Risk assessment of microgrid aggregators considering demand response and uncertain renewable energy sources
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Abstract
In power market environment, the growing importance of demand response (DR) and renewable energy source (RES) attracts more forprofit DR and RES aggregators to compete with each other to maximize their profit. Meanwhile, the intermittent natures of these alternative sources along with the competition add to the probable financial risk of the aggregators. The objective of the paper is to highlight this financial risk of aggregators in such uncertain environment while estimating DR magnitude and power generated by RES. This work develops DR modeling incorporating the effect of estimating power at different confidence levels and uncertain participation of customers. In this paper, two wellknown risk assessment techniques, value at risk and conditional value at risk, are applied to predict the power from RES and DR programs at a particular level of risk in different scenarios generated by Monte Carlo method. To establish the linkage between financial risk taking ability of individuals, the aggregators are classified into risk neutral aggregator, risk averse aggregator and risk taking aggregator. The paper uses data from Indian Energy Exchange to produce realistic results and refers certain policies of Indian Energy Exchange to frame mathematical expressions for benefit function considering uncertainties for each type of three aggregators. Extensive results show the importance of assessing the risks involved with two unpredictable variables and possible impacts on technical and financial attributes of the microgrid energy market.
Keywords
Aggregator Demand response Financial risk Value at risk Conditional value at risk Benefit analysis1 Introduction
The dependency on the microgrid is because of it provides the potential benefits of reliability, security, efficiency and being environment friendly [1, 2]. The participation of microgrid in the centralized energy market has been increasing dramatically in recent years. With the recent advancement of smart metering technology, there is a facilitation of the bidirectional communication that enables the participants in the microgrid operators to respond actively to the electricity prices in the energy market to maximize profit by the means of controllable distributed energy sources (DESs).
High penetration of renewable energy sources (RESs) necessitates the need for a new entity to handle the complexity associated with the RES [3, 4, 5]. This new entity is called renewable energy source aggregator (RESA) under whom solar and wind power producers act as independent power producers (IPPs) and RESA procures power from them. Reference [6] presented a multiobjective dayahead and reservemarket clearing model for RESA considering the security and economic objective of minimization of cost and maximization of voltage stability. The paper did not consider the uncertainty involved with the power generated by the RES and response of the customers during a DR event. Reference [7] proposed a twostage micro RESA model while the uncertainty of RES is determined using a meanvariance model in the upperlevel realtime market and the eventdriven mechanism is used for a lower intramarket level. Reference [8] proposed optimal points of residential microgrid for maximizing the RESAs profit using design space exploration methodology. The robustness of the dayahead bidding strategy for flexible demandside resources is evaluated using multiple stochastic scenarios [9]. References [6, 7, 8, 9] considered the uncertainty but did not consider the financial risk that RESA faces during bidding in a dayahead scenario.
DR is becoming an effective tool to change consumption of customer in order to maintain the balance between generation and consumption in real time. DR can be considered as negative load (or power generation) which helps in improving the reliability and economic efficiency of the system [10, 11]. To handle the complexity in implementing DR programs, a new entity has been introduced in the electricity market, which is known as a demand response aggregator (DRA). The main role of DRA is to implement the appropriate DR program at different DR events. Another function of DRA is to reduce the scalability issue of the residential customers. The DRA aggregates the entire DR magnitudes provided by different clusters. A hierarchical market model is introduced in [12, 13], which shows the competition between the set of DRAs by considering the incentives and DR quantities. In [13], this competition is quantified with the available stored energy between the aggregators using game theory. In [14, 15, 16], optimal consumer behavior is modeled to decide the optimal portfolio of DR contracts for a DRA participating in the electricity market. The works in [12, 13, 14, 15, 16] did not consider the RESs. In [17], the authors investigated the significance of automated DR for reducing the critical pressures on electricity supply industry, reducing the need for peaking plants and better utilization of RES. In [18], an optimal operation of DRA using mixed integer linear program (MILP) is proposed with the DR portfolio considering various load curtailment and flexible load contracts as the resources for DR.
The above analyses are carried out without considering any risk. But the response of the customer in modifying their consumption pattern is not certain so there is a requirement of studying DR considering the uncertainty associated with it. DR aggregation model is introduced in [19] which has considered the different DR contract options for hourly load reduction. In this model, the uncertainty of the customers is not investigated which is necessary for a voluntary response of customers. In [20], the authors present the combined effects of DR program, wind generator and network reconfiguration on distribution network considering uncertainties involved with DR and RES. In [21], profit maximization of DRA based on stochasticity is introduced by considering the bottomup approach in the dayahead and balancing markets. In this work, the uncertainty of the customers is quantified with the participation factors. The uncertain nature of the enduser responses and market prices are the basis for finding the shortterm selfscheduling for DRA using information gap decision theory (IGDT) [22]. In [17, 18, 19, 20, 21, 22], a simplified approach for load curtailment and load recovery is considered without using proper constraints. The load recovery model requires constraints like the constraints of starting and stopping of load recovery hours and the magnitude of load that may be recovered in a specific recovery event considering the base load of customers.
Financial risk implies the uncertainty regarding the expected returns, i.e. the actual return may not be equal to the expected return. This type of risk includes the chances of losing a part or whole investment. The risk can be understood as a potential for loss, it is not exactly same as uncertainty which means the absence of certainty in getting a particular outcome. There are certain instances wherein uncertainty is inherent with respect to the forthcoming event as in the case of the speed of the wind, cloud pattern which affects solar irradiance etc. There are different indices for estimation of risk like Sharpe ratio, Sortino ratio, value at risk (VaR) and conditional value at risk (CVaR) etc. The risk assessment measures—VaR and CVaR—have been used in many papers to reduce uncertainty in different areas of research like financial portfolio management [23, 24, 25, 26, 27]. Reference [26] highlights the noncoherent nature of VaR due to lack of subadditivity property and suggest the use of CVaR to overcome this drawback. Being a convex function, CVaR can also be used in the optimization procedures. In [27, 28, 29], analytical expressions for CVaR calculation and detailed comparative analysis of risk measure of VaR are described and CVaR are discussed. The concepts of VaR and CVaR are utilized by [23, 24, 25, 26, 27, 28, 29] in the area of finance. These concepts are incorporated in this paper for assessing the financial risk involved with both forecasted uncertain power and uncertain load curtailment or load recovery.
Some works have been reported so far addressing the risk involved in monetary gain while doing the microgrid aggregator. The authors in [30] addressed the uncertainties of the load aggregators and renewable sources by using ellipsoidal model wherein the risk is based on the Euclidean distance between the profiles of offered and desirable renewable productions. In [31], the CVaR is adopted for finding the optimal hourly bids in the dayahead market for maximizing the profit of the RESA, and the DR is also integrated into the operation of microgrid aggregator in power balancing purpose in risk neutral scenario. Meanwhile, the benefit analysis on the basis of load curtailment is reported as well. In [32], the scheduling of renewable sources is done on the basis of maximization of profit considering variation of electricity prices, and the risk management is done using CVaR technique. In [33], the problem of optimal power scheduling considering DR and various alternative sources is formulated in the framework of portfolio optimization and is done by employment of Sortino ratio as the objective function. Sortino ratio is a risk measure technique used in the area of finance for the measurement of downside risk. But the limiting constraints used in the paper are only for the maximum and minimum values of variables, other constraints like start time, stop time have not been used. Again, in [30, 31, 32, 33], the proper penalty function imposed on the aggregator is not considered and the effect of load recovered during valley periods is not properly addressed in benefit estimation.
 1)
This paper utilizes the risk measure indices, VaR and CVaR, very differently for estimating the uncertain power at different confidence levels by the aggregator and assessing the risk of the estimated power in the dayahead market scenario. VaR and CVaR, are applied for estimating the net financial benefit acquired from DR and RES on the dayahead market. VaR is used in estimating the RES power and magnitude of DR or load recovery at different confidence levels. CVaR is then used to reflect the amount of power that is liable for the financial risk. This representation helps user to understand the level of risk associated with uncertain generation and DR magnitude.
 2)
Both load curtailing and shifting have been considered in the paper which includes uncertain and fixed participation of customers to consider the effect of mandatory as well as nonmandatory participation. Further, a load recovery model is designed justifying the practical constraints during the day operation.
 3)
The potential effect on economic and technical issues in microgrid operation due to the difference in subjective judgment of different RES and DRAs on severity of risk has been investigated.
The remaining paper is organized as follows. Section 2 presents the segregation of aggregators. The implementation procedure of applying VaR and CvaR with a brief on these two techniques is given in Section 3. Section 4 describes the penalty function used in the paper for power deviation. Sections 5 and 6 present the mathematical modeling of DR and the benefit function of aggregators, respectively. Results and discussion are provided in Section 7. Finally, the paper concludes in Section 8.
2 Aggregator in decentralized energy market
2.1 Segregation of aggregators
Both the aggregators mentioned above may face a financial risk due to the uncertainty of their resources. To reduce this financial risk, these aggregators work at a certain confidence level. Owing to different aggregators commit at different confidence levels, we classify the aggregators into three different types based on the psychology of aggregators. The first type is risk neutral aggregator (RNA), which tries to commit a minimum or zero risk value. This type of aggregator commits at a value where there is no loss even though it gets a very less or zero benefit. The second type is risk averse aggregator (RAA). This type of aggregator always tries to reduce the risk with the motto of gaining higher benefits, and tries to get high riskadjusted returns by taking a minimum amount of risk. The third type of aggregator is the risk taking aggregator (RTA). This type of aggregator commits at a higher risk level for getting higher benefits. By segregating aggregators on the basis of risktaking capability, the different business strategies are highlighted and thus the profit and the financial risk due to the power deviation of the aggregator are compared in this paper.
3 Introduction of VaR and CVaR
For the financial and economic analysis where uncertainty is involved, risk analysis needs to be incorporated to analyze the effect of uncertainty on the profits. Here we use the risk measures VaR and CVaR to find out the benefit of the RES and DRAs. The uncertainty studies carried out here is basically to assess uncertainties in predicting the power to be committed and further to analyze the properties of the uncertainties for the future forecast. The uncertainty in the power generated by the RES and customers response is those that are inherent and cannot be removed. These uncertainties can often be modeled by probability distribution unlike the economic uncertainty that follows Brownian motion or discrete Markov chain.
3.1 Proposed implementation of risk using VaR and CVaR
In this paper, we propose a simple method for the use of \(VaR_{\alpha }\) as a committed value of power while the \(CVaR_{\alpha}\) as the value of power during a risky scenario. This approach is simple and briefly gives the idea about the probable risk of power deviation and financial risk caused due to these power deviations from the uncertain energy source. In the dayahead market, both RES and DRAs commit for their power at different \(\alpha\). Consideration of \(\alpha\) helps in converting the uncertainty into certainty to some extent as we are certain about the probability of power being greater than or equal to \(VaR_{\alpha }\) is \(\alpha\). A number of mathematical studies on VaR and CVaR lead to a problem of a confidence level choice. In practice, the level of \(\alpha\) lies in between 0.8 and 1 where 0.8 means 20% of risk and 1 means 0% of risk or riskfree.
In the dayahead market, each RES and DRA commits for the power that it can aggregate at that hour. The generated power from DR and RES is predicted using the probability distribution function (PDF) at different hours with different \(VaR_{\alpha }\) values given in (1). Each predicted power at \(\alpha\) confidence level has some risks associated with it, i.e. the 100% − \(\alpha\) worst value of power whose value is less than the value of power at \(VaR_{\alpha }\). Now for calculation of risk we have used \(CVaR_{\alpha }\). Power at \(CVaR_{\alpha }\) is calculated using (3).
4 Deviation and penalty charge
As already mentioned, the power at corresponding VaR indicates the confidence level associated with the generation. Penalty arises if any deviation happens from generation at specific VaR. We propose to calculate the penalty on the basis of percentage deviations if the generation deviates from VaR to CVaR. The penalty formation facilitates to understand the merit of the different business strategies adopted under risky environment.
5 DRA
The DRA operates the load shifting and load curtailment programs in order to decrease the load during peak demand hours. The PRLs under load shifting program, will recover their curtailed load in valley periods through load recovery programs, but the total consumption will be less for them. The reward for these reductions is determined based on agreements between aggregator and PRL. The mathematical modeling of the DR and load recovery is given briefly in the following section.
5.1 DR modeling
The constraint (8) limits the minimum and maximum capacity of the DR at time t where \(P_{DR,t}^{ \text{min} }\) represents the minimum capacity of DR and \(P_{DR,t}^{ \text{max} }\) represents the maximum capacity of DR. This constraint would run the DR program only if the required DR is in between the limits. The constraints (9) and (10) declare that the minimum and maximum durations for k^{th} DR event. \(U_{k,i}^{DR}\) is the status of the k^{th} DR event at time i; \(R_{k,DR}^{ \text{min} }\) and \(R_{k,DR}^{ \text{max} }\) are the minimum and maximum DR reduction durations in k^{th} DR event at time t, respectively; \(S_{k,t}^{DR}\) is the load reduction at the k^{th} event that would be started at time t; and \(Q_{k,i}^{DR}\) is the stop indicator of k^{th} DR event at time i. The simultaneous functioning of start and stop indicators of the k^{th} DR event is avoided by using (11) and (12). Finally, a number of DR events in a day should not exceed its maximum number of the DR event in a day as indicated in (13). \(T_{on}^{DR}\) represents the hours when DR event takes place; \(I_{k,t}^{DR}\) is the binary variable which checks the DR initiation at time t; and \(M_{DR}^{ \text{max} }\) is the number of times that DR program can be called in a day.
5.2 Load recovery modeling
5.3 Price based on load responsive model
Price elasticity can be defined as the responsiveness of demand to the change in price. High value of elasticity signifies that load is more elastic with price. If it is unity, there is a linear change between the price and demand. In power system economics, the price of electric power is highly dependent on the amount of electricity demanded by the consumers. Therefore, the price during the peak period is very high compared to the other periods. Meanwhile, during the valley hours when the demand is low, the generating companies become price taker. DR is employed during peak hours to reduce market clearing price. While in valley periods load recovery programs for the shifted load are employed resulting MCP becomes higher during these periods.
6 Benefit framework of aggregators in electricity market
6.1 Benefit of RESA
6.2 Benefit of DRA
6.3 Algorithm for calculation of committed power for RESAs and DRAs

Step 1: Historical data of wind, solar and DR are collected.

Step 2: From the historical data, the random samples within maximum and minimum limits for hourly wind power, solar power and DR power during the DR hours are generated by using the function below.
where \(P_{s,t}^{ \text{min} }\) and \(P_{s,t}^{ \text{max} }\) are the minimum and maximum power respectively at time t for a type of resource s; f_{r} is the random function with output between 0 and 1. The number of random samples generated greatly determined the accuracy of the prediction.$$RV_{s,t} = P_{s,t}^{ \text{min} } + \left( {P_{s,t}^{ \text{max} }  P_{s,t}^{ \text{min} } } \right)f_\text{r}$$(34) 
Step 3: The random samples are sorted and the PDF is generated. Through the PDF, the power at a specific confidence levels is calculated by using \(VaR_{\alpha }\).

Step 4: The committed resource risk value is measured with \(CVaR_{\alpha }\), as given in (3).

Step 5: The benefit analysis for the power at \(\alpha\) confidence level is then done considering risk.
7 Results and discussion
Input data
Data  Value 

Solar power price (₹/kW)  2.44 
Wind power price (₹/kW)  2.65 
Incentive price for customers (₹/kW)  2.19 
Incentive price for DRA (₹/kW)  3.81 
Load recovery time (h)  7–11 
Load reduction time (h)  18–22 
Risk level of RNA (%)  5 
Risk level of RAA (%)  10 
Risk level of RTA (%)  20 
Elasticity  0.8 
The DR has been utilized to reduce the peak load which in turns helps in reducing peak prices. The reduction in demand by using DR reduces the price of the energy market because of the demand elasticity of the price. Equation (27) is used to calculate the final price due to load change during DR hours with PoE of 0.8. The risk levels of the three aggregators are also shown in Table 1. The risk level of RTA is 20% which means the confidence level is 80%. Power deviation charge for different power deviations are given in (5).
In the distribution system, RESAs and DRAs are responsible for the aggregation of the power from distributed RESs and DR. In the dayahead market, both RESA and DRAs commit for its power at different confidence levels. In the dayahead market, the RESA and DRA commit for the power that they can aggregate at that hour. The power from DR and RES is predicted here by using the PDF curves at different hours using \(VaR_{\alpha }\). The selection of \(\alpha\) depends on the audacity of the aggregator.
7.1 Benefit analysis
7.1.1 Benefit of DRA
Effect on financial attributes in presence of different DRAs
DRA  Ratio of peak price to average price  Ratio of peak price to valley price  Peak price reduction (%)  Price volatility 

RNA  1.863  2.863  9.1436  4.680 
RAA  1.860  2.852  9.3570  4.556 
RTA  1.850  2.832  10.0120  4.530 
Base case  2.022  3.080  0  5.520 
Effect on technical attributes in presence of different DRAs
DRA  Ratio of peak power to average power  Ratio of peak power to valley power  Peak power reduction (%) 

RNA  1.279003  1.639784  7.231029 
RAA  1.277520  1.608610  7.367550 
RTA  1.274800  1.486070  7.617930 
Base case  1.373789  1.808075  0 
Financial benefit of different DRAs
DRA  \(VaR_{\alpha }\) (kW)  \(CVaR_{\alpha }\) (kW)  Power deviation (kW)  D (%)  Benefit at no risk (₹)  Benefit when actual power is equal to \(CVaR_{\alpha }\) (₹)  Net financial benefit during risky scenario (₹) 

RNA  780.35  758.90  21.45  2.145059  1263.25  1229.42  1229.42 
RAA  798.78  775.93  22.84  2.284893  1302.02  1264.77  1264.77 
RTA  855.25  810.76  44.48  4.448000  1394.06  1321.55  1321.55 
7.1.2 Financial risk assessment and benefit of RESA
Financial benefit of total power generated by solar and wind IPPs for risk averse RESA
Time (hour)  \(VaR_{\alpha }\) (kW)  \(CVaR_{\alpha }\) (kW)  Power deviation (kW)  Percentage error (%)  Benefit at no risk (₹)  Benefit when actual power is equal to \(CVaR_{\alpha }\) (₹)  Penalty rate applied (₹)  Total penalty (₹)  Net financial benefit during risky scenario (₹) 

0  467.63  280.93  186.70  6.220  344.300  206.84300  0  0  206.840 
1  273.36  149.43  123.92  4.130  156.880  85.76014  0  0  85.760 
2  171.84  90.05  81.78  2.720  − 25.410  − 13.32110  0  0  − 13.320 
3  338.80  155.90  182.89  6.090  150.180  69.10780  0  0  69.100 
4  485.08  230.45  254.62  8.480  305.730  145.25170  0  0  145.250 
5  293.10  165.75  127.35  4.240  176.410  99.76432  0  0  99.760 
6  485.89  253.78  232.11  7.730  281.880  146.15170  0  0  146.150 
7  1136.11  717.26  418.84  13.960  − 435.454  − 251.33400  0  0  − 251.334 
8  1383.11  900.65  482.46  16.080  15.490  28.94260  0.5  241.2319  − 212.289 
9  1301.01  956.14  344.86  11.490  752.040  568.43700  0  0  568.430 
10  968.88  650.22  318.66  10.620  864.690  589.66160  0  0  589.660 
11  878.66  595.65  283.00  9.433  917.580  630.82570  0  0  630.820 
12  604.53  359.43  245.09  8.169  523.590  313.99890  0  0  313.990 
13  626.13  381.13  244.99  8.160  593.140  364.26000  0  0  364.260 
14  637.05  453.85  183.19  6.100  638.590  465.01900  0  0  465.010 
15  644.42  462.09  182.32  6.070  638.250  471.24720  0  0  471.240 
16  627.68  340.28  287.40  9.580  374.220  208.71730  0  0  208.710 
17  556.12  278.96  277.15  9.230  247.900  124.35120  0  0  124.350 
18  302.46  166.16  136.30  4.540  1534.052  842.09180  0  0  842.090 
19  311.09  143.20  167.89  5.590  1433.983  660.10190  0  0  660.100 
20  411.90  185.34  226.55  7.550  1515.274  681.85010  0  0  681.850 
21  527.60  205.72  321.87  10.720  1509.680  588.67150  0  0  588.670 
22  897.68  443.52  454.16  15.130  1324.073  654.18900  0.5  227.0809  427.100 
23  886.34  449.82  436.51  14.550  962.720  488.59420  0  0  488.590 
Total  7700.860 
Comparison of net financial benefit and penalty of solar and wind IPPs with RESA
Type of IPP  Type of aggregator  \(VaR_{\alpha }\) (kW)  \(CVaR_{\alpha }\) (kW)  Penalty (₹)  Net financial benefit (₹) 

Solar IPP  Risk neutral  3299.073  2657.096  77.46568  2579.030 
Risk taking  4039.190  2936.606  421.58370  2515.022  
Risk averse  4423.170  3202.170  502.30070  2699.872  
Wind IPP  Risk neutral  5629.970  2796.110  151.35000  2644.760 
Risk averse  10760.680  5232.570  1123.14600  4109.430  
Risk taking  21886.820  10894.700  7033.69400  3861.020  
RESA  Risk neutral  8929.042  5453.200  0  5453.200 
Risk averse  14799.870  8169.180  468.31200  7700.869  
Risk taking  26310.000  14096.890  3597.91000  10498.980 
8 Conclusion
The paper investigates the impact on financial and technical attributes in microgrid operation due to financial risk taking behavior of the market players. DRA and RESA are considered as market players and they have been divided into three types in order to represent the diverse nature of risk taking ability of individuals. Monte Carlo method is used for the creating different scenarios on the basis of probable hourly DR magnitudes and RES powers. These scenarios are utilized to generate PDFs for each hour of the day. The paper introduces a new way of utilizing VaR and CVaR, to distinguish the audacity of different types of aggregators. In order to integrate the downside risk for deciding the magnitude of DR at different DR events, the load curtailment, load shifting and load recovery models have been modified accordingly. A benefit function has been developed to incorporate the uncertainty of the power generated by DR and RES considering the penalty function following in India for power deviations. An extensive result using the data taken from Indian Energy Exchange is given to justify the proposed work. It is demonstrated that the volatility of price reduces when the market players become more risk taking. Results also show that risk taking market players help to further flatten the load profile of the system which enhances the efficiency of the market operation however the higher risk takers may face a loss instead of making a profit at the same time. The authors are now working on finding the best confidence level for each type of aggregators considering both dayahead and balancing market scenarios.
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