Distributed power generation programming with waste incineration generation and hybrid energy storage equipment

Abstract

Under the current situation, distributed power generation becomes key solutions to the problems of environmental pollution and resources shortage that the electricity industry is facing. Rational power generation programming schemes will reduce energy consumption, and optimize energy structure on the premise of meeting the increasing requirements for electric energy. The multi-objective programming model was established to optimize economical and technical objectives of distributed generation system (DGS) containing waste incineration generation (WIG) and hybrid energy storage equipment (HESE), and then memorized-firefly algorithm (M-FA) is introduced to determine the model and installed capacity of various power generation units in distributed generation system. The case study demonstrated that the proposed programming model can obtain rational solutions with taking various objectives and constraints into consideration, and the M-FA shows the abilities of global search and better convergence in solving power generation programming problems, which will provide theoretic and practical references for the multi-objective programming problems of distributed generation system.

Keywords

Distributed generation system multi-objective programming waste incineration generation hybrid energy storage equipment memorized-firefly algorithm

1 Introduction

With the advantages of higher energy efficiency, less environmental pollution, more reliable power supply and flexible power generation, DGS has been greatly popularized in recent years. DGS is an effective way to relieve the power supply stress of large grid and promote the national energy conservation policy, for it lies close to the load centers, which can make full use of local renewable energy [1]. Influenced by wind generation (WG), Photovoltaic (PV), DGS is a little random and intermittent, which has great influences on reliability of power supply and on-grid connection. The influence degree is closely related to power installed capacity, so the study on DGS programming has become a hot issue. With full consideration of the characteristics of clean energy generation, DGS programming problem aims to supply stable and reliable power for load regions, and ultimately achieve the maximum of overall system benefits.

In the field of distributed generation system programming, current researches mainly focus on two issues: first, how to realize the effective participation of DGS in main grid programming and reduce the impact on main grid; second, how to determine objective function and constraint more reasonably. As for the first issue, Huang et al. [2] studied the impact of DGS on microgrid operation, controlling and economy. Wang et al. [3] discussed power distribution network programming containing DGS. What’s more, Zhang [4], Yang [5], Wu [6], et al. also made more researches in this issue. In term of the second issue, many scholars considered system reliability, investment cost, benefit, maintaining cost, energy utilization efficiency and pollution emission when set constraint conditions. For example, Bai et al. [7] established a multi-period and multi-scene nonlinear optimization model, which solved the locating and sizing problem of distributed power generation, and then minimized yearly power loss in distribution network; Motaleb and Bekdach [8] established optimization model for hybrid power system to minimize the one-time investment and annual operational costs, taking uncertainty of load demand and wind generation output into consideration; Li et al. [9, 10] built a multi-objective optimization model to solve DG grid-connection problem, which is viewed from environmental benefits, economic benefits and on-grid stability perspectives. From above we can see, current researches on DGS programming has been systematic, but it mainly focuses on few common distributed generations, such as wind power, photovoltaic power. Few researches take waste incineration generation and hybrid storage equipment into consideration. In addition, the researches which can fully consider environmental constraints and pollution controlling constraint are not yet mature.

DGS programming is a typical high-dimensional, nonlinear, stochastic programming problem. Aiming at such problems, bionic intelligent algorithm such as particle swarm optimization [11], improved genetic algorithm [12, 13], bee colony algorithm [14], shows great advantages. Firefly algorithm (FA) is a new swarm intelligent algorithm, and the position updating formula is the key point influencing searching ability. Max-Min method [15], chaos theory [16], variable parameters method [17] has been used to improve position updating formula in order to advance FA searching ability. In order to further improve FA searching ability, this paper introduces memory searching mechanism of particle swarm optimization algorithm (PSO) into FA to solve multi-objective programming problem. In particle swarm optimization algorithm, the best particle unidirectionally transmits information to other particles. In the whole searching process, other particles always follow the best particle [18], so they can faster converge to optimum solution. Therefore, memory searching mechanism of PSO is introduced into FA to improve algorithm searching ability.

Based on the analyses above, this paper first establishes a DGS which includes WG, PV, WIS and HESE; then, a model is built to analyze the objective function and constraints of DGS which takes environmental costs, units cost, power quality and system scale into consideration; finally, M-FA is introduced to solve this DGS optimization model, and a case study is designed to demonstrates the effectiveness of the established model and the algorithm applied in this paper.

2 Distributed power generation model

The DGS proposed in this paper consists of four components: power generation equipment, energy storage equipment, load and a micro-grid controller, as shown in Fig. 1. The function of each component can be expressed as follows: (1) Micro-grid controller is mainly responsible for internal power management as well as power dispatching between DGS and the large grid. (2) Power generation equipment is the main source of system power, and it includes WG, PV, and WIG. The WG and PV are clean but have strong randomness and cannot supply power to the demand regions alone [1]; while WIG can supply stable power, but may produce pollutants. Thus, the installed capacity of WIG should be constrained, in order to protect the environment. (3) Different energy storage equipment are used to meet different demands: energy storage equipment of power type has higher power density and faster response speed, but smaller energy density and higher cost; while energy storage equipment of energy type has larger capacity and lower cost, but slower response speed [19]. Then, the HESE in this paper includes super capacitor and battery, in order to quickly respond and store more energy. The capacity of HESE is closely related to the system investment, as shown in Fig. 2. Thus, the capacity of HESE should be determined from a comprehensive perspective, in order to avoid its negative effects on the stability and economy of DGS. (4) Load component describes the characteristics of system load.

Fig.1

System structure of distributed generation.

Fig.2

Influence of storage equipment capacity on investment of DGS.

DGS is a power management system that integrates power collecting, supplying, storing and allocating. A perfect DGS should have the advantages of low cost, high stability, environment-friendly generation and supplying power alone. The DGS proposed in this paper can not only supply clean and stable power, but also make full use of local clean energy and deal with urban garbage, which has great environmental and social benefits; the peak and valley load can be balanced with HESE; the environmental and economic benefits of programming schemes will be ensured by considering system scale rationality, system cost, and HESE cost.

3 Distributed generation system programming model

With considerations of strong randomness of WG and PV, the DGS programming model is proposed to integrate WIG, WG, PV, and HESE; units investment cost, operation and maintenance cost, environmental cost, power purchase cost and sales income are considered into the objective function as well as the cost of HESE, in order to maximize the comprehensive benefits of DGS.

3.1 Objective function

The purchase cost from large grid and sales income by selling electricity to large grid are two indicators to measure the scale rationality of DGS, and treat the prevention of environmental pollution as cost expressed in the objective function, and then maximize the income during the programming period based on constraints conditions, as (1) shows: $max F = G - (C_{mac} + C_{sca} + C_{env})$ (1)

Where F is net benefit of DGS; G is electricity sales income; C_mac is equipment cost; C_sca is scale rationality; and C_env is environmental cost.

3.1.1 Electricity sales income

$G = \sum_{i = 1}^{N_{y}} [(1 + r)^{- i} \sum_{j = 1}^{N_{i}} (π_{ij} E_{ij} + S_{ij})]$ (2)

Where N_y is programming years; N_i is number of units in the ith year; r is discount rate, and this paper takes r = 0.08; π_ij is on-grid price of unit j in the ith year, (CNY/MW·h); E_ij is power generation output of unit j in the ith year, (MW·h); S_ij is subsidy of unit j in the ith year.

3.1.2 Investment and operation cost

The cost of units includes the investment cost and operation cost of WG, PV, WIG units and HESE, which is calculated by (3): $C_{mac} = C_{inv} + C_{gen} + C_{sto}$ (3)

Where C_inv is the investment of DGS units; C_gen stands for operation and maintenance cost; and C_sto is the cost of HESE equipment.

Investment of units [20]

C_inv indicates investment cost of DGS units during programming period, which is calculated in way of dynamic investment, as described below: $C_{inv} = \frac{\sum_{i = 1}^{N_{y}} \sum_{j = 1}^{S^{new}} (1 + r)^{- i} I_{j} d_{ij} r (1 + r)^{N_{j}}}{((1 + r)^{N_{j}} - 1)}$ (4)

Where S^new is a collection of new units; d_ij represents whether to construct unit j or not in the ith year, d_ij = 1 if it is built, otherwise d_ij = 0; I_j represents the investment cost of unit j (100 million CNY/year); N_j is operation years of unit j.

Operation and maintenance cost

$C_{gen} = \sum_{i = 1}^{N_{y}} \sum_{j = 1}^{N_{i}} (1 + r)^{- i} c_{ij} E_{ij}$ (5)

Where c_ij is the unit generation cost of unit j in the ith year, CNY/MW·h, and c_ij is solved by: $c_{ij} = (M_{ij} + F_{ij} + D_{ij}) / E_{ij}$ (6)

Where, M_ij, F_ij, D_ij separately stands for maintenance cost, fuel cost and depreciation of unit j in the ith year, CNY/MW·h.

Cost of HESE

Referring to literature [19], the cost of HESE in DGS during the programming period can be calculated by (7), where $k_{eq}^{sc}$ , $k_{eq}^{ba}$ represents annual mean cost of super capacitor and battery. $C_{sto} = \sum_{i = 1}^{N_{y}} (1 + r)^{- i} (k_{eq}^{sc} + k_{eq}^{ba})$ (7)

Supposing that the time of battery charge/discharge is 530 times, and the battery is charged/discharged three times a day, then the annual depreciation of two storage equipment can be calculated:

$\begin{matrix} k_{eq}^{sc} & = & 1.05 \times (150 P^{sc} + 2700 E^{sc}) \\ k_{eq}^{ba} & = & 5.26 \times (150 P^{ba} + 100 E^{ba}) \end{matrix}$ (8)

3.1.3 Scale rationality

The scale of DGS is determined by the regional electricity demand, while the electricity demand is not constant, and the outputs of WG and PV are random, so situations of unreasonable system scale easily happen.

At current stage, most research [21 –23] use power load to measure DGS scale and be a constraint of DGS programming. However, in practice the level of scale rationality has direct influence on the level of economic benefit: ➀ If the installed capacity greatly exceeds the users demand, though it can result in excessive investment cost and a waste of resources, but DGS needs to sell redundant power to power gird and lead to revenue C_exp. ➁ If the installed capacity is too small to meet the electricity demand, DGS has to purchase electricity from the power grid, which results in higher power purchase cost C_pur. The C_exp and C_pur are the reflection of scale irrationality. Therefore, scale rationality in this paper is measured by C_pur and C_exp: $C_{sca} = C_{pur} + C_{exp}$ (9)

Electricity purchase cost

$C_{pur} = \sum_{i = 1}^{N_{y}} (1 + r)^{- i} U_{i} Q_{i}$ (10)

Where U_i is the unit price of electricity purchase in the ith year, CNY/MW·h; Q_i is quantity of electricity purchase, MW·h.

Output of power to the large grid

The output of power to large grid is the income of DGS on the surface, while it indirectly represents that the scale of DGS exceeds actual demand, thus this income is set as a part of the system comprehensive cost, as shown in (11): $C_{exp} = \sum_{i = 1}^{N_{y}} (1 + r)^{- i} C_{ex, i} D_{i}$ (11)

Where D_i represents output of power in the ith year; C_ex, i is the average price of electricity sales, which is calculated on the basis of comprehensive unit generation cost and on-grid price of different units, CNY/MW·h, as shown in (12): $C_{ex, i} = \sum_{j = 1}^{N_{i}} (\frac{E_{ij}}{\sum_{j = 1}^{N_{i}} E_{ij}}) π_{ij}$ (12)

3.1.4 Environmental cost [24]

Referring to literature [25, 26], environmental cost of WIG can be calculated: $C_{env} = \sum_{i = 1}^{N_{y}} \sum_{j = 1}^{N_{i}^{WIG}} \sum_{k = 1}^{N^{pol}} (1 + r)^{- i} v_{jk} E_{ij} (v_{k} + v_{k}^{'})$ (13)

Where $N_{i}^{WIG}$ is the collection of WIG in the ith year; N^pol is the species of pollutants; v_kj is pollutant emission coefficient of generation unit j, kg/(MW·h); v_k and $v_{k}^{'}$ represent environmental value and fine standard of pollutant k.

3.2 Constraints

Load constraint

To ensure the demand of power load, the installed capacity of DGS should meet the following requirements: ${\begin{matrix} \sum_{j = 1}^{N_{i}} P_{j} a_{ij} - \sum_{t = 1}^{T} P_{t}^{S} b_{it} \geq P_{i}^{max} \\ \sum_{j = 1}^{N_{i}} P_{j} a_{ij} + \sum_{t = 1}^{T} P_{t}^{S} b_{it} \geq P_{i}^{min} \end{matrix}$ (14)

Where P_j is the rated power of unit j, MW, and power generation model of WG and PV refers to literature [27]; a_ij is availability ratio of unit j; $P_{t}^{S}$ is charging/discharging power of HESE t, MW; b_ij is the utilization ratio of HESE t; $P_{i}^{max}$ is the system maximum load and $P_{i}^{min}$ is the minimum load in the ith year, MW.

Power constraints [24]

To meet the requirements of regional power demand, the DGS may not only purchase power from the large grid, but also sell power to the large grid. A real-time balance between demand and supply is almost impossible, so the probability of power constraint condition is β₁. $P_{r} {\sum_{j = 1}^{N_{i}} E_{ij} + Q_{i} - D_{i} = L_{i}} \geq β_{1}$ (15)

Where L_i is regional load demand in the ith year, MW·h; P_r {•} represents the probability of the event in the {•}; β₁ is the confidence value of balance between power supply and demand.

Voltage constraints

V_{k, min} \leq V_{k} \leq V_{k, max}

(16)

Where V_k,max and V_k,min are the maximum and minimum voltage of kth node, and V_k is the actual voltage of kth node.

Branch constraints

S_{z} \leq S_{z, max} z \in N_{line}

(17)

Where, S_z and S_z,max represent the transmission and the maximum transmission power of zth branch; N_line is the set of all branch.

Pollutant emission constraints [28]

The pollutant emissions of generation units should be below the ceiling of industrial requirements: $P_{r} {\sum_{j = 1}^{N_{i}} E_{ij} + Q_{i} - D_{i} = L_{i}} \geq β_{1}$ (18)

Where, $M_{ik}^{max}$ is industrial emission limit of pollutant k in the ith year, kg; β₂ is the confidence value that the pollutant emissions can meet the industrial limits.

Installed capacity constraint of WIG

$\sum_{n = 1}^{N_{i}^{WIG}} P_{n} \leq {M_{i, WIG}}^{max}$ (19)

Where, $M_{i, WIG}^{max}$ is the ceiling of installed capacity of new WIG units in the ith year.

State constraint of HESE

E_{t}^{min} \leq E_{t} \leq E_{t}^{max}

(20)

Where E_t is the state of HESE t; $E_{t}^{max}$ and $E_{t}^{max}$ represent the upper and lower bounds of equipment capacity.

4 Solution to programming model

4.1 Basic firefly algorithm

A firefly searches other fireflies within searching range by their luminous characters. It moves towards the brighter firefly in a neighborhood, which then optimizes its own position [18]. The FA abstracts the flashing characteristics of fireflies, and the following three idealized behaviors are assumed: ➀ All fireflies are unisex and can be attracted to other fireflies; ➁ the attractiveness intensity of a firefly is proportional to its light intensity, and light intensity is proportional to distance. If any two fireflies have the same light intensity, they move randomly; if no firefly around has more light, it move randomly; ➂ the light intensity of a firefly is closely related to objective function to be optimized. As mentioned above, the FA consists of two elements: the light intensity and attractiveness intensity. The light intensity of a firefly represents its present situation and determines its direction of movement; the attractiveness intensity determines its distance of movement. The light intensity and attractiveness intensity are both inversely proportional to the distance. The objective is optimized by constantly updating the light intensity and attractiveness intensity. Then, the mathematical description and analysis are as follow [29].

Definition 1. The relative brightness of each firefly $I = I_{0} \times e^{- γ \cdot rij}$ (21)

Where I₀ is the maximum brightness of a firefly when r = 0; γ is light intensity absorption coefficient, which represents that the brightness intensity gradually decreases with relative distance increasing, and γ can be set as a constant; r_ij is the Cartesian distance between two fireflies, which can be calculated as follows: $r_{ij} = | x_{i} - x_{j} | = \sqrt{\sum_{k = 1}^{d} (x_{ik} - x_{jk})^{2}}$ (22)

Definition 2. The relative attractiveness between two fireflies $β = β_{0} \times e^{- γ \cdot r_{ij}^{2}}$ (23)

Where β₀ is the attractiveness when r = 0.

Definition 3. Location updating formula

$\begin{matrix} x_{i} & = & x_{i} + β \times (x_{j} - x_{i}) \\ + α \times (rand () - 1 / 2) \end{matrix}$ (24)

Where x_i and x_j are spatial locations of fireflies; α is a step factor, and it is a constant on interval [0,1]; rand() represents a random number on interval [0,1], and it is normally distributed.

4.2 M-FA

The firefly algorithm shows great advantages in solving high-dimensional and non-linear optimization problem, and is less likely to fall into local optimum compared with particle swarm optimization (PSO). However, FA also has its deficiencies. For example, the search process of fireflies doesn’t adequately refer to the historical experiences, but rely on the random search of term α × (rand () -1/2), which may lose lots of valuable information and affect the search capability and purpose. Therefore, the memory search mechanism of particle swarm optimization algorithm is introduced into FA to enhance the local and global optimization capability of FA by taking full advantage of the relative best location and considering the extreme value in each iteration process. Then, the mathematical description and analysis are as follow. The location updating formula is described in (25).

$\begin{matrix} x_{i} & = & x_{i} + β \times (x_{j} - x_{i}) + z_{1} rand \times (P_{best} - x_{i}) \\ + z_{2} rand \times (rand () - 1 / 2) \end{matrix}$ (25)

Where P_best is the current global optimum; z₁ and z₂ are random disturbance parameters. The process of solving DGS programming problems by M-FA is shown in Fig. 3.

Fig.3

Process of M-FA.

5 Case study

5.1 Case 1: M-FA performance test

Eggholder function is used as a test function in order to evaluate the performance of optimization algorithms. This case is introduced to examine the performance of M-FA and FA. The Eggholder function shown in Equation (26) will be employed as objective function.

$\begin{matrix} f (x) & = & - (x_{2} + 47) sin \sqrt{| x_{2} + \frac{x_{1}}{2} + 47 |} \\ - x_{1} sin (\sqrt{| x_{1} - (x_{2} + 47) |}) \end{matrix}$ (26)

This function is difficult to solve because it has many local maximums and minimums which leads to the problem of trapping in local optimum. The searching range is [–512, 512, –512, 512]. Set α = 0.2 and γ = 1.0. The 100 fireflies’ final positions are shown in Fig. 4:

Fig.4

Eggholder testing result.

As shown in Fig. 4(a), MFA can reach global optimum at the coordinate (512,404.23) finally, but many fireflies in Fig. 4(b) have trapped in local optimum. The comparison presents that MFA has better global optimization capability. In addition, the time used by M-FA is 8.325 seconds, shorter than 13.642 seconds spent by FA. It strongly proves that MFA outperforms FA in searching ability, which makes M-FA a superior candidate for parameters optimizer. Therefore, M-FA is used as the optimization algorithm for DSG programming.

5.2 Case 2: DGS planning

5.2.1 Basic data

The load center chosen in this paper lies in northwestern China, whose solar resource belongs to the first grade and wind resource belongs to the second grade. The load demand in this region shows obviously randomness and volatility, and the 24-hour load curve of a typical day at the beginning of programming period is shown in Fig. 5. It is estimated that the load demand keeps growing during programming period, and corresponding increase data is shown in Table 1.

Fig.5

Typical daily load curve.

Table 1

Load variation during programming period

Year	AML	AEC	MDPVL
1	23.47	1.26	9.39
2	27.02	1.45	10.80
3	30.74	1.65	12.30
4	34.80	1.86	13.90
5	39.83	2.14	15.96
6	43.63	2.34	17.46
7	48.21	2.59	19.29
8	53.39	2.87	21.36
9	59	3.17	23.61
10	63.93	3.43	25.58

Note: AML = annual maximum load, MW; AEC = annual electricity consumption, hundred million kWh; MDPVL = maximum difference between peak and valley load, MW.

As the wind resource and solar resource of this load region are abundant, the clean energy generations like WG and PV are relatively more advantageous; the WIG is allocated in the DGS to ensure the minimum demand of regional power, as well as dealing with domestic waste problems; the HESE is allocated in the DGS to reduce resources waste and balance the relieve imbalance between power supply and regional load demand; the DGS can dispatch power with large grid if the power of this system is excessive or inadequate. Based on the above, the DGS in this paper will finally supply power of good reliability and low cost to the users, by coordinating power arrangement between power generation, storage equipment and large power grid.

The parameters for various units are shown in Table 2, of which the units construction period is the average period of similar units excluding uncontrollable factors; the number of units is the upper limit of similar units in DGS, not a number of units that DGS have to achieve; the pollutant emission limits of WIG follow national standards [30], and the standard of emissions penalties is in accordance with that of coal-fired plants, as shown in Table 3; the WG and PV models and parameters refers to literature [31]; on-grid prices during the programming period are shown in Table 4. Based on the previous experience, the confidence values are set β₁ = β₂ = 0.99; the parameters of M-FA are defined as follows: light absorption coefficient: γ = 1.0; maximum attractiveness: β₀ = 1.0; step factors: α = 0.2, z₁ = 0.4, z₂ = 1.

Table 2

Parameters of power plants to be built

Units	Single	Investment	Operation and	Construction	Life/a
	capacity	(million	maintenance	cycle/a
	(MW)	CNY/kW)	cost
			(CNY/MW×h)
WG	1.5	1.21	512.36	1	20
	2	1.05	509.50	1	20
	5	0.93	483.58	1	25
	10	0.79	459.82	1	25
PV	3	1.20	196.43	1	25
	5	1.14	181.82	1	25
	10	1.09	163.26	1	25
	12.5	1.06	160.06	1	25
WIG	6	2.629	340.23	2	22
	7.5	2.545	328.75	2	22
	9	2.485	313.62	3	25
	12	2.393	287.50	2	25

Note: The data above is collected and calculated by authors.

Table 3

Treatment cost of pollutants (CNY/kg)

Pollutants	NOx	CO2	CO	SO2
Environmental Value	8.000	0.023	1.000	6.000
Fine	2.000	0.010	0.160	1.000

Table 4

On-grid price and subsidy [32] (CNY/kW×h)

Units	On-grid price					Subsidies
	2016	2017	2018	2019	2020
WG	0.49	0.47	0.45	0.43	0.40	0.171
PV	0.90	0.87	0.84	0.81	0.78	0.42
WIG	0.66	0.243

Note: the subsidy of WG is the difference between the benchmark prices of WG and local coal power [33]; the subsidy of WIG is 68 CNY for per ton garbage, and per ton garbage can generate on-grid power of 280 kW·h [34].

5.2.2 Simulation result

The allocation problem of DGS should first take various factors into consideration, such as the regional natural environment and unceasingly changing load demand; then, rational system objectives are determined, such as clean generation, stable power supply and reasonable system income; finally, based on the available units in current market, the model and installed capacity of the power generation units are determined. Based on the above, M-FA is introduced to solve the DGS programming model proposed in this paper. The designed installed capacities of WG, PV, WIG, and HESE are calculated according to the objective function and constraint conditions, and then designed installed capacity is adjusted flexibly to meet the practical requirements of market and system. Finally, the calculation result of DGS installed capacity is shown in Fig. 6.

Fig.6

Accumulated capacity of new installed units.

Based on the Fig. 6, conclusions can be drawn: (1) Due to the higher initial investment and lower annual utilization hours, WG and PV haven’t been large-scale constructed during the early stage of programming period when the pollutant emissions of DGS can meet the related requirements of government and industry. In this period, WIG is the emphasis of investment for its higher profit, and the environmental cost rises rapidly with the installed capacity of WIG increasing. (2) With the pollutants approaching emission limits, environmental cost rising, and the constraints of renewable energy quota gradually increasing, WG and PV are gradually large-scale invested, and the DGS have to construct according energy storage equipment so as to avoid wasting power resource. Due to the higher investment of WG, PV, and HESE, the accumulated investment of DGS increases rapidly in later period.

The various costs of DGS are shown in Table 5 (converted to values of each year and represented by dynamic investment cost). In the early period, the electricity purchase cost of DGS is high. With the growth of installed capacity, the gap between power output of DGS and load demand gradually reduces and DGS transforms from electricity purchase to electricity sale. The income of DGS in early period is negative, which means that income of DGS is far away from comprehensive cost in the early period; while with installed capacity growing, electricity sales gradually increases and DGS gradually turns loss into gain.

Table 5

Profit and cost during programming period (unit: million CNY)

Year	Annual	Investment	Operation and	Power
	income		maintenance	purchase
			cost	cost
1	–55.44	2.10	1.62	100.82
2	–69.84	4.73	5.86	116.25
3	–30.58	2.64	9.47	92.47
4	–18.49	4.51	17.33	66.65
5	–6.45	8.85	24.56	29.04
6	13.53	4.93	36.14	0
7	27.57	5.06	42.51	0
8	43.07	9.38	53.69	0
9	51.30	2.13	69.17	0
10	60.92	4.03	74.89	0

5.3 Sensitivity analysis

5.3.1 Confidence coefficient analysis

Different emissions constraints

Based on the obtained optimal scheme, the emissions limits of various pollutants are respectively increased and decreased by 20%, and then the installed capacity of according schemes is shown in Fig. 7.

Fig.7

Influence of different emission limits on installed capacity.

The generation process of WG and PV is considered highly clean, so different emissions constraints directly influence the installed capacity of WIG, and indirectly influence the installed capacity of WG, PV, and HESE. While the latter ones don’t have the advantages over profit and investment cost, then WIG is prior to be built when emissions constraints are low, and WG, PV as well as HESE is gradually large-scale built with the installed capacity of WIG increasing; however, when emissions constraints are high, the comprehensive cost of DGS is much higher because of the higher investment and maintenance costs of WG, PV, and HESE.

Different confidence level

To study the influences of different confidence values on the economic indexes of different schemes, β₁ and β₂ are respectively taken different values, and the results are shown in Table 6. Seen from the figure, with the confidence values of constraint conditions changing, the installed capacity of DGS changes widely, which results in a wide range of investment cost, operation and maintenance cost; when the confidence value of installed capacity constraint of WIG changes, the installed capacity of clean generation units will change accordingly, and then installed capacity of HESE will greatly influenced. Though WG and PV have better environment benefit, they have no advantage over utilization efficiency and investment cost, for their utilization efficiency is greatly influenced by environment and the HESE with high investment cost have to be constructed to support them. In contrast, though WIG produces pollutants in generation process, it has widespread prospect in dealing with domestic waste for it can provide stable power for the load center. In summary, the installed capacity of each unit should be reasonably programmed in practice, in order to optimize the balance between economic income, social income and sustainable development.

Table 6

Influences of different confidence level on economic indexes of different schemes (units: million CNY/ MW)

β ₁	β ₂	Income	Investment	Operation/	Installed
				maintenance	capacity
				cost
0.90	0.99	39.98	384.64	231.32	98
0.99	0.99	72.24	328.13	189.71	82
0.99	0.90	45.25	352.26	262.23	73.5

5.3.2 Model rationality analysis

In this section, four models are established as shown in Table 7. All models are applied in Case 2, and the annual profit curves are presented in Fig. 8.

Table 7
Detailed information of built models

M1 M2 M3 M4

WIG √ √ √

PV+WG √ √ √

HSE √ √ √

	M1	M2	M3	M4
WIG	√		√	√
PV+WG	√	√		√
HSE	√	√	√

Fig.8

Annual profit curves of four models.

From Fig. 8 we can find that: For M2, M3 and M4, the total revenue will make up the deficits and get surpluses at the 8.9th year, 6.6th year and 6.7th year. For M1 proposed in this paper, positive profit can be achieved since the 5.6th year, much shorter than other models. In M1, WIG can provide stable power for DGS, PV and WG can supplement power when WIG construction scale is restrained, and HSE can improve power generation efficiency and lower the cost resulted by scale irrationality.

6 Conclusions

DGS plays an increasingly important role in power system of China, of which the rational layout can bring in huge social and economic benefits. The DGS programming model proposed in this paper contains waste incineration generation and hybrid storage equipment, and can fully consider the social, economic and technical optimization problems, those are, environmental cost, investment cost, operation and maintenance cost, reliability of power supply and scale rationality; the confidence of constraint conditions are considered, in order to raise its practical value. As for the nonlinear, multi-constraint and multi-objective characteristics of DGS programming problem, M-FA introduced in this paper can efficiently determine the types and volumes of various power units; based on the simulation results, the rationality of proposed model and the validity of applied algorithm are verified. With the enhancement of environment and resources constraints, the DGS programming problems with larger scale, more constraints and more power types will become future research emphasis.

Footnotes

Acknowledgments

This paper is supported byProject supported by the National Nature Science Foundation of China (71271085, 71471059) and Fundamental Research Funds for the Central Universities (2016XS73 and 2016XS75).

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Distributed power generation programming with waste incineration generation and hybrid energy storage equipment

Abstract

Keywords

1 Introduction

2 Distributed power generation model

3.1 Objective function

4.1 Basic firefly algorithm

5.1 Case 1: M-FA performance test

5.2.1 Basic data

5.3.1 Confidence coefficient analysis

Table 7 Detailed information of built models M1 M2 M3 M4 WIG √ √ √ PV+WG √ √ √ HSE √ √ √

Footnotes

Acknowledgments

References

Table 7
Detailed information of built models

M1 M2 M3 M4

WIG √ √ √

PV+WG √ √ √

HSE √ √ √