To make full use of distributed energy resources to meet load demand, this study aggregated wind power plants (WPPs), photovoltaic power generation (PV), small hydropower stations (SHSs), energy storage systems (ESSs), conventional gas turbines (CGTs) and incentive-based demand responses (IBDRs) into a virtual power plant (VPP) with price-based demand response (PBDR). Firstly, a basic scheduling model for the VPP was proposed in this study with the objective of the maximum operation revenue. Secondly, a risk aversion model for the VPP was constructed based on the conditional value at risk (CVaR) method and robust optimization theory considering the operating risk from WPP and PV. Thirdly, a solution methodology was constructed and three cases were considered for comparative analyses. Finally, an independent micro-grid on an industrial park in East China was utilized for an example analysis. The results show the following: (
Keywords: dynamic scheduling; VPP; CVaR; robust optimization; risk aversion
In recent years, under the dual pressures of energy shortages and environmental degradation, the development scale of distributed energy resources has gradually expanded, and its position in the energy grid has become increasingly prominent. However, due to their own limitations, the geographical distribution of the generators is dispersed, the unit capacity is small, and the intermittent fluctuation is obvious, so the direct grid connections of distributed energy resource (DER) units will have a great impact on the security and stability of the grid [[
Recently, the concept of VPP technology has attracted extensive attention in many industries, both domestically and internationally. In foreign countries, from 2001 to 2005, Germany, The Netherlands, and Spain jointly established the virtual fuel cell power plant program, consisting of 31 residential fuel cell combined heat and power (CHP) systems [[
At present, studies on VPP operation optimization mainly focus on three aspects: the capacity allocation, optimization scheduling, and uncertainty handle. In terms of capacity allocation, Muhammad et al. [[
Research on the optimization scheduling of VPP operation focuses on the economic value and the elimination of wind and photovoltaic power as the objective to optimize the output of each unit in the dispatching system. Mashhour et al. [[
Finally, researches on the power fluctuation of VPP operation focus on how to use the controllable units, energy storage, electric vehicles and controllable loads to ensure the stable output of a VPP. Hrvoje et al. [[
The optimization problem for VPP operation has been extensively discussed in all of the aforementioned studies. A capacity allocation method, scheduling model, and uncertainty handle technology have been proposed, which could greatly promote development. However, it should be noted that there are some gaps in the literatures. Firstly, most of the studies aggregated WPP, PV, ESS and conventional gas turbines (CGTs) into a VPP, and established a capacity allocation scheme, but for distributed power sources, small hydropower stations (SHSs), especially those with regulatory reservoirs, have a better application space for VPP. Secondly, the researches on the operation optimization of VPPs discussed the optimal operation strategies under different objective functions and different scenarios. Some studies considered the optimization effects of demand response on VPP. However, ESS and price-based demand response (PBDR) will flatten the load demand curve, which plays an important role in optimizing the VPP operation. It needs to be further discussed. Finally, some literatures studied the risks brought about by uncertainty. More studies used probabilistic methods to characterize uncertainty, but whether the DERs, whose capacity is small and quantity is large, have statistical properties remains to be verified, and probability distribution functions is difficult. In addition, uncertainty processing mainly relies on the stochastic programming method, which considers the probability distribution of uncertain factors, but the distribution law is difficult to describe. However, the optimal solution of robust optimization has certain inhibitions on the possible adverse effects of each element in the set. Adjusting the robust coefficient can decide the optimal scheduling schemes of different uncertainty degrees. This method does not need to consider numerous random schemes, so the calculation burden is small, and the applicable space is better. All of the above analyses motivate us to propose an optimization scheduling model of a VPP. The main contributions of this work are summarized as follows:
- A VPP coupled with WPP, PV, SHS, ESS, CGT, and an incentive-based demand response (IBDR) with the implementation of PBDR on the user side. Among these, the SHS equipped with regulating reservoirs can distribute the output according to the real-time load demand, which can provide reserve services for the WPP and PV coupling operation with CGT and ESS. WPP and PV have high environmental and economic benefits, as well as high risks, so balancing the benefits and risks is the key to the optimal operation of the VPP.
- A basic scheduling model for the VPP operation is put forward without considering uncertainty. The maximum revenue of the VPP operation is taken as the objective function of the optimization model, considering energy balance constraints, different power sources, and system rotating reserve constraints. The basic scheduling results could provide an important decision-making reference for determining the VPP operation risks and verifying the effectiveness of the risk aversion model.
- A CVaR-robust-based aversion scheduling model for the VPP operation is constructed with the objective function of minimum operation losses. First, the uncertainty analysis for WPP, PV, SHS, and the load are made, and WPP and PV selected as the main uncertainty factors. Second, the conditional value at risk (CVaR) method and robust optimization theory are used to reflect the operation risks brought about by uncertainty in the objective function and restrictions, respectively. Finally, a solution methodology is constructed after converting the mixed integer nonlinear programming (MINLP) model into a mixed integer linear programming (MIP) model with three cases for comparative analysis.
The rest of this paper is organized as follows: Section 2 describes the basic structure of the virtual power plant, then, the output model of the power sources is introduced. Section 3 presents the basic scheduling model for the VPP under the objective function of the maximum operating revenue. Next, in Section 4, the uncertainty analysis is made and the risk aversion scheduling model is proposed based on the CVaR method and the robust optimization theory. Finally, Section 5 presents an industrial park group in northern China which was chosen as a simulation system for the verification of the effectiveness and applicability of the proposed scheduling model. Section 6 highlights the contributions and conclusions of the paper.
This study integrated WPP, PV, SHS, CGT, ESS, and IBDR into the VPP. The energy scheduling of the VPP was mainly carried out by the energy management system (EMS). Based on the load demands of terminal users and the available outputs of different power sources, the optimal operation strategy of the VPP was established. Meanwhile, in order to fully motivate the user side to respond to the optimization scheduling, PBDR was implemented in this study, which could utilize time-of-use (TOU) prices to change the users' power consumption behavior and optimize the load curve. Moreover, assume the SHS was equipped with an annual regulating reservoir to improve the adjustment characteristics of the VPP, namely, the SHS could optimize the utilization of water storage according to the actual output of WP and PV, and participate in VPP optimization operation. IBDR was implemented through signing pre-agreements with the end users and providing a certain subsidy. When the content of the contract occurred, the scheduling agency could directly make the user adjust their power consumption behaviors to improve the power generation output or the spare output. Figure 1 is the basic structure of the virtual power plant.
In the VPP, WPP, PV, and CGT were the main power sources for satisfying the load demand. The surplus load demand was satisfied by SHS. The power generation of WPP and PV had great uncertainty, but system was pre-scheduled. The determined scheduling plan for the VPP was needed before knowing the actual output. In order to overcome deviation from the scheduling plan, the ESS and CGT provided reserve services. IBDR users provided virtual power generation by changing their power consumption behaviors, and participated in power generation dispatching in the energy market and reserve market. Meanwhile, the SHS equipped with regulating reservoirs could also provide reserve services by changing its power generation plans. WPP and PV have great environmental and economic benefits, but the high uncertainty of these sources also brings high risks. Balancing the benefits and risks is a critical issue in the optimization of VPP operation.
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The output of the VPP was mainly derived from WPP, PV, SHS, ESS, and IBDR. Among these, the outputs of WPP and PV mainly depend on natural wind and solar irradiance, respectively, which have highly random outputs. Correspondingly, the outputs of WPP and PV have great uncertainty. Simulating wind speed and irradiance is the key to calculating the outputs of WPP and PV. The Rayleigh distribution function and beta distribution function have been proved that they could be used to simulate wind speed and solar irradiance. The output models of WPP and PV have already been constructed based on the simulation distribution function in our previous research [[
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In order to increase the regulation capacity of the VPP, this study selected the small hydropower generation system with annual adjustment reservoirs. SHS could ensure the hydropower output by adjusting the amount of water according to power demand considering the water level of the adjustment reservoir. The output of a hydropower station mainly depends on the runoff and head height of the river. The expression is as follows:
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In IBDR, pre-agreements are generally signed with the users. When the response occurs, the users need to adjust their electricity consumption behaviors in accordance with the agreements, and receive financial compensation for this response. The IBDR program is mainly provided by demand response providers (DRPs). Because the revenue of DRPs is determined by the supply price of the demand response, DRPs participate in IBDR programs step-by-step according to the demand response (DR) price in accordance with the fluctuation of the electricity market price [[
According to Figure 2, the minimum required response for DRP i in step j is
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The energy storage system unit participated in VPP power generation scheduling by utilizing its own charge and discharge characteristics. During the valley periods, energy storage was performed, and power generation was performed during the peak periods, to provide a reserve service for the VPP. This study introduced the state of charge (SOC) to reflect the remaining capacity of the ESS battery, which varies with the charge and discharge of the system, and is expressed as the percentage of the remaining battery power and its total capacity, as follows:
When the ESS is charging:
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When the ESS is discharging:
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In the power generation scheduling of a VPP including WPP, PV, and SHS, with the objective of maximum operating revenue, a basic mathematical model is constructed. The specific objective function is as follows:
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The optimization operation of the VPP followed a load supply and demand balance constraint, unit operation constraints, and system rotation reserve constraints. The specific constraints are as follows:
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Small hydropower is constrained by season, due to the dry season and flood season. For the dry season, it is necessary to ensure that the water storage meets the night load; for the flood season, the water volume cannot exceed the maximum storage capacity, so it is necessary to adjust the water volume of the reservoir reasonably. Especially in the flood season, if the water volume of the reservoir has basically reached the maximum capacity, due to the maximum limit of the power generation drainage of the turbine unit, it is necessary to abandon the water to meet the reservoir storage requirements. Correspondingly, the reservoir water demand, power generation drainage, and water abandonment constraints are as follows:
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IBDR can be applied for both energy market scheduling and reserve market scheduling. Thus, the detailed constraints of the IBDR operation are expressed as follows:
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For the VPP, the operation constraints of CGT, ESS, and PBDR should also be considered. Among these, the CGT is mainly needed to meet the maximum and minimum power constraints, startup-shutdown time constraints, and upper and lower climbing constraints. The ESS needed to meet the maximum charge-discharge power constraints, charge and discharge state constraints, etc. The output generated by PBDR also needed to meet the maximum output constraints, upper and lower climbing constraints and cumulative maximum output constraints at each moment. We have already constructed the constraints of CGT, ESS, and PBDR as shown in our previous research [[
In the proposed VPP, four uncertainty factors exist, namely,
Similarly, the existing researches prove that the Rayleigh distribution function and the beta distribution function could be used to describe natural wind speed and solar irradiance [[
For the proposed model above, the uncertainty factors are distributed in the objective function and constraints. Determining how to describe the uncertainty factors was crucial to determining the optimal scheduling plan of the VPP. This paper proposes a risk aversion tool for the optimal operation of the VPP based on the CVaR method and the robust optimization theory.
In recent years, the financial sector has evolved a variety of risk analysis tools. Under normal market conditions and within a given confidence level, Value at Risk (VaR), which analyzes the risk characteristics quantitatively, can estimate the maximum possible loss of a portfolio over a specified period of time. However, VaR can only determine a risk situation under the given confidence level and doesn't consider the risk tail, so there are certain limitations in its practical applications. Conditional Value at Risk (CVaR) can describe the distribution of risk outside the confidence level. The basic principles are described as follows:
Set the portfolio vector as X and the random factor as random vector
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Considering the risk brought about by the uncertainty factors to the VPP operation, the CVaR theory is applied to describe the scheduling operation risk of the VPP. According to Equation (
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Second, apply the robust theory to convert the constraint conditions with uncertainty variables into stochastic constraint conditions by using the robust coefficient. Robust optimization theory is a mature theory that solves the problem of uncertain parameter optimization after multi-step stochastic optimization theory and fuzzy optimization theory [[
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Overall, CVaR-robust-based scheduling can realize the safe and stable operation of the system within a certain disturbance range when the system's operation information is incomplete, improve the system's immunity to uncertainty factors, and achieve the scheduling target.
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Furthermore, in order to analyze the applicability of the proposed CVaR-robust method in solving the optimization operation of the VPP, this study set three simulation cases, namely, reference scenario, CVaR scenario and comprehensive scenario, and analyzed the effectiveness of the CVaR method and robust optimization theory in measuring and controlling the risks of VPP operation caused by uncertainties. These cases are described as follows:
Case 1: The reference scenario, using self-scheduling for the VPP without considering uncertainties. This scenario did not consider the uncertainty of WPP and PV. It analyzed the operational characteristics of different components in the VPP, and focused on the complementary effects between different components to obtain the optimal scheduling results for the VPP under the objective of maximizing operating revenue.
Case 2: The CVaR scenario, using self-scheduling for only the VPP with the CVaR method. This scenario focused on the uncertainty of WPP and PV in the objective function, and used the CVaR method to transform the objective function (Equation (
Case 3: The comprehensive scenario, using self-scheduling for the VPP with the CVaR-robust method. This scenario further considered the influence of uncertainty factors on the operation of the VPP within constraints, and constructed random constraints (Equation (
An independent micro-grid located in an industrial park in East China (30°06′ N, 122°24′ E) was utilized for the simulation analysis of the proposed model. The park was equipped with two 0.25 MW WPPs, four 0.1 MW PVs, a 1 MW CGT, and a 0.2 MW·h ESS. An SHS was equipped with five small hydropower generating units of 50 kW each capacity, for which the annual average water flow was 40 m
Furthermore, in order to analyze the complementary effects between different power sources, the load data on a typical summer load day and on a typical winter load day were taken as input data. The maximum and minimum loads of the park were 0.9 MW and 0.709 MW in summer, respectively, and 0.879 MW and 0.737 MW in winter, respectively. According to [[
The on-grid prices of WPP, PV, SHS, and CGT in the park were 0.51 ¥/kW·h, 0.88 ¥/kW·h, 0.31 ¥/kW·h, and 0.42 ¥/kW·h, respectively. Meanwhile, in order to motivate the users to respond to the system's power generation scheduling, it was assumed that PBDR was implemented on the users' side, and the terminal users' electricity price before PBDR was 0.59 ¥/kW·h. The price elasticity of the power demand was set according to literature [[
After taking inputs from the above basic data, the model was solved by the GAMS software using the CPLEX 11.0 linear solver from ILOG_solver [[
This case focuses on the complementary effects of different power sources in the VPP, especially those between WPP, PV, and SHS. From the perspective of the load demand, on a typical winter day, due to the larger heating demand at night, the heating demand is relatively less during the daytime, so the peak-to-valley gap is lower. On a typical summer day, due to the higher cooling demand during the daytime, the cooling demand at night is relatively lower, so the peak-to-valley gap is relatively high. Figure 6 is the output distribution of VPP power generation in a typical day.
According to Figure 6, on the typical summer day, the main power sources for the load demand were CGT and SHS. The remaining load demand was satisfied by WPP. On the typical winter day, the main power sources were CGT and WPP. The remaining load demand was satisfied by SHS. This was due to the lower available output of WPP but higher available output of SHS and PV in summer, and lower available output of SHS and PV but higher available output of WPP in winter. It can be seen that there were significant complementary effects between different power sources on the different typical days. The VPP could form a stable power output to meet the load demand by aggregating different distributed power sources, and could thus get the maximum operating revenue. Table 2 shows the scheduling results of VPP operation on the different typical load days.
According to Table 2, in order to maximize the operating revenue, the VPP prioritized the utilization of clean energy to meet the load demand. The total output of WPP, PV, and SHS was 12.259 MW·h on a typical summer day and 12.297 MW·h on the typical winter day. Correspondingly, the operating revenue of the VPP on the typical summer day was ¥460.47, which was lower than that of the typical winter day. Since the peak-to-valley ratio on the typical summer day was higher than that of the typical winter day, the outputs of CGT, ESS, and IBDR were also higher. Furthermore, the clean energy output and revenue of the VPP in different periods was analyzed. Figure 7 shows the power output and operating revenue of VPP in different load periods.
According to Figure 7, considering the different load periods, whether in summer or winter, the clean energy output in the peak load period was higher than that in other load periods. The outputs of WPP, PV, and SHS were 2.529, 1.91 and 1.915 MW·h, respectively. Correspondingly, the operating revenue was also high in the peak load period, at ¥4.175 × 10
This scenario was mainly used to analyze the effectiveness of the CVaR method in measuring the uncertainty factor in the objective function. The initial confidence degree β was set to 0.9, and the optimal scheduling strategy of the VPP calculated. The respective total grid-connected outputs of WPP, PV, and SHS were 0.22, 0.417, and 0.242 MW·h for the typical summer day; and 0.123, 0.656 and 0.088 MW·h for the typical winter day, which were lower than those without considering uncertainty. The operating revenues of the VPP were ¥7645.5 on the typical summer day and ¥8137.68 on the typical winter day, which were lower than those without considering uncertainty. It can be seen that if the decision maker does not consider the uncertainty, the scheduling strategy of the VPP is arranged according to the risk neutral situation; when the actual output of WPP and PV deviates from the predicted results, the system will face a large operating risk. Figure 8 shows the output distribution of VPP power generation on typical load days.
According to Figure 8, in order to avoid the uncertainty risk of WPP and PV, the VPP increased the power output of CGT. Compared with Case 1, the output of CGT was relatively stable, and the total output of CGT was higher, at 0.928 MW·h on the typical summer day and 0.908 MW·h on the typical winter day. Correspondingly, in order to provide sufficient reserve services for WPP and PV, the outputs of ESS and IBDR were also higher. In total, when considering uncertainty, the VPP reduced the output of WPP and PV, which lead to lower operating revenue, but could also avoid the risk of a power shortage penalty. In general, the confidence degree is a crucial parameter for balancing benefits and risks. A reasonable confidence degree guarantees the establishment of the optimal scheduling strategy of a VPP. Table 3 shows the scheduling results of VPP operation under different confidence degrees β in typical load day.
According to Table 3, the confidence degree β reflects the risk attitude of the decision maker. When β is high, the decision maker is the risk aversion type, who will reduce the scheduling of WPP and PV power generation outputs to avoid the operating risk of the VPP. Conversely, when β is low, the decision maker is the risk preference type, who will increase the scheduling of WPP and PV to capture excess economic returns. It can be seen that as β increased from 0.8 to 0.98, the output of clean energy power generation gradually reduced, and the output of CGT, ESS, and IBDR gradually increased. This shows that as the risk aversion of policy makers increases, the unit output of VPP that can provide reserve services gradually increases, correspondingly, the CVaR value is gradually reduced. Further, when the decision maker considers the uncertainty risk, WPP and PV bring different degrees of risk to the VPP operation due to different supply and demand relationships in different time periods, so the changes in the operating revenue of the VPP in different load periods and confidence degrees need to be analyzed. Figure 9 shows the revenue of the VPP operation under different β in different load periods.
According to Figure 9, considering different time periods of the typical summer day, due to the heavy load during the peak period, the load supply and demand relationship was tight. So, when decision maker considered the uncertainty risk, the output of WPP and PV was significantly reduced, and the operating revenue significantly decreased with the increase of β. However, the supply and demand relationship in the valley period was not tight, so the dispatch of ESS and IBDR appropriately increased the grid-connected power of WPP and PV. For the typical winter day, the WPP's available output was higher at night, in order to avoid the risk to the VPP operation, the operating revenue in the valley period was significantly reduced with the increase of β. However, the ESS transferred part of the available output of WPP to the peak period. Correspondingly, the operating revenue did not decrease much in the peak period. In general, the CVaR method can measure the uncertainty factors in the objective function, reflect the risk attitude of the decision maker by setting the confidence degrees, and obtain the optimal operation strategy of the VPP.
This subsection further discusses the impact of uncertainties on the VPP operation within constraints by introducing robust stochastic optimization theory. The initial robust coefficient Γ was set as 0.9, and the optimal scheduling strategy of the VPP calculated. The respective total grid-connected outputs of WPP, PV, and SHS were 4.797, 1.760 and 4.407 MW·h for the typical summer day; and 6.984, 1.455 and 1.901 MW·h for the typical winter day. The values of revenue, VaR and CVaR are 204.8 ¥, −68.71 ¥, −98.76 ¥, 343.7 ¥, −15.07 ¥, −38.81 ¥ lower than those in Case 2, respectively. It can be seen that when considering the uncertainties in the constraint conditions, the sensitivity of the decision maker to the risk will increase. In order to avoid risk to the VPP operation, the decision maker will reduce the power generation of WPP and PV. Figure 10 shows the output distribution of VPP power generation on typical load days in Case 3.
According to Figure 10, when the robust optimization theory was introduced, the VPP further compressed the grid-connected space of WPP and PV. Taking the typical summer load day as an example, the outputs of WPP and PV were reduced by 0.11 and 0.307 MW·h, respectively. However, the power generation output of the CGT was scheduled more by the VPP because it was more stable and controllable, and it increased by 0.431 MW·h. Since the power generation outputs of WPP and PV were reduced, the scheduling outputs of ESS and IBDR were eliminated as well. In the peak period, only, the ESS discharged, and the output of IBDR was reduced. In the valley period, the ESS charged and the output of IBDR increased. Table 4 shows the scheduling results of the VPP operation in different cases.
According to Table 4, the values of revenue, VaR, and CVaR in different cases are compared. When robust stochastic optimization theory was introduced into the conversion constraints with the uncertainty variable, the risk brought about by WPP and PV to the VPP could be better considered. The decision maker would further control the power generation of WPP and PV. Correspondingly, the operating revenue of the VPP also decreased, but the VaR and CVaR values increased under the same confidence degree β, indicating that the benefits and risks are interrelated, and the decision makers need to consider the corresponding risk while pursuing high economic returns. When decision makers want to avoid risk, they will need to discard some of the economic benefits. Furthermore, since the uncertainty in the constraints is described by the prediction error and the robustness coefficient, it can directly affect the optimal operation of the VPP, so sensitivity analysis was conducted between the prediction error e, the robust coefficient Γ, and the confidence degree β, and the operation schemes of the VPP under different parameter combinations are discussed. Figure 11 shows the CVaR values of VPP operating under different robust coefficients.
According to Figure 11, the influence of prediction error e and robust coefficient Γ on the VPP operation is analyzed. When e was higher, the value of CVaR increased more than that when Γ increased by the same magnitude. When e
The ESS could use its own charge and discharge capacity to optimize the distribution of WPP and PV power generation outputs, and PBDR could smooth the load demand curve through time-of-use prices, which both have important optimization effects on the VPP operation. On the other hand, the linearization process (proposed in Section 4.3) could reduce the time for solving the proposed model and improve the optimization degree of the scheduling results. Correspondingly, the paper mainly comparatively discusses the operation results of the VPP with and without the ESS under different peak-to-valley price gaps in this section.
The ESS could charge in the valley period and discharge in the peak period. So, it could not only improve the flexibility of the VPP operation, but also smooth the load demand curve, which is conducive to improving the grid-connected space of WPP and PV in the valley period and reducing the risks of WPP and PV to the VPP operation. In particular, WPP is the main clean energy output. This section selects the typical winter day and compares the operation results of the VPP with and without the ESS, as shown in Figure 12.
According to Figure 12, the power structure and operating revenue are compared before and after ESS. For the power structure, if the VPP did not contain ESS, the outputs of WPP, PV, and SHS were reduced by 0.078, 0.659 and 0.101 MW·h. However, the output of WPP and PV increased in peak period. This is because when the VPP did not contain ESS, WPP and PV was utilized more to meet the high load demand and obtain greater economic benefits. But in flat and valley periods, the VPP reduced the output of WPP and PV to avoid the uncertainty risk. For the operation results, the values of revenue, VaR, and CVaR increased by −¥222.303, ¥71.641, and ¥69.315. During the peak period, the values increased by ¥227.30, ¥75.700, and ¥233.370. This is because when the VPP did not contain ESS, WPP and PV were difficult to store in peak periods. During the valley period, the outputs of WPP and PV were both reduced, resulting in a decrease in revenue and risk. In general, the ESS could utilize abandoned wind and solar energy for storage in the valley period, and release energy during the peak period, which was beneficial to alleviating the operating risk during the peak period, while improving the operating revenue of the VPP. Furthermore, the scheduling results of the VPP under different ESS capacities were measured. Table 5 shows the scheduling results of the VPP operation under different ESS capacities.
According to Table 5, when the ESS's capacity increased from 0 to 0.6 MW ((WPP, PV):ESS = 1.5:1), the values of revenue, VaR, and CVaR changed faster. When the capacity was higher than 0.6 MW, the value changed slower, which indicates that ESS could improve the grid-connected space of WPP and PV, but when the capacity was large enough, the ability to consume clean energy had basically reached the upper limit. At this time, other ways are needed to increase the output of WPP and PV with the objective of reducing the initial investment cost of the VPP and improving its operating revenue. Compared with the results when the capacity is 0, the outputs of WPP and PV increased by 1.082 and 0.183 MW·h, respectively, when capacity reached 1 MW·h. In general, with the increase of capacity, the operating revenue of the VPP increased, but the operating risk was improved as well. Hence, it is necessary to properly control the capacity of the ESS to balance the risks and benefits, which can ensure the optimal operation of the VPP.
PBDR can motivate the terminal users to respond to the VPP operation schedule through time-of-use prices, and transfer partial load demand in the peak period to the valley period, which has an important effect on improving the grid-connected space of clean energy generation during the valley period, and relieving the supply-demand relationship during the peak period. Therefore, this study selected the typical summer day with a large peak-to-valley gap, analyzed the load demand curve before and after PBDR, compared the operation results of the VPP, and discusses the influences of different peak-to-valley price gaps on VPP operation. Figure 13 shows the load demand of terminal customers in the typical day before/after PBDR.
According to Figure 13, the load demand curves before and after PBDR are compared. In a typical summer day, the maximum demands of the electrical load before and after PBDR were 0.900 and 0.882 MW, respectively. The minimum values were 0.709 and 0.730 MW. The peak-to-valley ratios of the load before and after PBDR in a typical summer day are 1.27 and 1.209. Similarly, the peak-to-valley ratios of the load before and after PBDR in a typical winter day are 1.194 and 1.144. It can be seen that PBDR is beneficial to reducing load demand in the peak period and increasing load demand in the valley period. Correspondingly, the flatter load demand curve also provides a greater grid-connected space for WPP and PV, which is beneficial to improving the operating revenue and reducing the operating risks of the VPP. Figure 14 shows the scheduling results of the VPP operating before and after PBDR.
According to Figure 14, the power structure and operation results before and after PBDR are compared. For the power structure, the output of WPP and PV after PBDR increased significantly, by 0.264 and 0.72 MW·h. Specifically, the output during the peak period and the valley period increased significantly. This is because the load curve after PBDR was smoother, and the reserve service space was larger during the peak period, and could support more grid-connected energy from WPP and PV. The increase of the load demand during the valley period also provided more grid-connected space for WPP and PV power generation. For the operation results, PBDR can smooth the load demand curves, the output of clean energy sources was more, correspondingly, and the revenue was also higher than that before PBDR. The operation revenue increased by ¥129.44, ¥40.62, and ¥262.74 in the three load periods, but VaR and CVaR were reduced in the flat period, and increased in both the peak period and the valley period. This is because the clean energy output increased after PBDR, but the load during the flat period remained unchanged, while PBDR released more reserve service space, so the risk was reduced. During the peak period and the valley period, the output of clean energy increased, so the risk caused by uncertainty increased. Furthermore, the influence of the peak-to-valley price gap on VPP operation was analyzed. Table 6 shows the scheduling results of the VPP operation with different peak-to-valley price gaps.
According to Table 6, with the increase of the peak-to-valley price gap, the revenue space for VPP also increased. Correspondingly, the total output of WPP and PV increased significantly. When the peak-to-valley price gap was lower than 3, the values of revenue, VaR, and CVaR changed faster, but when the peak-to-valley price gap was higher than 3, these values changed slower. For the operating revenue and operating risk, the growth rate of revenue generated by PBDR was higher than that of the risk, which indicates that PBDR is conducive to improving the operating revenue and controlling the risk. Hence, in order to acquire the optimal operation, decision makers need to actively implement PBDR on the user side, set reasonable peak-to-valley price gaps according to the actual conditions, and encourage end users to respond to system energy scheduling, which can maximize economic benefits while minimizing operating risk.
Quadratic terms exist in objective functions and a constraint condition, which results in the proposed model is a MINLP problems. However, the MINLP problem is complex, need much time to solve and hard to get the optimal solution. If the proposed model could be linearized, the above problem could be overcome. Figure 7 is the scheduling results of the VPP before/after linearizing model in typical summer day.
According to Table 7, the time for solving the model is lower in MIP model than that in MINLP model in three cases. This shows the linearization of the model will reduce the time for solving the model. Then, analyze the scheduling results in MIP model and MINLP model. Take Case 3 as example, the revenue is 135.25 ¥ lower in MIP model than that in MINLP model. However, the CVaR in MINLP is 80.77 ¥ higher than that in MIP model. This show the scheduling results could get more economic while rational controlling the operation risk after linearizing model. Overall, if the MINLP model is converted into MIP model, the optimization degree of the scheduling results is better.
To make full use of the distributed energy on the user side, this study integrated WPP, PV, SHS, ESS, and IBDR into a VPP. Firstly, a basic scheduling model was constructed based on the maximum net operating revenue. Then, a risk aversion model for the VPP was put forward considering the uncertainty risk. The CVaR method was introduced to handle the uncertainty variables in constraint conditions, while robust optimization theory was used to convert the constraint conditions with uncertainty variables into stochastic constraint conditions. Third, a solution methodology was constructed after converting a MINLP model into MIP, and three cases were set for comparative analysis. Finally, an independent micro-grid on an industrial park in East China (30°06′ N, 122°24′ E) was utilized for a case study. The conclusions can be summarized as follows:
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Graph: Figure 1 Basic structure of virtual power plant.
Graph: Figure 2 Step-wise DR price-demand curve.
Graph: Figure 3 Discretization method of load demand distribution function.
Graph: Figure 4 Solution flow of the proposed model.
Graph: Figure 5 Load demand and available output on typical load day: (left) summer and (right) winter.
Graph: Figure 6 Output distribution of VPP power generation on typical day: (a) summer and (b) winter.
Graph: Figure 7 Power output and operation revenue of VPP in different load periods.
Graph: Figure 8 Output distribution of VPP power generation on typical load days in Case 2.
Graph: Figure 9 Revenue of VPP operation under different β in different load periods.
Graph: Figure 10 Output distribution of VPP power generation on typical load days in Case 3.
Graph: Figure 11 The CVaR values of VPP operation under different β, Γ and e (typical winter day).
Graph: Figure 12 Operation results of VPP with/without ESS.
Graph: Figure 13 Load demand of terminal customers in typical day before/after PBDR.
Graph: Figure 14 Operation results of VPP before/after PBDR.
Table 1 Parameters of PBDR and IBDR in typical load day.
Time&price PBDR IBDR Peak Period Valley Period Flat Period Energy Market Reserve Market Up Down Time divide Summer 10:00−18:00 0:00−7:00 8:00−9:00&19:00−24:00 Winter 12:00−20:00 0:00−7:00 8:00−11:00&21:00−24:00 Power price (¥/kW·h) 0.69 0.33 0.55 0.5 0.2 0.6
Table 2 Scheduling results of VPP operation in typical load day.
Typical Day Power Output/MW·h Abandoned Energy/MW·h Revenue/¥ CGT PV WPP SHS ESS IBDR WPP PV SHS Summer 7.562 2.09 5.517 4.652 (0.25, −0.24) (0.36, −0.39) 0.48 0.11 0.245 7804.85 Winter 7.282 1.673 8.566 2.058 (0.20, −0.20) (0.21, −0.18) 0.745 0.146 0.179 8265.32
Table 3 Scheduling results of VPP operation under different confidence degrees β.
Summer Winter Power Output/MW·h CVaR/¥ Power Output/MW·h CVaR/¥ CGT PV WPP SHS ESS IBDR CGT PV WPP SHS ESS IBDR 0.8 8.06 1.95 5.43 4.50 (0.3, −0.3) (0.36, −0.30) 1764.58 7.61 1.61 8.43 2.01 (0.35, −0.33) (0.33, −0.27) 1878.18 0.85 8.18 1.92 5.32 4.47 (0.35, −0.36) (0.36, −0.24) 1740.27 7.80 1.59 8.26 2.00 (0.4, −0.36) (0.30, −0.24) 1852.30 0.90 8.49 1.87 5.10 4.41 (0.4, −0.4) (0.33, −0.18) 1725.59 8.19 1.55 7.91 1.97 (0.45, −0.44) (0.27, −0.18) 1836.67 0.95 8.53 1.83 5.02 4.39 (0.5, −0.4) (0.33, −0.15) 1713.89 8.31 1.51 7.79 1.96 (0.50, −0.48) (0.27, −0.15) 1824.22 0.98 8.83 1.75 4.85 4.36 (0.5, −0.44) (0.30, −0.15) 1703.36 8.67 1.45 7.53 1.95 (0.5, −0.48) (0.24, −0.15) 1813.01
Table 4 Scheduling results of VPP operation in different Cases.
Typical Day Power Output/MW·h Operation Results/¥ CGT PV WPP SHS ESS IBDR Revenue VaR CVaR Summer Case 1 7.562 2.09 5.517 4.652 (0.25, −0.24) (0.36, −0.39) 7804.85 Case 2 8.49 1.870 5.104 4.41 (0.40, −0.40) (0.33, −0.18) 7645.50 1716.77 1725.59 Case 3 8.921 1.760 4.797 4.407 (0.30, −0.28) (0.09, −0.15) 7440.70 1785.48 1824.35 Winter Case 1 7.282 1.673 8.566 2.058 (0.20, −0.20) (0.21, −0.18) 8265.32 − − Case 2 8.190 1.550 7.912 1.97 (0.45, −0.44) (0.27, −0.18) 8137.68 1827.29 1836.67 Case 3 9.342 1.455 6.984 1.901 (0.30, −0.24) (0.09, −0.09) 7793.98 1842.36 1875.48
Table 5 Scheduling results of VPP operation under different ESS Capacities (typical winter day).
Capacity/ Power Output/MW·h Operation Results/¥ CGT PV WPP SHS ESS IBDR Revenue VaR CVaR 0 9.941 1.419 6.517 1.834 0 (0.15, −0.15) 7645.54 1905.430 1938.840 0.2 9.342 1.455 6.984 1.901 (0.3, −0.24) (0.09, −0.09) 7793.98 1842.362 1875.48 0.4 8.983 1.497 7.176 1.935 (0.36, −0.3) (0.12, −0.12) 7867.843 1833.789 1869.525 0.6 8.682 1.539 7.316 1.965 (0.45, −0.39) (0.12, −0.15) 7937.503 1822.579 1860.852 0.8 8.351 1.581 7.504 1.975 (0.51, −0.45) (0.15, −0.18) 8028.115 1810.506 1851.539 1.0 8.199 1.602 7.599 1.982 (0.54, −0.48) (0.15, −0.18) 8065.874 1795.140 1836.481
Table 6 Scheduling results of VPP operation in different peak-to-valley price gaps.
Peak-to-Valley Price Gap Load Demand/MW Peak-to-Valley Clean Energy Output/MW·h Revenue/ VaR CVaR Max Min PV WPP SHS 1 0.900 0.709 1.270 1.76 4.797 4.407 7440.7 1785.48 1824. 35 2 0.891 0.723 1.233 1.848 5.037 4.440 7584.963 1805.447 1844.457 2.6 0.882 0.730 1.209 2.024 5.517 4.505 7873.49 1845.38 1884.67 3 0.878 0.733 1.197 2.141 5.837 4.549 8065.841 1872.002 1911.479 3.5 0.876 0.735 1.192 2.200 5.997 4.570 8162.017 1885.313 1924.883
Table 7 Scheduling results of the VPP before/after linearizing model in typical summer day.
cases MIP MINLP Time/s Revenue/¥ VaR/¥ CVaR/¥ Revenue/¥ VaR/¥ CVaR/¥ MINLP MIP Case 1 7804.85 7895.96 245 s 10 s Case 2 7645.50 1716.77 1725.59 7442.65 1785.27 1893.48 278 s 14 s Case 3 7440.70 1785.48 1824.35 7305.45 1805.45 1905.12 304 s 18 s
L.J. (Liwei Ju) and proposed the researching framework. L.J. (Liwei Ju) and P.L. (Peng Li) conducted the empirical analysis and wrote the manuscript. Q.T. (Qinliang Tan), Z.F. (Zhongfu Tan) and G.D. (GejiriFu De) provided several useful recommendations on the manuscript revision.
This research was funded by Supported by the Beijing Social Science Fund (18GLC058, 16JDYJB044) and the Science Foundation of China University of Petroleum, Beijing (No. ZX20170256), the National Science Foundation of China (Grant No. 71273090) and the Beijing Social Science Fund (18GLC058).
The authors declare no conflict of interest.
By Liwei Ju; Peng Li; Qinliang Tan; Zhongfu Tan and GejiriFu De
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