Unit Commitment with Ancillary Services in a Day-Ahead Power Market

: This paper integrates Discrete Particle Swarm Optimization (DPSO) and Sequential Quadratic Programming (SQP) to propose a DPSO-SQP method for solving unit commitment problems for ancillary services. Through analysis of ancillary services, including Automatic Generation Control (AGC), Real Spinning Reserve (RSR), and Supplemental Reserve (SR), the cost model of unit commitment was developed. With the requirements of energy balance, ancillary services, and operating constraints considered, DPSO-PSO was used to calculate the energy supply of each source, including the associated AGC, RSR, and SR, and the operating cost of a day-ahead power market was calculated. A study case using the real data from thermal units of Taipower Company (TPC) and Independent Power Producers (IPPs) demonstrated effective results for the “summer” and “non-summer” seasons, as classiﬁed by TPC for the two charging rates. According to the test cases in this research, costs without ancillary services in non-summer and summer seasons are higher than those with ancillary services. The simulation results are also compared with the Genetic Algorithm (GA), Evolutionary Programming (EP), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). DPSO-PSO shows effectiveness in solving unit commitment problems with enhanced sorting efﬁciency, and a higher probability of reaching the global optimum.


Introduction
Nuclear plants and large-scale thermal plants generally supply base loads, while medium thermal plants and water plants supply medium loads, and the peak load is supplied by gas turbines and diesel engines. The major purpose of unit commitment is to determine how to commit various units to satisfy the 24 h load demands under related constraints [1]. Ancillary services have now become indispensable in terms of operation [2,3]. If ancillary services are absent, there may be a series of problems related to safety, reliability, and power quality. Unit commitment with ancillary services is a more complicated issue than the traditional unit commitment problem, as unit commitment with ancillary services is a combinatorial, mixed-integer, continuous and multi-dimensional problem of "energy" and "capacity". In the power transaction market, the load forecast of energy supply and the ancillary service capacity need to be simultaneously evaluated. However, unit commitment in ancillary services must consider the fact that online units can rapidly adjust to satisfy the ancillary services' capacity to safely conform to the operational standards of a power system. As there are more variables and more confined constraints, optimal power dispatch becomes very tedious and difficult to achieve.
By considering the operations of various plants, they can rapidly respond to the load change with all units coordinating for energy balance. The appropriate supply of ancillary services requires the establishment of economic models that can pay for these services, whereby special attention is given to Automatic Generation Control (AGC), Real-time Spinning Reserve (RSR), and Supplemental Reserve (SR) in TPC [4]. AGC, including upregulation and downregulation, is the first level of regulation in reserve for the system operator. RSRs are units that can respond quickly to accidents or load increases. SR plays an important role in maintaining system security, as this reserve is more time-consuming, and is used when RSR cannot satisfy the reserve needs. Ancillary services, as required to ease the previously scheduled generating capacity, are based on online generating plants. Therefore, the operations of the energy market should consider ancillary services in unit commitment schedules.
Unit commitment for the power market is an urgent problem for the TPC. The scheduling strategy contains a sequential schedule that determines the unit on/off state in each time interval, and assigns the power scheduling and ancillary services' scheduling results. There are many constraints for unit commitment in the power market, such as unit generation limits, on/off states, operating time, and ramping rates. Many local minima could be expected with mixed integers, which increase the complexity of the problem. It is difficult to find the optimal solution using a traditional mathematical tool. Ref. [5] concluded that unit commitment, as addressed before 2003, may face problems of dimensionality, excessive computational time, and local optimality. Recently, artificial intelligence algorithms are being used in unit commitment optimization [6][7][8][9][10]; while part of the artificial intelligence algorithms can overcome various constraints, convergent rates are poor if there are numerous variables, and a long solving time can be expected. Among references regarding ancillary services, [11] used mixed-integer programming and an artificial neural network to analyze and simulate the condition of a power market in order to solve the competitive bidding strategy of ancillary services. Ref. [12] discussed the ancillary services of different reserve unit capacities, and combined the settlement price with an optimum allocation in order to properly implement the strategy of demand response in the system. Ref. [13] proposed a payment mechanism, and properly implemented energy costs and demand charges by considering energy dispatch in ancillary services. Ref. [14] used dynamic optimum power flow to analyze the dispatch of energy in relation to ancillary services. In terms of safety and unit commitment emergency analysis, [15] used N-k fault analysis to seek the work of the demand response in ancillary services, in order to address disasters caused by emergencies. Since microgrids have more flexibility in coordinating power sources and loads, they are usually [16] considered as a candidate for the provision of ancillary services. Ref. [17] used a renewable ancillary service to enhance power system operations. Regarding the ancillary services of frequency control, voltage regulation, and active power management, the allocation and management of costs are the most important issues of system operation [18][19][20][21]. Ref. [22] used pumped storage hydropower plants to provide the ancillary services for balancing supply and demand. The AGC unit's quantitative evaluation, unit selection [23], and power transmission line in ancillary service cost allocation [24] are all discussed. Real-time ancillary service is now a non-negligible function in an electrical deregulated environment. This paper proposes a hybrid DPSO-SQP by combining Discrete Particle Swarm Optimization (DPSO) [25] with Sequential Quadratic Programming (SQP) [26] to compute the power scheduling of various units and ancillary services in the power market. PSO is introduced with simplicity, easy implementation, and mutual independence in simulation, whereby the particles only need to exchange information once with the group optimum. However, the performance of the PSO is related to the initial distribution of the swarm, meaning that if the initial states of the swarm are near the local optimum region, the swarm may become trapped, which is the disadvantage of PSO. Unit commitment in ancillary services can be considered as two sub problems: "determining the on/off state of units in various time intervals" and "electricity generation assignment", which has many constraints. Generally speaking, while appropriate PSO parameter settings can accelerate the convergence, a good set of parameters may not be easy to come by. It is generally obtained from many experiences or from other settings with sophis-ticated enumeration process, thus, the problem is further complicated. This paper uses DPSO to compute the discrete mode of the "on/off state of units" for various time intervals, where parameter settings can be effectively reduced. SQP will then calculate power generation and ancillary services. The proposed DPSO-SQP used the thermal units of TPC and Independent Power Producers (IPPs) as the test sample, and the simulation results are compared with other algorithms, including the Genetic Algorithm (GA), Evolutionary Programming (EP), Particle Swarm Optimization (PSO), and Simulated Annealing (SA) [27][28][29][30]. The accuracy and robustness of the algorithm also show a higher probability of reaching a global optimum.

Problem Formulation
The unit commitment with ancillary services should satisfy the load demand, and must consider if the online units can respond to the load change in a short time period, i.e., the demands from AGC, RSR, and SR. The mathematical model involves multiple variables, which are mostly confined to the constraints of unit characteristics. This paper aims to minimize the total cost, including electric energy, AGC, RSR, and SR costs. That is, The startup cost is divided into hot-start and cold-start cost, as expressed by Other related constraints are [4,5] a. Load balance b.
Upper and lower limits of unit generation c.
Ramping down/up rate limitations d. Minimum up/down time The AGC rate for the load up/down is 3 min, RSR has a load up rate of 30 min, and SR has a load up rate of 60 min. Related constraints are described as follows [5]: The AGC demand is esxpresed as The response to the rise/down rate of 3 min can be expressed as B. RSR limitation a The RSR demand is expressed as The rise rate of 30 min is expressed as C. SR limitation a The SR demand is expressed as The rise rate of 60 min is expressed as

Proposed Methodology
Regarding the unit commitment problem, two types of variables must be computed: (1) unit state-U i (t) is an integer variable; (2) generation output: P i (t) is a continuous variable.
The proposed DPSO-SQP uses DPSO to compute the unit state in the state matrix, and uses SQP to compute the assigned generation output of various units. The proposed methodology is described below.

DPSO
The traditional PSO is modified with simplicity, easy implementation, and mutual independence, where the particles only exchange information once with the group optimum. In the traditional PSO, the position and the velocity of general particles can be expressed as [29] Position of the i − th particle : Velocity of the i − th particle : The self-cognition model can be expressed as and the social model can be expressed as The two behavior patterns can be integrated, and the updating of the PSO is expressed as Parameters c 1 and c 2 have a significant effect on the search result, but it is difficult to get the appropriate parameters. Since good parameters are difficult to come by, PSO is modified and improved in this paper, where parameter settings can be effectively reduced for the discrete mode by using the following formula: where round is the discriminant of rounding for simplifying the equation, which limits the output solution to binary states of 0 and 1. Since c 1 and c 2 are replaced, the computing process of DPSO will be relatively stable with binary values.

SQP
SQP is derived from Lagrangian relaxation. The idea is to convert the problem into a dual-optimization problem, where the problem and its numerous constraints are simplified. With the unit on/off state obtained from DPSO and the assigned generation output calculated by SQP, the minimum total production cost can be calculated. The cost function of units is described with a polynomial function, expressed as [26] Minimize x∈ n subject to : g i (x) = 0, i = 1, 2, . . . , m g i (x) ≤ 0, i = m + 1, m + 2, . . . , n x l ≤ x ≤ x u H : Hessian Matrix g i (x): the equal/inequal function x l /x u : thelower/upperlimitso f variablex The SQP solving process contains three steps.

a.
Update the Hessian matrix b.
Use Line Search and the Merit Function to update system parameters.
Line Search : Merit Function:

DPSO-SQP Implementation Procedure
The procedure of using DPSO-SQP to compute unit commitment with ancillary services is described as follows.
(1) Input the load demand, as well as the AGC, RSR, and SR demands on ancillary services. The flow chart of the DPSO-SQP problem is shown in Figure 1.

Simulation Results
Many study cases were conducted for the thermal units of TPC and IPP, including 14 coal-fired units, 23 gas-fired units, and 6 oil-fired units of TPC, and 5 coal-fired units and 9 gas-fired units of IPP. There are 57 units in total. The maximum generation output, minimum generation output, ramping rates, electric energy price, and startup costs are shown in [31]. The minimum operating time of a coal-fired unit is set as 8 h, the minimum operating time of a gas-fired unit is set as 4 h, and the minimum operating time of an oil-fired unit is set as 6 h. A typical day shown as an example is chosen from the middle ten days of March, and another single day example is taken from the first ten days of July in Taiwan in 2016. The single-day load demands represent the summer and non-summer seasons as shown in Figures 2 and 3. The daily load demand is from 1.2 MW to 2.35 MW for non-summer and from 1.9 MW to 2.6 MW for summer. The demand of AGC is assumed to be 2% of the load demand, the RSR is 3%, and the SR is 5% of the load.

Unit Commitment with Ancillary Services during Non-Summer
With 57 generator units, four costs per unit including energy, AGC, RSR, and SR, were used. Similarly, four assigned quantities per unit were used. Figure 4   The electric energy and the demands on ancillary services for non-summer are shown in Tables 1 and 2. The coal-fired unit of TPC and IPP provided 52.02% of the electric energy, while the gas-fired unit of TPC and IPP provided 47.32%. The most ancillary services are provided by gas units: AGC (98.58%), RSR (100.00%), and SR (99.83%). The oil-fired unit has a higher cost and provides much less electric energy and ancillary services.

Unit Commitment in Summer
A typical summer day solved by DPSO-SQP is shown in Figure 5. The total demands for the electric energy, AGC, RSR, and SR are 55,3734 MWh, 11,041 MWh, 16,605 MWh, and 27,681 MWh, respectively. The daily cost of the unit commitment on this summer day is MNT 1094.307.
The electric energy and demands on ancillary services on a typical summer day are shown in Tables 3 and 4. The gas-fired units of TPC and IPP provided 51.48% energy. The gas-fired units also provided most ancillary services: AGC (86.78%), RSR (89.02%), SR 46.28%. The electric energy of an oil-fired unit in the summer day is higher than that in the non-summer season by 8655 MWh (i.e., 2.15%) and the proportions of AGC (13.21%), RSR (10.98%), and SR (53.72%) also greatly increased.  This paper uses DPSO-SQP to calculate the minimum cost of electric energy in summer and non-summer, which are MNT 918.020 and MNT 900.081, respectively. According to the case study in this paper, costs in non-summer and summer are higher without ancillary services by MNT 17.939 and MNT 36.857, as shown in Table 5. The cost saving of unit commitment with ancillary services in summer is twice as high as that in non-summer. As power system operations are often accompanied by uncertainties-especially nowadays by the impact of renewable energies, where the generation could have a sudden change due to volatile weather conditions-appropriate ancillary service is important to ensure the safe and stable operation of the system, which must be considered in the power market.

Convergent Characteristic Analysis
The convergent characteristic of DSPO-SQP analysis is shown in Figure 6. The PSO, SA, GA, and EP are all compared. According to Figure 6, DPSO-SQP can reach convergence for about 65 iterations, and has a better convergent rate than other evolutionary algorithms. Table 6 shows the best values achieved by various algorithms. It shows that DPSO-SQP has the capability of reaching the global optimum better than other algorithms.   Table 7 shows the robustness of DPSO-SQP. It can be shown that DPSO-SQP is more robust and reaches the optimum level more often than other evolutionary algorithms, where the minimums may vary and often trapped in a local optimum. The number of trials reaching the optimum level (NRO) shows that DPSO-SQP is very robust.

Conclusions
Ancillary services are of crucial importance to power supply safety and reliability in the power market. The power scheduling must evaluate the demand on ancillary services, and procure sufficient ancillary services to meet that demand. For generator scheduling, the optimum unit commitment needs to consider ancillary services in terms of reducing costs. Our case study with real data from TPC and IPPs shows an efficient algorithm for power dispatch in a market environment with ancillary services. According to the case study, costs in non-summer and summer are higher by MNT 17.939 and MNT 36.857 without ancillary services. The cost savings of unit commitment with ancillary services in summer are twice as high as those in non-summer seasons. By considering the uncertainties of the new energy from renewables alongside the traditional load change, appropriate ancillary services are important to ensure a stable and safe power network that reduces operating risks.    Demand rise value of the i -th unit within 60 min Variables d Each particle has a d dimension c 1 Moving parameter of individual particle value updating c 2 Moving parameter of the particle following the overall value F i P t i The fuel cost of unit i F AGC,i P t AGC,i The AGC cost of unit i F RSR,i P t

RSR,i
The RSR cost of unit i F SR,i P t

SR,i
The SR cost of unit i in time interval t

Gbest j
The optimal solution in particle swarm after iteration j Self-optimal solution of particle i after iteration j X j i,d Position of particle i in iteration j