigma }_{\mathrm{EH}}$ = 73%,${\sigma }_{\mathrm{HE}}$ = 64%, $k_{\mathrm{ved}}$ = 2.78 kW·h/m³ and $E_{\mathrm{flex}}^{\min }$ = 0.05.

The optimization scheduling model is implemented using a computer with a 2.6 GHz CPU and 16 GB of memory. It is based on MATLAB 2020a software and utilizes YALMIP to invoke CPLEX 12.10.0 to solve the optimization problem.

4.2. Analysis of Typical Summer Day Scheduling

4.2.1. Day-Ahead Scheduling Analysis

Figure 2 and Figure 3 show the output power of each flexibility resource and the system flexibility demand during a typical scenario (Scenario A) in which renewable energy inflates the peak-to-valley difference of the load. Figure 4 and Figure 5 show the output power of each flexibility resource and the system flexibility in a typical scenario (Scenario B) where renewable generation curtails the peak-to-valley difference in the load.

Within Scenario A, pumped storage stations generate electricity during the busy peak load period from 09:00 to 12:00 while pumping water for storage during the off-peak period from 04:00 to 08:00. Wind power generation from 14:00–20:00 is large, which is consistent with the load curve. It can be seen from Figure 2 and Figure 3 that the flexibility demand of the system is large from 09:00 to 11:00, and the pumped storage stations, battery energy storages and hydrogen storage discharge during this period provide upward flexibility.

In Scenario B, as shown in Figure 4 and Figure 5, the renewable generation enlarges the peak-to-valley difference. The flexibility demand of the system is larger in comparison to that of Scenario A. Therefore, the pumped storage stations, battery energy storages and hydrogen storages generate power during the system load peak period to balance the system’s upward flexibility demand and absorb power during the off-peak period to balance the downward flexibility demand.

4.2.2. Intra-Day Scheduling Analysis

The intra-day scheduling results for the 15 min and 1 min time scales are presented in Figure 6 and Figure 7, respectively. On the 15 min time scale, from 9:00 to 12:00, the BESSs and the HESs generate power to provide upward flexibility. During the period from 2:00 to 8:00, the BESSs and HESs absorb power to offer downward flexibility. On the 1 min time scale, the power generation of each device is similar to that on the 15 min time scale. The reason is that the 1 min time scale flexibility demand is relatively small, and the real-time scheduling is based on the 15 min time scale plan and makes minor adjustments to guarantee low operation costs.

4.2.3. System Flexibility Constraint Analysis

The system upward and downward flexibility resources and demands in the simulation, without considering flexibility constraints, are shown in Figure 8A,B, respectively. Figure 8C,D exhibit the upward and downward flexibility resources and demands of the system that have incorporated flexibility constraints, respectively. As shown in Figure 8A, between 9:00 to 10:00, the system’s UFR falls below the UFD. This discrepancy suggests that neglecting flexibility constraints could lead to inadequate flexibility supply and potentially impact the secure operation of the power system. Even during the period from 10:00 to 12:00, where the system’s upward flexibility is greater than the UFD, there still remain risks of inadequate flexibility when there is a significant deviation between the actual and predicted renewable energy output.

As observed in Figure 8C, the system’s UFR is slightly greater than the UFD between 9:00 and 10:00. However, the risk of insufficient flexibility still exists when there are significant deviations between the actual and predicted amount of renewable energy created. Thus, merely considering flexibility constraints may not suffice, and the system must maintain a certain degree of the flexibility margin to enhance overall security.

4.2.4. System Flexibility Margin

The system flexibility margin, without considering the system flexibility margin index constraints, is shown in Figure 9A. The system flexibility margin under system flexibility margin index constraints is shown in Figure 9B. In Figure 9A, the upward flexibility margin index and downward flexibility index ranges are [0.005,0.193] and [0.025,0.205], respectively. In Figure 9B, the system flexibility margin is larger than that in Figure 9A, because the flexibility index constraints can guarantee that the flexibility margin is not below the threshold. To meet the flexibility demand during the day, it is necessary to consider the flexibility margin index constraints to cope with the uncertainty of renewable energy output.

4.3. Scheduling Scheme with Hydrogen Energy Storage

In order to investigate the effect of hydrogen storage stations, three scheduling schemes are conducted as below:

Scheme 1: No hydrogen storage stations participate in scheduling, and flexibility margin index constraints are not considered.

Scheme 2: No hydrogen storage power stations participate in scheduling, and flexibility margin index constraints are considered.

Scheme 3: Hydrogen storage stations participate in scheduling, and flexibility margin index constraints are considered. This approach is the method proposed in this paper.

The optimization outcomes for the three scheduling strategies are presented in

Table 2. Results of different scheduling schemes.

Scheduling Scheme	Total Operating Cost/$	Wind Power Curtailment Rate/%
1	1.1544 × 106	5.63
2	1.1333 × 106	3.41
3	1.1178 × 106	0.86

. Compared with Scheme 1, the operation cost and wind generation curtailment rate of Scheme 2 are both reduced. The reason is that in Scheme 1, the flexibility margin index constraints are ignored. When the actual wind generation deviates greatly from the predicted value, the system flexibility resources are not enough to meet the flexibility demand. As a result, the system can only reduce wind power generation to alleviate the imbalance of flexibility supply and demand. By constrsat, in Scheme 2 the flexibility margin index constraints are considered, and the system has sufficient flexibility resources to deal with the uncertainty of wind power.

The operation cost and wind generation curtailment rate are further reduced in Scheme 3 compared with Scheme 1 and Scheme 2. This is because the hydrogen storage stations are added in Scheme 3. The fast regulation characteristic of hydrogen storage stations provides more flexibility supply to the power system. An increase in wind farm output helps to reduce wind generation curtailment and lower the overall operation cost of the system.

5. Conclusions

This paper addresses the issue of improving the flexibility of integrated renewable energy power systems with high penetration rates. It constructs models for various flexibility resources, such as pumped hydro storage, hydrogen storage and electrochemical storage. A multi-time scale scheduling strategy is proposed for new high-proportion energy systems, considering the constraints of flexibility evaluation indicators and the participation of multiple flexibility resources. The feasibility of the proposed scheduling method is verified. The main conclusions are summarized as follows:

(1) Electrochemical and hydrogen storage have fast regulation capabilities and can effectively complement the regulation capabilities of pumped hydro storage, providing better storage capacity for wind power and thermal power during high-demand periods. The “peak shaving and valley filling” effect can be achieved in scenarios involving wind power peak and off-peak periods.

(2) The participation of energy storage systems in the scheduling plan can improve wind power integration. Energy storage systems can reduce the penalty cost of wind curtailment and thus reduce the overall operating cost of the power system. The daily operating cost is reduced by 3.1%.

(3) By considering the constraints of the flexibility supply–demand balance and flexibility margin index, the uncertainty of high-proportion new energy can be better addressed. After using the flexibility margin index constraints, the overall upward flexibility margin index of the system improves by 6.1%, and the downward flexibility margin index improves by 5.3%.

(4) As the penetration rate of renewable energy increases, the flexibility requirements of the system will also increase. An increase in the capacity of energy storage can be a reasonable measure to alleviate the pressure of the flexibility supply and demand balance in the system

High penetration of renewable energy will become an important feature of future power systems. Therefore, it is particularly important to analyze it from the perspective of system flexibility. Considering the participation of flexibility resources in power scheduling significantly improves the flexibility of power systems. The research results provide support for the flexible operation of high-proportion renewable energy power systems.