Coordinated Dispatch of Power Generation and Spinning Reserve in Power Systems with High Renewable Penetration

Abstract

The spinning reserve demand in high renewable penetration power systems is increasing significantly due to the stochastic and unpredictable nature of renewable power. This paper defines the expected load not supplied ratio (ELNSR) and models uncertainty factors such as unit forced outage rates, load and wind power output prediction errors based on probability density functions. It derives a quantitative relationship between system operating reserves and the ELNSR and uses this quantitative relationship as a constraint for power generation scheduling. Based on this, a coordinated generation and reserve scheduling model for power systems with large-scale wind power is established. Case study results demonstrate that the proposed model can balance both economy and reliability, coordinate the output allocation between wind power and thermal power, and provide an optimized allocation scheme for operating reserves among thermal power units to meet corresponding reliability requirements.

1. Introduction

With the rapid increase in renewable power installations across the world, great challenges have been brought to power system operation. Owing to the stochastic and fluctuating nature of renewable power, the accuracy of its forecast is relatively low, which introduces a new source of uncertainty to the power system generation dispatch.

In order to accommodate this uncertainty, as well as other stochastic factors such as generator outage, load forecast error, etc., a certain amount of spinning reserve is required. In conventional power systems, spinning reserve capacity is usually determined using deterministic methods. Due to the high accuracy of load forecasting and the good regulation performance of conventional units, reserve capacity is usually determined based on a fixed percentage of system load (for example, generally 12–15% in various provinces in China) or the capacity of the largest unit in operation. However, with the integration of large-scale renewable energy sources, which are characterized by low prediction accuracy and difficult regulation of their power output, the system needs to provide more operating reserves to cope with fluctuations in wind power output. Determine reserve capacity based on a fixed percentage would be either not sufficient or too much, which could lead to low economic efficiency. Therefore, the deterministic method for reserve dispatch is no longer applicable [1].

The current research on stochastic power system generation and reserve dispatch can be mainly classified into two categories [2]:

(1)

Sequential Dispatch [3,4,5,6]. The power generation of each unit is dispatched in the first place, and the spinning reserve is dispatched sequentially. This means the power generation and spinning reserve are scheduled independently. It is easy to understand and implement as the scale of the problem is relatively simple and small. However, the solution of sequential dispatch is not always economically optimized. Moreover, the difference in dispatch order will also affect the result.

(2)

Coordinated Dispatch [7,8,9,10,11]. Power generation and spinning reserve are dispatched and optimized at the same time. It aims to minimize the operational cost while satisfying the security and reliability constraints. As wind power installation increases, the need for reserve capacity rises greatly, which leads to the change in operation mode for some conventional units [7], some of which would be replaced by wind turbines while some would be providing reserve capacity rather than generating. Power generation and reserve supply are highly coupled and therefore should be optimized concurrently. Research into this field most focused on reserve-constrained economic dispatch, which gives out the generation scheduling [9,10,11]. The total amount of spinning reserve capacity and its allocation among units is usually not specified. However, in high renewable penetration systems, demands for spinning reserve are much more urgent and frequent. The quantification of spinning reserve requirements during different time periods would help the system operator to ensure system reliability and to cut operational costs. Thus, it is important to investigate the inner relationship between spinning reserve demand and system reliability demand.

The overall contributions of this paper are as follows:

(1)

The spinning reserve demand in high wind power penetration system is quantified based on reliability index: the expected load not supplied ratio (ELNSR). The forced outage rate of conventional units, load and wind power output forecast error are taken into consideration to deduce the formula which gives the quantitative relations between reserve demand and reliability requirement.

(2)

A coordinated dispatch model of power generation and spinning reserve is presented based on the reserve quantification formula. The model aims to minimize the total system operating cost by scheduling the power generation of each unit as well as the reserve allocation during each time period. The modified RTS-96 system is used to verify the effectiveness of the proposed model. The model is solved using CPLEX 12.2 (IBM Co., Ltd., Armonk, NY, USA).

The rest of this paper is organized as follows: In Section 2, the quantitative relationship between reserve demand and reliability requirement is obtained based on the ELNSR. The mathematical model of the coordinated dispatch problem is formulated in Section 3. Case studies and simulation results are given in Section 4, and finally the conclusions are given in Section 5.

2. Quantification of Reserve Demand

2.1. Reliability Index and Reserve Demand

Spinning reserve is intended to maintain system reliability. Thus, a reliability index that can appropriately reflect the system reliability level is crucial for the quantification of reserve demand. There are several reliability indices that can be used to measure the reliability level of the system, such as loss of load probability (LOLP), expected energy not supplied (EENS), expected load not supplied (ELNS), etc. [12]. In this paper, the normalized ELNS, the expected load not supplied ratio (ELNSR), is adopted as the reliability index. It is defined as follows:

$$N=E/L$$

(1)

where N is the ELNSR; E is ELNS; L is load demand. We can see from the equation that the ELNSR is actually the ratio of ELNS and load demand.

Note that for different types of load, usually different reliability levels are required [13,14]. Therefore, we have the following:

$$N_{m0}^t=E_{m0}^t/L_m^t$$

(2)

where $L_m^t$ is the m-th load demand during period t. $N_{m0}^t$ and $E_{m0}^t$ are the desired ELNSR and ELNS.

Now we establish the relationship between reserve demand and system reliability level based on the ELNSR. First, we consider the generator forced outage rate (FOR) and construct an outage scenario set containing all the possible forced outage situations. For each outage scenario, there are two possible sub-scenarios: the reserve capacity is sufficient to cover the loss of generation capacity; otherwise the reserve capacity is less than the loss of generation capacity, then part of the load would be curtailed to cover the energy deficiency. It is defined by the following:

$$L_{\mathrm{c}\mathrm{u}\mathrm{t},k}^t=P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t-R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t$$

(3)

where $L_{\mathrm{c}\mathrm{u}\mathrm{t},k}^t$ is the amount of load curtailed in scenario k during period t; $P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t$ is the sum of lost generation capacity; $R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t$ is the sum of reserve capacity that should have been supplied by faulted units during period t; $R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t$ is the sum of reserve capacity of all the units during period t. They are defined by the following:

$$P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t={\displaystyle \sum _{a\in F_k}{P}_{a,k}^t}$$

(4)

$$R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t={\displaystyle \sum _{a\in F_k}{R}_{a,k}^t}$$

(5)

$$R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t={\displaystyle \sum _i{R}_i^t}$$

(6)

where F_k is the faulted units in scenario k; $P_{a,k}^t$ is the scheduled output of the faulted unit a during period t; $R_{a,k}^t$ is the scheduled reserve capacity should have been provided by the faulted unit a during period t; $R_i^t$ is the reserve capacity provided by unit i during period t, which is defined by the following:

$$R_i^t=\min (P_{\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{p},i},P_{i\max }-P_i^t)$$

(7)

where P_ramp,i is the ramp rate of unit i; P_imax is the maximum output of unit i; $P_i^t$ is the scheduled output of unit i during period t.

As we can learn from (3), $L_{\mathrm{c}\mathrm{u}\mathrm{t},k}^t$ is the amount of load that needs to be curtailed. Note that different principles of load curtailment would lead to different results. In this paper, during an energy deficiency, all types of load demand would be curtailed in proportion to their desired ELNSR. This means the load with higher reliability requirement or lower ELNSR will take less responsibility. That is, during outage scenario k, the amount of load m to be curtailed is given by the following:

$$L_{\mathrm{c}\mathrm{u}\mathrm{t},mk}^t={\displaystyle \frac{E_{m0}^t}{{\displaystyle \sum _m{E}_{m0}^t}}}\times L_{\mathrm{c}\mathrm{u}\mathrm{t},k}^t$$

(8)

where $L_{\mathrm{c}\mathrm{u}\mathrm{t},mk}^t$ is the amount of load m to be curtailed during scenario k.

Combining (3) and (8), we obtain the following:

$$L_{\mathrm{c}\mathrm{u}\mathrm{t},mk}^t={\displaystyle \frac{E_{m0}^t}{{\displaystyle \sum _m{E}_{m0}^t}}}(P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t-R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t)$$

(9)

and from (9) we obtain the following:

$$E_m^t={\displaystyle \sum _k{\beta }_k\times L_{\mathrm{c}\mathrm{u}\mathrm{t},mk}^t}$$

(10)

where $E_m^t$ is the ELNS of load m; β_k is the probability of outage scenario k, which can be obtained using the following:

$${\beta }_k={\displaystyle \prod _{b\in N_k}(1-Y_b)}{\displaystyle \prod _{a\in F_k}{Y}_a}$$

(11)

where N_k is the normal units in scenario k; Y is the forced outage rate.

Combining (9) and (10), we obtain the following:

$$E_m^t={\displaystyle \sum _k{\beta }_k\frac{E_{m0}^t}{{\displaystyle \sum _m{E}_{m0}^t}}(P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t-R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t)}$$

(12)

To ensure the reliability requirement, $E_m^t$ satisfies the following:

$$E_{m0}^t\ge E_m^t$$

(13)

Thus, we obtain the following:

$$E_{m0}^t\ge {\displaystyle \sum _k{\beta }_k\frac{E_{m0}^t}{{\displaystyle \sum _m{E}_{m0}^t}}(P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t-R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t)}$$

(14)

which can also be written as follows:

$${\displaystyle \sum _m{E}_{m0}^t}\ge {\displaystyle \sum _k{\beta }_k(P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t-R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t)}$$

(15)

Now we rephrase (15) using the ELNSR. Combining (2) and (15) we obtain the following:

$${\displaystyle \sum _m(L_m^t{N}_{m0}^t)}\ge {\displaystyle \sum _k{\beta }_k(P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t-R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t)}$$

(16)

and (16) is the relationship between reliability demand the ELNSR and system spinning reserve demand during period t.

Furthermore, the minimum required spinning reserve capacity can be calculated using the following:

$$R_{\mathrm{d}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{d}}^t={\displaystyle \sum _k{\beta }_k(P_{\mathrm{out},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t)}-{\displaystyle \sum _m{L}_m^t{N}_{m0}^t}$$

(17)

where $R_{\mathrm{d}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{d}}^t$ is the minimum spinning reserve capacity demand during period t.

2.2. Uncertainty Description of Load

In this subsection, the impact of load forecast error on reserve demand is investigated. Load demand can be presented as follows:

$$L_{\mathrm{R},m}^t=L_m^t+{\xi }_m^t$$

(18)

where m is the type of load; $L_{\mathrm{R},m}^t$ is the actual load demand; $L_m^t$ is the predicted load demand; ${\xi }_m^t$ is the forecast error. The distribution of ${\xi }_m^t$ can be determined using statistical analysis of a large amount of historical data; generally, it is approximated to be a normal distribution with zero expectation and variance of ${\delta }_m^{t 2}$ [15], which is shown in Figure 1.

${\xi }_m^t$ is a continuous distribution which is not suitable for modelling. In this paper, it is divided into several discrete intervals. The expectation of each interval is taking the median of the interval, and the probability is the integral of the probability density function with respect to this interval length. Take five intervals as an example (see Figure 1), which means there are five possible values during each period t. Therefore, ${\xi }_m^t$ can be recognized as a special multi-state equivalent unit that has a negative output. So, it can be treated using a similar method in II.1 as a multi-state conventional unit. Adding this equivalent unit would expand the outage scenario set. Note that the forced outage rate of this equivalent unit is zero.

Now we introduce the load forecast error to β_k in (11), β_k is rewritten as follows:

$${\beta }_k={\displaystyle \prod _m{\eta }_{m,k}}{\displaystyle \prod _{b\in N_k}(1-Y_b)}{\displaystyle \prod _{a\in F_k}{Y}_a}$$

(19)

where η_m,k is the probability of the forecast error of load m in scenario k. In this paper, this equivalent unit cannot provide reserve capacity, which means $R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t$ and $R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t$ remains the same after introducing load forecast error.

The $P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t$ in (4) should be rewritten as follows:

$$P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t={\displaystyle \sum _{a\in F_k}{P}_{a,k}^t}+{\displaystyle \sum _m{\xi }_{m,k}^t}$$

(20)

where ${\xi }_{m,k}^t$ is the load forecast error in scenario k.

Combining (5), (6), (16), (17), (19) and (20), we obtain the system reliability constraint and the minimum reserve demand considering load forecast error.

2.3. Uncertainty Description of Wind Power

Wind power uncertainty is another important source that greatly impacts system operation in high renewable penetration systems. In this paper, wind power forecast error ${\xi }_W^t$ is also considered to obey a normal distribution with the zero expectation and variance of ${{\delta }_W^t}^2$ [16]. Similarly, the actual wind power output is given as follows:

$$P_{\mathrm{W}\max }^t=P_{\mathrm{W}}^t+{\xi }_{\mathrm{W}}^t$$

(21)

where $P_{\mathrm{W}\max }^t$ is the actual wind power output; $P_{\mathrm{W}}^t$ is the predicted output. Here we adopt a similar technique in II.2 to discretize the wind power forecast error and consider it to be another equivalent multi-state unit. Different from load forecast error, this equivalent unit has a forced outage rate, and the FOR of different states of this equivalent unit is the same as the FOR of the wind turbine.

If we introduce wind power forecast error to β_k in (19), it should be rewritten as follows:

$${\beta }_k={\displaystyle \prod _j{\alpha }_{j,k}}{\displaystyle \prod _m{\eta }_{m,k}}{\displaystyle \prod _{b\in N_k}(1-Y_b)}{\displaystyle \prod _{a\in F_k}{Y}_a}$$

(22)

where α_j,k is the probability of the forecast error state of wind turbine j in scenario k. $P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t$ in (20) also changes after introducing wind power, as follows:

$$P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t={\displaystyle \sum _{a\in F_k}{P}_{a,k}^t}+{\displaystyle \sum _m{\xi }_{m,k}^t}+{\displaystyle \sum _{c\in N_{w,k}}{\xi }_{\mathrm{W},c}^t}+{\displaystyle \sum _{d\in F_{w,k}}{P}_{\mathrm{W},d}^t}$$

(23)

where N_w,k is the normal wind turbine in outage scenario k; F_w,k is the faulted wind turbine in outage scenario k; ${\xi }_{\mathrm{W},c}^t$ is the forecast error of normal wind turbine c; $P_{\mathrm{W},d}^t$ is the scheduled output of the faulted wind turbine.

Combining (5), (6), (16), (22) and (23), we obtain the system reliability constraint with high renewable penetration, as follows:

$${\displaystyle \sum _m{L}_m^t{N}_{m0}^t}\ge {\displaystyle \sum _k{\beta }_k(P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t-R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t)}$$

(24)

$$R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t={\displaystyle \sum _{a\in F_k}{R}_{a,k}^t}$$

(25)

$$R_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}^t={\displaystyle \sum _i{R}_i^t}$$

(26)

$${\beta }_k={\displaystyle \prod _j{\alpha }_{j,k}}{\displaystyle \prod _m{\eta }_{m,k}}{\displaystyle \prod _{b\in N_k}(1-Y_b)}{\displaystyle \prod _{a\in F_k}{Y}_a}$$

(27)

$$P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t={\displaystyle \sum _{a\in F_k}{P}_{a,k}^t}+{\displaystyle \sum _m{\xi }_{m,k}^t}+{\displaystyle \sum _{c\in N_{w,k}}{\xi }_{\mathrm{W},c}^t}+{\displaystyle \sum _{d\in F_{w,k}}{P}_{\mathrm{W},d}^t}$$

(28)

and by combining (5), (6), (17), (22) and (23), we can obtain the minimum spinning reserve demand in high renewable penetration systems, as follows:

$$R_{\mathrm{d}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{d}}^t={\displaystyle \sum _k{\beta }_k(P_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t+R_{\mathrm{o}\mathrm{u}\mathrm{t},k}^t)}-{\displaystyle \sum _m{L}_m^t{N}_{m0}^t}$$

(29)

3. Coordinated Generation and Spinning Reserve Dispatch Model

The aims of our proposed dispatch model are to provide a power generation schedule and spinning reserve allocation among units, as well as the minimum reserve demand during each period. As is discussed in Section 1, once the output of conventional units and wind turbines are determined, the system spinning reserve capacity supplied during this period can be immediately calculated using (7). Therefore, the decision variables in this model are $U_i^t$, $P_{\mathrm{G},i}^t$, $P_{\mathrm{W},j}^t$, which are the on/off status of thermal units, thermal units output and wind turbine output, respectively.

In most previous research, wind power is usually treated as negative load for generation dispatch. This means that wind power is fully accepted by the grid under any condition [17,18]. But in high renewable penetration systems, because of the fluctuation and low forecast accuracy, it may be difficult or even impossible for the conventional units to accommodate such sharp and rapid output fluctuation. In this paper, the wind power output is considered as a decision variable; meanwhile, its cost is set to zero, so the system will accommodate as much as possible wind power and satisfy desired reliability demand.

The objective function to be minimized is the operational cost, as follows:

$$C={\displaystyle \sum _t{\displaystyle \sum _i{C}_i^{\mathrm{S}\mathrm{U}}(1-U_i^{t-1})U_i^t}}+{\displaystyle \sum _t{\displaystyle \sum _{i}F(P_{G,i}^t)}}$$

(30)

$$C_i^{\mathrm{S}\mathrm{U}}=\left\{\begin{array}{l}{C}_i^{\mathrm{h}},T_{i,\mathrm{o}\mathrm{f}\mathrm{f}}\le t_{i,\mathrm{o}\mathrm{f}\mathrm{f}}\le t_{i\mathrm{h}}\\ C_i^{\mathrm{c}},t_{i,\mathrm{o}\mathrm{f}\mathrm{f}}\ge t_{i\mathrm{h}}\end{array}\right.$$

(31)

$$t_{i\mathrm{h}}=T_{i,\mathrm{o}\mathrm{f}\mathrm{f}}+t_{i\mathrm{c}}$$

(32)

$$F(P_{\mathrm{G},i}^t)=a_i{P_{\mathrm{G},i}^t}^2+b_i{P}_{\mathrm{G},i}^t+c_i$$

(33)

where C is the total operational cost; the first half in (30) is the startup cost, where $U_i^t$ is the on/off status of unit i during period t; 1 means on and 0 means off; $C_i^{\mathrm{S}\mathrm{U}}$ is the startup cost of unit i; $C_i^{\mathrm{h}}$ is the hot startup cost; $C_i^{\mathrm{c}}$ is the cold startup cost; T_i,off is the minimum off time of unit i; t_i,off is the actual off time of unit i; t_ih is the hot startup time and t_ic is the cold startup time. The second half in (30) is the fuel cost, where F(.) is the fuel cost function of thermal units; a_i, b_i, c_i are the cost coefficient of thermal units i.

The constraints are as follows:

(1)

Output limits

$$P_{\mathrm{G},i\min }\le P_{\mathrm{G},i}^t\le P_{\mathrm{G},i\max }$$

(34)

$$0\le P_{\mathrm{W},j}^t\le P_{\mathrm{W},j\max }^t$$

(35)

where P_G,imin and P_G,imax are the minimum and maximum output of thermal unit i; $P_{\mathrm{W},j}^t$ is the output of wind turbine j; $P_{\mathrm{W},j\max }^t$ is the forecasted maximum available power of wind turbine j.

(2)

Power balance limits

$${\displaystyle \sum _i{P}_{\mathrm{G},i}^t}+{\displaystyle \sum _j{P}_{\mathrm{W},j}^t}={\displaystyle \sum _m{L}_m^t}$$

(36)

(3)

Ramp rate limits

$$P_{\mathrm{G},i}^{t-1}-T{P}_{\mathrm{G}\mathrm{D},i}\le P_{\mathrm{G},i}^t\le P_{\mathrm{G},i}^{t-1}+T{P}_{\mathrm{G}\mathrm{U},i}$$

(37)

where P_GD,i is the down ramp rate of unit i; P_GU,i is the up ramp rate of unit i; T is the dispatch time period interval, and in this paper, T = 1 h.

(4)

Minimum up/down time limits

$${\displaystyle \sum _{s=t}^{t+T_{i,\mathrm{o}\mathrm{n}}-1}{U}_i^s}\ge T_{i,\mathrm{o}\mathrm{n}}(U_i^t-U_i^{t-1})$$

(38)

$${\displaystyle \sum _{s=t}^{t+T_{i,\mathrm{o}\mathrm{f}\mathrm{f}}-1}(1-U_i^s)}\ge T_{i,\mathrm{o}\mathrm{f}\mathrm{f}}(U_i^{t-1}-U_i^t)$$

(39)

where T_i,on is the minimum on time of unit; i and T_i,off is the minimum off time of unit i.

(5)

Reliability limits

The reliability limits are Equations (24)–(28).

Figure 2 shows the flowchart of proposed coordinated generation and spinning reserve dispatch model.

4. Case Studies

The proposed coordinated dispatch model is a non-linear mixed integer programming (MIP) problem. The objective function (30) is quadratic; the non-linear constraints (31), (38) and (39) can be transformed into linear constraints using the technique proposed in [19]. Other constraints are all linear. Therefore, the problem is transformed into a quadratic MIP problem. The mathematical programming software CPLEX 12.2 is used to solve the model.

4.1. Test System

The illustrative example below is based on the modified RTS-96 test system [20]. There are ten thermal units with a total installed capacity of 3105 MW. Data of the thermal units are extracted from [21] and shown in

Table 1. Thermal units parameters.

Unit	PG,imin (MW)	PG,imax (MW)		FORi	ai (k$/MW2)	bi (k$/MW2)		ci (k$/MW2)
G1	12.0	60		0.02	0.02533	25.5472		24.3891
G2	16.0	180		0.10	0.01199	37.5510		117.7551
G3	60.8	304		0.02	0.00876	13.3272		81.1364
G4	75	300		0.04	0.00623	18.0000		217.8952
G5	108.5	310		0.04	0.00463	10.6940		142.7348
G6	108.5	310		0.04	0.00473	10.7154		143.0288
G7	206.8	591		0.05	0.00259	23.0000		259.1310
G8	140.0	350		0.08	0.00153	10.8616		177.0575
G9	100.0	400		0.12	0.00194	7.4921		310.0021
G10	100.0	400		0.12	0.00195	7.5031		311.9102
Unit	Ti,on (h)	Ti,off (h)	tic (h)	Init. Cond. (h)	Ch ($)	Cc ($)	PG,Ui (MW/h)	PG,Di (MW/h)
G1	0	0	0	−1	60	30	60.0	60.0
G2	0	0	0	−1	340	170	120.0	160.0
G3	3	2	2	3	60	30	154	300.0
G4	4	2	2	−3	840	420	151.0	214.0
G5–G6	5	3	3	5	1000	500	105.0	148.0
G7	5	4	4	−4	4500	2300	155.0	299.0
G8	8	5	5	10	4000	2000	70.0	120.0
G9–G10	8	5	5	10	11,000	11,000	50.5	100.0

and Figure 3.

A total of 300 × 2.5 MW wind turbines are added to the system. The wind power forecast and error distribution are drawn by the method from [22]. The data are presented in

Table 2. 24-hour wind power forecast.

T	PW,j\/ MW	t	PW,j\/ MW	t	PW,j\/ MW	t	PW,j\/ MW
1	510	7	690	13	750	19	450
2	570	8	540	14	720	20	480
3	600	9	600	15	660	21	360
4	660	10	540	16	420	22	390
5	630	11	600	17	309	23	540
6	660	12	720	18	270	24	630

.

The system load demands are classified into three types, with desired ELNSR of 2 × 10⁻⁴, 5 × 10⁻⁴, 1 × 10⁻⁴. The load forecast data are presented in

Table 3. 24-hour load forecast.

T	L1/ MW	L2/ MW	L3/ MW	Total/ MW	t	L1/ MW	L2/ MW	L3/ MW	Total/ MW
1	400	500	800	1700	13	600	700	1290	2590
2	410	520	800	1730	14	550	750	1250	2550
3	380	420	890	1690	15	600	800	1220	2620
4	400	500	800	1700	16	380	670	1600	2650
5	410	520	820	1750	17	400	600	1550	2550
6	450	300	1100	1850	18	310	520	1700	2530
7	500	400	1100	2000	19	550	600	1350	2500
8	500	630	1300	2430	20	540	610	1400	2550
9	640	500	1400	2540	21	600	800	1200	2600
10	600	550	1450	2600	22	630	750	1100	2480
11	380	590	1700	2670	23	580	420	1200	2200
12	740	550	1300	2590	24	400	540	900	1840

.

4.2. Simulation Results

The problem is programmed using CPLEX 12.2 on a 3.0 GHz computer. The 24 h generation and reserve dispatch results with and without wind power are, respectively, presented in

Table 4. Generation and reserve dispatching results without wind power.

t	G1		G2		G3		G4		G5		G6		G7		G8		G9		G10
	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Output/ MW	Reserve/ MW	Output/ MW
1	0	60	0	120	230	74	0	0	310	0	310	0	0	0	350	0	300	0	400	0
6	0	60	0	120	304	0	76	151	310	0	310	0	0	0	350	0	300	0	400	0
12	0	60	0	120	304	0	300	0	310	0	310	0	516	75	350	0	300	0	400	0
18	0	60	0	120	304	0	300	0	310	0	310	0	456	135	350	0	300	0	400	0
24	0	60	0	120	295	9	75	151	310	0	310	0	0	0	350	0	300	0	400	0
T									1	2	3	4	5	6	7	8	9	10	11	12
Reserve Demand/MW									156	156	156	156	156	165	168	190	198	198	200	198
Available Reserve/MW									254	224	264	254	204	331	254	279	305	245	200	255
T									13	14	15	16	17	18	19	20	21	22	23	24
Reserve Demand/MW									198	198	198	200	198	198	198	198	198	196	185	165
Available Reserve/MW									255	295	225	211	295	315	335	295	245	335	409	340

,

Table 5. Generation and reserve dispatching results with wind power.

t	G1		G2		G3		G4		G5		G6		G7		G8		G9		G10
	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW
1	0	60	0	120	0	0	0	0	173	105	167	105	0	0	350	0	300	0	400	0
6	0	60	0	120	0	0	0	0	173	105	167	105	0	0	350	0	300	0	400	0
12	0	60	0	120	200	104	0	0	310	0	310	0	200	155	350	0	300	0	400	0
18	0	60	0	120	304	0	286	14	310	0	310	0	200	155	350	0	300	0	400	0
24	0	60	0	120	0	0	0	0	183	105	178	105	0	0	350	0	300	0	400	0

and

Table 6. Reserve demand and available reserve with wind power.

T	1	2	3	4	5	6	7	8	9	10	11	12
Reserve Demand/MW	229	237	240	249	245	253	260	253	264	270	280	289
Available Reserve/MW	390	390	404	434	390	390	340	335	314	486	486	439
t	13	14	15	16	17	18	19	20	21	22	23	24
Reserve Demand/MW	294	289	290	253	248	229	255	261	243	247	242	249
Available Reserve/MW	469	479	605	379	449	349	486	505	369	486	294	390

(only parts of the results are shown because of page limitation. Full results can be found in Appendix A).

The “reserve” in the Table 4 and Table 5 represents the available reserve capacity of unit i. Here only the units in on status can provide spinning reserve except for G1 and G2 which are fast response units. Available reserve in Table 4 and Table 6 represents the total amount of reserve can be provided during period t, and reserve demand means the minimum reserve required to guarantee the reliability demand during period t. In this paper, the cost of providing spinning reserve is neglected. Note that the method is still applicable when there is a cost function for spinning reserve.

As can be seen from Table 4, Table 5 and Table 6, before wind power is integrated, G5, G6, G8, G9 and G10 are all operating in full load and do not provide reserve capacity. After wind power is integrated, some of the units change their status from generating to providing spinning reserve, and the allocation of spinning reserve also changes. The output of G5, G6 and G8 decrease in several periods to provide reserve capacities, and G3, G4 and G7, which provided reserve before wind power integration, provide more reserve capacities during more periods.

The comparison of system spinning reserve with and without wind power is shown in Figure 4. We can see from it that the system reserve demand increases when wind power is added to the system, meanwhile the available reserve also increases because some of the thermal units are substituted by wind power and provide reserve capacity instead of generating.

In some cases, instead of providing reserve capacity, the thermal units are replaced and just quit operation when wind power is integrated. Assuming the 310 MW unit G5 quit operation after wind power is integrated; the simulation results of generation and spinning reserve dispatch are listed in

Table 7. Generation and reserve dispatching results when G5 is replaced with wind power.

t	G1		G2		G3		G4		G5		G6		G7		G8		G9
	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW	Output/ MW	Reserve/ MW
1	0	60	0	120	60	154	0	0	280	30	0	0	350	0	300	0	400	0
6	0	60	0	120	60	154	0	0	280	30	0	0	350	0	300	0	400	0
12	0	60	0	120	304	0	206	94	310	0	200	155	350	0	300	0	400	0
18	0	60	0	120	304	0	300	0	310	0	496	95	350	0	300	0	400	0
24	0	60	0	120	60	154	0	0	300	10	0	0	350	0	300	0	400	0

and

Table 8. Reserve demand and available reserve when G5 is replaced with wind power.

t	1	2	3	4	5	6	7	8	9	10	11	12
Reserve Demand/MW	223	233	233	242	242	247	254	261	269	264	274	288
Available Reserve/MW	364	394	250	285	434	364	334	435	359	335	335	429
t	13	14	15	16	17	18	19	20	21	22	23	24
Reserve Demand/MW	293	288	281	250	245	228	249	255	242	239	242	242
Available Reserve/MW	459	469	393	278	335	275	335	335	295	280	284	344

. The comparison of system spinning reserve with and without G5 is shown in Figure 5.

As depicted in Figure 4, the system reserve demand varies little when G5 quit operation. This is easy to understand as the reserve demand is mainly due to wind and load uncertainty. Furthermore, the system available reserve decreases during most periods after G5 quit operation. When t = 3, the available reserve is merely enough to meet the system reserve demand. When more thermal units, for instance, G3 and G5 with a total capacity of 610 MW, quit operation, the simulation cannot obtain feasible results as there is not enough reserve to meet the system reliability demand. Note that there are 750 MW wind turbines added to the system, which in this case means that the wind power can only replace thermal units with capacities of about 30 to 40 percent of wind power added to the system. With more simulations on typical daily load demand curves, the model proposed here can also help to calculate how many conventional units could be replaced by wind power without harming system reliability.

A comparative analysis of the proposed reserve quantification and scheduling method in this paper with traditional reserve scheduling methods has been conducted. Specifically, in this paper, based on the principle of setting the spinning reserve rate at 12% of the maximum load, the reserve quantification constraints proposed in this paper were replaced and optimized calculations were performed. Compared to a scenario where the reserve rate is set at 12% of the maximum load, the overall reserve level of the model proposed is lower by 1.7%, while the system reliability levels meet the requirements overall. During some periods of high renewable energy generation, when the reserve rate is set at 12% of the maximum load, the reliability level of node L1 decreases to lower than 1.7 × 10⁻⁴, while the proposed model in this paper is 2.1 × 10⁻⁴. Additionally, the system operation cost of the model proposed in this paper is reduced by 2.3% on average.

5. Conclusions

In order to mitigate and tackle the impact of stochastic wind power on system operation, a quantification method of spinning reserve demand based on the ELNSR and a coordinated generation and reserve dispatch model are proposed in this paper. The simulation results proved that the proposed method and model can effectively quantify system reserve demand based on the reliability demand of different loads; it can give both generation schedule and reserve allocation among units at the same time.

In this research, modeling the uncertainty of wind power prediction errors through the establishment of a wind power scenario set is a crucial step in quantifying reserve requirements. The representativeness of the selected scenarios can potentially impact the accuracy of these reserve requirements. Further research can be conducted in the future to explore more precise algorithms for selecting representative scenarios and reducing scenario sets. Moreover, further research can also be focused on using the proposed model to help calculating the amount of thermal unit capacities that can be replaced with wind power while maintaining the same reliability level.