Optimal power dispatch for day-ahead power system operation considering demand elasticity

ABSTRACT

: The voltage angle between bus i and bus j at hour h

INTRODUCTION
Nowadays, the power system operation has created several techniques for increasing the marketbased energy efficiency of electric infrastructure.Demand response (DR) is one of the effective tools for balancing unexpected electricity price spikes and decreases in customer energy use to satisfy electricity price incentives.These price signals lower peak power demand when the cost of production is very high.This process also increases the reliability of electricity both in the short and long term.Therefore, the system's performance can be enhanced with the DR plan, for instance, boosting power system dependability, efficiency, stability, and mobility, as well as cutting down on electricity costs.As a result, a variety of roadmaps and initiatives are available for the DR scheme.New options for power system operation are now possible because of the DR technology's continual development.
Many DR's have planned the introduction of contemporary power supply responses to industrial needs.DR schemes have been proposed in various sources of literature [1].DR systems can be specifically divided into three basic groups [2].According to the kind of control mechanism, offered motivation, decision variable are provided to customers to lower their energy use.In general, programs can be categorized by their mechanism as shown in Figure 1 economically, DR can be classified into incentive base DR (IDR) [3], [4] and price-based DR (PDR) [5], [6].In this article, we will focus on PDR.
PDR is a strategy used by energy providers to manage electricity demand during peak periods.The idea is to incentivize customers to reduce their energy consumption during times of high demand by offering them lower prices for their electricity usage [7].Energy providers will offer different pricing tiers based on the time of day and the overall demand for electricity.During peak periods when electricity demand is highest, prices will be higher, while during off-peak periods, prices will be lower.This encourages customers to reduce their energy consumption during peak periods and shift their usage to off-peak periods.
PDR scheduling has lately been studied in [8]- [11].In [8] and [9], the operational challenge takes into account demand shifting and peak shaving.In [10], the day-ahead unit commitment model treats curtailable and changing requests separately.Best practices for scheduling the hourly demand response taking renewable energy uncertainties into account in the day-ahead market [11].
The PDR consists of a time of use (TOU) program [12], [13], critical peak pricing (CPP) [14], [15], extreme day CPP (ED-CPP), extreme day pricing (EDP) [16] and real-time pricing (RTP) [17]- [19].In [20] Int J Appl Power Eng ISSN: 2252-8792  Optimal power dispatch for day-ahead power system operation … (Pansa Kaikrathok) 375 overview of two types of demand response, namely price-based and incentive-based, and gives examples of price-based responses.by focusing on the role of electricity companies in influencing consumer behavior to reduce the stress on the electricity grid.The mechanism behind these programs is electricity prices that change over time.
The fluctuation in the price of electricity reflects the cost of electricity production in each period.The main aim of the program is to make the power consumption curve smoothest by charging high prices during peak times and lower prices during off-peak periods.RTP programs, in the opinion of many economists, are the most direct and effective DR programs appropriate for competitive electricity markets and need to be the main focus of policymakers [19].In this paper, demand elasticity (DE) is used to analyze the optimal power dispatch (OPD) for the PDR program using RTP.In the proposed RTP-PDR program the electricity users are informed of the dayahead RTP prior to the dispatch day.Therefore, the electricity load forecast is adjusted according to the DE.Then, the system operator re-dispatch with the smoother load profile, leading to a lower electricity price.
As shown in Figure 2, in the fixed price strategy or without price signal to consumers, the demand curve is the vertical line.In other words, the buyers are willing to pay whatever price to meet the demand.But with price signals to the consumer, the customers' electricity usage habits will vary depending on the price at the time in according to DE.If the price is high, the demand will be less.If the price is low, the demand will be high.Then, it is estimating the consumer response to the price by elasticity price [21] and obtaining the price-corrected load forecast.Finally, the price-corrected optimal power dispatch is obtained.Accordingly, in this paper, the optimal real power dispatch algorithm for market-based power system operation incorporating demand price elasticity for day-ahead operation using quadratic programming (QP) is proposed.The nodal real-time spot price algorithm for a power system with loss sensitivity and the DC line flow method is determined.The proposed method was tested by using the IEEE 30-bus system and investigate the solution with different elasticity coefficients.
The contributions in this paper are summarized as follows: − The optimal real power dispatch algorithm for market-based power system operation incorporating demand price elasticity for day-ahead operation using QP (for total cost minimization) is developed.− The algorithm for the nodal real-time spot price of power system using loss sensitivity and DC line flow method is incorporated into the proposed optimal real power dispatch.− Several different elasticity coefficients had been investigated and discussed.
The remainder of the paper is structured as follows.Section 2 focuses on the dynamic load economic model.The formulation of the proposed mathematical problem is described in section 3. Simulation results are in section 4. Section 5 serves as the paper's conclusion.

DAY-AHEAD ELASTIC LOAD MODEL
An economic load model that depicts the shifts in customer demand in response to changes in demand prices is needed to define client engagement in DR schemes.DE is used to represent the demand response behavior.The relative slope of the demand-price curve could be used to determine the demand-price elasticity as shown in Figure 2 This elasticity coefficient shows significantly a change in a commodity's price would alter the relative level of demand for that commodity.It shall be assumed throughout this paper that all prices and quantities have been normalized about a certain equilibrium.
The fixed-demand bids are inelastic to the market price in terms of demand.To represent the consumer's behaviors, the DE can be formulated by the matrix consisted of "self-elasticity" and "crosselasticity".The self-elasticity represents the DE of the demand corresponding to the price in the same hour.Therefore, if the higher price leads to the lower demand and the self-elasticity is then negative.On the other hand, the higher price in hour i (that reduce the consumption in hour j.Therefore, the cross-elasticity is then negative.An elasticity matrix can be followed as (1)-( 2). [ , ≤ 0, if  = , and  , ≥ 0, if  ≠ As was previously noted, the period under consideration affects how customers respond to changes in power prices.In this paper, we will focus on the response "short-term", which refers to the period between the price announcement for the subsequent 24-hour period and the actual demand periods.Therefore, hourly demand changes can be followed as ( 3)-(4).
The line flow sensitivity factors ( ,ℎ ) of line l to change in real injection power at bus  is followed as (10), then  ,ℎ is the change in power flow on line l when  ,ℎ  0 and  ,ℎ is the change in real injection power at bus i at hour h as (10).
The change of real power flow at line l will be  ,ℎ and the power flow at line l will be expressed as (11).

PROBLEM FORMULATION
The conception of the paper can be shown in Figure 3.The primary optimal power dispatch provides the day-ahead hourly spot price and is announced prior to the dispatch day [23], [24].The objective function is to minimize total operating cost considering demand response as (12).
Where, the quadratic generator cost function has the form (13).
Subjected to the power balance constraints in ( 14)-( 15 and the generator operating limit constraints in ( 16)-( 17), and line flow limit constraint in (18).
The proposed method's computational process is as in Figure 4.

SIMULATIONS RESULT AND DISCUSSION
This section examines the proposed method by using the IEEE 30-bus test system.The IEEE 30-bus system used in this simulation.Table 1 lists the quadratic cost functions for each generator in the IEEE 30bus system according to [25].To analyze the effects on different facets of the electricity system while incorporating price-elastic demand bids, the simulation for of 24 hours is used.The six generators are situated at buses 1, 2, 5, 8, 11, and 13 in the IEEE 30-bus system.Bus 1 has been designated as the slack bus.Optimal power dispatch for day-ahead power system operation … (Pansa Kaikrathok)

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The system's daily load profile in the summer peak day of Thailand 2018, which peaks of 20340.70MW at hour 20 and light-load of 13681.76MW at hour 8, as shown in Figure 5 is used.The peak in demand occurs between 7:00 p.m. and 12:00 a.m., which is when there could be a significant need for power because of human activity.

Figure 5. System daily load curve
The simulation study includes: -Case I: Base case.In this case, the price signal is not applied.
-Case II: Self-elasticity -0.1 without cross-elasticity.In this case, DE is considered for all buses in the system.The demand is changed after considering demand price-elasticity.-Case III: Self-elasticity -0.2 without cross-elasticity.In this case, DE is considered for all buses in the system.The demand curve with DE is the same as in case II, but a price elasticity is set to -0.2.-Case IV: Self-elasticity -0.23 and cross-elasticity 0.01.In this case, DE is considered for all buses in the system.The demand curve with DE has, a self-elasticity of -0.23 and a cross-elasticity of 0.01.We use this to represent the changes in the price of one hour affect the demand for another.Table 2 shows the spot prices for the peak and light-load hours of bus 5. Bus 5 is the highestdemand bus.The hourly price of each bus in cases I-IV are shown in Figures 6(a)-(d), respectively.The results of the fuel cost comparison in case I is served as a base case, with simulations indicating that the cost is higher in all scenarios as shown in Figure 6(a).In Figure 6(b), the result of case II, self-elasticity is applied with a value of -0.1.It is observed that the cost has slightly decreased in comparison to the base case.Figure 6(c) shows the result of case III, the self-elasticity is -0.2.Note that in this case, the total generation cost is the lowest.Finally, Figure 6(d) shows the result of case IV, self-elasticity is -0.23 and cross-elasticity is also applied at 0.01.
The optimal total power generator for all cases is shown in Table 3, representing the effect of price elasticity on the system demand.Comparing the experimental results in each case, it can be seen that in case III, the demand is 5503.423MW per day, which is the least.Moreover, due to the cross-elasticity, the lightload demand, is higher, resulting in a better system load factor, as shown in Figure 7.In case III, selfelasticity is utilized with a value of -0.2 resulting in the case with the lowest cost.Additionally, case IV takes into account the impact of changes to one product on the cost of another product, as illustrated in Table 4.
As shown in Figure 8(a), the hourly price during peak hour of case III is the lowest due to only selfelasticity is applied.In case IV, the total power generation is the same as in case I, but the demands in peak hours are lower as well as the demands in light-load hours are higher, leading to the lower total cost under the same total consumption as shown in Figure 8(b).The power produced in each case shown in Table 3 has the same trend as the cost in Table 4, in which case III has the least power output.Figure 8 address the hourly power generation of cases III and IV, respectively.Meanwhile, Table 5 shows the comparison of total cost for all cases.In case II, the total daily consumption was reduced from 5529.83 MW to 5516.624MW, due to the consumer response to the nodal spot price (NSP) with self-DE, leading to the reduction in total daily operating cost from $17677.25 to $17615.69.Similarly, in case III the total daily consumption and total daily operating cost were reduced to 5503.423MW and $17554.26,respectively, with the consideration of larger self-DE of -0.2.Meanwhile, with the balance seif-and cross-DEs, the total daily operating cost can be reduced to $17674.63 under the same total daily consumption of base case, due to the consumers' load shifting in response to the NSP.Accordingly, self-elasticity and cross-elasticity are both important measures of price elasticity in the electricity market.Selfelasticity measures the responsiveness of quantity demanded to changes in electricity use according to the NSP, while cross-elasticity measures the responsiveness of quantity demanded to changes in the price of other

CONCLUSION
An integrated OPD with DE model was proposed in this paper.The spot pricing concept has been successfully incorporated into the power system operation plan by using DE with self-elasticity and crosselasticity.The effectiveness of the proposed methodology has been comparatively tested and validated on the IEEE 30-bus system.The results showed that the proposed method can lower the total system cost.
Figure 1.DR program

Figure 3 .
Figure 3.The conception of the proposed framework

Figure 6 .
Figure 6.Fuel cost (a) case I, (b) case II, (c) case III, and (d) case IV

Figure 8 .
Figure 8. Hourly power generator (a) case III and (b) case IV

:
The initial real power flow at line l at hour h  ,ℎ : Change in power flow on line l   ( ,ℎ ) : The fuel cost of the generator at bus i at hour h The voltage magnitude at bus i at hour h | ,ℎ | : The voltage magnitude at bus j at hour h |  | : The magnitude of the   element of Ybus  ,ℎ : The demand elasticity matrix at bus i at hour h  , : Position in the demand elasticity matrix representing self and cross demand elasticity  ,ℎ : Change in spot price at bus i at hour h  ,ℎ : The spot price at bus i at hour h  ,ℎ : The marginal transmission loss component at hour h  ,ℎ : The network quality of supply component at hour h ℎ : The real power demand at bus i with demand response at hour h  ,ℎ : The real power generation at bus i at hour h  ,ℎ  : The maximum real power generation at bus i ℎ : The system marginal price at hour h   : The angle of the   element of Ybus  ,ℎ ,ℎ =  ℎ +  ,ℎ +  ,ℎ ,  = 1, ..., , ℎ = 1, ...,24,(6) ,ℎ =  ℎ ⋅ (− ,ℎ ) =  ℎ ⋅ ( Optimal power dispatch for day-ahead power system operation … (Pansa Kaikrathok) 377

Table 2 .
Spot price at bus 5

Table 3 .
Comparison of the results of the generator in a 30-bus system

Table 4 .
Comparison of the results of the fuel cost the in the 30-bus system

Table 5 .
Total cost for different price elasticity