# The Role of Demand Response Aggregators and the Effect of GenCos Strategic Bidding on the Flexibility of Demand

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

_{k}− 1}, is a time period, and assume that the number of time interval T

_{k}satisfies T

_{k}= 24/k (k = 1 h duration interval). Therefore, the set, $\mathbb{T}$, has 24 components. The proposed market model can be framed as a bi-level programming problem given by Equations (1)–(16). Equations (1)–(10) and (11)–(16), respectively, represent the upper-level and lower-level problems.

#### 2.1. SCED’s Problem at Upper-Level

_{b}buses, and N

_{l}transmission lines are considered [25]. In the model, $\mathcal{N}$

_{𝒷}is the set of busses and $\mathcal{N}$

_{𝓁}the sets of the transmission lines, respectively. Further, define $\mathcal{N}$

_{ℊ}:= {1, 2,…, N

_{g}} is the set for the generation companies. The demand at the ith bus is denoted by D

_{i},∀i ∈ $\mathcal{N}$

_{𝒷}. The operation cost in (1) consists of two terms. The first term, c

_{n}$(P{g}_{nk}^{}$), refers to the offers cost of the generation $P{g}_{nk}^{}$ units. The second term, ${\lambda}_{mk}^{d},$ refers to the demand reduction cost for the ${d}_{mk}^{}$ is for the DR amount provided by aggregator m in time k. The equality constraint (2) represents the grid wise supply-demand balance. The first term on the right-hand side of this constraint is a DR regulating factor. The B

_{b}is for the bus admittance matrix. The term, (ϑ

_{ik}− ϑ

_{jk}), is for the voltage phase angles. Representing x

_{ij}for the reactance of the transmission line from the bus i and j, the diagonal element of the B

_{b}is the sum of all 1/x

_{ij}. The off-diagonal element of the B

_{b}is equal to the negative of 1/x

_{ij}, between the bus i and j. The power flow in the lines connecting the bus i and j are represented by Equation (3). The details refer to [25,45,46]. The transmission line and generation supply limits are provided in Equations (4)–(6), respectively. The associated dual variables contracting to the constraints are presented by the double-headed arrow. The ramping rate constraints are given in Equation (6). The constraint Equation (7) imposes voltage phase angle limits. The nonzero decision variables in Equation (10) are found by solving the lower-level DRX optimization model.

#### 2.2. DRX’s Problem at Lower-Level

_{𝒶}: = {1, 2, …, N

_{a}} and $\mathcal{N}$

_{𝓇}: = {1, 2, …, N

_{r}}, corresponding for the DR aggregator and DR purchaser (as see Figure 2). The DR buyers are simplified as those price-sensitive load buses where the unit load reduction save more operation cost.

_{a}and A

_{r}. For three aggregators (N

_{a}= 3) and two buyers, (N

_{r}= 2), the matrices, A

**and A**

_{a}**, in Equation (14), take the arrangement as shown in Figure 2.**

_{r}_{a}and A

_{r}is equal to the number of aggregators and buyers, respectively. It is assumed the aggregator can sell the DR to several buyers, and each of the DR buyers can buy the DR from several aggregators. The total number of possible deals between the DR buyer and aggregators denote the number of columns of the A matrix. Any DR quantity, d

_{mj}(d

_{mj}> 0), associated with arc, (m, j) ∈ A, represent the DR transaction from the aggregator node, m ∈ $\mathcal{N}$

_{𝒶}, to the DR buyer node, j ∈ $\mathcal{N}$

_{𝓇}. The objective function (13) specifies the DR resource cost function (s

_{m,,u}) of the end-user customer, u, under the aggregator, m. The bidding price rises with the growing level DR as represented by:

_{m}, is the aggregator’s bidding factor, which is used to characterize aggregator price-taking behaviour [26]. The lower the ω

_{m}value; the lesser is the price escalation and vice versa. The ω

_{m}value can be determined by tracking the LMPs and end-user’s consumption flexibility [47]. The quadratic (α

_{m}) and linear (β

_{m}) coefficient terms are assumed to be unity. The Γ

_{u}, ∀i is called end-user type, which takes values between 0 and 1. The non-negativity of type value scales user wiliness to adjust compensation price [48,49,50]. At a higher value of Γ

_{u}, users are likely to waive compensation for the equal quantity of DR. This intern reduces the DR transaction cost.

_{mj}(also called primal variable), of length, N

_{a}× N

_{r}, the objective function (11) returns a scalar DR transaction cost. The constraint (10) specifies the sum of DR from all aggregators is equal to the total DR provided to DR buses. The coupling constraint (12) refers to the summation of the DR from all the DR buses is as large as the DR limits imposed by the operator.

_{w}(χ

_{w}∈ R), introduced in the upper-level is a regulation parameter for the DR level settings, which limits load demand, D

_{i}

_{,}at a power system bus, i, i ∈ $\mathcal{N}$

_{𝒷}. Based on the exogenous variables, such as the adjustment required for the renewables, the total DR from the reference consumption is to be increased or decreased.

^{th}step Ψ

_{nk}: = [Pg

_{1k}, Pg

_{2k}, …, Pg

_{Ngk}]’ to represent the generation profile. Define further dispatch decisions considering the DR are Ψ

_{nk}

^{DR}: = [Pg

_{1k}

^{DR}, Pg

_{2k}

^{DR}, …, Pg

_{Ngk}

^{DR}]’ accordingly. Where the Ψ

_{nk}to Ψ

_{nk}

^{DR}, respectively, denote generation without and with DR, respectively. The aggregator’s profit (0 < R

_{m}, ∀m) is the difference of a percentage of total cost saving due to the DR and the compensation given to the end-user customers.

^{S}

_{nk}(Ψ

_{nk}) and λ

^{S}

_{nk}(Ψ

_{nk}

^{DR}) are the LMP without and with the DR, respectively. The term in the bracket in Equation (18) corresponds to the total LMP reduction. The term, α

_{m}, is for a percentage of monetary reward; aggregator obtains from the operator. The term, γ

_{m}, equals to unity reflect the aggregator gets paid at a rate of the LMP. The γ

_{m}> 1 means the payment is made at a rate that is higher than the LMP. This indirectly subsidizes the end-user to increase the incremental curtailment. The γ

_{m}< 1 refers a partial amount of the LMP is given to limit the DR trading.

_{n}Pg

_{n}+ b

_{n}, where Pg

_{n}is the generation output of unit n, and a

_{n}, b

_{n}are the cost coefficients. It is customary to submit generation blocks, q > 0, ∀q ∈{1, 2, 3, …, Q}; the seller wants to sell at a price, constitute stepwise price-generation block pair expressed by:

^{th}time step. Table 1 shows the cost coefficients and the generation limit values [26].

_{n}) as shown in Figure 3. The GenCo manipulate α

_{n}to increase its revenue when the system load level changes from one critical load level to another.

## 3. System Model

_{1}and G

_{2}at Bus#1, G

_{5}at Bus#5); two high-cost generation units (G

_{3}at Bus#3, G

_{4}at Bus#4); and the aggregated loads (D

_{2}, D

_{3}, and D

_{4,}at Bus#2, #3, and #4 respectively). The PJM is a regional electric power trading pool market that dispatches the generation and coordinates’ day-ahead capacity and real-time balancing market. It determines the LMP and the generation supply share considering bid-based pricing in a competitive manner. The LMP represents the value of the electricity at the specific location. In the day-ahead capacity market, hourly LMP is determined based on forecasted loads for each hour of the following day. The over or under-estimated loads are adjusted in the real-time balancing market. The test system data, such as generation limits [53] and transmission line parameters [47], are listed in Table 1. The offer prices for all the possible capacities are given in Table 2. The colored numbers in 7

^{th}coloumn are the marginal cost (strategic pursuit to achieve higher profit) to the G

_{1}and G

_{4}to deliver an additional unit of electricity at a specific location of the system. The line data, generation capacity, and load demand are at a base of 100 MVA. The upper bound of each aggregator and the DR bidding price for the users under each aggregator are provided in Table 3. The EMO collects the supply offer bid and the load demand data. Further, it settles the generation supply share and the LMP. The LMP also was known as the marginal cost to the EMO to deliver an additional unit of electricity at a specific location of a power system. The LMPs ($/MWh) are Lagrangian multipliers determined at the upper-level. The solution of the model assigns the required system load demand among the generation units in such a way that minimized the operation cost.

## 4. Numerical Result

**Case#1**discusses the congestion-free and congested conditions and the identification of the critical load buses.

**Case#2**discusses the competitive bidding (offering bids at a true marginal price) by GenCos and its impact on LMP and the aggregator’s payoff.

**Case#3**discusses the strategic bidding (includes a rebidding at higher price and generation capacity withholding when the system load demands exceed crucial load levels) and its impact at the lower-level market clearing.

#### 4.1. Case#1 (Sensitivity Analysis)

_{1}, G

_{2}, G

_{3}, and G

_{5}, provide 1.10, 1.00, 0.90, and 6.00 p.u., respectively. The expensive unit, G

_{4}, does not get dispatched in this instance. Non-zero Lagrange multipliers of value $16.58/MWh and $10.83/MWh are found at the Bus#1 and the Bus#5 as generators G

_{1}, G

_{2}, and G

_{5}hit their upper limits, respectively. The results are summarized in Table 4.

_{3}increases from 0.90 to 4.06 p.u., while the G

_{5}reduces from 6.00 to 2.84 p.u. The non-zero Lagrangian multipliers due to hitting the upper limits of G

_{5}are now zero as they are within their limits. The upper limit multipliers for the G

_{1}and G

_{2}still exist. The transmission line constraint allowed the G

_{3}to increase its output and does not hit its upper limit anymore.

#### 4.2. Case#2 (Competitive Bidding)

**Operation Cost and LMPs**

**:**The market model is simulated twice, without and with a DRX mechanism, to quantify the benefits of reduced LMP and operating cost. The operation cost without a DRX is determined to be k$747.49 and an average (over a day) LMP at Bus#4 is found to be $56.49/MWh. The reduction of the LMP ($49.14/MWh LMP at Bus#4) and the operation cost (k$724.16) is evident even with a modest amount of incremental DR (1.95%) for few hours. The effect of different levels of DR on the operating cost with, without DRX transaction cost, is summarized in Table 5 and Figure 5. The operation cost without considering DRX gradually decreases due to serving a reduced load demand. It is interesting to note that with DRX, the operation cost reduces with the DR up to 15.28% and increases for any further increase in DR levels. This is because, at higher DR levels, the DR transaction cost outweighs savings from the reduction in the market clearing cost (the DR transaction cost and the DR amount among the aggregators and users are the decision variables determined by solving the market at the lower-level). The DR transaction cost is reasonably small for up to 12.94% DR and increases sharply beyond it. The DR transaction cost progressively increases with the increasing level of DR. A larger value of DR yields a higher selling revenue for the DRX participants. The DR transaction cost at the lower-level equivalently provides monetary benefit for the end-user customers. The end-user proportionately shares this based on the disutility price they offered. However, the increased DR transaction cost exceeds the overall operation cost provide an argument for limiting the DR payments to periods when the LMP are likely to exceed a specific threshold. The emission without DRX was 19,077 ton a day. With 1.95% and 5.92% DR, the emission reduced to 18,806 and 18,167 ton, respectively. A 1.42% and 6.88% emission, respectively, reduces in each day.

_{5}get paid as its bid. These values are almost the same irrespective of the DR level. At Bus#2, #3, and #4, the LMPs of the peak demand period are responsive to the incremental DR level. The peak hour LMP at Bus#4, without DR, is found to be $82.67, which reduces to $67.45 at 10.60% DR. At Bus#3, those values are $80.85 and $66.10. At Bus#2, the LMPs are $75.86 and $62.40. Increasing the DR level decreases the peak hour durations. With a DR level of up to 5.92%, the duration of the LMP spike reduces to 4 h in a day and is further reduced to only 3 h for DR level of 8.26% and can be totally avoided with the DR level of 10.60%.

**Aggregators’ Payoff**

**:**The lower-level model allows the aggregators to participate in the DR exchange in the same way that supply-side Genco’s bid into day-ahead electricity markets. The proposed DRX integrated market clearing model promotes the true market value of DR in daily scheduling intervals. Figure 7 illustrates the aggregators’ payoff with different incremental DR levels and Table 7 presents the DR amount supplied by the aggregators. The aggregator’s payoff not only depends on the amount of DR traded, but also on the LMP. The aggregator payoff is a difference of the DR selling revenue at LMP, and the compensation provided to end-users and is determined using Equation (18). Assuming, the reward scale factor, γ

_{m}, as unity, with a 1.95% DR, the aggregator, A

_{1}, A

_{2}, and A

_{3}, earn k$15.15, k$13.74, and k$14.41, offering the DR amounts of 2.69, 2.66, and 2.66, respectively, in the DR trading period in a day. Irrespective of the equal DR provided by both the J

_{2}and J

_{3}, the payoff difference happens due to different compensation price among the user group. The payoff rises and becomes maximum at the 8.26% DR level. After a 12.94% DR, a payoff reduction is observed, because of the decrease in the LMP and increase in the rate of compensation price. At the 15.28% DR level, A

_{1}becomes marginally profitable and both A

_{2}, A

_{3}outweigh compensation paid to the end-users than the LMP at which the A

_{2}and A

_{3}get paid. For any DR levels greater than 17.72%, all the aggregators lose. The polynomial fit (second order) of the payoff is also shown in the figure. As observed, with the increasing DR level, the payoff increases, reaches a maximum value, then decreases before finally becoming zero, at which point, the EMO also loses. Until such a critical DR level, the DR payoff resulting from new revenue generation driven by DRX market is considerable.

**DR and Compensation Share among the End-Users**

**:**In the proposed model, aggregators compensate the users for the DR that they provide. The transaction cost and compensation price are determined in DRX markets. The magnitude of possible DR transaction cost depends on how much the users can afford and the marginal disutility price. Figure 8 shows a disutility price for different user groups. Three types/groups of users under each aggregator are considered. The disutility price for user group, U

_{1,}under the aggregator, A

_{1}, is the stepper. The DR price is smallest for the U

_{1}, while it is highest for the U

_{3}. The user, U

_{1}, under the A

_{2}has minimum disutility ($21.71), while a maximum for the group, U

_{3}($26.43). The offer price for the U

_{1}under aggregator, A

_{3}, is $19.2. The price for the rest of the two group, U

_{2}and U

_{3}, is around $24.60. The aggregator, A

_{1}, has a maximum DR supply capacity of 2 p.u. and A

_{2}and A

_{3}whereas having the capacity of 1.75 p.u. The end-users get paid by the aggregator at a compensation price, which is a dual multiplier associated with Equation (12) of the lower-level problem. Due to receiving compensation (payback), the users reduce the energy consumption cost. However, from the EMO perspective, the DR benefit can be obtained if the operation cost reduction at the upper-level does not outweigh the compensation given to the end-users at the lower-level. This possibly occurs when the DR demand rises significantly higher if the user seeks higher compensation. Multiplying the DR price with the allocated DR is regarded as overall DR compensation benefit for the users.

_{2}, under the aggregators do not provide any DR amount. From 10.60 to 15.28% DR; both the U

_{1}and U

_{2}deliver with a varying amount. At a 17.62% DR and onward, all the user group under the aggregator, A

_{3}, contribute to supply.

_{1}, while for the A

_{2}and A

_{3}, DR transaction is profitable. Now, if the LMP scaled parameter, γ

_{m}, is increased, then the payoff margin also increases to transact higher amount of DR, provided end-users kept their compensation price fixed.

**Generation Dispatch**

**Share:**The solution of the upper-level economic market clearing problem finds the optimal generation dispatch. The G

_{1}, G

_{2,}and G

_{5}bid a lower price than others. In the market clearing model, the generation units’ output is arranged according to the transmission security and economy-based merit order. Figure 10, Figure 11 and Figure 12 compare the optimal generation dispatch without and with DRX (with two different DR level), respectively. Without DRX, the generation unit, G

_{1}and G

_{2}, are at their maximum capacity, while the G

_{3}and G

_{4}change within its generation limits across the scheduling hour (as in Figure 10). The amount supplied by G

_{5}is restricted by line capacity constraint, thereby, most of the time, its output changes around 2.85 p.u. The dotted line in red colour indicates the total load demand served by all the generators.

_{4}is not dispatched at hours 7 am to 9 am as peak loads are curtailed. The G

_{4}dispatches a few hours around evening peak. Further, in Figure 12, with 5.92% DR, the G

_{4}only dispatches around evening peak periods. Such dispatch results are economical, since the most expensive unit got restriction. The reduced dispatch of G

_{4}is compensated mainly by the second least expensive unit, G

_{3}, to meet the load.

#### 4.3. Case#3 (Strategic Bidding)

**Scenario#1**: The unit, G

_{3}, bids $83.85 instead of $66.10 in the hour 7 pm, 8 pm, and 9 pm. The unit, G

_{4}, and others bid as completive.

**Scenario#2**: The unit, G

_{4}, bids $103.92 instead of $82.67 in those hours indicated in

**Scenario#1**. The unit, G

_{3}, and others bid as completive.

**Scenario#3:**Both the G

_{3}and G

_{4}bid simultaneously with the new offer price, while others bid as completive.

_{3}only, the unit G

_{4}only, and both the G

_{3}and G

_{4}simultaneously. The rest of the conditions, like loading level, transmission constraints, and the capacity of the rest of the units, are the same. The impact on dispatch share, LMPs, and operation cost are investigated.

_{3}is strategic, the operation cost rises to k$764.99. In Scenario#2 and #3, the cost is k$753.61 and k$772.08, respectively. The relative decrease in operating cost compared to the competitive case found to be maximum at Scenario#3 is 3.69%.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\mathcal{N}$_{𝒶}: m, N_{a} | set, index, number of aggregators |

$\mathcal{N}$_{𝓇}, j, N_{r} | set, index and number of DR buyer |

$\mathcal{N}$_{𝓁}, N_{g} | number and set of generation companies (GenCos) |

$\mathcal{N}$_{ℊ}, i, N_{b} | set, index and number of power system buses |

$\mathcal{N}$_{𝒷}, l, N_{l} | set, index and number of transmission lines |

B_{b} | matrix of dimension N_{b} ×N_{b} for admittance |

ϑ_{ik} | voltage angle at bus i in time k |

α_{m}, β_{m} | DR offer cost coefficient for aggregator |

ω_{m} ∈ (0 ~ 1) | aggregator bidding parameter/end-user type |

a_{n}, b_{n} | cost-coefficient for the GenCos n ∈ $\mathcal{N}$_{𝓁} |

Δd_{mj} | ramp-down limit of the DR provided by m ∈ $\mathcal{N}$_{𝒶} |

${d}_{mk}^{\ast}$ | DR amount provided by aggregator m |

${d}_{mk}^{max},\text{}{d}_{mk}^{min}$ | limit of DR provided by aggregator m |

$P{g}_{nk}^{max},P{g}_{nk}^{min}$ | limit of generation amount provided by GenCo |

${F}_{ij}^{k}$ | power flow from the bus i to j |

${F}_{ij}^{max},-{F}_{ij}^{max}$ | line maximum capacity limit between the bus i and j |

${R}_{n}^{dn}$ | ramp-down limit of generator |

${R}_{n}^{up}$ | ramp-up limit of generator n |

D_{ik} | load demand at power system bus i |

d_{mj} | DR sells by aggregator |

${\lambda}_{jk}^{D}$ | Lagrangian multipliers of upper-level problem |

${\lambda}_{mk}^{d}$ | Lagrangian multipliers of lower-level problem |

χ_{w} ∈ R | the DR tunng parameter to deal wind-generated power variability |

c_{n}$(P{g}_{nk}^{}$) | cost of the GenCos, n |

s_{m,u}($\xb7$) | aggregated DR selling offer cost of m |

${\mathsf{\Psi}}_{nk}^{D}\left({\mathsf{\Psi}}_{nk}\right)$ | LMP without DR at bus n, in time k [$/MWh] |

${\lambda}_{nk}^{D}\left({\mathsf{\Psi}}_{nk}^{DR}\right)$ | LMP with DR at bus n, in time k [$/MWh] |

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**Figure 2.**The DR transaction mechanism, (

**a**) a trading network presenting two DR procuring points (N

_{r}= 2) and three aggregators (N

_{a}= 3); (

**b**) a segmentation of the

**A**matrix indicating the DR aggregator node, N

_{a}, and the DR procuring node, N

_{r}.

**Figure 4.**The 5-Bus PJM power network with aggregated loads are at Bus#2 and #3 and Bus#4. The line supply data are provided in Table 1.

**Figure 10.**Generation dispatch mix among the units without DRX assuming no elasticity to the demand.

**Figure 11.**Generation dispatch mix in the DRX integrated market clearing with 1.95% DR participation.

**Figure 12.**Generation dispatch mix in the DRX integrated market clearing with 5.92% DR participation.

Gen (Fuel type) | Capacity Limits[P_{n}^{min} P_{n}^{max} ] (p.u.) | Carbon Emissions (kgCO_{2}/kWh) [54] | |||
---|---|---|---|---|---|

G_{1} (Coal), Bus#1 | [0.25, 1.10] | 0.940 | |||

G_{2} (Diesel), Bus#1 | [0.25, 1.00] | 0.778 | |||

G_{3} (Coal), Bus#3 | [1.50, 5.20] | 0.940 | |||

G_{4} (Gas), Bus#4 | [0.50, 3.00] | 0.581 | |||

G_{5} (Coal), Bus#5 | [2.25, 6.00] | 0.940 | |||

Transmission Lines and Load Data | |||||

From Bus i | To Bus j | Reactance (x_{ij}) | Capacity Limit [F_{ij}^{min} F_{ij}^{max}] | Load Demand D_{i} (p.u.) | |

1 | 2 | 2.81 | [−8.75, 8.75] | Bus#2 = 3.00 | |

2 | 3 | 1.08 | [−8.75, 8.75] | Bus#3 = 3.00 | |

4 | 3 | 2.97 | [−8.75, 8.75] | Bus#4 = 3.00 | |

5 | 4 | 2.97 | [−8.75, 2.40] | ||

5 | 1 | 0.64 | [−8.75, 8.75] | ||

1 | 4 | 3.04 | [−8.75, 8.75] |

Gen | Block | Generation Supply Offer Price | ||||
---|---|---|---|---|---|---|

[a_{n}, b_{n}] | Size | [1st Block] | [2nd Block] | [3rd Block] | [4th Block] | [5th Block] |

($/MWh, $/MWh^{2}) | (MWh) | |||||

G_{1} [0.115, 11.50] | 50.00 | 11.61, 0.5 | 17.36, 1.1 | 23.11 | 28.86 | 34.61 |

G_{2} [0.115, 11.50] | 50.00 | 11.61, 0.5 | 17.36, 1.0 | 23.11 | 28.86 | 34.61 |

G_{3} [0.355, 12.50] | 100.0 | 12.85, 1.0 | 30.60, 2.0 | 48.35, 3.0 | 66.10, 4.0 | 83.85, 5.0 |

G_{4} [0.425, 18.50] | 60.00 | 18.92, 0.6 | 40.17, 1.2 | 61.42, 1.8 | 82.67, 2.4 | 103.92, 3.0 |

G_{5} [0.265, 10.50] | 120.0 | 10.76, 1.2 | 24.01, 2.4 | 37.26,3.6 | 50.51, 4.8 | 63.76, 6.0 |

Aggregator | Capacity | DR Cost Coefficients | The DR Offer Price Segments for the User Group at ω_{m} = 1 | |||
---|---|---|---|---|---|---|

d_{max} | α_{m} | β_{m} | U_{1} | U_{2} | U_{3} | |

A_{1} | 1.90 | 0485 | 12.15 | 16.97 | 23.06 | 27.42 |

A_{2} | 1.70 | 0.092 | 10.35 | 21.71 | 24.72 | 26.43 |

A_{3} | 1.70 | 0.068 | 11.05 | 19.20 | 24.65 | 24.66 |

The bidding parameter, ω_{m} in Equation (18), is varied from 1:5.50 with a different increment to rescaled price coefficient, α_{m} and β_{m}, for the different DR levels. |

**Table 4.**The generator output and the LMPs to serve load {D

_{2}, D

_{3}, D

_{4}} = {3.00, 3.00, 3.00} p.u.

Scenarios | {G_{1}, G_{2}, G_{3,} G_{4,} G_{5}} | LMP_{Bus # i} {λ_{i}} ($/MWh) | Total Cost (k$) |
---|---|---|---|

Without Line Constraints | {1.10, 1.00, 0.90, 0.00, 6.00} | {30.17, 30.17, 30.17, 30.17, 30.17} | 12.22 |

Line 5–4 is Constrained | {1.10, 1.00, 4.06, 0.00, 2.84} | {28.19, 28.86, 30.60, 31.23, 10.60} | 18.48 |

ΔD_{2} = ±0.01 p.u. | {1.10, 1.00, 4.05 ± 0.01, 0.00, 2.84} | ±$28.86 | |

ΔD_{3} = ±0.01 p.u. | {1.10, 1.00, 4.05 ± 0.01, 0.00, 2.84} | ±$30.60 | |

ΔD_{4} = ±0.01 p.u. | {1.10, 1.00, 4.05 ± 0.01, 0.00, 2.84} | ±$31.23 |

DR (p.u.) | Base Demand (p.u.) | DR (%) | Operation Cost with DRX (k$) | Operation Cost w/o DRX (k$) | DR Transaction Cost (k$) | Net Emissions (tonCO_{2}) |
---|---|---|---|---|---|---|

0 | 202.26 | 0 | 747.49 | 747.49 | 0 | 19077 |

4.02 | 198.18 | 1.95 | 724.16 | 716.41 | 7.75 | 18806 |

12.21 | 194.08 | 5.92 | 686.31 | 656.96 | 29.34 | 18167 |

17.03 | 189.25 | 8.26 | 672.61 | 623.84 | 48.76 | 17764 |

21.86 | 184.42 | 10.60 | 679.22 | 591.78 | 74.32 | 17335 |

26.69 | 179.59 | 12.94 | 687.10 | 560.78 | 107.28 | 16881 |

31.52 | 174.76 | 15.28 | 734.44 | 529.78 | 178.48 | 16427 |

36.35 | 169.94 | 17.72 | 802.55 | 498.79 | 266.92 | 15974 |

39.96 | 166.32 | 19.37 | 909.64 | 475.36 | 382.34 | 15634 |

43.57 | 162.71 | 21.21 | 1040.62 | 451.93 | 516.08 | 15294 |

The DR Amount | Average LMP ($/MWh) | ||||
---|---|---|---|---|---|

% DR | Bus#1 | Bus#2 | Bus#3 | Bus#4 | Bus#5 |

0 | 50.51 | 51.82 | 55.25 | 56.49 | 16.28 |

1.95 | 47.92 | 49.14 | 52.30 | 53.46 | 16.28 |

5.92 | 46.30 | 47.45 | 50.46 | 51.55 | 16.28 |

8.26 | 45.76 | 46.89 | 49.85 | 50.92 | 16.28 |

10.60 | 44.14 | 45.21 | 48.00 | 49.01 | 16.28 |

12.94 | 44.14 | 45.21 | 48.00 | 49.01 | 16.28 |

15.28 | 44.14 | 45.21 | 48.00 | 49.01 | 16.28 |

17.72 | 44.14 | 45.21 | 48.00 | 49.01 | 16.28 |

19.37 | 44.14 | 45.21 | 48.00 | 49.01 | 16.28 |

21.21 | 44.14 | 45.21 | 48.00 | 49.01 | 16.28 |

The DR amount | DR (p.u.) Provided by the Aggregators | The Payoff (k$) Achieved by the Aggregators | ||||
---|---|---|---|---|---|---|

% DR | J1 | J2 | J3 | J1 | J2 | J3 |

1.95 | 2.69 | 2.66 | 2.66 | 15.15 | 13.75 | 14.41 |

5.92 | 4.27 | 3.97 | 3.97 | 23.05 | 19.35 | 20.59 |

8.26 | 6.70 | 5.17 | 5.17 | 26.09 | 17.33 | 19.27 |

10.60 | 8.99 | 6.43 | 6.44 | 22.93 | 15.89 | 16.19 |

12.94 | 11.56 | 7.57 | 7.57 | 26.37 | 15.98 | 16.09 |

15.28 | 13.98 | 8.77 | 8.77 | 2.92 | −1.65 | −1.47 |

The DR Amount | Aggregator, A1 | Aggregator, A2 | Aggregator, A3 | ||||||
---|---|---|---|---|---|---|---|---|---|

% DR | U1 (k$) | U2(k$) | U3(k$) | U1(k$) | U2(k$) | U3(k$) | U1(k$) | U2(k$) | U3 (k$) |

1.95 | 2.31 | 0 | 0 | 2.88 | 0 | 0 | 2.553 | 0 | 0 |

5.92 | 9.06 | 0 | 0 | 10.76 | 0 | 0 | 9.519 | 0 | 0 |

8.26 | 17.05 | 0 | 0 | 16.82 | 0 | 0 | 14.88 | 0 | 0 |

10.60 | 30.14 | 4.28 | 0 | 25.37 | 1.23 | 0 | 23.22 | 1.22 | 0 |

12.94 | 36.84 | 14.75 | 0 | 30.82 | 6.59 | 0 | 30.73 | 6.57 | 0 |

15.28 | 52.66 | 32.97 | 0 | 42.37 | 17.22 | 0 | 42.25 | 17.17 | 0 |

17.62 | 71.33 | 55.01 | 0 | 53.93 | 32.29 | 0 | 53.78 | 36.46 | 0.943 |

19.37 | 95.62 | 76.20 | 0 | 69.33 | 52.65 | 0 | 69.15 | 60.34 | 10.98 |

21.21 | 121.28 | 96.33 | 0 | 86.88 | 76.94 | 10331 | 84.54 | 82.37 | 30.01 |

All GenCos Competitive (Case#2) | The G3 Strategic (Scenario#1) | The G4 Strategic (Scenario#2) | The G3, G4 Both Strategic (Scenario#3) | |
---|---|---|---|---|

Aggregator’s Payoff ($) without DR | 0 | 0 | 0 | 0 |

Aggregator’s Payoff (k$) with 5.92% DR | {23.05, 19.35, 20.59} | {23.42,19.70, 20.95, | {21.69, 18.06, 19.31} | {24.72, 20.94, 22.18} |

Aggregator’s Payoff (k$) with 8.26% DR | {26.09, 17.32, 19.27} | {23.42, 19.70, 20.94} | {30.16, 20.72, 22.67} | {32.22, 22.43, 24.37} |

Total Payoff with 5.92% DR | 62.99 | 64.07 | 59.07 | 67.84 |

Total Payoff with 8.26% DR | 62.69 | 73.86 | 73.56 | 79.01 |

Relative payoff variation with 5.92% DR | (64.07 – 62.69) = 2.20 | (59.07 − 62.99) = −6.22 | (67.84 − 62.99) = 7.69 | |

Relative payoff variation with 8.26% DR | (73.86 − 62.99) = 17.33 | (73.56 − 62.69) = 17.33 | (79.01 − 62.69) = 26.03 |

All GenCos Competitive (Case#2) | The G3 Strategic (Scenario#1) | The G4 Strategic (Scenario#2) | The G3, G4 Strategic (Scenario#3) | |
---|---|---|---|---|

Operation cost (k$) without DR | 747.49 | 772.07 | 753.61 | 764.99 |

Operation cost (k$) with 5.92% DR | 686.31 | 706.04 | 687.97 | 711.65 |

Operation cost (k$) with 8.26% DR | 672.60 | 690.65 | 681.31 | 697.08 |

Relative increase (%) in cost at 5.92% DR | 2.87 | 0.24 | 3.69 | |

Relative increase (%) in cost at 8.26% DR | 2.68 | 1.29 | 3.64 | |

Average LMP ($/MWh) in Bus#4 without DR | 54.72 | 54.98 | 56.49 | 56.49 |

Average LMP ($/MWh) in Bus#4 at 5.92% DR | 51.55 | 51.94 | 53.32 | 53.32 |

Average LMP ($/MWh) in Bus#4 at 8.26% DR | 50.92 | 51.94 | 52.57 | 52.57 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mohammad, N.; Mishra, Y. The Role of Demand Response Aggregators and the Effect of GenCos Strategic Bidding on the Flexibility of Demand. *Energies* **2018**, *11*, 3296.
https://doi.org/10.3390/en11123296

**AMA Style**

Mohammad N, Mishra Y. The Role of Demand Response Aggregators and the Effect of GenCos Strategic Bidding on the Flexibility of Demand. *Energies*. 2018; 11(12):3296.
https://doi.org/10.3390/en11123296

**Chicago/Turabian Style**

Mohammad, Nur, and Yateendra Mishra. 2018. "The Role of Demand Response Aggregators and the Effect of GenCos Strategic Bidding on the Flexibility of Demand" *Energies* 11, no. 12: 3296.
https://doi.org/10.3390/en11123296