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applied sciences Article A Time-Varying Potential-Based Demand Response Method for Mitigating the Impacts of Wind Power Forecasting Errors Jia Ning, Yi Tang * and Bingtuan Gao Jiangsu Provincial Key Laboratory of Smart Grid Technology & Equipment, Southeast University, Nanjing 210096, Jiangsu, China; ningjia@seu.edu.cn (J.N.); gaobingtuan@seu.edu.cn (B.G.) * Correspondence: tangyi@seu.edu.cn; Tel.: +86-138-5199-2330 Received: 3 October 2017; Accepted: 27 October 2017; Published: 3 November 2017 Abstract: The uncertainty of wind power results in wind power forecasting errors (WPFE) which lead to difﬁculties in formulating dispatching strategies to maintain the power balance. Demand response (DR) is a promising tool to balance power by alleviating the impact of WPFE. This paper offers a control method of combining DR and automatic generation control (AGC) units to smooth the system’s imbalance, considering the real-time DR potential (DRP) and security constraints. A schematic diagram is proposed from the perspective of a dispatching center that manages smart appliances including air conditioner (AC), water heater (WH), electric vehicle (EV) loads, and AGC units to maximize the wind accommodation. The presented model schedules the AC, WH, and EV loads without compromising the consumers’ comfort preferences. Meanwhile, the ramp constraint of generators and power ﬂow transmission constraint are considered to guarantee the safety and stability of the power system. To demonstrate the performance of the proposed approach, simulations are performed in an IEEE 24-node system. The results indicate that considerable beneﬁts can be realized by coordinating the DR and AGC units to mitigate the WPFE impacts. Keywords: wind power forecasting error (WPFE); demand response (DR); DR potential (DRP); wind accommodation 1. Introduction As intermittent renewable energies continue to enter the power grid, more and more operational and regulatory challenges emerge. Wind power is one of the most mature renewable energies around the world [1], but the wind power forecasting error (WPFE) can be up to 10–15% with a look-ahead time of 1 h. The variability and unpredictability of wind power generation increase the amplitude and occurrence rate of power imbalance in the power system [2–4], which is mainly regulated by automatic generation control (AGC) units in real-time. At present, the base output of AGC units is conﬁrmed in the process of formulating the dispatching plan based on the forecasting information of load and wind, which is optimized every 15 min. If the WPFE is large, then AGC units are limited in their ability to alleviate its impacts on the generator ’s active power ramp rate and the spinning reserve [5,6]. To cope with the abovementioned challenges, additional ﬂexible resources are required in smart grids. Supplemental energy resources such as storage devices [7], pumped-storage hydro plants [8], gas turbines, and compressed air energy storage [9] are feasible solutions proposed to reduce the variability and uncertainty of wind power. Although storage can reduce the imbalance that stems from wind power ﬂuctuations, the current high investment cost of storage makes it an uneconomical solution. In recent years, it has been suggested to utilize the ﬂexibility potential available from residential demand-side resources. Compared with traditional generation resources, DR resources have some advantages [10,11] in terms of operational control in the power system. Firstly, according to Appl. Sci. 2017, 7, 1132; doi:10.3390/app7111132 www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 1132 2 of 20 a report by the Federal Utility Regulatory Commission, demand response (DR) is capable of offsetting 20% of the peak demand in the US [12]. Secondly, without the regulating inertia, the DR resources can respond to the control order rapidly. In addition to the two mentioned advantages, the DR resources can also cope with emergency conditions because of their geographical decentralization. Hence, coordinating the AGC units and DR is a reasonable consideration to mitigate the WPFE impacts in real-time to maximize the wind accommodation. In general, the loads are classiﬁed into three types: residential load, commercial load, and industrial load [13]. In this paper, we focus on the residential loads. Among the various residential load types, thermostatic loads such as air conditioner (AC) and water heater (WH) loads, and deferrable loads such as electric vehicle (EV) loads are placed at the top of the merit list of DR appliances due to their greater load shifting potential and larger daily energy demand share [14–16]. Recently, the load management beneﬁts of controlled appliances for the increased deployment of intermittent renewable generation have been investigated [17–21]. A stochastic unit commitment model is presented for assessing the reserve requirements resulting from the integration of renewable sources in [17], where alternative DR paradigms for assessing the beneﬁts of demand-side ﬂexibility on absorbing the variability and uncertainty of renewable supply are investigated. Aghaei et al. [18] considered ﬂexible loads as a storage device in a hybrid power plant of a wind farm to compensate for wind power imbalances and proposed a procedure to derive the strategic offer for a hybrid power plant selling energy in the pool-based market. The joint operation of wind farms and DR producer is demonstrated, and DR is effective in coping with the wind power uncertainties in the intraday market. Pourmousavi et al. [19] evaluates thermostat set point control of aggregate electric water heaters (EWHs) for load shifting and providing a desired balancing reserve for the utility at the presence of wind generation. Çiçek et al. [20] developed a DR model that offers optimal levels for both production and consumption in a smart grid that consists of a wind farm along with conventional sources. Although these studies have studied the DR role in power systems with wind generation, they lack the considerations of the demand side’s DRP and security constraints. To the best of the authors’ knowledge, until now, few studies have thoroughly investigated the optimization of DR and AGC units to smooth the power imbalance considering the real-time DR potential (DRP) and security constraints. The major contribution of this paper is to develop a mathematical model to mitigate the WPFE impacts through the collaboration of DR and AGC units. It is necessary to evaluate how much power smart appliances including ACs, WHs, and EVs can respond, which is regarded as DRP. The DRP varies with different working conditions of the smart appliances. The operational status has features of continuity and accumulation as a result of their operating characteristics. If the smart appliances respond, the subsequent operational power would change. Therefore, this paper proposes a method of evaluating the DRP quantitatively in real-time. Combining the DR and AGC units, the framework is presented to take advantage of their potential for balancing supply and demand considering the security constraints. The rest of the paper is organized as follows. Section 2 covers the model formulation for wind power and its forecasting error. The proposed computational method of aggregated DRP is presented, and the preliminary basics are discussed in Section 3. Section 4 presents the framework for wind forecasting error balancing via DR and AGC units. The case studies and their subsequent results are outlined in Section 5. Finally, the paper is concluded in Section 6. 2. Wind and WPFE Model In this paper, the actual wind power is the summation of the wind forecasting power and its error DP . The actual wind power is modelled in Equation (1): P = P + DP (1) w wind w Appl. Sci. 2017, 7, 1132 3 of 20 where P is the actual wind power; P is the wind forecasting power; and DP is the difference w w wind between actual power and forecasting power, namely the wind forecasting error. It is assumed that the wind forecasting error obeys a normal distribution with a certain deviation [22]. Assuming that the wind prediction was made 24 h prior to the ﬁrst hour of the schedule for an ensemble of wind farms contained in a region with a diameter of 140 km, the standard deviation of the wind forecasting error can be approximated by: 1 1 s = P + W (2) w z wind 5 50 where s is the standard deviation, and W is the installed wind capacity. w z 3. DR and AGC Unit Capabilities In this section, the models of smart appliances, including ACs, WHs, and EVs, are built. Based on their operating characteristics, the DRP which can respond to both load reduction and increment signals is quantiﬁed considering the consumers’ comfort. Finally, the AGC units’ regulating capability is illustrated. 3.1. Modeling of Residential Smart Appliances The residential appliances include heating, ventilation, AC, WH, clothes dryer, clothes washer, dishwasher, range, refrigerator, light, plug load, and EV. AC and WH have the characteristics of a thermal storage such that homeowners can control their power consumption by adjusting the room/hot water temperature set points. Usage of EV can be deferred based on homeowner preference. All other loads (e.g., cooking appliances and TVs) are not controlled. 3.1.1. AC Model An AC system with a thermostat works in an “on–off” manner and the AC will simply run at its rated power when turned on. In general, a thermostat control is set so that the room temperature will s d ﬂuctuate around the thermostat set point T within the dead band of T /2. AC AC Controlling the AC load is carried out by adjusting cooling set points. The AC status is related to the current room temperature, cooling set point, and the thermostat dead band. The relationship is presented in Equation (3): s d P , T (t) T (t) + T /2 AC AC AC AC s d p (t) = (3) 0, T (t) T (t) T /2 AC AC AC AC s d s d p (t 1), T (t) T /2 T (t) T (t) + T /2 AC AC AC AC AC AC where p (t) is the working power of the air conditioner in time interval t (kW); P is the rated AC AC power of AC (kW); T (t) is the room temperature in time interval t ( F); T (t) is the cooling set AC AC point in time interval t ( F); and T is the thermostat dead band ( F). AC The AC is controlled by changing the cooling set point T (t). Increasing the cooling set point to AC some value can stop the AC working. The controlled formula is presented in Equation (4): s set T (t) = s (t) T (4) AC AC AC set where s (t) is the DR control signal which is received from the in-home controller, and T is the AC AC cooling set point ( F). For each time interval t, the room temperature is calculated in Equation (5): G(t) C p (t) AC AC T (t + 1) = T (t) Dt + Dt (5) AC AC Dc Dc P AC Appl. Sci. 2017, 7, 1132 4 of 20 where Dt is the length of time interval t (hour); G(t) is the heat gain rate of the house during time interval t, positive for heat gain and negative for heat loss (Bth/h); C is the cooling capacity (Bth/h); AC and Dc is the energy needed to change the temperature of the air in the room by 1 F (Bth/ F). 3.1.2. WH Model The water heater model is a temperature-based model rather than an energy-based one. This means that the duration of the ON period of the heating coils depends on the temperature set point and the current water temperature. The WH working power is presented in Equation (6): s d 0, T (t) T + T /2 > WH WH WH s d p (t) = (6) P , T (t) T T /2 WH WH WH WH WH : s d s d p (t 1), T T /2 T (t) T + T /2 WH WH WH WH WH WH where p (t) is the working power of water heater in time interval t (kW); P is the rated power of WH WH WH (kW); T (t) is the water temperature in time interval t ( F); T (t) is the desired temperature WH WH set point in time interval t ( F); T is the thermostat dead band ( F). WH The WH is controlled by changing the water set point T (t). Decreasing the water set point to WH some value can stop the WH from working. The controlled formula is presented in Equation (7): s set T (t) = s (t) T (7) WH WH WH set where s (t) is the DR control signal which is received from the in-home controller, and T is the WH WH water set point ( F). The water temperature in the tank is calculated as shown in [23]. 3.1.3. EV Model Here, an on–off strategy is used for EV response, which means that each EV is charged by a constant and maximum power. The beneﬁts of charging with an on–off strategy instead of adjustable power are as follows: First of all, it was suggested that charging the EV with a constant power could prolong the battery’s service time. Secondly, smaller communication overhead is required to contact a small subset of EVs, and hence it is more practical to turn charging on or off rather than adjusting the charging rate when a large amount of EV charging is scheduled. Finally, it is expected that using an on–off strategy can fully charge the EVs in a shorter timeframe [24]. To model EV charging proﬁles, three parameters are essential: the rated charging power, the plug-in time, and the battery state-of-charge (SOC). The plug-in time is related to the time of vehicle arrival at home and arrival at work. The calculation of the EV charging proﬁle is described in Equation (8): p (t) = P N (t) w (t) s (t) (8) EV EV EV EV EV where p (t) is the EV charge power in time interval t (kW); P is the EV rated power (kW); N (t) is EV EV EV the EV connectivity status in time interval t (“1” if EV is connected to the plug and “0” if EV is not connected); w (t) is the EV charging status without control in time interval t, which depends on the EV battery SOC as shown in (9) (“0” if EV is not being charged and “1” if EV is being charged); and s (t) EV is the DR control signal for EV in time interval t, 0 = OFF, 1 = ON. 0, SOC(t) SOC min w (t) = (9) EV 1, SOC(t) < SOC min where SOC(t) is the state of charge in time interval t, and SOC is the minimum SOC limit of EV at min the desired ﬁnish time. Appl. Sci. 2017, 7, 1132 5 of 20 The battery SOC after EV charging completes should fulﬁll customers’ demand, which is determined by: SOC 1 (10) E Q EV EV where SOC is the initial SOC of EV; L is the travel distance of EV (mile); E is the efﬁciency of driving 0 EV (mile/kWh); and Q is the full capacity of battery (kWh). EV The EV battery charging model is as follows: p (t) Dt EV SOC(t + 1) = SOC(t) + h (11) EV where Q is the full battery capacity (kWh), and h is the coefﬁcient of charging. EV 3.2. Aggregated Model The AC load parameter values obey a certain probability distribution [25]. The initial room temperature obeys a discrete uniform distribution T ~ U (19,24). Suppose that the ACs are distributed in in a close geographic area so the thermostat set point and its dead band are the same for all the ACs. The parameters of the aggregated WHs are set randomly within speciﬁc ranges. Each WH has a different demand ﬂow rate, tank insulation thermal resistance, tank volume, and different initial water temperature. For the aggregated WH model, the demand ﬂow rate is randomly obtained from [26], which includes 18 kinds of demand ﬂow rate for one day. The thermal resistance of the tank insulation obeys a random uniform distribution R ~ U (10,20). The tank volume obeys a random normal distribution V ~ N (40,6.272), whose range is approximately 20 to 65 gallons. The initial water temperature is randomly distributed from 45 C to 50 C [19]. Each EV has different initial SOC, plug-in time, and travel mileage. Based on the report of the US Department of Transportation for all American private cars in 2009 [27], when an EV starts charging in a residence, it is assumed that it will not travel any more in a day. The initial SOC obeys a uniform distribution SOC ~ U (0,0.1). On account of the driving pattern data in [27], the statistical data is normalized, and it is obtained that the EV plug-in time approximately meets the Gaussian distribution [28], which can be described as: (xm ) 1 s exp 17 x 20 s 2p 2s s s f (x) = (12) 0 else where s = 3.4, m = 19. s s The daily travel mileage obeys a Gaussian distribution, and the density function can be described as: " # 1 (ln(x) m ) f (x) = exp (13) 2s xs 2p where s = 0.88 and m = 3.66. l l 3.3. Aggregated DRP Responsive loads are controlled to satisfy the demand requirements, which include load increment and load reduction. DRP is deﬁned that the smart appliances can switch their working status in response to the DR signal without affecting the consumer ’s comfort. This section discusses the condition when there is a DR signal which needs smart appliances to stop working or continue to work. Figure 1 shows the DRP of AC and WH in different conditions in response to a load reduction signal. Appl. Sci. 2017, 7, 1132 6 of 20 Appl. Sci. 2017, 7, 1132 6 of 20 Air Conditioner Water Heater Tcomfort_upper DR potential None Tset+Deadband/2 T T room water DR potential No DR potential Tset No DR potential DR potential Tset-Deadband/2 None DR potential Tcomfort_lower Figure 1. Demand response potential (DRP) of air conditioner (AC) and water heater (WH) in Figure 1. Demand response potential (DRP) of air conditioner (AC) and water heater (WH) in response response to a load reduction signal. to a load reduction signal. set d set d seTT t − d 2 sTT et +2 d For the AC, when the room temperature is between and , the AC has AC AC AC AC For the AC, when the room temperature is between T T /2 and T + T /2, the AC has AC AC AC AC DRP if the room temperature has a downward tendency, and has no DRP if it has an upward DRP if the room temperature has a downward tendency, and has no DRP if it has an upward tendency. tendency. In order to guarantee the comfort of consumers, the comfort range is set previously. In In order to guarantee the comfort of consumers, the comfort range is set previously. In general, set d set d AC the range of thermostat set point T within the dead band of T /2 is between T and T ±T 2 general, the range of thermostat set point within the dead band of is between AC AC AC ACcom f ort_lower AC AC AC T , except the condition of AC responding. When the room temperature goes above the Tcom f ort_up an per d T , except the condition of AC responding. When the room temperature goes comfort _lower comfort _upper set d AC T + T /2 which is below T , the AC has DRP until the room temperature is higher than set d AC AC AC com f ort_upper TT+2 T above the which is below , the AC has DRP until the room temperature is AC AC comfort _upper the maximum temperature of comfort range. Similar logic is suitable for WH. For the EV, when it is higher than the maximum temperature of comfort range. Similar logic is suitable for WH. For the EV, connected to the charging station and can charge to the minimum SOC before the desired ﬁnish time, when it is connected to the charging station and can charge to the minimum SOC before the desired it has DRP [29]. finish time, it has DRP [29]. The DRP index of the three appliances in time interval t + 1 are obtained based on the parameters The DRP index of the three appliances in time interval t + 1 are obtained based on the parameters of time interval t, “1” if the appliance has DRP and “0” if the appliance has no DRP, which are described of time interval t, “1” if the appliance has DRP and “0” if the appliance has no DRP, which are in Equations (14)–(16): described in Equations (14)–(16): set d set d (T (t + 1) < T (t)&&T (t + 1) 2 (T T /2, T + T /2)) set d set d > AC AC AC AC AC AC AC < (( T t+<1) Tt()&&Tt( +1)∈(T −T 2,T +T 2)) 1, AC AC AC AC AC AC AC set d AC 1, DP (t + 1) = jjT (t + 1) 2 (T + T /2, T ) (14) AC AC set d AC AC AC com f ort_upper DP (1 t+=) ||Tt ( +∈ 1) (T +T 2 ,T ) (14) > AC > AC AC AC comfort _ upper 0, others 0, others set d set d > set d set d (T (t + 1) > T (t)&&T (t + 1) 2 (T T /2, T + T /2)) > WH WH WH (( Tt+>1) Tt()&&Tt( +1)∈(WHT −T WH 2,TWH+T WH2)) WH WH WH WH WH WH WH 1, 1, WH set d DP (t + 1) = (15) jjT (t + 1) 2 (T , T T /2) WH WH WH set d com f ort_lower WH WH DP (1 t >+=) ||Tt ( +∈ 1) (T ,T −T 2) (15) WH > WH comfort _ lower WH WH 0, others 0, others P (Tt1) EV 1, N (t) = 1&&SOC(t + 1) + h SOC EV min EV PT⋅−(1t−) DP (t + 1) = (16) EV EV 1, N (t )=+ 1 & &SOC (t 1)+ ⋅η≥ SOC 0, others EV min DP (1 t+=) Q (16) EV EV where DP (t + 1), DP (t +0, 1), and DP (t + 1) are the other DRP s statuses of the AC, WH, and EV in AC WH EV time interval t + 1, respectively. where DP (1 t + ) , DP (1 t + ) , and DP (1 t + ) are the DRP statuses of the AC, WH, and EV in time AC WH EV In the condition of the DR requirement which requires more loads work, it is assumed that only interval t + 1, respectively. the WHs and EVs respond to the increment signal. The reason is that when the WHs and EVs respond In the condition of the DR requirement which requires more loads work, it is assumed that only to the increment signal, the water temperature increases and then decreases slightly because of its the WHs and EVs respond to the increment signal. The reason is that when the WHs and EVs respond high heat preservation, and the EV’s SOC increases and then stays constant in the condition of no to the increment signal, the water temperature increases and then decreases slightly because of its charging or discharging because of its storage capacity. These characteristics are beneﬁcial to the later high heat preservation, and the EV’s SOC increases and then stays constant in the condition of no DR actions responding to the reduction signal. The DRP index of these three kinds of appliances in charging or discharging because of its storage capacity. These characteristics are beneficial to the later DR actions responding to the reduction signal. The DRP index of these three kinds of appliances in time interval t + 1 are obtained based on the parameters in time interval t, “1” if the appliance has DRP and “0” if the appliance has no DRP, which are described Equations (17)–(19): Appl. Sci. 2017, 7, 1132 7 of 20 time interval t + 1 are obtained based on the parameters in time interval t, “1” if the appliance has DRP and “0” if the appliance has no DRP, which are described Equations (17)–(19): DP (t + 1) = 0 (17) AC set d set d (T (t + 1) < T (t)&&T (t + 1) 2 (T T /2, T + T /2)) > WH WH WH WH WH WH WH 1, set d WH DP (t + 1) = jjT (t + 1) 2 (T + T /2, T ) (18) WH WH WH WH com f ort_upper 0, others 1, N (t) = 1&&SOC(t + 1) SOC EV min DP (t + 1) = (19) EV 0, others where DP (t + 1), DP (t + 1), and DP (t + 1) are the DRP statuses of the AC, WH, and EV in AC WH EV time interval t + 1, respectively. The aggregated DRP of each agent is presented in Equation (20). N N N 1 2 k j j i i k k DRP (t + 1) = P DP (t) + P DP (t) + P DP (t) (20) total å å å AC AC EV EV WH WH i=1 j=1 k=1 where DRP (t + 1) is the DRP of all the appliances in one agent in time interval t + 1 (kW); N is the total 1 i i total number of ACs; P is the rated power of the ith AC (kW); DP (t) is the DRP index of the ith AC AC j j AC in time interval t; N is the total number of WHs; P is the rated power of jth WH (kW); DP (t) WH WH is the DRP index of the jth WH in time interval t; N is the total number of EVs; P is the rated power EV of kth EV (kW); DP (t) is the DRP index of the kth EV in time interval t. EV 3.4. AGC Units Regulating Capability Coal-ﬁred generating units have a response delay, slow regulation speed, and are difﬁcult to change the regulating direction. Normally, the adjustable range of a coal-ﬁred generating AGC unit is 50–100% P (P is the rated capacity of unit), whose response delay time is 1–2.5 min. The load e e regulation speed of most coal-ﬁred generating units can reach 1.5 P /min. However, the maximum allowable is generally 3% P /min. 4. Proposed Methodology This section presents a sequential procedure to maximize the joint beneﬁts of coordinating DR and AGC units for balancing wind power ﬂuctuations. In doing so, it is considered that there is a power system with high wind power ﬂuctuation and a large population of smart appliances. The optimization routine is performed in real-time, and the schematic diagram is illustrated in Figure 2. The output of an AGC unit is controlled by two signals, which contains area control error DP updated by seconds ACE and a base value updated every 15 min. Although the dispatching center can already update the base value of AGC units in real-time, the control algorithm relies on the prediction of the load every 15 min. As a result of the regularity of load variation, the prediction of the load becomes more accurate. With the wind penetration increasing, the high forecasting error of wind power would lead to the actual output of AGC units deviating from economical operating point, which increases the operating cost. Meanwhile, the large ﬂuctuation of wind power requires more reserve, so the AGC units have less regulating capacity. Therefore, this paper proposes a real-time control method by coordinating DR and AGC units to alleviate the WPFE impacts. In Figure 2, the output of the AGC units, wind farm, and smart appliances are controlled by the combination of dispatching order (DO) and real-time control order (RTCO). The actual power of AGC units are restricted by the ramp and transmission constraints. The dispatching center collects information from the wind forecasters and sends the WPFE to the sublocal controllers of the AGC units. The local controller obtains information from all the sublocal controllers and makes control decisions. Appl. Sci. 2017, 7, 1132 8 of 20 Appl. Sci. 2017, 7, 1132 8 of 20 Dispatching Center DO DO DO DO RTCO RTCO RTCO RTCO ΔP ΔP ACE ,1 ACE ,2 Smart Wind Farm Appliances WPFE P WPFE Governor Governor Sublocal Sublocal Sublocal Sublocal Controller Controller Controller Controller Turbine Turbine G1 W L G2 Ramp limit Ramp limit Local Controller C Power limit Power limit G ,1 G,2 Figure 2. Schematic diagram of coordinated real-time control of DR and automatic generation control Figure 2. Schematic diagram of coordinated real-time control of DR and automatic generation (AGC) units. DO: dispatching order; RTCO: real-time control order; WPFE: wind power forecasting control (AGC) units. DO: dispatching order; RTCO: real-time control order; WPFE: wind power error. forecasting error. 4.1. Optimization Model 4.1. Optimization Model (1) Objective Function (1) Objective Function Considering the wind power forecasting error and smart appliances’ DRP, this paper focuses on both the supply side and demand-side strategies to maximize the wind accommodation. The formula Considering the wind power forecasting error and smart appliances’ DRP, this paper focuses on is as follows: both the supply side and demand-side strategies to maximize the wind accommodation. The formula TNw is as follows: max F=Δ PT (21) T Nw wi ti == 11 t max F = P DT (21) å å wi t=1 i=1 where T is the number of time intervals; Nw is the number of wind farms; P is the wind output in wi where the ti T is me i thennumber terval t; aof nd time ∆T isintervals; the time inN terva is lthe . number of wind farms; P is the wind output in the wi time interval t; and DT is the time interval. (2) Active Power Balance Constraint (2) Active Power Balance Constraint Once the smart appliances participate in the DR program and response, the total load energy varies. Meanwhile, the forecasting error on load prediction can also lead to the variation of total load. Once the smart appliances participate in the DR program and response, the total load energy Therefore, there is load fluctuation as a result of DR actions and load forecasting error, which is as varies. Meanwhile, the forecasting error on load prediction can also lead to the variation of total follows: load. Therefore, there is load ﬂuctuation as a result of DR actions and load forecasting error, which is Δ= P PP − +P −P (22) lj lj lj 0 aj fj as follows: DP = P P + P P (22) where ∆Plj is the load fluctuation of the jth household; Plj is the total power after DR of smart lj lj lj0 aj f j appliances in the jth household; Plj0 is the prediction load power of smart appliances in the jth where DP is the load ﬂuctuation of the jth household; P is the total power after DR of smart appliances lj lj household; Paj is the actual power of non-smart appliances in the jth household; and Pfj is the in the jth household; P is the prediction load power of smart appliances in the jth household; P is lj 0 aj forecasting power of non-smart appliances in the jth household. the actual power of non-smart appliances in the jth household; and P is the forecasting power of The active power balance constraint is shown in Equation (23). fj non-smart appliances in the jth household. PP++ΔP = P The active power balance constraint is shown in Equation (23). (23) giwind w lj ij == 11 g N where N is the number of generators; N is the number of households; P is the output power g gi P + P + DP = P (23) å gi wind å lj P ΔP of the ith generator; is the wind forecasting power; is the fluctuation of the wind power; wind i=1 jw=1 and is the output power of the jth household’s total loads. lj where N is the number of generators; N is the number of households; P is the output power of the L gi (3) Generator Capacity Constraint ith generator; P is the wind forecasting power; DP is the ﬂuctuation of the wind power; and P is wind lj the output power of the jth household’s total loads. PP≤≤P (24) gi,min gi gi,max (3) Generator Capacity Constraint P P P (24) gi,min gi gi,max where P and P are the minimum and maximum capacities of the ith generator, respectively. gi,min gi,max Appl. Sci. 2017, 7, 1132 9 of 20 (4) Generator Ramp Constraints P P R DT gi,t gi,t1 u,i (25) P P R DT gi,t1 gi,t d,i where P is the output power of the ith generator in time interval t; DT is the time interval; and R gi,t u,i and R are the ascending and descending ramp, respectively, whose units are MW/min. d,i (5) Power Flow Transmission Constraint l l l P P P (26) line,max line line,max l l where P is the power ﬂow at the lth line, and P is the maximum limit at line l. line,max line (6) Demand Response Capacity Constraint When the loads increase: P P P + DRP (27) j0 lj j0 j When the loads decrease: P DRP P P (28) j0 j lj j0 where P is the initial power of the jth household’s total loads, and DRP is the DRP of the jth j0 j household’s responsive loads. (7) Consumers’ Comfort Constraints AC T T (t) AC com f ort_upper 0 C (t) = 1 (29) AC AC AC T T com f ort_upper com f ort_lower WH T (t) T WH com f ort_lower 0 C (t) = 1 (30) WH WH WH T T com f ort_upper com f ort_lower 1 a N(t) SOC(t) SOC min 0 C (t) = 1 (31) EV 0 SOC(t) < SOC min where C (t), C (t), and C (t) are the comfort indices of the air conditioner, water heater, AC WH EV AC WH and electric vehicle in time interval t, respectively; T and T are the upper com f ort_upper com f ort_upper AC WH limit of room temperature and water temperature, respectively; T and T are the com f ort_lower com f ort_lower lower limits of room temperature and water temperature, respectively; T (t) is the room temperature AC in time interval t and T (t) is the water temperature in time interval t; N(t) is the total charging WH times during the t period, SOC(t) is the SOC of EV in time interval t; and SOC is the minimum min SOC limit of EV at the desired ﬁnish time. 4.2. Solution Method The way of determining the optimal combination of AGC units and DR reserve power for maximizing the wind accommodation is presented as the following ﬂowchart (see Figure 3). First, the wind power and load curve are forecasted and the output power of thermal units is scheduled using the direct current optimal power ﬂow (DCOPF) method in Matpower [30]. Based on the wind model described in Section 2, the wind power ﬂuctuation DP is calculated. Considering the operating characteristics of smart appliances, including ACs, WHs, and EVs, it is obvious that their working status are the accumulated results of previous operation, and there is a load ﬂuctuation DP calculated in Equation (22). The wind and load ﬂuctuations result in the system imbalance, and the wind Appl. Sci. 2017, 7, 1132 10 of 20 Appl. Sci. 2017, 7, 1132 10 of 20 ΔP working status are the accumulated results of previous operation, and there is a load fluctuation calculated in Equation (22). The wind and load fluctuations result in the system imbalance, and the accommodation is maximized with the combination function of the supply-side and demand-side wind accommodation is maximized with the combination function of the supply-side and demand- considering the constraints in Section 4.1. side considering the constraints in Section 4.1. Start Forecast wind power and load curve Generation scheduling using the DCOP F m ethod Calculate wind power fluctuation ΔPw based on wind m odel t=1 Calculate load fluctuation ΔPl Calculate the DRP of smart appliances Generation re-scheduling and smart Calculate wind appliances response to smooth the energy curtailment power imbalance No Check for No Negative Load t=t+1 convergence fluctuations shedding Yes Yes Expand the Export optimal results comfort range Update the s tatus of smart appliances No Acceptable Yes No t=T Yes End Figure 3. Solution method’s flowchart. DCOPF: direct current optimal power flow. Figure 3. Solution method’s ﬂowchart. DCOPF: direct current optimal power ﬂow. When the AGC units regulating capability and DRP are not large enough to smooth the power When the AGC units regulating capability and DRP are not large enough to smooth the power imbalance, there would be wind energy curtailment with a negative fluctuation or load shedding imbalance, there would be wind energy curtailment with a negative ﬂuctuation or load shedding with a positive fluctuation. In the condition of positive fluctuation, the comfort range is expanded to with a positive ﬂuctuation. In the condition of positive ﬂuctuation, the comfort range is expanded to increase the DRP within the consumers’ acceptable limits. increase the DRP within the consumers’ acceptable limits. 5. Case Study 5. Case Study The proposed model was tested on a modified IEEE 24-node system over a daily time horizon The proposed model was tested on a modiﬁed IEEE 24-node system over a daily time horizon whose data was taken from Reference [31]. The system comprises 34 transmission lines, illustrated in whose data was taken from Reference [31]. The system comprises 34 transmission lines, illustrated in Figure 4. The wind farm is located at bus 20. The load profile used for testing was obtained as given Figure 4. The wind farm is located at bus 20. The load proﬁle used for testing was obtained as given in Figure 5. The 24-node system includes 17 loads. Both the nodal location of these loads and their in Figure 5. The 24-node system includes 17 loads. Both the nodal location of these loads and their contribution in percentage to the total system demand are listed in Table 1. It was assumed that there contribution in percentage to the total system demand are listed in Table 1. It was assumed that there were smart appliances in 10 nodes, including nodes 3, 4, 5, 6, 8, 9, 10, 14, 19, and 20. The time interval were smart appliances in 10 nodes, including nodes 3, 4, 5, 6, 8, 9, 10, 14, 19, and 20. The time interval was 1 min. was 1 min. Appl. Sci. 2017, 7, 1132 11 of 20 Appl. Sci. 2017, 7, 1132 4 of 8 Appl. Sci. 2017, 7, 1132 11 of 20 G7 G8 G9 G7 G8 G9 18 21 18 21 G10 G10 16 19 20 23 16 19 20 23 G6 G6 15 G4 15 G4 G5 G5 11 12 9 10 1 2 7 G1 G2 G3 G1 G2 G3 Figure 4. The modified IEEE 24-node system. Figure 4. Figure 4. The The m modiﬁed odified I IEEE EEE 24-node sy 24-node system. stem. Figure 5. The daily load profile. Figure 5. The daily load proﬁle. Figure 5. The daily load profile. Table 1. The 24-node system: node location and distribution of the total system load. Table 1. The 24-node system: node location and distribution of the total system load. Table 1. The 24-node system: node location and distribution of the total system load. Load Node Percentage Load Node Percentage Load Node Percentage Load Node Percentage Load Node Percentage Load Node Percentage 1 1 3.8 10 10 6.8 1 1 3.8 10 10 6.8 2 2 3.4 11 13 9.3 1 2 2 1 3.83.4 11 10 13 10 9.3 6.8 3 3 6.3 12 14 6.8 2 3 3 2 3.46.3 12 11 14 13 6.8 9.3 4 4 2.6 13 15 11.1 3 4 4 3 6.32.6 13 12 15 14 11.1 6.8 5 5 2.5 14 16 3.5 5 5 2.5 14 16 3.5 4 4 2.6 13 15 11.1 6 6 4.8 15 18 11.7 6 6 4.8 15 18 11.7 5 5 2.5 14 16 3.5 7 7 4.4 16 19 6.4 7 7 4.4 16 19 6.4 6 6 4.8 15 18 11.7 8 8 6.0 17 20 4.5 8 8 6.0 17 20 4.5 7 7 4.4 16 19 6.4 9 9 6.1 9 9 6.1 8 8 6.0 17 20 4.5 9 9 6.1 An ensemble of wind farms with a total installed capacity of W = 600 MW is connected to the An ensemble of wind farms with a total installed capacity of W = 600 MW is connected to the base system as an example. The wind forecast power data is taken based on [32], and its forecasting base system as an example. The wind forecast power data is taken based on [32], and its forecasting An ensemble of wind farms with a total installed capacity of W = 600 MW is connected to the base error is distributed normally as shown in Section 2. Figure 6 shows the actual and prediction wind error is distributed normally as shown in Section 2. Figure 6 shows the actual and prediction wind system as an example. The wind forecast power data is taken based on [32], and its forecasting error is power. power. distributed normally as shown in Section 2. Figure 6 shows the actual and prediction wind power. Appl. Sci. 2017, 7, 1132 12 of 20 Appl. Sci. 2017, 7, 1132 5 of 8 Appl. Sci. 2017, 7, 1132 5 of 8 -150 -300 -150 00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:00 Time (h) -300 Wind prediction error Wind prediction power Actual wind power 00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:00 Figure 6. The actual and prediction wind power. Figure 6. The actual and prediction wind power. Time (h) Wind prediction error Wind prediction power Actual wind power To showcase the benefits offered from the proposed methodology, four distinct case studies To showcase the beneﬁts Fig offer ure ed 6. fr The om act the ual and proposed predictimethodology on wind power,. four distinct case studies were were conducted as follows, in which the wind installed capacity was 600 MW and the DR percentage conducted as follows, in which the wind installed capacity was 600 MW and the DR percentage was was 15%. The operator maximizes the wind accommodation for which, in Case 1, generating units To showcase the benefits offered from the proposed methodology, four distinct case studies 15%. The operator maximizes the wind accommodation for which, in Case 1, generating units provide provide energy and reserve and there is no DR participation to absorb as much wind power, but in were conducted as follows, in which the wind installed capacity was 600 MW and the DR percentage energy and reserve and there is no DR participation to absorb as much wind power, but in Case 2, Case 2, in addition to generators, smart houses can also participate in balancing the wind prediction was 15%. The operator maximizes the wind accommodation for which, in Case 1, generating units in addition error. Thto e ge generators, nerator ramp smart constra houses int is can not con also siparticipate dered in Casin e 3balancing , and the po the wer wind flow pr transm ediction ission error. provide energy and reserve and there is no DR participation to absorb as much wind power, but in constraint is not taken into account in Case 4 in the condition of a wind percentage of 20% and DR The generator ramp constraint is not considered in Case 3, and the power ﬂow transmission constraint Case 2, in addition to generators, smart houses can also participate in balancing the wind prediction percentage of 15%. The simulations were conducted in Matpower and Matlab [33]. The observations is not taken into account in Case 4 in the condition of a wind percentage of 20% and DR percentage of error. The generator ramp constraint is not considered in Case 3, and the power flow transmission are reported in the following subsection. 15%. The simulations were conducted in Matpower and Matlab [33]. The observations are reported in constraint is not taken into account in Case 4 in the condition of a wind percentage of 20% and DR the following subsection. percentage of 15%. The simulations were conducted in Matpower and Matlab [33]. The observations 5.1. Simulation Results are reported in the following subsection. 5.1. Simulation Results Figure 7 shows the generator’s ability to smooth the wind fluctuation in Case 1. It is clear that the generator capability deviated from the imbalanced power. The generator capability varies owing 5.1. Simulation Results Figure 7 shows the generator ’s ability to smooth the wind ﬂuctuation in Case 1. It is clear to the wind fluctuation, negative or positive, and the different generator output for every time Figure 7 shows the generator’s ability to smooth the wind fluctuation in Case 1. It is clear that that the generator capability deviated from the imbalanced power. The generator capability varies interval. The generator capability was smaller than the imbalanced power most of the time, which the generator capability deviated from the imbalanced power. The generator capability varies owing owing to the wind ﬂuctuation, negative or positive, and the different generator output for every time indicates that the AGC units cannot smooth the wind prediction error, and hence the curtailment of to the wind fluctuation, negative or positive, and the different generator output for every time interval. The generator capability was smaller than the imbalanced power most of the time, which renewable generation, or even load shedding, are inevitable during large fluctuations. The estimated interval. The generator capability was smaller than the imbalanced power most of the time, which indicates that the AGC units cannot smooth the wind prediction error, and hence the curtailment of load shedding was 130.77 kWh. It can be obviously anticipated that additional balancing reserves are indicates that the AGC units cannot smooth the wind prediction error, and hence the curtailment of renewable generation, or even load shedding, are inevitable during large ﬂuctuations. The estimated required in order to accommodate the wind output as much as possible. renewable generation, or even load shedding, are inevitable during large fluctuations. The estimated load sheddi As ng disc was ussed 130.77 earlier kWh. , the Itsm can art be appl obviously iances—anticipated including AC, that Wadditional H, and EV balancing loads—are reserves highly are load shedding was 130.77 kWh. It can be obviously anticipated that additional balancing reserves are flexible, and the shifting of the smart appliances in time to smooth the wind power fluctuation will required in order to accommodate the wind output as much as possible. required in order to accommodate the wind output as much as possible. bring greater benefits. The questions of how the smart appliances respond and how much DRP As discussed earlier, the smart appliances—including AC, WH, and EV loads—are highly ﬂexible, As discussed earlier, the smart appliances—including AC, WH, and EV loads—are highly supports the balancing of wind power forecasting error are now explored. and the shifting of the smart appliances in time to smooth the wind power ﬂuctuation will bring flexible, and the shifting of the smart appliances in time to smooth the wind power fluctuation will greater beneﬁts. The questions of how the smart appliances respond and how much DRP supports the bring greater benefits. The questions of how the smart appliances respond and how much DRP balancing of wind power forecasting error are now explored. supports the balancing of wind power forecasting error are now explored. Figure 7. The system operational power without DR. Figure 7. The system operational power without DR. Figure 7. The system operational power without DR. Power (MW) Power (MW) Appl. Sci. 2017, 7, 1132 13 of 20 Appl. Sci. 2017, 7, 1132 6 of 8 Figure 8 indicates the DRP and AGC unit capabilities and the unbalanced power. The red line Appl. Sci. 2017, 7, 1132 6 of 8 represents Figthe ure AGC 8 indiunit cates capability the DRP ,an which d AGC is assumed unit capabilitie negative s anwhen d the unbalanced it provides r po eserve, wer. Th and e red vice line versa. represents the AGC unit capability, which is assumed negative when it provides reserve, and vice The green line expresses the summation of DRP and AGC unit capability. The DRP is unlocked thanks Figure 8 indicates the DRP and AGC unit capabilities and the unbalanced power. The red line versa. The green line expresses the summation of DRP and AGC unit capability. The DRP is unlocked to the represent domestic s the thermal AGC uni storages t capabithat lity, wh enable ich is load assume shifting d negin ative order when to smooth it provid the es re wind servefor , an ecast d vicerr e or. thanks to the domestic thermal storages that enable load shifting in order to smooth the wind forecast It isversa worth . Th stating e green that line the expcustomers’ resses the summ comfort—including ation of DRP and the AGC temperatur unit capability e prefer . The ences, DRP travel is unlocked distance error. It is worth stating that the customers’ comfort—including the temperature preferences, travel thanks to the domestic thermal storages that enable load shifting in order to smooth the wind forecast ,and charging times—are respected at all times. However, as has been discussed in an earlier part of distance ,and charging times—are respected at all times. However, as has been discussed in an earlier error. It is worth stating that the customers’ comfort—including the temperature preferences, travel this paper, the DR strategy is not restricted to some speciﬁc method. The DR strategy could affect the part of this paper, the DR strategy is not restricted to some specific method. The DR strategy could distance ,and charging times—are respected at all times. However, as has been discussed in an earlier following DRP, which varies at different time intervals. The DRP may not likely be large enough to affect the following DRP, which varies at different time intervals. The DRP may not likely be large part of this paper, the DR strategy is not restricted to some specific method. The DR strategy could smooth the wind forecast error. This phenomenon is observed during 01:50–02:44 a.m. The load-supply enough to smooth the wind forecast error. This phenomenon is observed during 01:50–02:44 a.m. The affect the following DRP, which varies at different time intervals. The DRP may not likely be large matching is disturbed because of large wind forecast error and little DRP. Consequently, the utilization load-supply matching is disturbed because of large wind forecast error and little DRP. Consequently, enough to smooth the wind forecast error. This phenomenon is observed during 01:50–02:44 a.m. The of wind power could be enhanced if the system had more allowed DRP. It is worth revealing that the utilization of wind power could be enhanced if the system had more allowed DRP. It is worth load-supply matching is disturbed because of large wind forecast error and little DRP. Consequently, the mismatching, wind power curtailment, and load shedding are a result of large ﬂuctuations and revealing that the mismatching, wind power curtailment, and load shedding are a result of large the utilization of wind power could be enhanced if the system had more allowed DRP. It is worth DRP uncertainty. fluctuations and DRP uncertainty. revealing that the mismatching, wind power curtailment, and load shedding are a result of large fluctuations and DRP uncertainty. Figure 8. DRP and AGC unit capabilities and wind prediction error power. Figure 8. DRP and AGC unit capabilities and wind prediction error power. Figure 8. DRP and AGC unit capabilities and wind prediction error power. Figure 9 shows the smart appliance results with and without the proposed method. In the Figure 9 shows the smart appliance results with and without the proposed method. In the process process of optimization, the smart appliances provide up and down reserve based on the time- Figure 9 shows the smart appliance results with and without the proposed method. In the of optimization, the smart appliances provide up and down reserve based on the time-varying DR varying DR potential. It is obvious from the upper figure that the smart appliance power before DR process of optimization, the smart appliances provide up and down reserve based on the time- potential. It is obvious from the upper ﬁgure that the smart appliance power before DR is different from is different from the power with no DR, which means the DR potential under these two conditions varying DR potential. It is obvious from the upper figure that the smart appliance power before DR the power with no DR, which means the DR potential under these two conditions are also different. are also different. The difference between smart appliance power after DR and before DR is within is different from the power with no DR, which means the DR potential under these two conditions The difference between smart appliance power after DR and before DR is within the DR potential the DR potential value. When the DR potential is not sufficient with negative unbalanced power, are also different. The difference between smart appliance power after DR and before DR is within some other loads would be shed, like the green line of the lower figure. value. When the DR potential is not sufﬁcient with negative unbalanced power, some other loads the DR potential value. When the DR potential is not sufficient with negative unbalanced power, would be shed, like the green line of the lower ﬁgure. some other loads would be shed, like the green line of the lower figure. Figure 9. The smart appliance results with and without the proposed method. Figure 9. The smart appliance results with and without the proposed method. Figure 9. The smart appliance results with and without the proposed method. Appl. Sci. 2017, 7, 1132 14 of 20 Appl. Sci. 2017, 7, 1132 7 of 8 The The conventional conventional DRP DRP is is calculated calculated in in advance, advance, such such that that the the DRP DRP is is constant. constant. It It is is assume assumed d that that the upward DRP is 100 MW and the downward DRP is 45 MW. Figure 10 shows the comparative the upward DRP is 100 MW and the downward DRP is 45 MW. Figure 10 shows the comparative r result esults s between between the the pro proposed posed time-varying time-varying DRP DRP and and c constant onstant DRP DRP.. During During 00:00–01:20 00:00–01:20 a.m., a.m., the the total total fluctuation is positive and the smart appliances respond to the increment signal. The lower figure ﬂuctuation is positive and the smart appliances respond to the increment signal. The lower ﬁgure depicts depicts that that the the gr gre een en shadow shadow is is the the wind wind curtailment curtailment ener energy gy because because the the DRP DRP is is lower lower than than the the required response capacity of the load side. During 01:29–03:00 a.m., the total fluctuation is negative required response capacity of the load side. During 01:29–03:00 a.m., the total ﬂuctuation is negative and the smart appliances respond to the reduction signal. The purple shadow is the load shedding and the smart appliances respond to the reduction signal. The purple shadow is the load shedding energy. The amount of load shedding is greater with constant DRP than with the time-varying DRP. energy. The amount of load shedding is greater with constant DRP than with the time-varying DRP. Demand response potential Required response capacity of load side Wind curtailment or load shedding -50 -100 -150 -200 00:00 00:30 01:00 01:30 02:00 02:30 03:00 Time (h) (a) Demand response potential Required response capacity of load side Wind curtailment or load shedding -50 -100 -150 -200 00:00 00:30 01:00 01:30 02:00 02:30 03:00 Time (h) (b) Figure 10. Comparative results: (a) load response results with time-varying DRP; and (b) load Figure 10. Comparative results: (a) load response results with time-varying DRP; and (b) load response response results with constant DRP. results with constant DRP. When the wind forecast error is large, there should be DR participation because of the AGC When the wind forecast error is large, there should be DR participation because of the AGC units’ units’ output restrict. If the generator ramp constraint is not considered, the AGC units can provide output restrict. If the generator ramp constraint is not considered, the AGC units can provide an an adequate up and down reserve, which is not correct in reality. The results are indicated in Figure adequate up and down reserve, which is not correct in reality. The results are indicated in Figure 11 11 compared with taking the ramp constraint into account. compared with taking the ramp constraint into account. After the wind accommodation is maximized with the combination of generators and smart appliances, the line power varies and may be beyond the limit. Table 2 shows the line active power without and with power ﬂow transmission constraint at a given time. As shown in Figure 4, the branches 15–21, 18–21, 19–20, and 20–23 are double circuit lines. Therefore, their power limit and line active power are depicted as the corresponding parameter of the single line multiplied by two in Table 2. It can be seen that the active power of branch 14–16 shown in red frame exceeds the power limit in the condition of not considering the power ﬂow transmission constraint. Power (MW) Power (MW) Appl. Sci. 2017, 7, 1132 15 of 20 Appl. Sci. 2017, 7, 1132 15 of 20 Figure Figure 11. 11. Results Results of DR and of DR and generator generator outp output ut vari variation ation without/with the ramp constraint. without/with the ramp constraint. Appl. Sci. 2017, 7, 1132 16 of 20 After the wind accommodation is maximized with the combination of generators and smart Table 2. Line power without/with transmission constraint. Table 2. Line power without/with transmission constraint. appliances, the line power varies and may be beyond the limit. Table 2 shows the line active power without and with power flow transmission constraint at a given time. As shown in Figure 4, the Branch Power Limit (MW) Line Power w/o Transmission Constraint (MW) Line Power with Transmission Constraint (MW) 1–2 140 21.88 21.45 branches 15–21, 18–21, 19–20, and 20–23 are double circuit lines. Therefore, their power limit and line 1–3 140 −58.96 −58.04 active power are depicted as the corresponding parameter of the single line multiplied by two in 1–5 140 12.76 12.26 2–4 140 −6.72 −6.96 Table 2. It can be seen that the active power of branch 14–16 shown in red frame exceeds the power 2–6 140 14.46 14.27 limit in the condition of not considering the power flow transmission constraint. 3–9 140 35.81 34.98 3–24 408 −257.13 −253.79 4–9 140 −73.72 −72.44 Table 2. Line power without/with transmission constraint. 5–10 140 −51.92 −51.02 Branch6–10 1 Power Li40 mit (MW) Line Power w/o Transmiss −108.88 ion Constraint (MW) Line Power with Transm −107.55 ission Constraint (MW) 71–8 1 –2 140 40 −2 271..88 00 −2 271..45 00 8–9 140 −104.33 −103.39 1–3 140 −58.96 −58.04 81–10 1 –5 140 40 −1 752..76 95 −1 752..26 37 9–11 408 −145.52 −143.76 2–4 140 −6.72 −6.96 92–12 4 –6 108 40 −15314.46 .56 −15214.27 .42 10–11 408 −201.36 −198.90 3–9 140 35.81 34.98 130–1–24 4 2 408 08 −−209 257.41 .13 −−207 253.56 .79 11–13 400 −115.47 −115.36 4–9 140 −73.72 −72.44 151–1–10 1 4 400 40 −− 231 51..40 92 −− 227 51..30 02 12–13 400 −101.29 −100.09 6–10 140 −108.88 −107.55 12–27–8 1 3 400 40 −− 261 27..67 00 −− 259 27..90 00 13–23 400 −236.49 −235.17 8–9 140 −104.33 −103.39 184–1–10 1 6 400 40 −− 405 75..49 95 −−75 400 .37 195–1–11 4 6 400 08 −8 1458.09 .52 −8 1436.98 .76 9–12 408 −153.56 −152.42 15–21 400 × 2 −237.51 × 2 −235.28 × 2 1510–1–241 4 4008 0 −25 2017.13 .36 −25 1983.79 .90 10–12 408 −209.41 −207.56 16–17 400 −347.17 −342.54 116–11–19 4 3 400 00 −7 1157.30 .47 −7 1151.17 .36 11–14 400 −231.40 −227.30 17–18 400 −205.58 −200.99 117–22–12 4 3 400 00 −−141 101.59 .29 −−141 100.55 .09 1812–2–213 4 400 00 × 2 −4−6 261 .70 × .67 2 −4−8 259 .94 × .90 2 1913–2–203 4 400 00 × 2 −4−3 236 .92 × .49 2 −4−6 235 .20 × .17 2 20–23 400 × 2 −25.60 × 2 −27.15 × 2 14–16 400 −405.49 −400 21–22 400 −158.41 −158.45 15–16 400 88.09 86.98 15–21 400×2 −237.51×2 −235.28×2 15–24 400 257.13 253.79 The wind forecasting power and its error are 225.78 MW and −74.06 MW, respectively. The load 16–17 400 −347.17 −342.54 The wind forecasting power and its error are 225.78 MW and 74.06 MW, respectively. The load 16–19 400 77.30 71.17 forecasting power is 2545.45 MW. Table 3 shows the results with and without considering power forecasting power is 2545.45 MW. Table 3 shows the results with and without considering power ﬂow flow transmission constraint. In the condition of with power flow transmission constraint, even transmission constraint. In the condition of with power ﬂow transmission constraint, even though though the line power is lower because of less load fluctuation, the smart appliances respond to the the line power is lower because of less load ﬂuctuation, the smart appliances respond to the 4.06 MW 4.06 MW load reduction signal in order to keep the line power within the limitation. The DR power load r is eduction 0 without consi signal d in eri or nder g the power fl to keep the ow tra linen power smission within constraint, in the limitation. which the ge The DR nerator re powergulating is 0 without capability is abundant to balance the fluctuation. Therefore, it is indispensable to consider the power flow transmission constraint in the process of optimizing the utilization of DR. Table 3. Results without/with transmission constraint. Transmission Constraint Generator Power (MW) Load Fluctuation (MW) DR Power (MW) with 2390.58 0.92 −4.06 without 2405.53 11.81 0 5.2. Wind and Smart House Penetration Level In the basic simulation, it was supposed that the wind penetration percentage is 20% and the DR percentage is 15%. However, this may not be considerate in practice. Therefore, it is imperative to evaluate the impact of the wind penetration and smart houses enrollment level on the wind energy curtailment and load shedding. There are several assumptions for the wind percentage and DR percentage, which are shown as follows. (1) The wind penetration percentage equals the installed capacity of wind generation divided by the maximum total load. (2) The maximum power of a house in one day is 12 kW. The total number of houses is maximum total load divided by 12 kW. Appl. Sci. 2017, 7, 1132 16 of 20 considering the power ﬂow transmission constraint, in which the generator regulating capability is abundant to balance the ﬂuctuation. Therefore, it is indispensable to consider the power ﬂow transmission constraint in the process of optimizing the utilization of DR. Table 3. Results without/with transmission constraint. Transmission Constraint Generator Power (MW) Load Fluctuation (MW) DR Power (MW) with 2390.58 0.92 4.06 without 2405.53 11.81 0 5.2. Wind and Smart House Penetration Level In the basic simulation, it was supposed that the wind penetration percentage is 20% and the DR percentage is 15%. However, this may not be considerate in practice. Therefore, it is imperative to evaluate the impact of the wind penetration and smart houses enrollment level on the wind energy curtailment and load shedding. There are several assumptions for the wind percentage and DR percentage, which are shown as follows: (1) The wind penetration percentage equals the installed capacity of wind generation divided by the maximum total load. (2) The maximum power of a house in one day is 12 kW. The total number of houses is maximum total load divided by 12 kW. (3) All the smart houses contain three kinds of smart appliances, whose working parameters are indicated in Table 4. (4) The DR percentage is a number of smart houses expressed as a fraction of all houses. Table 4. Parameters of smart appliances. EV: electric vehicle. Parameter Value Unit Cooling set point 22 C AC thermostat dead band 1 C AC power consumption 3 kW WH temperature set point 47 C WH thermostat dead band 6 C WH power consumption 4 kW EV power consumption 3.3 kW EV efﬁciency of driving 3.846 mile/kWh EV charging efﬁciency 0.9 - Quite a few simulations have been performed by changing the wind and smart house penetration percentages. Based on the mentioned assumptions, the simulation data are shown as follows: If the maximum load is 2658 MW, then the installed wind capacities are approximately 265 MW, 530 MW, and 795 MW when the wind penetration percentages are 10%, 20%, and 30%, respectively, and the total number of smart houses in the studied system are roughly 11,050, 22,100, 33,150, and 44,200 when the DR percentages are 5%, 10%, 15%, and 20%. The wind generation curtailment and load shedding are listed in Table 5 with different wind and DR percentages. Here, the comfort ranges of smart appliances are ﬁxed. The wind energy curtailment decreases from 645.71 MW to 158.4 MW when the wind percentage is 30% and the DR percentage is from 0% to 20%. From the relation between DR percentage and wind energy curtailment with 10% and 20% wind percentage, it is easily derived that the wind curtailment could reduce to 0 with the DR percentage increasing as the wind percentage is 30%. There is a similar variation tendency for load shedding as the wind and DR percentage change. Appl. Sci. 2017, 7, 1132 8 of 8 Appl. Sci. 2017, 7, 1132 17 of 20 Table 5. Wind energy curtailment and load shedding energy with different wind and DR percentage. Wind Percentage DR Percentage Wind Energy Curtailment (MWh) Load Shedding (MWh) 00:00 01:00 02:00 03:00 04:00 05:00 0% 29.50 95.85 Time (h) 5% 0 42.30 10% 0 23.21 10% 15% 0 7.52 1500 20% 0 0.29 0% 148.74 262.28 1000 5% 41.87 175.20 20% 10% 3.26 148.36 15% 0 130.77 20% 0 108.21 0% 645.71 385.38 00:00 01:00 02:00 03:00 04:00 05:00 5% 443.40 318.88 Time (h) 30% 10% 329.52 290.79 Actual load power Load prediction power Generator prediction power 15% 224.10 264.24 Actual wind power Wind prediction power Actual generator power 20% 158.40 239.70 Figure 11. Results of DR and generator output variation without/with the ramp constraint. This result will serve as a strong motivation to provide an incentive to distribution companies to to utilize more DR. Figure 12 shows the impact of DR and wind percentage on wind curtailment utilize more DR. Figure 12 shows the impact of DR and wind percentage on wind curtailment and and load shedding using the interpolation method based on the information in Table 5. load shedding using the interpolation method based on the information in Table 5. Figure 12. Impact of DR and wind percentage on wind curtailment and load shedding. Figure 12. Impact of DR and wind percentage on wind curtailment and load shedding. Figure 12 shows the correlation among wind percentage, DR percentage, and wind power Figure 12 shows the correlation among wind percentage, DR percentage, and wind power curtailment/load shedding. The wind curtailment or load shedding reduce as the number of enrolled curtailment/load shedding. The wind curtailment or load shedding reduce as the number of enrolled smart houses increases and wind power decreases. Power (MW) Power (MW) Appl. Sci. 2017, 7, 1132 18 of 20 6. Conclusions This paper proposes a real-time optimal method to mitigate the WPFE impacts by the coordination of AGC units and residential DR. Consequently, a comprehensive model is proposed that enables AGC units and DR to function to mitigate the effect of wind power forecasting error. The model is applicable no matter what kind of DR load control method is used. Since the wind forecasting error may not be offset by employing conventional generation resources and further leads to wind curtailment or load shedding, the smart appliances’ loads—including AC, WH, and EV—are applied in the optimal scheduling to alleviate the WPFE impacts. Furthermore, the quantifying DR potential method is presented considering consumers’ comfort and smart appliances’ dynamic characteristics, which reﬂect the time-scale variability of DRP. To ensure the safety and stability of the power system, the generator ramp constraint and power ﬂow transmission constraint are necessarily considered. The proposed method could reveal the correlation among the wind percentage, DR percentage, and wind curtailment/load shedding, which can provide ancillary decisions under diverse operational conditions. The obtained results conﬁrmed that the collaboration of residential DR and AGC units can improve the ability of wind accommodation and reduce load shedding. Other DR categories, such as the industrial DR and commercial DR, should be considered in future studies. Acknowledgments: This work is supported by the National Natural Science Foundation of China (grant no. 51577030). Author Contributions: Jia Ning, Yi Tang and Bingtuan Gao contributed in developing the ideas of this research. Jia Ning performed this research. All the authors read and approved the ﬁnal manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest. Abbreviations AC Air Conditioner AGC Automatic Generation Control DCOPF Direct Current Optimal Power Flow DO Dispatching Order DR Demand Response DRP Demand Response Potential EV Electric Vehicle EWH Electric Water Heater SOC State-of-Charge RTCO Real Time Control Order WH Water Heater WPFE Wind Power Forecasting Error References 1. Menemenlis, N.; Huneault, M.; Robitaille, A. Computation of dynamic operating balancing reserve for wind power integration for the time-horizon 1–48 hours. IEEE Trans. Sustain. Energy 2012, 3, 692–702. [CrossRef] 2. Tamrakar, U.; Shrestha, D.; Maharjan, M.; Bhattarai, B.P.; Hansen, T.M.; Tonkoski, R. Virtual inertia: Current trends and future directions. Appl. Sci. 2017, 7, 654. [CrossRef] 3. Zhang, D.; Eseye, A.T.; Zhang, J.; Li, H. Short-term wind power forecasting using a double-stage hierarchical ANFIS approach for energy management in microgrids. Prot. Control Mod. Power Syst. 2017, 2. [CrossRef] 4. Zhang, N.; Kang, C.; Xia, Q.; Liang, J. 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Applied Sciences – Multidisciplinary Digital Publishing Institute
Published: Nov 3, 2017
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